Prediction of fatigue crack growth and residual stress relaxations in shot-peened material

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玻璃纤维铝合金层板(FMLs)的疲劳损伤特性及S-N曲线

玻璃纤维铝合金层板(FMLs)的疲劳损伤特性及S-N曲线马玉娥;王博;熊晓枫【摘要】根据国内外标准和参考文献,针对玻璃纤维增强铝合金层板(FMLs)的特点设计出FMLs疲劳试验件,进行了不同载荷下的R=0.1等幅拉-拉疲劳试验.疲劳试验过程中FMLs最先在表面铝层内出现裂纹,随后表面铝层可见多条裂纹.随着循环载荷数的增加,裂纹不断扩展,并在界面出现分层现象,然后分层损伤快速扩展直至完全断裂破坏.测得了FMLs的疲劳裂纹起裂寿命和裂纹扩展寿命,给出了其疲劳寿命的规律性.得到了FMLs和同样厚度碳纤维复合材料CCF300的S-N曲线,并进行了对比.FMLs的疲劳寿命随载荷变化平缓,近似成对数趋势;在载荷大于400 MPa时FMLs的疲劳寿命与CCF300碳纤维复合材料层板相当;当疲劳载荷最大值低于300 MPa,FMLs的疲劳寿命比CCF300复材板要低.为飞机结构设计师们提供了材料基础性能和信息.【期刊名称】《西北工业大学学报》【年(卷),期】2016(034)002【总页数】5页(P222-226)【关键词】玻璃纤维增强铝合金层板;疲劳裂纹起裂寿命;裂纹扩展寿命;分层扩展;S-N曲线【作者】马玉娥;王博;熊晓枫【作者单位】西北工业大学航空学院118号,陕西西安 710072;西北工业大学航空学院118号,陕西西安 710072;中航工业成都飞机设计研究所,四川成都 610041【正文语种】中文【中图分类】V215.5材料的疲劳性能是飞机结构设计选材考察的重点之一。

为克服传统铝合金结构疲劳性能相对较差的问题，同时充分利用复合材料对疲劳载荷不敏感的特性，国外研究者提出了金属和复合材料的混杂材料。

根据金属和复合材料的不同，研制出不同的纤维增强合金层合板类型，如第一代的Arall(aluminum with aramid fibers)是由铝合金层和芳纶纤维交替组成，CARALL(aluminum with carbon fibres)由铝合金和碳纤维组成，GLARE(aluminum with glass fibers)是由铝合金和玻璃纤维组成，还有最近发展由钛合金和碳纤维组成的TiGr(titanium with carbon fibers)和由镁合金和玻璃纤维组成的MgFML(magnesium with glass fibers)。

某机中央翼下壁板疲劳裂纹扩展寿命估算

某机中央翼下壁板疲劳裂纹扩展寿命估算ΞPRE DICTION OF FATIGUE CRACK GR OWTH LIFE OF THE CENTRALWING JOINT PANE L IN AN AIRCRAFT朱青云ΞΞ1　李曙林1ΞΞΞ　薛　军ΞΞΞΞ2　王　智ΞΞΞΞ2　陈志伟ΞΞΞΞ2(1.空军工程大学工程学院,西安710038)(2.北京航空工程研究中心,北京100076)ZHU QingY un 1　LI ShuLin 1　X UE J un 2　WAN G Zhi 2　CHEN ZhiWei2(1.Air Force Engineering Univer sity ,Xi ′an 710038,China )(2.Beijing Aeronautical Technology Research Center ,Beijing 100076,China )摘要　为评估某型飞机中央翼下壁板萌生疲劳裂纹后的使用安全性,进行结构模拟件疲劳试验,并利用AFG ROW 软件对其疲劳裂纹的扩展寿命进行估算,与试验结果进行对比,初步确定出该部位裂纹扩展速率,为裂纹故障部位的修理提供参考依据。

关键词　疲劳裂纹　裂纹扩展　寿命估算中图分类号　V215.5Abstract Fatigue crack was found in the lap joint panel of the central wing lower structure in an aircraft.T o assess the safety of the structure ,simulated structure specimen was designed and fatigue test was per formed under design fatigue load.T est results were re 2ported ,and analyzed crack growth cycles predicted by the AFG ROW s oftware package com pared and agreed well with test results.I t als o gave suggestion for the repair of crack failure.K ey w ords F atigue crack ;Crack grow th ;Life predictionCorresponding author :ZHU QingYun ,E 2mail :zqingyun -0@ ,Tel :+86210266713598,Fax :+86210268753560Manuscript received 20040428,in revised form 20040714.1　引言某型飞机在特检时发现中央翼连接板第1墙处有裂纹,裂纹部位基本情况如图1所示。

齿轮疲劳断裂数值模拟 finite element simulation of fatigue crack growth in a spiral bevel pinion gear

Three-dimensional,parallel,ﬁnite element simulationof fatigue crack growth in a spiral bevel pinion gearAnıUral a,*,Gerd Heber a ,Paul A.Wawrzynek a ,Anthony R.Ingraﬀea a ,David G.Lewicki b ,Joaquim o caCornell Fracture Group,Rhodes Hall,Ithaca,NY 14850,USA b US Army Research Laboratory,NASA Glenn Research Center,Cleveland,OH 44135,USAc Federal University of Ceara,Fortaleza-CE 60455-760,BrazilReceived 23February 2004;received in revised form 25August 2004;accepted 31August 2004Available online 11November 2004AbstractThis paper summarizes new results for predicting crack shape and fatigue life for a spiral bevel pinion gear using computational fracture mechanics.The predictions are based on linear elastic fracture mechanics theories combined with the ﬁnite element method,and incorporating plasticity-induced fatigue crack closure and moving loads.We show that we can simulate arbitrarily shaped fatigue crack growth in a spiral bevel gear more eﬃciently and with much higher resolution than with a previous boundary-element-based approach [Spievak LE,Wawrzynek PA,Ingraﬀea AR,Lewicki DG.Simulating fatigue crack growth in spiral bevel gears.Engng Fract Mech 2001;68(1):53–76]using the ﬁnite element method along with a better representation of moving loads.Another very signiﬁcant improvement is the decrease in solution time of the problem by employing a parallel PC-cluster,an approach that is becoming more common in both research and practice.This reduces the computation time for a complete simulation from days to a few hours.Finally,the eﬀect of change in the ﬂexibility of the cracking tooth on the location and magnitude of the contact loads and also on stress intensity factors and fatigue life is investigated.Ó2004Elsevier Ltd.All rights reserved.Keywords:Finite element method;Fatigue crack growth;Computational fracture mechanics;Gears;Three-dimensional ﬁnite element contact analysis;Parallel computation0013-7944/$-see front matter Ó2004Elsevier Ltd.All rights reserved.doi:10.1016/j.engfracmech.2004.08.004*Corresponding author.Tel.:+16072548822;fax:+16072548815.E-mail address:au14@ (A.Ural).Engineering Fracture Mechanics 72(2005)1148–1170/locate/engfracmechA.Ural et al./Engineering Fracture Mechanics72(2005)1148–117011491.IntroductionPredicting crack shapes is important in determining the failure mode of a gear.Cracks propagating through the rim may result in catastrophic failure,whereas the gear may remain intact if one tooth fails allowing for early detection of impending failure.Being able to predict crack trajectories is insightful for the designer.However,predicting growth of three-dimensional arbitrary cracks is complicated due to the diﬃculty of creating and evolving three-dimensional geometry and mesh models,the computing power re-quired and absence of closed-form solutions of the problem.Previously,tooth-bending fatigue failure in spiral bevel gears was investigated using the boundary ele-ment method[1].These analyses were signiﬁcant in developing a method for predicting three-dimensional, non-proportional,fatigue crack growth incorporating moving loads.Prior to that study,there were few examples of three-dimensional crack growth studies on gears[2,3].Most of the gear studies in the literature employing computational fracture mechanics employed two-dimensional analyses[4–8].Furthermore, moving contact loads following a path along the tooth surface starting from the root and moving up to the top of the tooth on the heel end had not been considered in these analyses.The predictions from[1]were helpful to determine areas in need of further research.These were:improv-ing accuracy of simulation by switching from the boundary element(BEM)to theﬁnite element method (FEM),decreasing computation time by employing parallel FEM analysis,and improving modeling of con-tact tooth loads.The main objective of this paper is to demonstrate that we can improve accuracy and eﬃciency of crack growth simulations in a spiral bevel pinion gear through the use of a new computational fracture mechanics environment that synthesizes these improvements.A complete description of this environment is given in [9].It is composed of components capable of performing parallel FEM simulations of arbitrary,non-pla-nar,3D crack growth,creating volume meshes of bodies with curved surfaces and internal boundaries,and performing fracture analysis tasks such as calculating stress intensity factors(SIF)using the J-integral in an integrated manner.Another focus of this paper is performance and interpretation of three-dimensional con-tact analysis of a spiral bevel gear set incorporating cracks.These analyses are signiﬁcant in determining the inﬂuence of change of toothﬂexibility due to crack growth on the magnitude and location of contact loads. This is an important concern since a change in contact loads might lead to diﬀerences in stress intensity factors and therefore result in alteration of the crack shape and rate of crack growth.2.Three-dimensional FEM simulations of fatigue crack growth in a spiral bevel pinion gearAn example of tooth-bending failure can be observed in a spiral bevel pinion gear used in the main rotor transmission of the US ArmyÕs OH-58Kiowa Helicopter(Fig.1).This gear is composed of19teeth and meshes with a71-tooth gear under operating conditions of6060rpm and3099in.-lb of torque.The material used for OH-58spiral bevel gears is AISI9310steel.Material properties of this steel are given in Table1as well as the Paris model parameters[10]used in the fatigue life calculations described in Section2.1.The OH-58spiral bevel pinion gear,shown in Fig.1,was tested in an actual helicopter transmission test facility at full speed under increasing loading conditions at the NASA Glenn Research Center(NASA/ GRC).Several electron-discharge-machined(EDM)notches with diﬀerent sizes were introduced at theﬁllet of a toothÕs concave side to serve as fatigue crack initiators.The test was run for one million cycles at 2479in.-lb,one million cycles at3099in.-lb,one million cycles at3874in.-lb and1.9million cycles at 4649in.-lb.At the end of a total of4.9million cycles,ﬁve fractured teeth were observed.No crack growth measurements were taken during the test.In this respect,this test only provided an upper bound on fatigue life of a tooth of4.9million cycles.However,qualitative information on the fracture surfaces and fatiguecrack growth were extracted from the test.A detailed study of the fracture surfaces using a scanning elec-tron microscope (SEM)can be found in [1].2.1.ApproachIn the current study,as in [1],LEFM theories were used for fatigue crack growth predictions.Fatigue crack growth rates were determined using a modiﬁed Paris model accounting for crack closure.A crack is assumed to advance when its SIF is large enough to overcome closure and is larger than the SIF of the pre-vious load step.All fatigue life predictions were based on plane strain assumptions.Crack direction predic-tions were made using the maximum circumferential stress theory [11].Moving loads were takenintoFig.1.OH-58spiral bevel pinion gear showing tooth-bending fatigue fracture:(a)whole pinion;(b)close-up view of the fractured pinion;(c)broken pinion tooth.Table 1Material properties and Paris model parameters of AISI 9310steelMaterial properties of AISI 9310steelYoung Õs modulus30,000ksi Poisson Õs ratio0.3Tensile strength185ksi Yield strength160ksi Fracture toughness,K Ic85ksi in.1/2Paris model parameters of AISI 9310steelC6.19·10À20(in./cycle)/(psi in.1/2)n n 3.361150 A.Ural et al./Engineering Fracture Mechanics 72(2005)1148–1170account by discretizing loading of a tooth as it rolled through mesh into15steps.This loading created a non-proportional load history at the tooth root meaning that the ratio of Mode II to Mode I SIFs changed during the load cycle.Complex cracking problems,such as the current gear problem,require computation of mixed mode SIFs due to the combined loading that they receive.Several fundamentally diﬀerent approaches for computing SIFs have been developed.Among these methods,the displacement correlation method[12–15]and equivalent domain J-integral methods[16–21]are widely used in numerical computations.In the previous BEM-based simulations of this spiral bevel pinion gear,the displacement correlation method was used for calculating SIFs.This method only requires displacement information on the boundary near the crack front and is computationally eﬃcient.Since the BEM solves for displacement information only on the bounda-ries,this method is directly suitable for the BEM analysis.This method is only as accurate as the computed displacements at the correlation points.In the current FEM-based simulations,we used the equivalent do-main,J-integral approach.SIFs calculated by this method are known to produce more accurate values than those from displacement correlation,from the same local displacementﬁelds,because it involves numerical integration over computedﬁelds rather than point sampling.The overall methodology used in the present simulations is composed of the following steps:1.Create initial geometry model of the spiral bevel pinion gear with the Object Solid Modeler(OSM)[22]using the gear geometry information provided by the NASA/GRC.2.Specify boundary conditions and material properties in Fracture Analysis Code-3D(FRANC3D)[23].3.Insert the initial crack in FRANC3D at the location where the EDM defect was inserted in the testpinion.4.Create a surface mesh composed of triangular elements in FRANC3D.5.Create a3D FEM mesh composed of tetrahedra using JMesh[24]using a geometry descriptionﬁlewritten out from FRANC3D.6.Calculate the magnitude and location of the nodal contact loads resulting from continuous meshing ofthe pinion and the gear(Fig.2).7.Run the FEM analysis on a parallel PC-cluster for15discrete load ing the J-integral method,calculate SIF values at each speciﬁed crack front point for each load step.8.Calculate crack extension and crack growth angle due to one non-proportional load cycle using theapproach developed in[1].For each discrete crack front point:(a)Calculate amount of crack growth,d a i corresponding to each load step i=1, (15)d a i¼K iIÀK iÀ1ID K effd ad ad N¼CðD K effÞn D K eff¼K maxIÀK opð1ÞFig.2.Single,left-handed,spiral bevel pinion tooth.Note the moving load path on the tooth surface.A.Ural et al./Engineering Fracture Mechanics72(2005)1148–11701151(b)Calculate the angle of crack growth corresponding to each load step using maximum circumferen-tial stress theory.h i ¼2tan À114K i I K i II Æ14ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃK i I K i II2þ8s 2435ð2Þ(c)Calculate the ﬁnal coordinates of the crack front points and trajectory angles by approximating thecontributions from each load step by a straight line (Fig.3).(d)Determine the number of cycles,N ,for a maximum of approximately 0.01in.of crack growth forany point along crack front which is small compared to the tooth thickness.9.Perform a least squares curve ﬁt through the new discrete crack front points and update geometryusing the new ﬁtted crack front in FRANC3D.10.Remesh locally and repeat steps 5–10.2.2.Modeling of moving tooth loadsContact in a spiral bevel gear occurs in three dimensions following a path along the tooth surface start-ing from the root and moving up to the top of the tooth on the heel end (Fig.2).In order to model this three-dimensional eﬀect the magnitude and location of contact loads at diﬀerent instants of time over one loading cycle have to be determined.There are no closed-form solutions for the contact loads on a pin-ion tooth due to the complexity of the gear geometry and three-dimensional eﬀects.To this end,numerical tools were developed by Litvin and Zhang [25]to determine the mean contact points on the spiral bevel pinion tooth.In analyzing the present spiral bevel gear,it is assumed that the contact between the gear and pinion follows Hertz theory of elastic contact which takes into account only normal pressure between two bodies and produces an elliptical contact area with a semi-ellipsoidal pressure distribution.The continuous meshing process between a gear and a pinion is modeled by 15discrete load steps.Load steps 5–11are single tooth contact and 1–4and 12–15are double tooth contact.Single tooth contact steps create larger contact areas and larger loads on the tooth surface.Load step 11corresponds to the highest point of single tooth contact.The location of the 15contact ellipses and the magnitude of the contact loads applied over these areas were provided by NASA/GRC.In Ref.[1],contact ellipses were a part of the geo-metry models.Since the ellipses overlapped,four diﬀerent geometry models were needed for each crack conﬁguration.In the current approach,contact loads are no longer a part of the geometry model.This ap-proach brings a substantial decrease in computation time since only one geometry model for each crack conﬁguration is now needed.In the current work,moving contact loads are approximated by interpolation using the shape functions on the surfaces of the loaded elements.This procedure starts with reading the1152 A.Ural et al./Engineering Fracture Mechanics 72(2005)1148–1170mesh information created by JMesh and retrieving the geometry information of the n th (n =1,2,...,15)contact ellipse.After the nodal points deﬁned in three-dimensional coordinates are transformed into a two-dimensional contact space according to the mapping described in [25],mesh nodes falling into the con-tact area bounded by the n th ellipse are determined.If the node is within the contact area work equivalent nodal contact forces are calculated following standard ﬁnite element procedures.All the information for nodes found by this search and the corresponding loads are written out to a ﬁle completing the procedure.2.3.ResultsThree-dimensional,parallel ﬁnite element analyses were performed for an OH-58spiral bevel pinion gear for 54crack growth steps.In the previous serial BEM-based analysis,only 13crack growth steps were per-formed.One crack growth step in the FEM analyses consists of 15static ﬁnite element analyses in order to simulate moving loads on the pinion tooth.After the 54th crack growth step the analysis was stopped be-cause it was concluded that propagating the crack further would not provide additional insights into the simulations and results.All predictions were based on the methodology outlined in Section 2.1.Fig.4shows the initial surface FE mesh of the spiral bevel pinion gear.As seen in the ﬁgure,the mesh is ﬁner on the tooth where the initial crack is located.The volume mesh of the gear is composed of 10-noded tetrahedra which model quadratic variation of displacement over the element domain.Modeling only three teeth of the pinion was adequate to obtain accurate results.A study was done in [26]which showed the comparison of SIFs between explicit modeling of three and nine teeth of the pinion.For both models,K I and K II values were very similar leading to the conclusion that the three teeth model is suﬃcient for the simulations.The initial ﬂaw is modeled as a semi-elliptical crack with dimensions 0.125in.long and 0.05in.deep,although the actual EDM notch was rectangular.This diﬀerence is introduced by the attempt to avoid sharp corners which create stress concentrations leading to inaccurate numerical results.However,the initial notch shapes are still very similar in size and location and the predictions from the simulations and experimental results can still be compared.The initial crack is introduced into the ﬁllet of the middle tooth of the concave side.The displacements in all directions with respect to the global coordinate system at the end of the long shaft of the pinion and the normal component of displacements on the surfaces of the smaller shaft are set tozero.Fig.4.A spiral bevel pinion model with surface FE mesh:(a)whole pinion,(b)close-up view of pinion teeth.Note the location of the initial crack in the middle tooth.(c)Initial crack shape and dimensions.A.Ural et al./Engineering Fracture Mechanics 72(2005)1148–11701153Figs.5–7show Mode I,II and III stress intensity factors,respectively,for the initial crack conﬁguration for the ﬁrst eleven load steps.Only load steps 1,5,9and 11are shown in the ﬁgures for clarity.Since a crack is not assumed to advance when its SIF is smaller than the SIF of the previous load step,only the ﬁrst 11steps practically contribute to crack growth calculations.In these ﬁgures,crack front position cor-responds to the points near the crack front at which SIF values are evaluated.The orientation of the initial crack is shown in Fig.4c.In the initial step of crack growth simulation,the crack front was discretized such that there were 222points at which SIF values were calculated.This is compared to only 61points previ-ously used with the BEM-based model [1].In Fig.5,Mode I SIFs show an increasing trend as the load moves up the tooth surface (i.e.the load step number increases)since more load is transferred to the pinion tooth and the lever arm between the contact points and the crack increases.Maximum SIFs occurfor1154 A.Ural et al./Engineering Fracture Mechanics 72(2005)1148–1170A.Ural et al./Engineering Fracture Mechanics72(2005)1148–11701155step11after which SIF values decrease due to switching to double tooth contact.The inﬂuence of Mode III SIFs on the crack shape predictions was not taken into account.Fig.8shows the crack shape predictions by the parallel FEM on the tooth surface and cross-section of the tooth for several crack growth steps including the initial andﬁnal conﬁgurations of the crack.Fig.9 contains a close-up view of the last step of crack growth viewed from the toe end of the tooth,and a detail of the corresponding mesh.Fig.9b shows that JMesh is capable of meshing very complex crack shapes while still producing well-shaped elements.parison of present and previous resultsThis section compares the present results with those reported in[1]in terms of accuracy and eﬃciency. One of the most signiﬁcant improvements in the present work is the diﬀerence in the solution time of the problem with the use of a better simulation environment and state-of-the-art hardware.This comparison is presented for historical progress reasons only.It is not to show parallel FEM is better than serial BEM.A parallel PC-cluster at the Cornell Theory Center was used to perform the crack growth simulations with an in-house-developed,parallel,FEM solution framework.The cluster is ranked49th(1068GFlops) in the21st list of the Top500supercomputer sites(published in June,2003).Its hardware consists of192 Dell PowerEdge2650servers with a Gigabit Ethernet interconnect,running Microsoft Windows2000Ad-vanced Server as its operating system.Each node is equipped with2Intel Xeon processors clocked at 2.4GHz and having4GB of RAM.For our simulations,a maximum of128nodes was used and only one processor per node was utilized(Table2).One load step of the largest problem(3,044,077DOF)takes about10min on64processors.Gigabit Ethernet is by no means a very fast(low latency)interconnect,and that is the main reason why going to128processors reduces the solution time by only about20%.Fortu-nately,all load steps can be dealt with independently and we can run two of them simultaneously on two sets of64processors each.This increases the overall throughput and lets us complete one load cycle in about1.5h on128processors.With advances in solver technology(optimized matrix ordering/storage, more eﬀective preconditioners)and faster I/O,this time can be reduced further.Preliminary tests indicate that a further50%reduction of the execution time can be achieved this way.The performance comparison in Table 2clearly shows that there is a very signiﬁcant improvement in computation time with the development of a parallel FEM solver,even when adding signiﬁcant resolution to the solution.The solution time for the previous serial BEM simulations was about 65h for onecrackFig.8.Crack shape predictions by parallel FEM on tooth surface and tooth cross-section.1156 A.Ural et al./Engineering Fracture Mechanics 72(2005)1148–1170growth step,whereas the parallel FEM simulations took much less time for each crack growth step,even though the models have much higher resolution.The number of unknowns for the FEM was about a mil-lion at the initial step,and increased to more than 3million as the crack front advanced.3D volume mesh-ing of one model,still performed in sequential and not parallel mode,ranged from 20min for thesmallest Fig.9.(a)Close-up view of the simulated crack after the last step of crack growth and (b)detail of mesh corresponding (a).Table 2Comparison of performance between present parallel FEM and previous serial BEM simulationsItemFEM BEM Computer power128nodes a Single DEC-Alpha PC-cluster,2.4GHz Workstation,175MHz Number of unknowns$1–3million 6700(coeﬃcient matrix)(sparse,symmetric)(dense,non-symmetric)Max.solution time per load cycle$1.5h $60h (one load cycle =15load steps)(4models)Typical time for one crack step$4.5h b $65h c aOnly one processor per node is used.bSolution time plus 3h post-processing and remeshing.c Solution time plus 5h post-processing and remeshing.A.Ural et al./Engineering Fracture Mechanics 72(2005)1148–11701157model to about an hour for the largest models.Of course,solution time for a single crack step using the previous serial BEM-based approach would be substantially reduced with use of a similar,faster processor. However,resolution in terms of length of crack step,and,therefore,crack geometry and accuracy of SIFs would still be wanting.Improvement in the computation time for each crack growth step allowed us to increase solution reso-lution by taking smaller crack increment steps and to simulate more steps of propagation.Figs.10–12show the comparison of crack area,depth and crack front length by FEM and BEM.The summary of the infor-mation from theseﬁgures is also given on Table3.These plots indicate that the current fatigue growth rate is marginally lower when we compare the crack area and the crack front length,and more cycles are re-increasequired to achieve the same amount of crack growth when compared with previous results.A rapidTable3Comparison of crack growth amount between present and previous simulationsResults Present Previous[1] Number of steps5413Total number of cycles383,000311,000 Final crack front length 1.55in. 1.42in. Final crack area0.319in.20.186in.20.188in.Final crack depth0.268in.in the slope of the curves at high cycles can be observed in Figs.10and11which indicates that the simu-lations cover most of the useful fatigue life of the pinion.Figs.13–15show the SIF comparisons for load steps3,7and11.Theseﬁgures show that Mode I SIF calculations using displacement correlation and the BEM are higher than those from using J-integral and the FEM for load step3and7.However for load step11,the values are almost the same throughout the crack front.Figs.16and17present the comparison of SIF variation over one load cycle and non-proportional load history.In Fig.16,it is seen that K I predictions are lower in the J-integral/FEM analysis than the displace-ment correlation/BEM analysis over most of the steps.As seen in Fig.17,the ratio of K II to K I over15load steps shows a similar trend as observed in the BEM-based analysis with a slight diﬀerence in values.These diﬀerences in SIFs inﬂuence the fatigue life predictions which depend on K I values and also crack growth direction which depend on the ratio of K II to K I.Crack shape comparisons in Fig.18show that,on the tooth surface,crack trajectory predicted by cur-rent FEM-based simulation is similar to the previous BEM-based results.The deviation of crack path at thetoe end in the previous predictions was also observed in current predictions.On the heel end,current results exhibit a less steep propagation angle than the experimental trajectory.On the tooth cross-section it is ob-served that the current predicted crack trajectory is less steep than previous BEM and experimental results.Current results also exhibit a shallower ridge formation than the experiment.Although the FEM-predicted crack path still does not exactly reproduce the crack shape observed in experiments,it captures the global behavior of the crack propagation shape.An important remark is that the crack trajectory at the cross-sec-tion changes along the crack front.The comparison shown in Fig.18is one sample for the cross-section at the midpoint of the initial crack.The reason for the deviation of crack path on the toe end is most probably the end product of the inac-curate representation of the contact loads.Hertzian model used in the simulations assumes that the location and magnitude of the contact loads are constant.However,the pinion tooth becomes more ﬂexible as the crack grows and the amount of load transferred decreases,also changing the SIFs.Therefore,a better rep-resentation of the contact loads accounting for these eﬀects is necessary.This can be achieved through ex-plicit 3D contact analysis which is capable of capturing the change in magnitude and location of contact.In the following section,we demonstrate the eﬀect of a growing crack on the contact loads by performing 3D,FEM-based contact analysis.3.Three-dimensional,FEM-based contact analysisThe meshing of a gear and pinion produces loads on the tooth surface that change in magnitude and position in time.In Section 2,analyses assuming Hertzian contact theory were described.This assumption,however,is a simpliﬁcation for a number of reasons:(1)the teeth and rims that transmit the load are ﬂex-ible,(2)assumed elliptical contact area on the tooth surface may not be accurate since the curvatures of the teeth surfaces in contact are not constant over the contact zone,(3)the center of contact,where the maxi-mum contact stress occurs,may diﬀer from the theoretical contact point and (4)most importantly for the current investigation,the tooth ﬂexibility changes as the crack propagates in a tooth.The change in ﬂex-ibility due to cracking may shift the contact area,and change the magnitude of the contact loading.In this section a series of three-dimensional ﬁnite element analyses that model the contact conditions be-tween the gear and pinion explicitly are described.The purpose of this study is to assess what inﬂuence the details of the load transfer through the contact conditions have on the computed stress intensity factors,and through them the predicted crack shape.Three-dimensional,ﬁnite element contact analyses in spiral bevel gears have been undertaken by sev-eral researchers to study the stresses induced at the root and on the surface of the tooth.Earlierworkparison of crack shape predicted by the serial BEM,the parallel FEM and an experiment on the tooth surface and tooth cross-section at the midpoint of crack.by Bibel et al.[27]utilized gap elements to simulate the contact boundary conditions and to evaluate the stresses on the tooth surface.Further study on this subject eliminated the need for using gap elements through the use of contact capabilities of commercialﬁnite element programs.Preliminary results showing the moving contact patches over the tooth surface are reported in Bibel and Handschuh[28].These analyses also incorporated automatic meshing of the gear and pinion via the addition of user subroutines to a com-mercialﬁnite element program.The same authors performed additional analyses in order to compare experimentally measured tooth bending stresses in spiral bevel gears to FEM results[29].Other studies on the contact analysis of spiral bevel gears,including the development of a methodology combining a sur-face integral and aﬁnite element solution,are described by Vijayakar[30].Numerical examples carried out using this approach show the change in the contact area as a result of the misalignment of the gears.The changing stiﬀness of a cracking tooth was investigated in2D spur gears by an analytical model where the gear geometry was mapped to an elastic half-plane and stiﬀness of a cracked spur gear was calculated as a function of Mode I and II SIFs[31].3.1.ApproachThe goal of the present study is to perform contact analyses incorporating cracking to determine the ef-fect of changing toothﬂexibility on the magnitude and location of the contact load and,therefore,on the stress intensity factors.A commercialﬁnite element program,ABAQUS[32],was used to perform the con-tact analysis in conjunction with software developed by the Cornell Fracture Group to calculate fracture-related parameters.A general outline of the approach is as follows:1.Create initial geometry model of the spiral bevel pinion and gear with OSM using the geometry infor-mation provided by the NASA/GRC.2.Specify boundary conditions,material properties and contact surfaces in FRANC3D.3.Specify initial crack in FRANC3D.4.Create a surface mesh composed of triangular elements in FRANC3D.5.Create a3D FE mesh of the model composed of tetrahedra using JMesh.6.Transform the FRANC3D model into an ABAQUS inputﬁle.7.Perform contact analysis in ABAQUS and determine the location and magnitude of the contact loads.8.Calculate SIFs using the results of FEM contact analysis and also using the results from analysis withHertzian contact loads in pare these values and investigate their eﬀects on the crack shape predictions.Geometries of a one-tooth sector of the spiral bevel pinion and gear were created separately in OSM using the information provided by NASA/GRC.This information regarding the geometric positions of points deﬁning the gear set was determined analytically using the method developed by Litvin and Zhang [25].The one-tooth gear and pinion models were created in a common coordinate system with the same axis of rotation(z-axis).Additional teeth of the gear and pinion were created by copying and rotating the orig-inal tooth by an angle equal to360°divided by number of gear teeth.The resulting models were further rotated to orient them in the proper meshing position.At the meshing orientation,there was no interference between the gear and pinion teeth.The analyses used both FRANC3D and ABAQUS.FRANC3D was used to generate the complicated geometry of the gear,to specify the analysis attributes and to deﬁne the crack.Also,it was used as a post-processor to calculate the SIFs.ABAQUS was utilized forﬁnite element contact analysis of the model. In order to perform contact analysis on models with cracks,features that complement FRANC3D and ABAQUS were needed.In this respect FRANC3D was extended to include a capability of specifying the master and slave contact surfaces and to include a translator to convert the information regarding。

基于有限元仿真腐蚀疲劳试验方案研究

基于有限元仿真腐蚀疲劳试验方案研究■ 丰世林李浩（中国民用航空飞行学院航空工程学院）摘要：当前很多研究做了各种有关腐蚀介质对铝合金疲劳寿命影响的试验。

发现很多环境都会加速疲劳裂纹的扩展。

考虑到腐蚀和疲劳的相互作用影响，两者并不仅仅是简单的先后作用关系，同时目前主流试验方案都有需要完善的方面，因此本课题提出一种优于现存腐蚀研究的试验方案：“腐蚀-腐蚀疲劳循环试验”，可以较为全面的实现飞机的飞-续-飞和疲劳预腐蚀同时作用的实际工况，更加完善腐蚀与疲劳的试验方法，并设计一种基于有限元仿真的寿命预测方法。

关键词：航空铝合金，腐蚀疲劳试验，预腐蚀疲劳试验，有限元仿真DOI编码：10.3969/j.issn.1002-5944.2021.08.044Study on Corrosion Fatigue Test Scheme Based on Finite ElementSimulationFENG Shi-lin LI Hao(Aviation Engineer Institute, the Civil Flight University of China）Abstract: Many studies have been conducted on the influence of corrosion media on the fatigue life of aluminum alloys. Many environments are found to accelerate fatigue crack growth. Considering the interaction of corrosion and fatigue, this paper proposed a testing scheme that is superior to the existing corrosion research, “erosion - corrosion fatigue cycle”. This method enables the simultaneous operation of more comprehensive aircraft fly - continue to fly and pre-corrosion fatigue test. It optimizes corrosion and fatigue test method, and provides lifecycle prediction method based on finite element simulation. Keywords: aerospace aluminum alloy, corrosion fatigue test, pre-corrosion fatigue test, finite element simulation2024航空铝合金具有较好的性能，凭借制造与维修检测的优势，这种材料在飞机蒙皮、机翼等构成中十分常见。

钢轨滚动接触疲劳裂纹萌生和磨耗共存预测方法验证

11.1×104 cycles，which is close to that of the specimen
with the maximum crack length in the experiment. It is
observed that the average value of the angle between the
Rail
ZHOU Yu1，2，WANG Zheng1，2，LU Zhechao1，2，LIANG
Xu3，LI Junpeng1，2
loading cycles is about 11×104 to 12×104 cycles. In the
simulation， the predicted crack initiation life is about
次，基本与试验结果中裂纹萌生时出现极大值的试样所对应
的荷载作用次数接近。试验观测到试样表面裂纹开口与滚
动方向的角度平均值约为 45°；仿真预测的裂纹开口与滚动
方向的角度平均值基本与观测到的裂纹开口与滚动方向的
coexistence of rail rolling contact fatigue(RCF） crack
耗共存发展过程，建立轮轮试验条件下的钢轨滚轮
增加润滑或摩擦控制介质，以模拟干摩擦状态下轮
试样裂纹萌生和磨耗共存预测模型，对比试验和仿
轨材料磨耗和疲劳共存过程。
真中的磨耗、裂纹萌生等情况，从而验证裂纹萌生和
2. 1
磨耗发展共存预测方法。
试样设计与制作
试验采用重载铁路 75 kg·m−1 热处理钢轨材料。
fatigue （RCF） experiment was applied to reproduce the

科技文献检索与利用_2015年期末试题及答案_天津大学

《科技文献检索与利用》期末考试试卷(A卷)(2014—2015学年第一学期)姓名: XXX 学号: 3012XXXXXX 座位号:100一、确定下列课题的检索式（每题2分，共10分）1. 重金属污染土壤的微生物生态效应及其修复研究进展重金属*土壤*微生物*（生态效应+修复）2. RFID技术在物联网中的应用及研究（RFID+射频识别）*（物联网+感知中国）3. 基于云计算的WLAN和GPRS融合方案研究云计算*（WLAN+无线局域网）*（GPRS+通用分组无线服务技术）4. 航空发动机涡轮叶片冷却技术综述航空发动机*（涡轮+叶轮）*冷却5. ASON技术在高铁通信系统中的应用（ASON+自动交换光网络）*（高铁+高速铁路）*（通信+通讯+信息）二、通过检索数据库写出答案（每题4分，共40分）1. 请列出《减压膜蒸馏过程中的钙镁污染研究》这篇会议论文的来源信息？【作者】宋震宇；李保安；高晓飞；【Author】SONG Zhenyu,LI Baoan,GAO Xiaofei (School of Chemical Engineering and Technology,Tian Jin University,Tian Jin 300072,China)【机构】天津大学化工学院；【摘要】以膜蒸馏过程中钙镁污染为研究对象,通过模拟海水成分,分别考察了单组分及多组分难溶盐对膜通量和膜污染的影响.结果表明,碳酸钙和碳酸镁易于在膜表面形成结晶堵塞膜孔,硫酸钙沉淀主要在膜组件进口端发生堵塞.料液中存在多组分难溶盐时,碳酸钙为污染物的主要形式.【关键词】减压膜蒸馏；钙镁污染；海水淡化；中空纤维；【文内图片】【基金】国家科技支撑计划(2006BAB0A06)【会议录名称】第四届中国膜科学与技术报告会论文集【会议名称】第四届中国膜科学与技术报告会【会议时间】2010-10-16 【会议地点】中国北京【分类号】TQ028.8【主办单位】中国膜工业协会、北京工业大学2. 天津大学冯亮的博士论文题目是什么？《电动汽车充电站规划研究》3.检索德温特专利数据库中高通公司的专利数量，要求：利用专利权人代码。

基于临界距离理论预测T型管节点的疲劳强度

基于临界距离理论预测T型管节点的疲劳强度贺琦;潘军;唐雪松【摘要】依据已有支管受轴向荷载的T型焊接圆管节点的实验数据,使用ANSYS 进行了有限元分析,并利用临界距离理论的点法和线法,预测了构件的疲劳强度.选取第一主应力点沿其最大梯度方向作为临界距离理论的聚焦路径.研究结果表明:预测的疲劳强度与疲劳强度实测值的误差在20％以内.临界距离理论能够在实验数据不足的情况下对焊接管节点的疲劳性能提供较精确的理论预测,为工程应用提供有价值的参考.【期刊名称】《交通科学与工程》【年(卷),期】2019(035)001【总页数】5页(P61-65)【关键词】临界距离理论;焊接管节点;疲劳强度;有限元分析【作者】贺琦;潘军;唐雪松【作者单位】长沙理工大学土木工程学院,湖南长沙410114;长沙理工大学土木工程学院,湖南长沙410114;长沙理工大学土木工程学院,湖南长沙410114【正文语种】中文【中图分类】O346.1管结构广泛应用在海洋平台、桥梁和塔等结构中[1]。

焊接管节点是结构的关键部位，也是结构的薄弱环节。

焊接管节点在焊缝处的结构形式复杂，会产生严重的局部应力集中；载荷作用下，焊接过程中产生的宏观和微观缺陷使其易出现疲劳破坏[2]。

焊接管节点的疲劳问题一直是各国学者研究的热点[3]。

研究焊接管节点的疲劳性能，对高强管结构的安全性具有十分重要的意义。

各国的学者们针对管节点疲劳性能开展了大量的研究工作。

国际管结构协会(CIDECT)发表的空心管结构设计简介中，重点对圆管和矩形管焊接相贯节点疲劳性能设计提供了指南[4]。

国际焊接协会(IIW)对各国研究成果进行了总结，给出焊接管节点疲劳性能评估方法[5]。

此外，美国焊接协会(AWS)和美国石油协会(API)等也开展了一系列的研究，形成了相应的焊接管节点疲劳规范。

在焊接结构的疲劳强度分析过程中，形成了4种不同层次的方法，即：名义应力法、热点应力法、缺口应力法和断裂力学法。

Fatigue crack growth behaviour in the LCF regime in a shot peened

Fatigue crack growth behaviour in the LCF regime in a shot peened steam turbine blade materialB.Y.He a ,⇑,K.A.Soady a ,1,B.G.Mellor a ,Gary Harrison b ,P.A.S.Reed aa Engineering Materials,Engineering and the Environment,University of Southampton,Highﬁeld,Southampton SO171BJ,UK bMaterials Science Centre,University of Manchester,Oxford Road,Manchester M139PL,UKa r t i c l e i n f o Article history:Received 12November 2014Received in revised form 12March 2015Accepted 18March 2015Available online xxxxKeywords:Fatigue crack initiation and propagation Low cycle fatigue (LCF)Shot peeningResidual stress and strain hardening Evolution of crack aspect ratioa b s t r a c tIn this study,short fatigue crack initiation and early growth behaviour under low cycle fatigue conditions was investigated in a shot peened low pressure steam turbine blade material.Four different surface con-ditions of notched samples have been considered:polished,ground,T0(industry applied shot peened process)and T1(a less intense shot peened process).Fatigue crack aspect ratio (a/c )evolution in the early stages of crack growth in polished and shot peened cases was found to be quite different:the former was more microstructure dependent (e.g.stringer initiation)while the crack morphology in the shot peened cases was more related to the shot peening process (i.e.surface roughness,position with respect to the compressive stress and strain hardening proﬁles).Under similar strain range conditions,the beneﬁcial effect of shot peening (in the T0condition)was retained even at a high strain level (D e 11=0.68%),N f ,ground <N f ,T1<N f ,polished <N f ,T0.The a/c evolution effects were incorporated in K -evaluations and used in calculating da/dN from surface replica data.Apparent residual stress (based on crack driving force D K difference)was applied to describe the beneﬁt of shot peening and was seen to extend signiﬁcantly below the measured residual stress proﬁle,indicating the importance of the strain hardening layer and stress redistribution effects during crack growth.Ó2015Published by Elsevier Ltd.1.IntroductionShot peening is one of the most effective surface engineering approaches to improve fatigue resistance,and has been widely applied in a range of components,such as industrial steam turbine components (in the severe stress concentration areas).The shot peening process,as detailed elsewhere [1–3],produces inhomoge-neous plastic deformation in the near surface layer which induces not only residual stress but also an increase in hardness,surface roughness,dislocation density,and also surface defects.The shot peening process is typically controlled by measuring intensity and coverage.The intensity of shot peening can be characterized by an Almen type gauge,which is a thin strip of SAE1070desig-nated as ‘‘A’’,‘‘N’’and ‘‘C’’type which differ in thickness but have the same width and length;while coverage is deﬁned as the ratio of the area covered by peening indentations to the overall treated specimen surface and is expressed as a percentage.Many investigations have focussed on the effect of shot peening on fatigue behaviour in different material systems such as steel,Al and Ti alloys [4–8].The rough surface induced is generally consid-ered to be detrimental to fatigue resistance [4],while both the residual stress and strain hardening proﬁles at,and just below,the surface are considered to improve fatigue resistance [9,10].The beneﬁt of shot peening in the high cycle fatigue regime is well documented [9,11,12],however,in the low cycle fatigue regime,this beneﬁt is more service condition dependent and more com-plex to assess,especially when it comes to residual stress relax-ation or strain hardening changes during the fatigue process.Recent reviews [13,14]have detailed at some length the effects of the shot peening process (surface roughness,plastic deformation as well as residual stress)on fatigue behaviour as well as how the magnitude of these effects can be determined both experimentally and numerically.Although there has been substantial investigation into the effect of shot peening on the fatigue life of different mate-rial systems,systematic research on fatigue crack initiation and propagation behaviour (especially when operating in the LCF regime)in a notch stress ﬁeld has not yet been fully explored.Whilst a few studies have tried to investigate the effect of the near surface layer induced by shot peening,generally only the total fati-gue life has been focused upon,not the speciﬁc evolution of fatigue/10.1016/j.ijfatigue.2015.03.0170142-1123/Ó2015Published by Elsevier Ltd.⇑Corresponding author.Tel.:+442380599450;fax:+442380593016.E-mail address:Binyan.he@ (B.Y.He).1Present address: E.ON Technologies (Ratcliffe)Limited,Technology Centre,Ratcliffe-on-Soar,Nottingham NG110EE,UK.method with incremental layer removal by the electropolishing method which was detailed in[15](electrolyte8%(by volume)of60%perchloric acid solution mixed in solution with92%(by vol-ume)of glacial acetic acid).The fatigue crack behaviour was evaluated by three point bend tests at ambient temperature with a sinusoidal waveform and fre-quency of20Hz on a servo hydraulic Instron8502machine.To simulate the stress concentration feature in the steam turbine, the fatigue samples contain a U-notch that provides a stress con-centration factor$1.6(which has been calculated using an elastic ﬁnite element analysis).This U-notched fatigue sample as well as the relevant S/N data has been reported elsewhere[15,17],as reproduced in Fig.5.Although the fatigue test was under load con-trol with a load ratio of0.1,the true strain range experienced at the notch root was simulated by an elastic plasticﬁnite element model.In the present study,crack initiation and propagation beha-viour were investigated under the same local strain range condi-tions.The true strain in the sample loading direction(D e11)was 0.68%.The effect of any modiﬁcations to material behaviour induced by surface processing,such as surface work hardening, was neglected in this calculation.This allowed a representative comparison to be drawn between the samples tested under differ-ent surface conditions.Interrupted fatigue tests were carried out to evaluate the evolu-tion of crack aspect ratio.Fatigue tests were interrupted at about 65–75%of the estimated fatigue life(based on the S/N curve); the samples were then removed from the test apparatus and oxi-dized in an furnace at600°C for2h.After that,they were kept in liquid nitrogen for up to10min to allow samples to cool down thoroughly to below the ductile to brittle transition temperature. These cooled samples were then broken open with a hammer man-ually and the fracture surfaces were allowed to warm up to ambi-ent temperature in acetone.The interrupted fatigue test with subsequent heat tinting process allows the evolution of crack shape in the depth of the sample to be assessed,since the fatigue crack region after heat tinting is clearly different from the subse-quent brittle fracture area.In addition,a silicone replica technique was used during fatigue testing at differing numbers of cycles to monitor crack initiation and short crack growth behaviour in polished,ground,T0and T1 shot peened cases.Crack length measurement from replication as well as the crack growth rate assessments are extensively described in[17].Stress intensity factor(SIF)K calculations in the present study were based on Scott and Thorpe’s review paper of semi-elliptical cracks[20].The fatigue crack was assumed to be a semi-elliptical crack in aﬁnite thickness plate under a bending condition.1.FEGSEM(SEI mode)micrograph of polished and etched(by Vilella’s Reagent) sample revealing the microstructure of FV448[17].Fig. parison of tensile behaviour in the longitudinal and transverse directions.3.ResultsA comparison of surface roughness obtained by both optical and tactile line measurement techniques for each surface condition is shown in Fig.6.In each case,surface roughness Ra (or Rz )in line proﬁle measurement are comparable in both the optical and con-tact approach.However,area roughness Sa (the arithmetic average of the 3D roughness)and Sz (maximum height of surface rough-ness)in all these four cases are apparently higher than Ra and Rz obtained by 2D proﬁle measurements,respectively.In the ground case,grinding marks play an important role in fatigue crack prop-agation behaviour [17].Roughness Ra in the longitudinal direction (parallel to the grinding marks)is less than that in the transverse direction (normal to the grinding marks).In the shot peened case,Ra in T0is 3.69±0.35l m and 1.40±0.16l m in the less intense shot peened case (T1).3D reconstruction of the as-shot peened sur-face were obtained by Alicona Mex based on SEM images tilted at À5°,0°,5°,as shown in Fig.7.In both the T1and T0cases,shot pee-ned lips at the bottom or edges of shot peened dimples and some crack-like regions are clearly revealed.However,these defects induced by severe plastic deformation in the T0condition appeared more frequently.Quite a thin compressive residual stress layer ($20l m)near surface can be observed in the polished condition,as can be seen in Fig.8.Residual stress obtained in the ground condition was based on measurements on the U-notched geometry,which was detailed in [15].Tensile stress was found on the ground surface in the longitudinal direction while a compressive stress (a very thin layer,$5l m)was observed in the transverse direction.In both directions,tensile residual stress increased gradually up to a maximum point ($400MPa in the longitudinal direction and $250MPa in the transverse direction)at $20l m beneath the sur-face.After that,the value of tensile residual stress decayed to a bal-ancing compressive stress as the depth increased.The total depth of the affected layer in the ground condition is around 100–150l m.For T1,the stress distributions in the longitudinal and transverse direction showed no signiﬁcant difference:the maxi-mum compressive stress was À620MPa at 50l m depth and the total residual stress affected layer extended to about 200l m beneath the surface.For T0,the residual stress is also similar in two directions:the maximum compressive residual stress in both the longitudinal direction and the transverse direction is $600MPa.The depths where the compressive stress reached the maximum value in both directions were all around $150l m,aftermicrographs of the four different surface conditions:(a)polished,(b)ground,(c)T0shot peened condition and (d)illustration in (a)shows the positions of the stringers in the barstock;inclusions of aluminium oxide/silicate and manganese (a)on the L–T face;(b)on the L–S face within the FV448matrix.which the compressive stress decreased gradually to a tensile stress at $340l m depth.There are several different methods that can be applied to the plastic strain proﬁle,such as micro-hardness,X-ray diffraction (XRD)line broadening and electron backscatter diffrac-(EBSD)local misorientation techniques.As discussed exten-sively in [16],the results calculatedfrom the microhardness technique indicated a greater plastic strain depth (resulting deeper yield strength proﬁle)than the other two methods.would lead to non-conservative estimates of component remnantFig.7.3D as-shot peened surface reconstruction by Alicona Mex based on SEM images tilted at À5°,0°,5°:(a)T0and (b)T1Comparison of surface roughness measurements for each surface condition both contact and optical approaches.4B.Y.He et al./International Journal of Fatigue xxx (2015)xxx–xxxdeeper hardening proﬁle (150l m)than that in the less intense process (T1).The fracture surfaces of the interrupted fatigue tests after heat tinting for polished,T0and T1samples are illustrated in Figs.10–12respectively.The remnant crack opening after the fati-gue process allowed oxidation to occur in the fatigued regions dur-ing the heat tinting process.The distinction between the fatigue and brittle failure region was apparent under SEM observation,since the brittle fracture area is more faceted or rough,while the fatigue damage area is relatively smooth.Fig.10(a)shows the overview of the fracture surface in the polished case after the fati-gue test was interrupted at 18,292cycles (about 65–75%of thefatigue life based on the previously established S /N curve).As shown in Fig.10(b)and (c),the cracks identiﬁed were still quite small and individual,since no apparent crack coalescence was observed.Fig.10(b)was the longest crack found in this specimen,with a surface projected crack length of 700l m (measurement based on the fracture surface).Crack shapes were semi-elliptical or near semi-circular;within the central fatigue region,aluminium oxide stringers (e.g.in Fig.10(b))and MnS (e.g.in Fig.10(c))were revealed clearly,and are likely to be the crack initiation sites.However,early crack behaviour in the T0shot peening condi-tion was quite different,as shown in Fig.11.This was probably due to the complex surface condition associated with local plastic(a)(b)(c)region Aregion B(a)Overview of polished case fracture surface after interrupted heat-tinted test;(b)fatigue crack region A and (c)fatigue crack (a)(b)(c)region A region BOverview of T0shot peened case fracture surface after interrupted heat-tinted test;(b)fatigue crack region A and (c)fatigue crack B.Y.He et al./International Journal of Fatigue xxx (2015)xxx–xxx5deformation as well as the residual stress distribution.The fatigue process was interrupted at 36,163cycles (60–70%of the established fatigue life).Fatigue crack shapes were very shallow;ratchet marks in the fatigue region indicate crack coalescence has already occurred at this fatigue stage,and also there were sev-eral crack initiation sites,but these were not from inclusions.However,in the less intense shot peening process (T1),early fatigue crack initiation and propagation behaviour exhibits the features of both the polished (baseline)and T0case,as evidenced in Fig.12(a)and (b).Fig.13(a)illustrates the difference between the real surface crack length 2c and the projected surface crack length 2c project .In the present study,the crack length,2c project ,can be measured from the fracture surface after the interrupted fatigue test.Crack mor-phology during the fatigue process was not only dependent on microstructure,but also varied with load/stress condition.One approach to obtain crack aspect ratio a/c is to measure half surface crack length c project and crack depth a at the deepest position directly.However,since the crack shape was not regular (as shown in Fig.13(b))this deﬁnition of a/c was not considered sufﬁciently(a)(b)Cracks iniƟated from inclusionsT1shot peened case after interrupted heat-tinted test:(a)fatigue cracks initiated from inclusions and (b)shallow (a)2c projecta2c project(b)tensile stressreal fatigue crack region semi-elliptical crack regiontensile stress2ccrack showing (a)the difference between the real crack length 2c and 2c project and (b)crack aspect ratio (a/c )calculationnotched_polished notched_T0notched_T11.01.21.4a /c6 B.Y.He et al./International Journal of Fatigue xxx (2015)xxx–xxxrepresentative.If all these cracks are considered to be semi-elliptical in the present investigation,then crack aspect ratio a/c can be derived more systematically and consistently from mea-sured surface crack length 2c projec t and the approximation of an equivalent semi-ellipse with this value of c project ,based on the total measured fatigue area A .The variation of aspect ratio (a/c )with surface crack length 2c project as well as the nominal crack depth a in both the polished notch and shot peened samples are illustrated in Fig.14(a)and (b),respectively.Generally speaking,crack aspect ratio in the baseline test was around $1,higher than observed in the T0shot peened case,at longer crack lengths the a/c ratio for the baseline condition tended to a value of 0.8.In terms of the baseline condition,for shorter cracks,a/c tends to be slightly higher,for example,the shortest crack identiﬁed in this case is 117l m in length with an aspect ratio a/c of 1.27,whereas it is only 0.94for the longest crack (711l m in length,as illustrated in Fig.10(b)).Thus it appears that in the early stages of crack growth the crack length in the depth direction is longer than the projected half surface crack length,indicating that the crack propagated faster in the depth direction than along the surface.It is thought that the effect of the initiation process via cracking of brittle,vertically aligned stringers in the microstructure produces an initially higher aspect ratio at smaller crack sizes.Under the effect of shot peening,however,the crack aspect ratio was initially very small,indicating a shallow crack shape.The aspect ratio tended to increase gradually as the surface crack length increased.After the aspect ratio reached its maximum value (a/c =0.8),it decreased somewhat with increase of the surface crack length,this is thought to be due to frequentcrackB.Y.He et al./International Journal of Fatigue xxx (2015)xxx–xxx7coalescence.The effect of shot peening on aspect ratio can be seen more clearly if a/c is plotted against crack depth,as shown in Fig.14(b).The depth where the aspect ratio reaches the maximum value of a/c was $120–150l m,similar to the position of the max-imum compressive residual stress ($150l m,as shown in Fig.8)and/or the depth of the shot peened plastic deformation layer ($160l m,as can be seen in Fig.9)for the T0shot peened condi-tion.This shallow crack shape indicated the crack growth rate in the depth direction (i.e.growing into an increasing compressive residual stress ﬁeld)was actually slower than the growth rate at the surface.In the less intense shot peening case (T1),both microstructure and the shot peening effect played an important role in fatigue crack shape evolution.Crack morphology/aspect ratio evolution shows features of both the polished (baseline)and T0shot peened cases and distinction between these two regimes can be visualized in Fig.14(a):where it can be seen that some of these aspect ratios fall into the data cluster for the polished condition while the others ﬁt well with aspect ratios of the T0condition.Fig.5shows that under similar applied strain range conditions,the fatigue life of the ground,T1and polished cases are quite similar,while the T0case still shows signiﬁcant beneﬁt from the shot peen-ing process,even in this low cycle fatigue regime.The variations in c at different number of cycles in polished,ground,T0and T1condi-tion are shown in Fig.15(a),(b),(c)and (d),respectively.What should be noted here is that all the fatigue cracks studied in the pre-sent research are all dominant cracks which coalesced and led to the ﬁnal failure.To make a clear comparison between the different sur-face conditions,all these data points in (a–d)are combined together as shown in Fig.15(e).Half surface crack length c at different fatigue life ratios in all these four conditions are illustrated in Fig.15(f).Fatigue cracks in the baseline condition (polished and ground)appeared at around 50%of fatigue life and after that these cracks developed at a constant rate and accelerated near the end of fatigue life,when the main cracks coalesced,leading to failure.Although the cracks in the T1case were also clearly picked up at 50%of fatigue life,crack coalescence in the later fatigue stages was obvious.However,some of the cracks observed in the T0case in the very early stages of fatigue life were pre-existing (for example,one of the initiating cracks was 51l m,while the other one was 242l m before any cyclic loading had been applied).This indicates that they were pre-existing on the shot peened surface and these pre-initiated cracks started to grow very slowly at $0.1–0.2of fatigue life but the crack lengths did not increase dramatically until 0.7–0.8of fatigue life,where crack coalescence occurred frequently and secondary cracks also began to grow.Based on the number of ratchet marks on the fracture surface,crack initiation sites in the T0condition were as many as 18,while only about 11initiation sites were observed in the polished and ground baseline cases (Fig.16).However,there are only 7initiation sites observed in the less intense shot peening process (T1).Based on the replication studies,cracks in the early fatigue stages were very small and ratchet marks left by early stage crack coalescence were not easy to pared to the shot peened case,crack coalescence in the ground sample occurred infrequently even near the end of fatigue life,partly because there were signiﬁcantly less initiation sites during the fatigue process.4.DiscussionMaterial microstructure played an important role in fatigue crack initiation and propagation.Alumina and MnS are two of the most common non-metallic inclusions present in steel,and these stringers can be clearly identiﬁed in the present study.Since in this study,the fracture surface (crack plane)is actually parallel to the longitudinal direction where these stringers are dis-tributed,in the baseline conditions,these stringers tended to be favoured crack initiation sites.The cracks initiated along the brittle aluminium oxide stringers or inclusions,which were either on the surface or slightly beneath the surface.Since the stringers are in the longitudinally aligned direction,which is parallel to the crack depth direction,at the very early fatigue stage,those fatigue cracks initiated at stringers (or inclusions)were encouraged to propagate in the depth direction,due to the higher stress intensity around these elongated,brittle and mechanically mismatched inclusions.So the initiating inclusion position and shape will strongly affect the initial fatigue crack morphology leading to an initially larger crack aspect ratio (around 1.2).As the crack propagated,the range of stress intensity factor around the initiation sites became less dominant and the crack grew to the more expected equilibrium shape,where the stress intensity factor at both the crack surface and depth are the same.Whilst in the less intense shot peening process (T1),the effect of these inclusions was still signiﬁcant,more intense shot peening (T0)overcame the microstructure dominated initiation process as evidenced by inclusions being seldom found in the fatigue region.In this case,almost all the cracks initiated from the surface with no clear evidence of subsurface crack initiation.Furthermore,for a crack initiated from the rough shot peened surface,cracks tended to propagate along the surface direction rather than the depth direction when the crack tip process zone is within the shot peened affected zone;once it breaks through this region,crack growth in the depth direction becomes faster.This explains why the smaller cracks are shallow (low a/c )in shot peened samples.Compared to the ground surface condition,the fatigue life is slightly longer for the polished notch surface,showing about a 12%improvement.For the T0case,the fatigue life is almost twice that for the polished,ground,or less intense shot peened speci-mens under a similar applied local strain condition (D e 11=0.68%).The improvement of fatigue life is due to a complex interrelation of the effect of the surface roughness induced by the shot peening process,the compressive residual stress distribution as well as the work hardened layer.For many engineering components and structures,short fatigue crack behaviour controls the majority of total fatigue life.A num-ber of researchers have reported that these short cracks propagate much faster than long cracks under equivalent stress intensity fac-tor ranges D K [21–23].Conventionally,small crack data analysis approaches employ secant or polynomial data reduction,assuming that small crack shapes are semi-circular (a/c =1).However,the results of Ravichandran’s study [24,25]strongly indicate that some8 B.Y.He et al./International Journal of Fatigue xxx (2015)xxx–xxxof these apparent characteristics of small cracks,often referred to as anomalous,are in fact partly due to the assumption that a/c =1.He found that allowing for the lower levels of crack closure found naturally in small cracks,and for the a/c variations in D K cal-culations,the scatter in the growth data of small cracks was signif-icantly reduced and was found to be of the same order as in large cracks.In the present study,it is also noteworthy that the crack aspect ratio varies with crack length c (and,ergo,also crack depth a ).The change of aspect ratio in the shot peened condition is espe-cially obvious,varying between 0.38and 0.83,while it is more con-sistent between 0.9and 1.2in the polished notch condition.Therefore,it is necessary to consider the aspect ratio evolution when analyzing fatigue crack initiation and propagation behaviour in terms of the crack tip stress intensity factor.A Linear Elastic Fracture Mechanics (LEFM)calculation of K -equilibrium around the crack front was conducted based on Scott and Thorpe’s review paper [20].A local stress level (D r 11)of 1500MPa in the loading direction was used in calculating the short crack D K levels in the notch root.This stress range was esti-mated using ﬁnite element modelling,implementing an isotropic hardening model based on the monotonic tensile data obtained in the direction perpendicular to rolling.Assuming a notional crack in the polished condition (not considering the shot peening effect),its crack shape area A is ﬁxed,the crack depth a at varying crack aspect ratio a/c (a/c =0.1,0.2,0.3,...,1.8,1.9,2.0)can be obtained.The variation of D K surface and D K depth for cracks with the same fati-gue area but different a/c ratios is illustrated in Fig.17(a).At low aspect ratios,the expected K in the depth direction is greater than that at the surface;whilst at a high aspect ratio the expected K in the surface direction is greater than that in the depth direction when a/c is 0.8,D K surface and D K depth are in equilibrium.This is con-sistent with the experimental crack aspect ratio evolution,where the aspect ratio ($0.8)was achieved in both the baseline and shot peening tests once the crack had grown away from the effect of microstructural initiation and the shot peened affected layer respectively.In fact,the equilibrium a/c also varies with absolute crack size.But it is a challenge to unambiguously characterize this feature through these interrupted fatigue tests,since when the crack length 2c is longer than 1000l m,the fatigue test is in the last stages of fatigue life and crack coalescence events are happening frequently and affecting the aspect ratio measurement for differing reasons.In Fig.17(b),the characterization of the change of equilib-rium a/c at different surface crack lengths was based on the assumption of isolated individual cracks with different surface crack length 2c (50,100,200,500,1000,2000l m).When the sur-face crack length 2c is no more than 500l m,the equilibrium a /c isB.Y.He et al./International Journal of Fatigue xxx (2015)xxx–xxx 90.8,as is the case in observations from the interrupted fatigue test cases.However,as the surface crack length increases,this equilib-rium value decreases gradually,for example,a/c equilibrium is0.75at 1000l m while it drops to0.52if the surface crack length2c is 5000l m.This trend is expressed as equation g(x)in Fig.18(a)and(b),which shows the evolution of crack aspect ratio in both non-peened and shot peened conditions.In the polished and ground case,the evolution of a/c will be given by equation k(x)when crack length2c62065l m,while equation g(x)will be applied to describe a/c if the surface crack length2c>2065l m. While for shot peening cases,equation f(x)describes the trend of crack aspect ratio when2c6289l m and equation g(x)is the appropriate one for cracks longer than289l m.Fig.19(a),(b),(c)and(d)illustrates the fatigue crack growth rates dc/dN(calculated by the secant method)for polished,ground,T0and T1notch samples plotted as a function of D K surface.The crack tip stress intensity factor in terms of D K surface and D K depth discussed in this study consider the evolution of crack aspect ratio, respectively.Again,all these data points in(a–d)are put together for comparison,as shown in Fig.19(e).Fig.19(f)shows the fatigue crack growth rates da/dN as a function of D K depth in these four con-ditions.Although these data are highly scattered,this exhibits typ-ical short fatigue crack behaviour.The dc/dN versus D K surface data gives a reasonable comparison of crack growth rates under similar externally imposed stress/strain states,ignoring any local effects of work hardening or compensating residual stresses.Short crack growth behaviour in both the polished and ground cases is similar. For the T0case,almost all the data points are well below those in polished and ground cases,which indicates the intrinsic beneﬁt of shot peening,even when the varying evolution of crack aspect ratio10 B.Y.He et al./International Journal of Fatigue xxx(2015)xxx–xxx。

疲劳寿命的计算流程

疲劳寿命的计算流程Calculating the fatigue life of a material is a crucial aspect in engineering design. 疲劳寿命是材料工程设计中至关重要的一个方面。

Fatigue life refers to the number of cycles a material can withstand before failing under repeated loading conditions. 疲劳寿命指材料在重复加载条件下能承受的循环次数。

It is essential to understand fatigue life to ensure the structural integrity and reliability of components in various machines and structures. 了解疲劳寿命对于确保各种机器和结构中零部件的结构完整性和可靠性至关重要。

Fatigue failure can lead to catastrophic consequences, so accurate calculation and prediction of fatigue life are crucial. 疲劳失效可能导致灾难性后果，因此准确计算和预测疲劳寿命至关重要。

One of the key components in calculating fatigue life is the concept of stress amplitude. 计算疲劳寿命的关键组成部分之一是应力幅概念。

Stress amplitude refers to the difference between the maximum and minimum stresses experienced by the material during a loading cycle. 应力幅指的是材料在加载周期中经历的最大和最小应力之间的差异。

论文英文翻译

Intelligent lighting control systemAbstractThis paper studies of intelligent street lamp energy saving control system is aiming at existing in urban lighting on the huge energy consumption and development based on SCM system, set the soft starter to function , automatic starting and stopping, intelligent pressure regulating control and new energy-saving control voltage control in one body. Intelligent street lamp energy saving control systems will be theorist power changing unit and intelligent control system by combining, high voltage and low voltage variable reactor isolation, a winding variable reactor (HVT) and street lamp in series, will be secondary windings and thyristor and fuzzy control algorithm with associated the control system by changing its low voltage to control the winding voltage hv winding, so as to achieve the change, the effects of voltage change street lamps in order to realize the soft start and pressure regulatingI. INTRODUCTIONwith the rapid development of our economy, electricity consumption is subsequently fast growth. Electric power resource has become shortage resources. How to energy consumption has become the hot topic research in recent years., the power of AE analysis is the possibility to directly observe the process of deterioration. For this reason, AE has the potential to provide critical information about the structural integrity. The AE technique offers a distinct advantage over conventional nondestructive testing techniques because it allows for the real time, in-situ monitoring of in-servicestructures.This paper describes the AE techniques applications in civil engineering. The main contents included are: Part .Review of AE technique. Part . Structure health monitoring system, including offshore platform, dam, masonry arch bridge, concrete structure, steel structure, etc. Part .Structural crack detection and monitoring, including concrete and steel structures. Part .Structure integrality detection and residuallife prediction. At last, Part .A prospect is made about the research direction in this field.II. REVIEW OF AE TECHNIQUEAcoustic emission (AE) is defined as the class of phenomena whereby transient elastic waves are generated by the rapid release of energy from localized sources within a material [1].In order to quantify the material behavior under this type of stress, the signals are processed to develop one or more of the following parameters [2]:Total counts (the number of threshold crossings above an arbitrary signal level are counted).Count rate (the number of threshold crossings above an arbitrary signal level per unit of time is measured).Events (the number of discrete signals above a specified threshold are counted; e. g., each of the traces of Fig. 1 would be considered single events); or event rate.Amplitude (the signal strength is measured); or amplitude distribution.In comparison with other non-destructive techniques, acoustic emission technique has two important advantages [3]: one is that AE technique can give valuable information what’s going on inside of the material, and the other one is that it gives a capability of on-line monitoring during in-service of structures or facilities. So, the AE technique has emerged as a powerful non-destructive tool to detect or evaluate damages and monitor in the field of safety of civil engineering structures.III. STRUCTURE HEALTH MONITORING SYSTEMUntil this time, AE technique has been applying in many fields, e.g., aircraft structure[4], offshore platform[5], pressure equipment[6], dam[7], concrete[8], steel[9], etc.AE technique was applied into civil engineering later compared with other fields, but developed rapidly. Structure health monitoring systembased Acoustic Emission (AE) Techniques on civil engineering structures developed fleetly during 1980s.Bassim, M. Nabil [10] (1985) invented and patented a new system for continuous monitoring of large structures using acoustic emission was. This system is based on a two-step approach and uses small size, low cost surveillance unitscontaining a microprocessor and which is software controlled to continuously monitor the structure and extract features of the acoustic emission activity.Rogers, L. M [5] (1987) gives results of acoustic emission (AE) monitoring of structures to provide information on integrity and fitness for purpose. Applications both locally to monitor known defects or weld repairs in areas of hot spot stress and globally, in search of the most severe defects present in large areas of the structure are considered. By studying AE during the fatigue testing of full scale tubular elements under controlled laboratory conditions it has been possible to define levels of acoustic emission activity by which the severity of defects in normally inaccessible areas can be determined, e. g. in the sub sea node joints of offshore structures.With the high associated costs of commercial AE systems, AE techniques were limited wider exploitation of in the field of structural monitoring. In 2003, Holroyd.T.J and his partners [11] had explored whether simpler solutions might be usefully applied to the field of structural health monitoring. They developed an AE system that makes additional information readily accessible to civil and structural engineers. Figure 1 shows the prototype system that they had developed is comprised of a combination of three elements; AE sensors, mufti channel measurement nodes and a controller module.Various rig and field tests have provided evidence that when productionised it will successfully combine sensitive detection flexibility and autonomous operation.IV. STRUCTURAL FATIGUE CRACK DETECTION ANDMONITORINGNowadays, concrete and steel are widely used structural material for civil structures. The development of non-destructive techniques to evaluate deterioration of concrete and steel structures is one of the most important issues for an effective maintenance. Especially, structural fatigue crack that occurs under long-term service diction and monitoring is very concernful technology in this field. Figure 2shows the schematic diagram of the Fatigue-cracking specimen with transducers mounted.Before 1970, several previous studies about structural fatigue crack detection and monitoring based AE technique had been developed [13], [14].In 1971, NAKAMURA.Y [15] expatiated that an acoustic emission monitoring system designed to detect, in real time, initiation and growth of cracksin a complex structure during static as well as fatigue testing has been developed. The system is being used successfully in static and fatigue testing of full- scale, as well as small-scale specimens of aircraft components and structures. Then, in 1989 Bowles, S.J. [16] studied how to discriminate between AE due to different sources, and the activity in each zone was analyzed in terms of its load-cycle dependence. Wang, Z.F. et al. [17] (1992) investigated the relation between AE characteristics and fatigue crack closure, and tries to find a new way of monitoring crack closure. Results showed that AE monitoring can be used to determine fatigue crack closure very accurately and conveniently.To achieve the practical monitoring of AE signals from fatigue cracks with effective noise filtering, several new researches have been developing. Neural networks were used for detection of crack growth and estimation of crack depth. [18]. Laser based ultrasonic (LBU) technique had been developed to characterize materials properties and detect flaws in materials [19].V. STRUCTURE INTEGRALITY DETECTION AND RESIDUAL LIFE PREDICTIONThe modern structures mostly receives circulation load more or less, but from this the fatigue damageaccumulation which causes the main reason which the structure finally expires. Therefore, it is very significative to carry on fatigue damage degree and residual life prediction accurately and effectively for structures.In 1983, Simons, Fuller, Michael.D.et el. [20] firstly used the AE technique for the Offshore platform integrity.Rogers L. M [21] (1987) given the results of acoustic emission (AE) monitoring of structures to provide information on integrity and fitness for purpose. By studying AE during the fatigue testing of full scale tubular weldments under controlled laboratory conditions it has been possible to define levels of acoustic emission activity by which the severity of defects in normally inaccessible areas can be determined, e. g. in the sub sea node joints of offshore structures.As practical illustrations, in 1991 Royles.R [22] used the AE technique in the testing of masonry arch bridges. Theimplications for the use of an acoustic signature in the integrity assessment of masonry arch bridges were considered.Colombo, S. et al[23](2003) presented the description and results of an acoustic emission (AE) monitoring exercise on concrete bridge beams in situ, as part of a larger project aimed to develop an Advice Note on the use of AE to evaluate the structural conditions of concrete bridges. From the results one is able to distinguish between the different structural behaviors of the beams - thus showing that the AE method is a promising way to evaluate the condition of an in-situ structure.Up to the minute, Carpinteri.A.et al. [24] (2007) used AE technique to identify defects and damage in reinforced concrete structures and masonry buildings. In addition, based on fracture mechanics concepts, a fractal or multiscale methodology is proposed to predict the damage evolution and the time to structural collapse.VI. THE PROSPECT OF AE TECHNIQUEThe predominance of the AE technique is obvious and affirmative, but at present the disadvantage of AE is also incontestable. First, AE signals are usually very weak; thereby background and extraneous-noise rejection is extremely important in the practical application. Thus, signal discrimination and noise reduction are very difficult, yet extremely important for successful AE applications. Second, a perfect and effective data analysis method that tends to reject noise from testing sources is still nonexistent. Third, the higher precise data gathering system is still expectant in the future. Thus, the technique which devotes to solve the above-mentioned problems becomes the hotspots in this field, and can sum up to the following several aspects:-New type AE sensors, include: low-profile fiber optic-based AE sensor [25], fiber-optic sensor based Doppler Effect in a curved light waveguide, [26], wireless AE sensor [27]-New data gathering systems include: advanced acoustic emission system with accurate source location [28], AE measurement system with laser interferometer [29].-New data analysis methods, include: neural networks [30, 31], wavelet analysis [32], [33] VII. CONCLUSIONNon Destructive Testing and Health Monitoring on civil engineering structures based Acoustic emission (AE) techniques have been brief summary. Indubitably, Acoustic emission techniques can play a significant role for the detection and monitoring of civil engineering structures since they are able to reveal hidden defects leading to structural failures long before a collapse occurs. However, currently most of the existing AE data analysis techniques which include AE sensors, data gathering systems and data analysis methods seem not be appropriate for the requirements of an accurate and effective AE system. Further developments based on this field will bring AE techniques into greater far-ranging applications and make this technology more perfect in the future.VIII. ACKNOWLEDGMENTThe authors would like to acknowledge the following individuals for their support and contributing work on this project:[1]Vizimuller, P.: ‘RF design guide-systems, circuits, and equations’ (ArtechHouse, Boston, MA, 1995)[6]R. Dye, “Visual Object-Orientated Programming,” Dr. Dobbs MacintoshJournal, Sept. 1st ( 1991).[1]Weilian QU, Professor of Wuhan University of Technology.[2]Beilei XU, Graduate student of Nanchang University.IX. REFERENCES[3]ASTM Standard Definitions of Terms Relating to Acoustic Emission,ASTM subcommittee E07, ASTM E610-82, 1982.[4]R. M. Koerner, W. M. McCabe, and A. E. Lord, Jr., "Overview of Acoustic Emission Monitoring of RockStructures," Rock Mechanics, 14, pp.27-35, 1981.[5]Dong-Jin Yoon, Philip Park. "Assessment of Crack Activity by Acoustic Emission in ConcreteStructures," presented at the 12th A-PCNDT 2006– Asia-Pacific Conference on NDT, Auckland, New Zealand., 2006.[6]Bailey, C. D. "Acoustic Emission for In-Flight Monitoring on Aircraft Structures, "Materials Evaluation,vol. 34, n 8, pp.165-171, Aug, 1976.[7]Rogers, L. M. "Detection and Monitoring of Cracks in Offshore Structures by Acoustic Emission,"American Society of Mechanical Engineers, vol.10, pp.55-60, 1987.[8]Lovaas, Steina."Acoustic Emission of Offshore Structures Attenuation Noise Crack Monitoring," inSpec Suppl J Acoust Emiss, pp.161-164, 1985.[9]Simons, Daryl B., Li.Rug-Ming, Chen.Yung Hai, V onderHaar and Thomas.H. Brubaker, Thomas A."Acoustic Emission For Dam Safety Monitoring," In Proc. 1983. Conference on Frontiers in Hydraulic Engineering pp. 465-466.[10]H oiseth, K. "Monitoring of concrete structures by means of acoustic emission and strain," NordicConcrete Research, n 7, pp.135-151, 1988.[11]Y oon, Dong-Jin Jung, Juong-Chae, Park.Philip, Lee.Seung-Seok."AE characteristics for monitoringfatigue crack in steel bridge members," InProc.2000 SPIE - The International Society for Optical Engineering, pp.153-162.[12]H off, A. B. M and Arrington.M."Acoustic Emission Monitoring of a Node in an Off-Shore Platform,"Spec Suppl J Acoust Emiss, pp 165-170, 1985.[13]H olroyd, Meisuria.H.M, Lin and D., Randall. N. "Development of a practical acoustic emission-basedstructural monitoring system. Insight,"Destructive Testing and Condition Monitoring, vol.45, n 2, pp.127-129,Feb. 2003.[14]S. Smith and T. M. Morton. "Acoustic-emission Detection Techniques for High-cycle-fatigueTesting,"Experimental Mechanics .pp.193-198, 1973.[15]C. E. Hartbower, W. W. Gerberich, and P. P. Crummins. Welding Journal Research Supplement vol.47,pp.1-18.1968.[16]W. W.Gerberich and C. E. Hartbower.International Journal of Fracture vol.3, pp.185-187.1967.[17]N AKAMURA.Y. "Acoustic emission monitoring system for detection of cracks in a complexstructure ,".Mater Eval, vol. 29, pp. 8-12 , Jan, 1971,[18]B owles.S.J. 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不锈钢的疲劳裂纹扩展有限元模拟-英文版(另有中文翻译)

Modeling of fatigue crack growth of stainless steel 304LFeifei Fan,Sergiy Kalnaus,Yanyao Jiang *Department of Mechanical Engineering (312),University of Nevada,Reno,NV 89557,USAa r t i c l e i n f o Article history:Received 7November 2007Received in revised form 9June 2008Keywords:Damage accumulation Fatigue crack growth Fatigue criteriona b s t r a c tAn effort is made to predict the crack growth of the stainless steel 304L based on a newly developed fatigue approach.The approach consists of two steps:(1)elastic–plastic ﬁnite element (FE)analysis of the component;and,(2)the application of a multiaxial fatigue cri-terion for the crack initiation and growth predictions based on the outputted stress–strain response from the FE analysis.The FE analysis is characterized by the implementation of an advanced cyclic plasticity theory that captures the important cyclic plasticity behavior of the material under the general loading conditions.The fatigue approach is based upon the notion that a material point fails when the accumulated fatigue damage reaches a cer-tain value and the rule is applicable for both crack initiation and growth.As a result,one set of material constants is used for both crack initiation and growth predictions.All the mate-rial constants are generated by testing smooth specimens.The approach is applied to Mode I crack growth of compact specimens subjected to constant amplitude loading with differ-ent R -ratios and two-step high–low sequence loading.The results show that the approach can properly model the experimentally observed crack growth behavior including the notch effect,the R -ratio effect,and the sequence loading effect.In addition,the early crack growth from a notch and the total fatigue life can be simulated with the approach and the predictions agree well with the experimental observations.Ó2008Elsevier Ltd.All rights reserved.1.IntroductionLoad-bearing engineering components are often sub-jected to cyclic loading and failure due to fatigue is of a great concern.Generally,fatigue process consists of three stages:initiation and early crack growth,stable crack growth,and ﬁnal fracture.Traditionally,the crack growth rate (d a /d N )is expressed as a function of the stress inten-sity factor range (D K )on a log–log scale.The stable crack growth results under constant amplitude loading with dif-ferent R -ratios (the minimum load over the maximum load over a loading cycle)are often represented by the Paris law (Paris and Erdogan,1963)and its modiﬁcations (Walker,1970;Kujawski,2001).Different materials behave differ-ently under constant amplitude fatigue loading.Some materials display a R -ratio effect:crack growth rate curves are coincided for the same R -ratio,but a higher R -ratio re-sults in a higher crack growth rate (Kumar and Garg,1988;Pippan et al.,2005;Wu et al.,1998;Zhao et al.,2008).Other metallic materials do not reveal any R -ratio effect,and the curves for constant amplitude loading overlap in a log–log scale (Crooker and Krause,1972;Kumar and Pan-dey,1990;Wang et al.,to appear ).The fatigue crack growth behavior under variable amplitude loading is another subject that has been studied for a number of years.The application of an overload (ten-sile load of high magnitude applied over one cycle pre-ceded and followed by constant amplitude loading)or change in the loading amplitude (so-called high–low se-quence loading experiments)can introduce profound effects on the fatigue crack growth.For most metallic materials,the application of the abovementioned loading schemes results in a crack growth rate retardation.Based on the linear elastic fracture mechanics (LEFM)concept,such a transient behavior is often modeled by using the stress intensity factor concept and by introducing correc-tion factors to the Paris law on the stable crack growth0167-6636/$-see front matter Ó2008Elsevier Ltd.All rights reserved.doi:10.1016/j.mechmat.2008.06.001*Corresponding author.Tel.:+17757844510;fax:+17757841701.E-mail address:yjiang@ (Y.Jiang).Mechanics of Materials 40(2008)961–973Contents lists available at ScienceDirectMechanics of Materialsj o u r n a l h o m e p a g e :/loc ate/mechmatregime.A model of such a type was introduced by Wheeler (1972)and can be viewed as a practical way of treating the effects of variable amplitude loading.Several modiﬁcations on Wheeler’s model have been proposed(Kim et al.,2004; Yuen and Taheri,2006;Zhao et al.,2008)targeting the par-ticular shapes of the crack growth curves for different materials subjected to variable amplitude loading.These models have little or no physical basis and the results of the crack growth experiments are needed in order to ob-tain a set ofﬁtting constants to calibrate the models.Since its introduction by Elber(1970),the crack closure concept is often used to explain crack growth behavior.The retardation in crack growth rate generated by a single ten-sile overload was explained by using the crack closure con-cept in Elber’s later study(Elber,1971).The concept of K op was introduced as a stress intensity factor corresponding to the crack opening load,and the effective stress intensity factor range from K op to K max was considered as a crack driving parameter.As a result,the contribution to crack propagation comes from a part of the total stress intensity factor range corresponding to the part of the cycle when the crack is open.Such an approach is used to explain the R-ratio and variable loading effects.However,the crack closure method has been under criticism based upon experimental observations(Lang and Marci,1999;Sada-nanda et al.,1999;Silva,2004;Feng et al.,2005)and numerical simulations(Jiang et al.,2005;Mercer and Nich-olas,1991;Zhao et al.,2004).Crack-tip blunting has been used to explain the crack advance(Gu and Ritchie,1999;Tvergaard,2004).The retardation caused by an overload is attributed mainly to the compressive residual stresses ahead of the crack tip, plasticity induced crack closure behind the crack tip,or the combination of these two.The initial acceleration in the crack growth immediately after the application of an overload was explained as a result of the tensile residual stress due to crack-tip blunting(Makabe et al.,2004).The ﬁnite element analysis was used to analyze the stress dis-tribution and the crack opening displacement which was related to the variable amplitude loading effects(Zhang et al.,1992;Ellyin and Wu,1999;Tvergaard,2006).Generally,a fatigue crack is nucleated at a notch due to the stress concentration.The so-called notch effect on short crack behavior exists and the crack growth rate may be higher or lower than that expected based on the stable growth.Extensive research has been carried out to study the crack initiation and early crack growth behavior from a notch.Around a notch,a transition zone exists and the fatigue crack growth rate may decelerate,accelerate,or non-propagate after the crack initiation under constant amplitude loading.In order to model the short crack growth behavior from a notch,efforts were concentrated on the‘‘effective stress intensity factor”near the notches (Sadanandam and Vasudevan,1997;Dong et al.,2003; Teh and Brennan,2005;Vena et al.,2006),notch tip plas-ticity(Li,2003;Hammouda et al.,2004),and the combina-tion of crack tip cyclic plasticity and the contact of the crack surfaces(Ding et al.,2007a).A recent effort by Jiang and co-workers(Ding et al., 2007a,b;Feng et al.,2005;Jiang and Feng,2004a)at-tempted to use a multiaxial fatigue criterion to unify the predictions of both crack initiation and crack growth.The notion is that both crack initiation and the subsequent crack growth are governed by the same fatigue criterion.A material point fails to form a crack once the accumula-tion of the fatigue damage reaches a certain critical value. The approach has been applied to1070steel with success. The predictions of the early crack growth from notches (Ding et al.,2007a;Jiang,Ding and Feng,2007),the stable crack growth(Feng et al.,2005;Jiang and Feng,2004a; Jiang,Ding,and Feng,2007),the overload effect(Jiang and Feng,2004a;Jiang,Ding,and Feng,2007),the R-ratio effect(Jiang and Feng,2004a;Jiang,Ding,and Feng, 2007),and the crack growth under direction-changing loading(Ding et al.,2007b)agreed well with the experi-mental observations.All the predictions of the crack growth were based on the material constants generated from testing the smooth specimens.In the present investigation,the aforementioned ap-proach is used to simulate the crack growth from the notched specimens made of the AISI304L austenitic stain-less steel.The notch effect on the early crack growth,the R-ratio effect,and the inﬂuence of the loading sequence are modeled.The stress analysis is conducted by using theﬁ-nite element method implementing a robust cyclic plastic-ity model.The predicted results are compared with the results of the crack growth experiments.2.Crack growth modelingIn the present investigation,the fatigue approach devel-oped by Jiang and co-workers(Jiang and Feng,2004a;Jiang et al.,2007)is used to model the crack growth of the stain-less steel304L.The approach is based on the assumption that any material point fails if the accumulation of the fa-tigue damage reaches a critical value on a material plane.A fresh crack surface will form on the material plane at the material point.Essentially,the approach consists of two major computational steps:a)Elastic–plasticﬁnite element(FE)stress analysis forthe determination of the stress and strain history atany material point of a component,and,b)Application of a multiaxial fatigue criterion utilizingthe stress and strain obtained from the previous stepfor the determination of crack initiation and crackgrowth.The following sub-sections describe the methods em-ployed in the current study.2.1.Cyclic plasticity model and multiaxial fatigue criterionEarlier studies indicate that an accurate stress analysis is the most critical part for the fatigue analysis of the mate-rial(Jiang and Kurath,1997a,b;Jiang and Zhang,2008; Kalnaus and Jiang,2008;Jiang et al.,2007).If the stresses and strains can be obtained with accuracy,fatigue life can be reasonably predicted by using a multiaxial fatigue criterion.The elastic–plastic stress analysis of a notched or cracked component requires the implementation of a962 F.Fan et al./Mechanics of Materials40(2008)961–973cyclic plasticity model into FE software package.The selec-tion of an appropriate cyclic plasticity model is crucial for an accurate stress analysis of a component subjected to cyclic loading.Cyclic plasticity deals with the non-linear stress–strain response of a material under repeated external loading.A cyclic plasticity model developed by Ohno and Wang (1993,1994)and Jiang and Sehitoglu (1996a,b)is used in the present FE simulations of the stress and strain response in a notched or cracked component.The model is based on the kinematic hardening rule of the Armstrong–Frederick type.Basic mathematical equations constituting the model are listed in Table 1.A detailed description of the plasticity model together with the procedures for the determination of material constants can be found in corresponding refer-ences (Jiang and Sehitoglu,1996a,b ).The choice of the cyc-lic plasticity model was based on its capability to describe the general cyclic material behavior including cyclic strain ratcheting and stress relaxation that occur in the material near the notch or crack tip.The plasticity model listed in Table 1was implemented into the general purpose FE package ABAQUS (2007)through the user deﬁned subroutine UMAT.A backward Euler algorithm is used in an explicit stress update algo-rithm.The algorithm reduces the plasticity model into a non-linear equation that can be solved by Newton’s meth-od.The corresponding consistent tangent operator is de-rived for the global equilibrium iteration,which ensures the quadratic convergence of the global Newton–Raphson equilibrium iteration procedure (Jiang et al.,2002).A critical plane multiaxial fatigue criterion developed by Jiang (2000)is used for the assessment of fatigue dam-age.The criterion can be mathematically expressed as follows,d D ¼r mrr 0À1m 1þr r fb r d e p þ1Àb s d cpð1ÞIn Eq.(1),D represents the fatigue damage on a material plane and b and m are material constants.r and s are the normal and shear stresses on a material plane,and e p and c p are the plastic strains corresponding to stresses r and s ,respectively.r 0and r f are the endurance limit and the true fracture stress of the material,respectively.r mr is a memory stress reﬂecting the loading magnitude.For constant amplitude loading,r mr is equal to the maximum equivalent von Mises stress in a loading cycle.The use ofMacCauley bracket hi ensures that when r mr 6r 0the fati-gue damage is zero.The critical plane is deﬁned as the material plane where the fatigue damage accumulation ﬁrst reaches a critical value,D 0.The Jiang multiaxial fatigue criterion has been success-fully applied to the fatigue predictions of a variety of mate-rials (Ding et al.,2007a,b;Feng et al.,2005;Gao et al.,to appear;Jiang,Ding,and Feng,2007;Jiang et al.,2007;Zhao and Jiang,2008).The incremental form of the criterion (Eq.(1))does not require a separate cycle counting method for general loading conditions.Any fatigue criterion making use of the stress/strain amplitude or range requires the deﬁnition of a loading cycle or reversal.Therefore,a cycle counting method is needed to deal with the variable ampli-tude loading.Although the rain-ﬂow cycle counting meth-od is widely accepted for counting the loading reversals/cycles,it is not well deﬁned for general multiaxial loading.The second feature of the criterion expressed by Eq.(1)is its capability to predict the cracking behavior.The Jiang fa-tigue criterion is a critical plane approach which is capable of predicting different cracking behavior through the intro-duction of constant b in Eq.(1).The value of constant b is selected to predict a particular mode of cracking based on the smooth specimen experiments.It has been shown (Jiang et al.,2007;Zhao and Jiang,2008)that the predic-tions of the cracking behavior based on the Jiang criterion are generally more accurate than the predictions based on the other multiaxial criteria such as the Fatemi–Socie mod-el (Fatemi and Socie,1988),the Smith–Waltson–Topper model (Smith et al.,1970)and the short-crack based crite-rion (Döring et al.,2006).Table 2lists the material constants used in the cyclic plasticity model and the fatigue model for stainless steelTable 1Cyclic plasticity model used in the ﬁnite element simulations Yield functionf ¼ðe S À~a Þ:ðe S À~aÞÀ2k 2¼0e S ¼deviatoric stress~a¼backstress k =yield stress in shear Flow lawd ~e p ¼1hh d ~S :~n i ~n ~n¼normal of yield surface h =plastic modulus function ~e p ¼plastic strain Hardening Rule~a¼P Mi ¼1~aði Þ~aði Þ¼i th backstress part d ~a ði Þ¼c ði Þr ði Þ~n À~a ði Þk k r ði Þ v ði Þþ1~a ði Þ~aði Þk k !dp M =number of backstress parts (i =1,2,3,...M )dp =equivalent plastic strain increment c (i ),r (i ),v (i )=material constantsTable 2Material constants for SS304L Cyclic plasticity constantsElasticity modulus E =200GPa Poisson’s ratio l =0.3k =115.5MPac (1)=1381.0,c (2)=507.0,c (3)=172.0,c (4)=65.0,c (5)=4.08r (1)=93.0MPa,r (2)=130.0MPa,r (3)=110.0MPa,r (4)=75.0MPa,r (5)=200.0MPa v (1)=v (2)=v (3)=v (4)=v (5)=8.0Fatigue constants r 0=270MPa;m =1.5;b =0.5;r f =800MPa;D 0=15000MJ/m 3F.Fan et al./Mechanics of Materials 40(2008)961–973963304L.The cyclic plasticity material constants were ob-tained from the cyclic stress–strain curve which was ob-tained from the experiments on the smooth specimens under fully reversed tension-compression loading.A com-plete description of procedure for determination of mate-rial constants can be found in corresponding references (Jiang and Sehitoglu,1996a,b ).The fatigue material con-stants were determined by comparing the fatigue data un-der fully reversed tension-compression and that under pure torsion (Jiang,2000).2.2.Finite element modelRound compact specimens with a thickness of 3.8mm were used in the crack growth experiments.The geometry and the dimensions of the specimen are shown in Fig.1.The crack growth experiments were conducted in ambient air.The specimens were subjected to constant amplitude loading with different R -ratios (the minimum load over the maximum load in a loading cycle)and high–low se-quence loading.All of the experiments started without a pre-crack,except two specimens tested under the follow-ing loading conditions:R =0.85,D P /2=0.54kN and R =À1,D P /2=5.0kN.More detailed information of the experiments and the experimental results were reported in a separate presentation.Due to the small thickness,plane-stress condition was assumed for the round compact specimen.Four-node plane-stress elements were used in FE mesh model.The FE mesh model shown in Fig.2was created by using the FE package HyperMesh (Altair HyperMesh,2004).Due to the symmetry in geometry and loading,only half of the specimen was modeled.To properly consider the high stress and strain gradients in the vicinity of the notch or crack tip,very ﬁne mesh size was used in these regions.The size of the smallest elements in the mesh model was 0.05mm.There were approximately 3058to 5067ele-ments used in the mesh model depending on the cracksize.The knife edges for the attachment of the open dis-placement gage in the specimen (Fig.1)were not modeled because the free end of the specimen does not affect the stress and strain of the material near the crack tip or notch.Referring to the coordinates system employed in Fig.2,the tensile external load,P ,is applied in the y direction uni-formly over nine nodes on the upper surface of the loading hole.To mimic the actual loading condition,the compres-sive load is applied in the negative y direction uniformly over nine nodes on the lower surface of the loading hole.The displacements in the x direction of the middle nodes on the upper edge of the loading hole are set to be zero.The displacements in the y direction for all the nodes on the plane in front of the crack tip or the root of the notch are set to be zero.In order to consider the possible contact between the upper and lower surfaces of a crack,the FE model incorpo-rates the contact pairs deﬁned in ABAQUS (2007).The crack surface of the lower symmetric half of the specimen is considered as a rigid surface which acts as the master surface.The corresponding crack surface of the upper half of the specimen serves as the slave surface.2.3.Determination of crack growth rateFor continuous crack growth under constant amplitude loading with small yielding,a simple formula was derived for the determination of the crack growth rate (Jiang and Feng,2004a ),d a d N ¼AD 0;ð2Þwhere,A ¼Zr 0D D ðr Þd r ;ð3Þr is the distance from the crack tip and r 0is the damaging zone size ahead of the crack tip where the fatigue damage is non-zero.D D (r )is the maximum fatigue damage per loading cycle with respect to all possible material planes at a given material point.D D (r )is determined by integrat-ing Eq.(1)over one loading cycle,D D ¼Icycler mrr 0À1m 1þr r fb r d e p þ1Àb s d cpð4ÞFig.1.Geometry and dimensions of the round compact specimen (all dimensions inmm).Fig.2.Finite element mesh model.964 F.Fan et al./Mechanics of Materials 40(2008)961–973for a given material point once the stress–strain response at the point is known.In Eq.(3),A denotes the damaging area enclosed by the D D(r)–r curve.Fig.3shows the distribution of D D(r)along the x-direc-tion for Specimen C01which was subjected to constant amplitude loading with R=0.1and D P/2=2.475kN. According to the fatigue criterion,Eq.(1),a material plane will accumulate fatigue damage when the memory stress is higher than the endurance limit and the material point experiences plastic deformation.For a cracked component, only the material near the crack tip accumulates fatigue damage.The values of D D(r)are determined along all ra-dial directions in a polar coordinate system with its origin being at the crack tip.The direction at which the crackgrowth rate is a maximum or the value of A is a maximum is the predicted cracking direction.The corresponding crack growth rate is the predicted crack growth rate.2.4.Crack initiation and early crack growth from notchThe approach described in the previous sub-sections as-sumes that a material point fails to form a fresh crack on the critical plane when the accumulation of the fatigue damage on the critical material plane reaches a critical va-lue,D0.The rule applies to the initiation of a crack and the crack extension after a crack has been formed.Therefore, the approach uniﬁes both the initiation and the subse-quent crack propagation stage.The distribution of the stress-plastic strainﬁeld in the vicinity of a notch root, however,inﬂuences the early crack growth,which should be properly considered.The deﬁnition of crack initiation used in the current study is different from that of the traditional way.The crack initiation of a fatigue crack is judged by using the fa-tigue criterion,Eq.(1).Once the fatigue damage on a mate-rial plane for the material point at the notch root reaches the critical fatigue damage,D0,the notched member is called to have initiated a fatigue crack.The FE stress analysis is conducted with the notched member for the designated loading condition.For a notched component,the maximum fatigue damage occurs at the notch root.The fatigue damage per loading cycle can be determined and it can be plotted as a distribution along the radial direction from the notch root.Fig.4shows an example for Specimen C20(R=0.2,D P/2=2.0kN,notched depth a n=7.38mm,notch radius=2.0mm).The distance,r,from the notch root is along the x-axis(refer to Fig.1).D D i denotes the fatigue damage per loading cycle on the critical plane during crack initiation.D D i is a function of the location of the material point.The maximum fatigue damage occurs at the notch root during crack initiation.The crack initiation life is predicted to be,N i¼D0D D in;ð5Þwhere N i is the predicted crack initiation life,D0is a mate-rial constant,and D D in is the fatigue damage per loading cycle on the critical plane at the root of the notch.D D in is D D i shown in Fig.4when r=0.During crack initiation,the fatigue damage is also accu-mulated in the vicinity of the notch root and should be considered in the determination of the crack growth near the notch.The area where the fatigue damage accumula-tion is non-zero during crack initiation(Fig.4)is referred to as the notch inﬂuencing zone(NIZ).For a specimen un-der a given loading condition,the NIZ can be determined by applying the fatigue criterion,Eq.(1),with the stress and strain histories outputted from the FE analysis.For Specimen C20shown in Fig.4,the NIZ size is approxi-mately0.85mm ahead of the notch root.For each material plane at any material point,the total fatigue damage at the end of the fatigue crack initiation is N i D D i.It should be reiterated that the discussion is based on the assumption that the material is stable in stress–strain response and the applied loading is constant ampli-tude.The crack growth rate within the NIZ can be deter-mined by using the following equation with the consideration of pre-existing fatigue damage accumulation (Ding et al.,2007a):d ad N¼AD0ÀN i D iðrÞ:ð6Þwhere A is the damage area enclosed by the D D(r)–r curve, as explained in Section2.3.In Eq.(6),N i and D D i(r)are re-lated to the fatigue damage accumulation during crack ini-tiation in the NIZ.For a given crack size within the NIZ the FE analysis is conducted.The distribution of the fatigue damage per loading cycle,D D(r),can be determined as a function of the distance from the crack tip,as shown in Fig.3.The enclosed area made by the D D(r)–r curve is A in Eq.(6).For any direction radiated from the crack tip, the direction which has the highest crack growth rate isF.Fan et al./Mechanics of Materials40(2008)961–973965the predicted cracking direction and the corresponding crack growth rate is the predicted crack growth rate.It can be seen that the difference between the crack growth rate determination near the notch(Eq.(6))and that away from the notch root(Eq.(2))lies in the consideration of the fatigue damage caused during the crack initiation stage.Generally,the stress–strain response becomes stabi-lized after a limited number of loading cycles.It was shown (Jiang and Feng,2004a)that the predicted crack growth re-sults obtained based on the stress–strain response from the10th loading cycle were very close to those based on the stabilized stress and strain response.Therefore,the FE analysis for a given notch or crack length under a desig-nated loading amplitude is conducted for10loading cycles. The stress and strain results at the10th loading cycle are used for the fatigue analysis.The stress and strain results obtained from analyzing the notched component during crack initiation will deter-mine the fatigue damage per loading cycle for each mate-rial plane at each material point.Eq.(5)is used to determine the crack initiation life.FE stress analyses are conducted with different crack lengths for a given loading condition.When the crack tip is within the notch inﬂuenc-ing zone,Eq.(6)is used for the crack rate determination.D D i(r)in Eq.(6)is the fatigue damage per loading cycle for a given material point during crack initiation.Once the crack grows out of the NIZ,Eq.(2)is used for the crack growth rate determination.In fact,D D i(r)is determined during crack initiation.As a result,Eq.(6)can be used for both situations since D D i(r)is zero for the material points out of the notch inﬂuencing zone.It should be noticed that the FE simulation is conducted cycle by cycle mimicking the real crack growth procedure. The crack initiation life is determinedﬁrst.The crack growth rates at several crack lengths are predicted by using the approach.Therefore,the prediction is the relationship between the crack growth rate,da/dN,and the crack length for a given notched component.With the crack initiation life obtained from using Eq.(5),the relationship between the crack length and the number of loading cycles can be established through a numerical integration.Simulations are also conducted for the high–low step loading conditions.In a high–low step loading experiment, an external load with higher loading amplitude is applied until a crack length reaches a certain value.The amplitude of the external load is switched to a lower value in the sec-ond loading step.In the simulations for the high–low load-ing sequence,one special consideration is made.The memory stress,r mr,in Eq.(1)is kept the same before and immediately after the change of the external load from a higher amplitude to a lower amplitude.After an extension of the crack in the second loading step,the memory stress returns to that under the lower constant amplitude loading.3.Results and discussion3.1.Crack growth experimentsThe material under consideration in the present study is AISI304L austenitic stainless steel which belongs to the class of metastable steels of300-series.Austenitic steels display a R-ratio effect when subjected to constant ampli-tude loading,as has been shown for AISI304(Mei and Morris,1990)and AL6-XN(Kalnaus et al.,2008).The experimental data used in the present investigation was the results of a series of experiments conducted by the authors.Fatigue crack growth experiments were performed using round compact specimens made of stainless steel 304L.The compact specimens were machined from an as-received cold rolled round bar.The bar had a diameter of41.28mm.The dimensions of the specimens are shown in Fig.1.The U-shaped notches were made through EDM (Electric Discharge Machining).The width of the slot in the specimen is0.2mm.One side of the specimen was pol-ished to facilitate the observation of the crack growth using an optical microscope with a magniﬁcation of40. The loading conditions included constant amplitude load-ing with R-ratios ranging fromÀ1to0.85and two-step high–low sequence loading.Detailed description of the experiments and the results were reported in a separated presentation.Fig.5shows the experimental results under constant amplitude loading with different R-ratios.Ten specimens were subjected to constant amplitude loading with different loading amplitudes and six R-ratios.Clearly, the R-ratio has an effect on the crack growth of the mate-rial.The notch effect is reﬂected in the crack growth results presented in Fig.5.It can be found that,except in the case of the specimen with a relatively large notch radius under R=À1loading,the notch effect on the crack growth is not signiﬁcant.For the R=À1case(Specimen C24,notch966 F.Fan et al./Mechanics of Materials40(2008)961–973。

Fatigue crack growth behaviour and life prediction for 2324-T39 and 7050-T7451 aluminium alloys

Fatigue crack growth behaviour and life prediction for 2324-T39and 7050-T7451aluminium alloys under truncated load spectraRui Bao a,*,Xiang Zhang ba Institute of Solid Mechanics,School of Aeronautic Science and Engineering,Beihang University (BUAA),Beijing 100191,China bDepartment of Aerospace Engineering,School of Engineering,Cranﬁeld University,Bedford MK430AL,UKa r t i c l e i n f o Article history:Received 17September 2009Received in revised form 14December 2009Accepted 21December 2009Available online 29December 2009Keywords:Fatigue crack growth Fatigue load spectra Crack branching Retardation Life predictiona b s t r a c tThis paper presents a study of crack growth behaviour in aluminium alloys 2324-T39and 7050-T7451subjected to ﬂight-by-ﬂight load spectra at different low-stress truncation levels.Crack branching was observed in the higher truncation levels for the 2324and in all truncation levels for the 7050.Mode I crack growth life can be predicted for the 2324alloy by the NASGRO equation and the Generalised Wil-lenborg retardation model.However,quantitative prediction of the fatigue life of a signiﬁcantly branched crack is still a problem.Material properties,test sample’s orientation and applied stress intensity factor range all play dominant roles in the fracture process.Ó2009Elsevier Ltd.All rights reserved.1.IntroductionFor the damage tolerance design of aircraft structures,fatigue tests are required at all structural levels according to the airworthi-ness regulations [1]to support and validate the crack growth life predictions.There are several aspects in both the practical fatigue testing and the development of predictive models.Since a representative service loading spectrum can contain a large number of low-amplitude load cycles that do not cause fati-gue damage but consume unacceptable testing time and cost in the full scale fatigue tests (FSFT),an economic and common practice is to eliminate these low amplitude stress cycles in the test spectrum.Tests and analysis on laboratory specimens are necessary to deter-mine an acceptable load truncation level for the FSFT of a structural component.These laboratory sample tests are used to demonstrate that the elimination of certain low-range loads will not change the characteristic of the crack growth and have little inﬂuence on crack growth life while considering the scale of time saving.The second aspect is the requirement of life prediction tools.Fa-tigue crack growth (FCG)behaviour and life prediction methods under the constant amplitude loads (CAL)have been well estab-lished for commonly used aluminium alloys.The problem of pre-dicting FCG life under the variable amplitude loads (VAL)is still challenging due to the load sequence and load interaction effects [2,3].For simple VAL sequences,rge numbers of CAL cyclesplus occasional tensile overload cycles,or an overload followed by an underload,current prediction methods include the Wheeler [4],the Generalised Willenborg [5,6],and the crack closure models [7,8].These models and a few others have now been implemented in computer packages,such as the AFGROW crack growth analysis code [8].However,the problem of life prediction gets more com-plex when randomly ordered ﬂight-by-ﬂight loading spectrum is used.In most of the cases,the low-amplitude load cycles that tend to be eliminated contribute little to the fatigue crack growth.How-ever,for some circumstances,the elimination of small load cycles might shift the balance between the crack initiation and crack growth phases [9].Moreover,the overload retardation effect is found to be very sensitive to subsequent underload cycles [2,10,11]as well as to the cycle numbers of subsequent lower amplitude stresses [10].Thirdly,the inﬂuence of the low-amplitude load cycles on crack growth rates also depends on the material properties and test sam-ple’s material orientation.In the last four decades,most research efforts in the aircraft applications have been focused on the 2024and 7075aluminium alloys (AA).Consequently,adequate crack growth prediction models are now available [12].In recent years,trend in the aircraft industry is to gradually introduce new versions of the 2000and the 7000series alloys due to their superior mechanical properties.Their performance in terms of FCG life in ﬂight-by-ﬂight loads needs to be investigated.The materials investigated in this study are the AA 2324-T39and AA 7050-T7451,which are widely employed in the current generation of aircraft components.The former is a higher strength0142-1123/$-see front matter Ó2009Elsevier Ltd.All rights reserved.doi:10.1016/j.ijfatigue.2009.12.010*Corresponding author.Tel.:+861082338663.E-mail address:rbao@ (R.Bao).International Journal of Fatigue 32(2010)1180–1189Contents lists available at ScienceDirectInternational Journal of Fatiguejournal homepage:w w w.e l s e v i e r.c o m/l o c a t e /i j f a t i g ueversion of AA 2024-T351and is a high-purity controlled composi-tion variant of 2024,and is mainly applied on the lower wing skin and center wing box components of new commercial transport air-craft.The fracture behaviour and crack growth behaviour of 2324have been widely investigated in recent years for better under-standing and further application of this material [13].Alloy 7050is the premier choice for aerospace applications requiring the best possible combination of strength,stress corrosion cracking (SCC)resistance and toughness.However,it is one of these highly aniso-tropic alloys;consequently,crack growth behaviour along the short transverse direction (L-S)is found to be quite different from that along the long transverse direction (L-T).Nevertheless,the L-S orientated plates have found some applications in the spar caps and stringer webs of machined integral skin–stringer panels.Pro-gress has been made in understanding the crack growth behaviour in L-S orientated AA 7050-T7451plates under CAL at different stress ratios [14,15],in which comparisons of the failure modes be-tween the L-S and T-L plates under truncated loading spectra are also presented.Small crack growth rates in AA 7050-T7451sub-jected to simple load sequences containing underloads are re-ported in [16]to generate constant amplitude crack growth data for use in life predictions.The experimental tests conducted in this study were designed to achieve two objectives:(1)to select a suitable low-load trunca-tion level for the FSFT;(2)to investigate the characteristics of crack growth behaviour under different load spectra with various trun-cation levels.The ﬁrst objective was achieved and reported in [17].The purpose of this paper is to present the investigation ﬁnd-ings towards the second objective,which covers the studies of crack growth behaviour under a ﬂight-by-ﬂight loading spectrum of a civil transport aircraft wing at different small-stress rangetruncation levels and the performance of current predictive models in spectrum loads.2.Experimental procedures 2.1.MaterialsCrack propagation tests were conducted using the middle-crack tension,M(T),specimens made of AA 2324-T39and AA 7050-T7451.The conﬁguration and orientation of the specimens are shown in Fig.1and Table 1.The material data is found in reference [18,19].For alloy 2324,(wt.%),Si 0.1,Fe 0.12,Cu 3.8–4.4,Mn 0.3–0.9,Mg 1.2–1.8,Cr 0.10,Zn 0.25,Ti 0.15,others each 0.05,others total 0.15,aluminium remainder.For alloy 7050,(wt.%),Si 0.12,Fe 0.15,Cu 2.0–2.6,Mn 0.10,Mg 1.9–2.6,Cr 0.04,Zn 5.7–6.7,Zr 0.08–0.115,Ti 0.06,others each 0.05,others total 0.15,balance alu-minium.The mechanical properties are fully deﬁned in [18,19]and presented in Table 2.Crack growth rate and fatigue properties are available for the L-T orientation (refer to Fig.1)for both alloys [20].A total of 66specimens were tested;for each load truncation le-vel six specimens were tested for AA 2324-T39and ﬁve specimens for AA 7050-T7451.2.2.Load spectraThe baseline load spectrum is a ﬂight-by-ﬂight spectrum with each load block simulating 4200ﬂights.The gust and manoeuvres loads are represented by ten load levels ﬂatulating around the mean load corresponding to the 1g ﬂight condition.The ﬂights in each load block are classiﬁed into ﬁve types,stated as A,B,C,D and E,respectively,according to the stress levels.Flight type A is the most severe loading condition occurring only once in each block,whereas ﬂight type E is the least severe occurring 2958times in each block.The ﬁve ﬂight types were arranged randomly within one block except that ﬂight type A was arranged to occur near the middle and in the second half of a block.The taking-off and landing taxiing loads were taken into account by eight equiv-alent loading cycles in each ﬂight.Fig.2a illustrates a loading seg-ment of the baseline spectrum containing the ﬂight types A,B and E.It can be seen that the spectrum is dominated by tension loads.The baseline spectrum (S0)was ﬁltered by removing small-stress range cycles to obtain different truncated spectra,while the taxiing loads during each ﬂight were retained.A 9.82%trunca-Fig.1.Conﬁguration of M(T)specimen and deﬁnition of material orientation.Nomenclature a ,a 0half crack length,half of initial crack length in middle-crack tension,M(T),specimenC ,n ,p ,q material constants in the NASGRO fatigue crack growthrate lawC f 0parameter in AFGROW crack closure model d a /d N crack growth rate E Young’s modulus f parameter in NASGRO equation taking account of thecrack closure effectK ,K max stress intensity factor (SIF),maximum SIF D K ,D K th SIF range,SIF thresholdK crit apparent fracture toughnessN number of cycles in crack growth laws and NASGRO equationN f fatigue crack growth life in terms of ﬂightsR nominal stress intensity factor ratio (R =K min /K max =r -min /r max )SORshut-off Ratio in Willenborg retardation modelTable 1Specimen dimensions (mm)and orientation.Length (L )Width (W )Thickness (t )Half length of the saw-cut (a n )Orientation 2324-T3935098.5 4.54L-T 7050-T745135098.564L-SR.Bao,X.Zhang /International Journal of Fatigue 32(2010)1180–11891181tion level indicates that those load cycles with stress range less than9.82%of the maximum stress range in the S0were removed, while the other parts of the spectrum were kept unchanged.So no matter what the load truncation level is,the mean stress level re-mains to correspond to the1g acceleration.There areﬁve trunca-tion levels resulting inﬁve different truncated load spectra,named as S1,S2,S3,S4and S5,shown in Table3.Fig.2b shows the load sequences ofﬂight type A in S0and S5.2.3.Fatigue testingPre-cracking was accomplished under constant amplitude load of r max=90MPa,R=0.06which resulted in an initial crack length a0of about5.5mm.The FCG tests were subsequently carried out under the aforementioned six load spectra until the half crack length a was greater than24mm.All the tests were conducted using the MTS880fatigue test sys-tem.Specimens were held in a pair of100mm wide hydraulic wedge grips.An observation system consisting of a digital microscope,servo motor and raster ruler was used to record the crack tip position. Incremental crack length measurements were made on both the right and left sides of the front surface of the specimens.The fol-lowing rules were adopted when recording the crack length:(1) if it is an ideal mode I crack,which is perpendicular to the applied loads and propagating along the x-axis,the crack length is the true distance from the symmetric axis of the specimen to the crack tip, Fig.3a;(2)if the crack has deviated from the horizontal x-axis, then the crack length refers to the projected length of the crack on the x-axis,Fig.3b;(3)if the crack has branched,the recorded crack length is the projected length of the longest branch,Fig.3c.3.Prediction method3.1.Review of available crack growth prediction modelsBased on the principle of the linear elastic fracture mechanics (LEFM),FCG rates can be correlated with the stress intensity factor range D K.There are many empirical FCG laws to describe this rela-tionship.Paris law[21]is theﬁrst and most popular,which corre-lates crack growth rate d a/d N with only the D K.During the following decades,modiﬁcations to the Paris law have been devel-oped by taking into account of different factors.For example,the Forman[22]and Walker equations[23]were proposed to encom-pass the mean stress effect.Both the Paris and Walker equations work well for the stable crack growth stage showing good linearity in double logarithm coordinate of d a/d N vs.D K.The Forman equa-tion[22]introduces the parameter of critical stress intensity factor K c therefore can be applied in the prediction of theﬁnal fracture re-gime.Hartman and Schijve[24]suggested a modiﬁed form of Paris law by adding a parameter of stress intensity factor threshold which depended strongly on the alloy and the environment.The NASGRO equation[8]takes account of the inﬂuences of the mean stress,the critical and threshold SIF,and plasticity-induced crack closure by introducing several empirical constants.Most of the empirical constants in the above mentioned crack growth laws are obtained byﬁtting measured crack growth test data under con-stant amplitude stresses.Table2Material mechanical properties.Tensile strength(MPa)Yield strength(MPa)Elongation(%)KI C (plane strain)(MPaﬃﬃﬃﬃﬃmp)2324-T39475370838.5–44(t=19.05–33.02mm) 7050-T7451510441931.9(L-T),27.5(T-L)(t=25.42–50.80mm)Table3Details of the truncated loading spectra.Name of spectrum S0S1S2S3S4S5Truncation level(%)09.8211.7213.9817.1121.36Cycles eliminated in each block(%)026.5646.8762.9573.3578.581182R.Bao,X.Zhang/International Journal of Fatigue32(2010)1180–1189When variable amplitude loading is applied,crack growth behaviour shows more complicated characters.One of the most important factors that should be taken into account is the profound overload retardation effect[2,12].However,this effect is much re-duced when the tension overload is immediately followed by com-pressive underload[2,12].Furthermore,if a load history has peak loads with a long recurrence period,i.e.peak overload cycle is fol-lowed by large numbers of baseline stress cycles,it will result in large retardation in the crack growth curve,while an almost regu-lar crack growth curve may be resulted by a load history which has peak loads with a short recurrence period[10].These two factors were paid more attention in this study,since the loading spectra in this study all contain a tensile overload in theﬂight type A which is followed by a negative underload,and with the increase of load truncation levels,the recurrence periods between the two overload peaks become shorter and shorter.A number of crack growth models have been developed to ac-count for the load interaction effects and thereby enable predic-tions of crack growth lives.Most of the retardation models are based on either the crack tip plastic zone concept or the crack clo-sure argument.Five retardation models are available in the crack growth prediction software AFGROW;they are the Closure model [7,8],the FASTRAN model[25],the Hsu[26],the Wheeler[4]and the Willenborg models[5,6].Each retardation model has one or more user adjustable parameter(s),which are used to tune the model toﬁt the actual test data.Ideally,any parameter in crack retardation models should be a material constant,which is inde-pendent of other variables such as the spectrum sequence and load level.The Generalised Willenborg model is a modiﬁed version of the original Willenborg model.Physical arguments were used to account for the reduction of the overload retardation due to subse-quent underloads.The AFGROW code has adapted the treatment of the underload acceleration effect by using the Chang’s model[8,27] to adjust the overload induced yield zone size.Therefore the effect of compressive stresses after a tension overload is considered.This model is suitable to the overload/underload pattern found in the load spectra used in this study as shown in Fig.2b.The AFGROW Closure model is based on the original Elber’s crack closure concept [7]and developed by Harter et al.[8].This type of crack closure models has been very popular in both the constant and variable amplitude loads because they correlate crack growth rates with the effective stress intensity factor range,which is affected by the applied loads and crack opening displacements;both can be re-lated to the cyclic plasticity effect.The AFGROW Closure model uses a single adjustable parameter(C f0)that is determined at stress ratio R=0in order to‘‘tune”the closure model for a given material. The suggested C f0value by AFGROW for aluminium alloys is0.3[8].3.2.Crack growth and retardation laws used in this studyIn this study,FCG life predictions were accomplished by using the AFGROW computer package[20]and employing the NASGRO equation[8],Eq.(1).Since this equation takes account of the inﬂu-ences of the mean stress,the critical and threshold SIF,and plastic-ity-induced crack closure,it usually gives more accurate predictions provided that the required material constants are available.The material constants used in the NASGRO equation for commonly used aluminium alloys,including2324-T39studied here,are provided in the database of the AFGROW package.d ad N¼C1Àf1ÀRD Kn1ÀD K thp1ÀK maxK critqð1ÞIn order toﬁnd a suitable crack retardation model for further analyses of the truncated load spectra,attempts have been made to predict FCG life from a=5.5mm to22mm under the S0spec-trum using the Generalised Willenborg model and Closure model. The prediction results are shown in Table4.It indicates that both the No-retardation model and the Generalised Willenborg model have achieved good agreement with the test result,whereas the Closure model underestimated the life by13%using the recom-mended C f0=0.3.Prediction is found to be sensitive to the value of parameter C f0.The following crack life predictions are performed by the NASGRO equation(no retardation)and NASGRO equation plus the Generalised Willenborg model.4.Results and discussion4.1.Crack growth morphology4.1.1.AA2324-T39L-T oriented specimenIt has been observed during the experiments that cracks sub-jected to load spectra S0,S1,S2and S3are perfect mode I cracks which areﬂat and straight and perpendicular to the applied loads direction.However,signiﬁcant crack meandering and/or branching are observed when the low-load range truncation is increased to a certain level,i.e.S4and S5,shown in Fig.4.A typical branched crack occurred under spectrum S4is illustrated in Fig.5.It is amaz-ing that the crack always tended to grow away from the centerline of the specimen rather than taking a zigzag route.The crack growth rate dropped signiﬁcantly after the crack had branched.Some evidence has been found for therelationship Fig.3.Recorded crack lengths with respect to different crack morphologies.Table4Predicted FCG life using two different retardation models(spectrum S0,AA2324-T39).Model and parameter NoretardationClosure model WillenborgmodelTestresultC f0=0.3C f0=0.5SOR=3.0aFCGL(ﬂights)12,73911,755551713,72913,495Error(%)–5.6–12.9–59.1 1.7–a SOR=3.0is recommended by AFGROW technical manual[8]for aluminiumalloys.R.Bao,X.Zhang/International Journal of Fatigue32(2010)1180–11891183between the crack growth path change and the peak stress in the ﬂight type A.This will be discussed in Section 4.4.However,branching was not observed immediately after the maximum over-load.It can be deduced that the tension overload had introduced a few secondary cracks in the subsurface of the specimen,which were later observed at the surface of the specimen.The lead crack and the secondary cracks kept growing for a period of loading cy-cles until they were linked up,which has resulted in the observed branched crack.The appearance of the secondary cracks and the linking up process are shown in Fig.6.The ﬁnal failure mode of the branched crack under tension load is almost the same as the perfect mode I crack,showing the typical characteristic of mode I crack in ductile materials,see insert of Fig.5. 4.1.2.AA 7050-T7451L-S oriented specimenCrack turning,meandering,branching and splitting (90°turn)were observed on some specimens whatever the load truncation level was applied as shown in Fig.7a.However,not all the speci-mens showed signiﬁcant crack turning or branching.It is quite dif-ferent from the 2324-T39L-T specimens,in which crack branching occurred only under the spectrum S4and S5.Schubbe also ob-served crack branching and splitting in 7050-T7451L-S oriented specimens [14,15].He has pointed out that signiﬁcant forward growth retardation or splitting is evident at a threshold D K valuein the range of 10–15MPa ﬃﬃﬃﬃﬃm p and a distinct crack arrest point where vertical growth is dominating is found when D K is between18and 20MPa ﬃﬃﬃﬃﬃm p [14].In this study,the D K value corresponding to the peak stress range in ﬂight type A at initial cracklengthFig.4.Crack morphologies under different loading spectra;(a)–(f)are for the S0,S1,S2,S3,S4and S5spectrumrespectively.Fig.5.Crack turning,meandering and branching for 2324-T39(L-T)(the example shown here is under the spectrum S4of low-load range truncation level of17.11%).Fig.6.Appearance of secondary surface cracks and cracks linking up (the example shown here is under the spectrum S5of truncation level about 21.36%):(a)lead crack r ,secondary crack s (b)another secondary crack t ;(c)link-up of the two secondary cracks with the lead crack.1184R.Bao,X.Zhang /International Journal of Fatigue 32(2010)1180–1189a 0=5.5mm is already above 22MPa ﬃﬃﬃﬃﬃm p ,therefore the reason for observed crack branching and splitting is understood,whether or not the load spectrum was truncated.However,it should be men-tioned here that slight crack branching was also observed occa-sionally during the pre-cracking stage with fatigue crack length no more than 0.5mm from the edge of the saw-cut andD K <10MPa ﬃﬃﬃﬃﬃm p ,see Fig.7b.It was hard to get the normal mode I failure strength when per-forming the residual strength testing after the half crack length a had reached 24mm.Longitudinal splitting occurred parallel to the load direction,as shown in Fig.8.4.2.Crack growth livesSince the loading cycle numbers are different in different load spectra corresponding to different truncation levels,FCG life is de-ﬁned as the number of ﬂights,N f ,rather than the number of load cycles N .Initial crack length a 0was 5.5mm for all the specimens.Measured a vs.N f data corresponding to the S0,S2and S4load spectra are shown in Fig.9a and b for the two aluminium alloys,which indicate good linearity in the log-linear coordinate.For the clarity of illustration,measured data for spectra S1,S3and S5are omitted in these ﬁgures.They do follow the same trend and similar scatter range.Fig.9c and d present the best ﬁtted curves of the test data with respect to all the loading spectra using exponential linear least square method,a ¼Ae BN fð2Þwhere,A and B are ﬁtting parameters.Since a 0=5.5mm,ﬁnd A =5.5.Crack growth retardation due to overload effect are not obvious in this ﬁgure for spectra S0,S1,S2,and S3.The signiﬁcant retardation found in the S4and S5spectra tests was partially caused by the crack branching described in Section 4.1and partially by the removal of large numbers of load cycles at these two higher trunca-tion levels.4.3.Prediction of crack growth livesCrack growth life predictions were performed using the AF-GROW code.Predicted a –N f curves for AA 2324-T39are shown in Fig.10.The loading spectra and specimen conﬁguration used in the prediction are the same as those used in the experimental tests.In the ﬁgures,‘‘No Retardation”means no load sequence effect was considered;‘‘Willenborg”demotes the Generalised Willenborg model.Following observations can be made:(1)For S0,S1,S2and S3,i.e.load range truncation level of 0%,9.82%,11.72%and 13.98%of the maximum load range,the predicted lives agree well with the test results.(2)Under the spectra S4and S5,17.11%and 21.36%truncation levels,measured crack growth lives are much longer than the predicted by Willenborg model.Such differences in the model and measurement cannot be related to the overload retarda-tion effect alone.The main reason is the occurrence of signiﬁcant crack meandering and branching under these two loading spectra,as mentioned in Section 4.1,which slow down the lead crack growth rate signiﬁcantly.This kind of crack growth retardation mechanism is very different from that due to the overload induced plastic zone effect.Crack path deviation was not observed in the tests subjected to load spectra S0,S1,S2and S3.Hence,the FCGlifeFig.7.Crack morphology of the L-S oriented 7050-T7451specimens:(a)crack branching and splitting during propagation under spectrum S0,(b)crack branching during pre-cracking under constant amplitudeloads.Fig.8.Final splitting failure of a L-S oriented 7050-T7451specimen under static residual strength test.R.Bao,X.Zhang /International Journal of Fatigue 32(2010)1180–11891185predictions are fairly accurate,even though the same tensile over-loads exist in these spectra as in the S4and S5.(3)Predicted lives obtained by the ‘‘No Retardation”model and ‘‘Willenborg”model do not differ from each other too much;both are located within the scatter band of the test data.This is mainly due to the overload pattern:an underload is immediately following the overload,see Fig.2b,reducing the retardation effect.Considering the preferred conservativeness in practical applications,NASGRO equation with-out overload retardation is applicable for such kind of load spec-trum investigated in this study with low-stress range truncation levels no higher than 14%of the maximum stress range.Since the crack growth rate data in terms of d a =d N –D K is not available for the 7050-T7451L-S orientation in the AFGROW package,FCG life prediction for this material under spectrum loads was not con-ducted.Schubbe published some d a =d N –D K crack growth data for AA 7050-T7451L-S orientation under constant amplitude loads at different stress ratios in [14].Attempts have been made to use these data and the Harter T-method to predict crack growth lives for 7050-T7451under spectrum loads.However,the d a =d N –D K curves in [14]have a characteristic divergent sinusoidal trend ofgrowth when D K >10MPa ﬃﬃﬃﬃﬃm p ,where the growth mode alter-nates between arrested forward growth and splitting,or arrested vertical growth and continuing forward progression.This crack growth data cannot be used in the crack growth life prediction with the AFGROW,because there is no crack growth model that can take account of such sinusoidal trend of crack growth.4.4.Crack growth rateIt has been mentioned in Section 4.3that the ‘‘No Retardation”option in AFGROW gives good FCG life predictions under the load spectra S0,S1,S2and S3.However,when the crack branching or splitting occurred under S4and S5,the observed signiﬁcant crack growth retardation is not caused by the overload induced yield zone effect;hence it cannot be predicted by these retardation mod-els in AFGROW.Another point is that the crack branching was not observed immediately after the maximum stress in the block.Since it is difﬁcult to observe the overload effect from these a –N f curves,the crack growth rate data may shed light on the effect immedi-ately after each overload.Attempts have been made to ﬁnd expla-nations for the relationship between crack growth retardation and tensile overloads.Fig.11shows the measured d a /N f –N f curves for the 2324-T39L-T and 7050-T7451L-S specimens under different load truncation levels.Locations of the peak loads in the ﬂight A are marked by the vertical lines.The effect of these peak loads on crack growth rate can be observed.These crack growth rate vs.ﬂights curves show periodic changes in both aluminium alloys.Following obser-vations can be made:(1)The occurrences of crack retardation fol-low the maximum tension overload regularly in each load block.(2)Retardation is more signiﬁcant at higher truncation levels,S4and S5,than that at lower truncation levels,S0,S1,S2and S3.(3)Crack growth retardation in 2324-T39L-T specimens is more1186R.Bao,X.Zhang /International Journal of Fatigue 32(2010)1180–1189。

XFEM裂纹扩展范例

Add Weight Traditional Sensors Data Convert Data to Stress History Damage Growth on Digital Twin Life Estimate of Panel/Airplane
Uncertainty in Location/Size
In Development
Conditional Maintenance
1Black, 2Coppe,
Structural health monitoring: Composites get smart, 2008. Simplified damage growth models can still yield accurate prognosis, submitted. 3An, Experimental study on identifying cracks of increasing size using ultrasonic excitation, 2011. Structural & Multidisciplinary Optimization Group Mechanical and Aerospace Engineering Department
4/36
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Structural & Multidisciplinary Optimization Group Mechanical and Aerospace Engineering Department
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Overview
• Fatigue crack growth • Stress intensity factor evaluation – Extended Finite Element Method (XFEM) – Exact XFEM reanalysis algorithm • Integration of fatigue crack growth models – Surrogate models for high-order integration – Surrogate models for variable integration step size • Variable amplitude fatigue crack growth from flight data – Crack tip plasticity – Conversion of flight data to biaxial stress histories – Example problem and discussion • Conclusions

An energy based fatigue crack growth model-Pandey-2003

2. Fatigue crack growth model development Uni-axial elastic–plastic behaviour of materials under cyclic loading are often described by Ramberg-Osgood relation [21,26] as given by Eq. (1): ⌬e ϭ ⌬s ⌬s ϩ2 E 2kЈ
ͩ ͪ1/nЈຫໍສະໝຸດ (1)where kЈ is the cyclic strength coefﬁcient and nЈ is the cyclic strain hardening exponent. ⌬ε / 2 and ⌬s / 2 are the
0142-1123/03/$ - see front matter 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0142-1123(03)00049-5
Abstract A fatigue crack growth (FCG) model under constant amplitude loading has been developed considering energy balance during growth of the crack. Plastic energy dissipated during growth of a crack within a small area, known as process zone at the tip of the crack and area below cyclic stress–strain curve was used in the energy balance. The predictions of model are in good agreement with the experimental results. 2003 Elsevier Science Ltd. All rights reserved.

MTO失活催化剂再生新技术诞生

fatigue crack growth rate[S].The International Organiza-tion for Standardization，2008.[3]Lake G J，Clapson B E.Truck tire groove cracking，theoryand practice[J].Rubber Journal，1970，152（12）：36-52.[4]Radek S，Zlín R S.Study of the relationship between fa-tigue crack growth and dynamic chip&cut behavior of re-inforced rubber materials[J].Kautschuk Gummi Kunst-stoffe，2014，67（4）：26-29.[5]Rowlinson M，Herd C R，Moninot G，et al.The effect ofcarbon black morphological characteristics on tear propaga-tion in rubbers[J].Kautschuk Gummi Kunststoffe，1999，52（12）：830-835.第1期张晨昊，等：用疲劳裂纹扩展分析仪来表征胎面配方的耐切割性能天津大学构建致密储能锂电池，为微米硅碳穿上金刚软甲近日，天津大学化工学院杨全红教授领衔的研究团队及其合作者将致密储能的设计思想运用于锂离子电池，在高致密微米硅碳负极材料构建方面取得重要突破。

受植物细胞吸脱水过程中结构稳定性的启发，该团队为微米硅颗粒设计了一种独特的“金刚软甲”碳包覆结构。

利用水脱出产生的毛细收缩力，石墨烯片层高度交联并紧密地黏附在通过化学气相沉积得到的碳壳表面，形成致密收缩的“金刚软甲”结构，实现了应力释放、电子传输网络“一体化”。

孔边倒角和预腐蚀作用下航空铝合金疲劳性能及断裂机理研究

孔边倒角和预腐蚀作用下航空铝合金疲劳性能及断裂机理研究周松;王磊;马闯;杨林青;许良;回丽【摘要】基于航空铝合金带孔结构材料在服役过程中常因腐蚀损伤而导致疲劳断裂问题,通过对未腐蚀和预腐蚀24h后的7075铝合金双孔未倒角和双孔倒角试样进行疲劳实验研究,分析腐蚀预损伤和孔边倒角对试件疲劳性能的影响及疲劳断裂特性差异.结果表明:腐蚀预损伤对7075铝合金材料疲劳寿命的影响显著,双孔未倒角和倒角试样预腐蚀24h后试样中值疲劳寿命比未腐蚀试样最大下降了31.74％和26.92％;孔边倒角对材料疲劳寿命有一定的影响,未腐蚀和预腐蚀24h孔边倒角试样中值疲劳寿命比未倒角试样最大下降了28.02％和15.36％,主要原因是由于孔边倒角过程中产生加工刀痕,引入了“预损伤”,且倒角后疲劳裂纹萌生位置变多,导致材料发生疲劳断裂的概率变大.【期刊名称】《材料工程》【年(卷),期】2016(044)006【总页数】6页(P98-103)【关键词】铝合金;孔边倒角;腐蚀预损伤;腐蚀坑;疲劳;断裂【作者】周松;王磊;马闯;杨林青;许良;回丽【作者单位】沈阳航空航天大学航空制造工艺数字化国防重点学科实验室,沈阳110136;东北大学机械工程与自动化学院,沈阳110004;沈阳航空航天大学航空制造工艺数字化国防重点学科实验室,沈阳110136;沈阳航空航天大学航空制造工艺数字化国防重点学科实验室,沈阳110136;沈阳航空航天大学航空制造工艺数字化国防重点学科实验室,沈阳110136;沈阳航空航天大学航空制造工艺数字化国防重点学科实验室,沈阳110136;沈阳航空航天大学航空制造工艺数字化国防重点学科实验室,沈阳110136【正文语种】中文【中图分类】V252;V216飞机在实际服役过程中会受到有害环境的严重影响[1]，特别是沿海一带服役的军机，随着服役时间的增加，腐蚀对其造成的损伤越来越严重[2]。

大量飞机失效分析实例表明，腐蚀和疲劳是飞机两类最主要的损伤形式，而腐蚀损伤和破坏又常发生在机械连接部位、孔边和应力集中处等[3,4]。

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Materials Science and Engineering A 527 (2010) 5962–5968Contents lists available at ScienceDirectMaterials Science and EngineeringAj o u r n a l h o m e p a g e :w w w.e l s e v i e r.c o m /l o c a t e /m s eaPrediction of fatigue crack growth and residual stress relaxations in shot-peened materialJinxiang Liu a ,∗,Huang Yuan b ,Ridong Liao aa School of Mechanical Engineering,Beijing Institute of Technology,Beijing 100081,ChinabDepartment of Mechanical Engineering,University of Wuppertal,Wuppertal 42103,Germanya r t i c l e i n f o Article history:Received 16March 2010Received in revised form 25May 2010Accepted 26May 2010Keywords:Shot peeningFatigue crack growth Cohesive zone model Finite element methoda b s t r a c tThe fatigue crack growth,incorporating effects of shot peening,is investigated using two-dimensional ﬁnite element analysis.The cohesive zone model,which takes into account the damage evolution under cyclic load,is adopted in the ﬁnite element analysis to simulate the potential fracture surfaces.The effects of shot peening on the fatigue crack growth and the relaxation of residual stress under cyclic load are studied.It is shown that the residual stress retards the fatigue crack propagation and the retardation effect depends not only on the shot peening intensity but also on the cyclic load amplitude.The residual stress relaxes nonlinearly as the load cycles increase.© 2010 Elsevier B.V. All rights reserved.1.IntroductionFatigue life is an important speciﬁcation in the design of com-ponents subject to constant or variable amplitude loads.The basic mechanism of a fatigue failure is that a slowly spreading crack extends with each cycle of the applied mechanical load.Practi-cally tensile stress is responsible for nucleating and propagating the crack across a certain component,while a compressive stress will only close the crack and cause no damage [1].One effective way to extend the fatigue life of components is to reduce or elimi-nate the tensile stresses by inducing a constant compressive stress in the surface of the components.Shot peening is widely used as a method to create such compressive stress ﬁeld in the surface layers of machine parts [2].Shot impacts result in local plastic deforma-tions on the surface.Since the plastically stretched surface layer tends to expand and the adjacent elastically responding material in vicinity and below the impact location restrains the expansion,a compressive residual stress ﬁeld is formed in the near surface lay-ers [3].Compressive residual stress close to the surface of material may prolong fatigue life by decelerating the initiation and growth phases of the fatigue process [4–7].In damage tolerant design the durability of the fatigue crack growth is a major concern.The process of shot peening affects the initiation of small cracks and the growth of cracks near surfaces.Because the compressive residual stress layer is very thin it is very∗Corresponding author.Fax:+861068913041.E-mail address:liujx@ (J.Liu).challenging to experimentally quantify the interaction between the residual stress ﬁeld and the fatigue crack development.Even in conventional FEM computations the effects of the residual stresses cannot be considered.On the other hand,the quantitative relation between the residual stress state and the crack growth is of great signiﬁcance in component design optimization.In this paper,the cohesive zone model (CZM)is used to simulate the crack growth of shot-peened specimens.The parameters of CZM are identiﬁed using Paris’law in common cracked specimens and are directly applied to 2D shot-peened specimens.Fatigue crack growth and residual stress relaxation of shot-peened specimens have been studied for different load amplitudes and different shot peening intensities.The main purpose of the study is to examine the role of residual stress on fatigue crack initiation and growth.2.Cohesive zone model and parameter identiﬁcationDuring crack propagation,a fracture process zone exists in front of the crack tip where micro-voids initiate,grow,and ﬁnally coa-lesce with the main crack.In the fracture process zone,material degradation is obvious.The conventional elastic–plastic consti-tutive relation used in bulk material is not suitable for the local material degraded region.To consider the material degradation in the fracture process zone,one simple way is to use the cohesive zone model.The fundamental idea behind the cohesive zone model can be traced back to the strip yield models of Dugdale [8]and Baren-blatt [9].In this way,the unrealistic continuum mechanics stress singularity at the crack tip could be avoided.Contrary to the0921-5093/$–see front matter © 2010 Elsevier B.V. All rights reserved.doi:10.1016/j.msea.2010.05.080J.Liu et al./Materials Science and Engineering A 527 (2010) 5962–59685963standard concept in continuum mechanics,the cohesive zone model allows for a displacement jump inside material and for the separation of material surfaces which ﬁnally leads to the failure of the material.No continuum elements are involved in the cohe-sive zone.Cohesive interfaces or elements are deﬁned between the continuum elements instead,which open when damage occurs and loose their stiffness at failure so that the continuum elements are disconnected.In a cohesive zone model,the fracture process zone is treated with its own constitutive relationship in form of the traction–separation law (TSL).Since the cohesive zone model is a phenomenological model there is no direct evidence for formu-lation of the traction–separation law.The fracture behavior of a cracked specimen is mainly determined by the energy release rate and the effect of the TSL form is secondary.We take the popular law suggested by Needleman [10]asT n = max eıı0exp−ıı0,(1)where T n and ıare the normal traction and normal separation,respectively.The model parameters are the cohesive strength, max ,and the cohesive length,ı0,i.e.where the traction reaches a peak value, max .Under monotonic load conditions max and ı0are supposed to be material parameters.The area under the T n –ıcurve is called the separation energy, ,which is deﬁned as=∞T n d ı= max ı0e.(2)The cohesive zone model has been extensively used for anal-ysis of fracture under monotonic load cases [10–14].The results seem to conﬁrm the cohesive zone model,even though the present applications of cohesive models are still far away from practical engineering employment in structural integrity assessments [15].The application of cohesive zone model for fatigue cracking is,however,still at initial stage.The general treatments of the cohesive zone model for fatigue analysis is to introduce additional parame-ters to describe the degradation of material.The main difﬁculty is constructing a realistic damage evolution equation for the damage variable.In the model suggested by Siegmund et al.[16,17]a damage variable,D ,is introduced for cyclic load and is described by D =| ı|ıT nmax − f max ,0H (ıC −ı0),(3)where D is the damage increment, ıis the separation incre-ment,ıC is the accumulated separation,H stands for Heavisidefunction.Two additional parameters are introduced in the dam-age evolution Eq.(3):the cohesive endurance limit, f ,and the accumulated cohesive length,ı .Because the material damage is irreversible,the damage increment should not be less than zero.The incremental damage, D ,is proportional to the normalized incre-mental separation,| ı|/ı ,and weighted by a measure of current traction reduced by the endurance limit.The current value of the damage,D ,is then used to calculate the current cohesive strength, max ,asmax =(1−D ) max ,0.(4)In the above equation max,0denotes the initial cohesive strength.Obviously,the cohesive strength decreases with the dam-age indicator,D ,which represents the material degradation.The TSL,taking into account the damage accumulation under cyclic load,is given by substituting the current cohesive strength, max ,into Eq.(1).The deﬁnition of unloading/reloading path is indispensable for cyclic cohesive zone model.The unloading/reloading path intheFig.1.The traction–separation relationship for the cohesive zone model under sim-ple and cyclic load condition.present investigation follows a linear relationship with a slope equal to that of the current traction–separation curve at zero sep-aration.The value of current unloading/reloading stiffness is given by k n =max eı0.(5)The traction and separation relationships for monotonic and cyclic loads are depicted in Fig.1.Since max decreases with cycling,k n is not a constant even within one loading step.The cohesive zone model presented above has been imple-mented into the commercial ﬁnite element code ABAQUS [18]via the interface UINTER.For the mode I problems the crack propa-gates along the symmetric plane where the cohesive zone can be assumed.The cohesive model with the modiﬁcation for fatigue is used in the computations for 2D crack growth.In the cyclic cohesive zone model,there are four parameters,i.e.the initial cohesive strength max,0,the cohesive length ı0,the cohesive endurance limit f and the accumulated cohesive length ı .In general,the ﬁrst two parameters are determined by the fracture energy under monotonic load condition [13,14].For sim-pliﬁcation,in this study they are assumed to be material parameters and constant through the whole specimen.The small variations due to constraint effects are neglected [19].The void growth and nucleation process,which is the physical phenomenon behind the cohesive zone model,in the specimens under nominal plane strain condition,a rather highly constrained state,are generally characterized by values of max,0between 3and 4times of material yield stress y [20].For thin sheet,a plane stress case,the cohesive strength max,0at the crack tip is approximately 2 y [21,13].Based on previous studies,the value of the cohesive strength max,0is taken to be 3 y for all computa-tions.For the crack initiation under small scale yielding,the mode I cohesive energy can be identiﬁed with the value of the J -integralat crack initiation, =J IC .With J IC =(1− 2)K 2IC/E and Eq.(2),the value of cohesive length ı0is determined.For Inconel 718alloy[22],taking the crack initiation value of K IC =120MPa √m and yield stress value of y =710MPa under room temperature,the cohesive strength max,0and cohesive length ı0are 2130MPa and 0.0055mm,respectively.To understand the interactions between crack growth and f as well as ı ,we have conducted several 2D simulations on compact tension specimens,which is in the square geometry of size 250mm with an initial crack of 100mm.For the mode I problem,the crack is constrained to grow along the symmetrical plane of the specimen.Due to symmetry,only half of the specimen has to be modeled.The constitutive relation governing the deformation behavior of5964J.Liu et al./Materials Science and Engineering A527 (2010) 5962–5968Fig.2.The crack growth versus load cycles under different load conditions K ,i.e.20.6MPa √m,24.8MPa √m,28.9MPa √m and 41.3MPa √m.The cohesive endurance limit f and accumulated cohesive length ı are 0.25 max,0and 4ı0,respectively.the bulk material is the elastic–plastic constitutive relation using the Mises yield criterion.Crack growth in the 2D specimen versus load cycles is shown in Fig.2under stress controlled loading condition with loading ratio R =0.The stress intensity factor range K is used to serve as an indi-cator of load intensity.In present work the stress intensity factor,K ,is calculated from the J -integral by K =JE/(1− 2).It should be carefully noted that as the amplitude of the load is held constant, K gradually creeps up as a result of the steady increase in crack length.However,when crack growth is relatively small compared with the initial crack length,the change of K is negligible.For all load cases,the crack growth speed increases after crack initia-tion and becomes stationary rapidly.Due to mesh limits,we cannot simulate larger crack growth amount.From the ﬁgures we obtain two features which have been conﬁrmed in experiments:(1)The crack initiation is sensitive to the load amplitudes.The initiation time decreases nonproportionally as load amplitude increases.(2)After initiation the crack grows linearly with the load cycles,i.e.the crack growth rate becomes constant for small amount of crack growth.Based on the above described parameter study and experimen-tal data,appropriate accumulated cohesive length ı and cohesive endurance limit f can be determined.Fig.3plots experimental fatigue data [23]and numerical prediction together.For tested material,the heat treatment is water quenching from 960◦C fol-lowed by tempering in 718◦C for 8h.Crack propagation test was done in room temperature and stress ratio is 0.Here,ı equals 30ıparison of experimental [23]and numerical crack growth rates.The cohesive endurance limit f and accumulated cohesive length ı are 0.25 max,0and 30ı0,respectively.Fig.4.Residual stress ( yy and zz ,see Fig.5)distribution in specimens peened by the Almen’s intensity 0.12and 0.25mmA,respectively.The experimental data are taken from the published works [24,25].and f equals 0.25 max,0.The predicted line is in a good agreement with experimental data and has approximately the same slope.This comparison demonstrates that the cohesive zone model is capable of matching long-crack constant amplitude fatigue data at least as well as Paris’law.3.2D simulations of fatigue crack propagationIn shot peening life assessment,inﬂuence of the specimen sur-face damage will not be considered explicitly.This means,the fatigue prediction can be performed just based on the stress and strain states.The fatigue life variations are induced by the local residual stress.In the study,no other effects of shot peening are considered,as in most other works.With the help of ABAQUS subroutine SIGINI [18],two intensities of shot peening,0.12and 0.25mmA,are used.The experimental data have been taken from the papers by Hessert et al.[24]for 0.12mmA and by Hoffmeis-ter et al.[25]for 0.25mmA.The residual stress of 0.12mmA is not generated by shot peening but by ultrasonic peening.Since no other effects but only residual stress is considered in the study,ultrasonic peening,in a sense,has no difference with shot peening.The residual stresses of two shot peening intensities are shown in Fig.4.The main differences between the two residual stress proﬁles are the depth of compressive zone and the maximum compressive stress.The stronger peening intensity leads to the greater depth of compressive zone and the greater value of maximum compressive stress.For comparison,two cyclic load amplitudes are considered for each shot peening intensity.One half of a square plate with a single-edge-crack is modeled utilizing its geometrical symmetry.The two-dimensional FE model is shown in Fig.5.The bottom plot shows the initial mesh and the top plot zooms in to show the tip region.The plane strain element with 4nodes is used for continuum elements.Since the surface layer affected by the shot peening process is very thin and the stress gra-dient in this layer is very high,extremely ﬁne elements are needed for not only the crack area but also the whole affected layer.There-fore,only a very small specimen can be modeled in order to keep the total number of nodes within acceptable bounds.The specimen is 2.5mm long and 1.25mm wide.As shown in the ﬁgure,the ele-ments in the shot peening affected layer are 0.004mm in the depth direction (x direction).The initial crack is 0.012mm,i.e.three ele-ments,and the potential fracture surface is assumed to be 0.6mm.The symmetric line is y =0,and the initial crack is from x =0on the symmetric line.The boundary and loading conditions are as in the preceding section for all of following computations.J.Liu et al./Materials Science and Engineering A 527 (2010) 5962–59685965Fig.5.The two-dimensional FEM model with initial crack length of 0.012mm (upper:near-tip detail,lower:overallview).Fig.6.The crack growth with the number of load cycles under different loading forces for unpeened specimen.The crack tip position is measured from free surface.Fatigue crack growth for unpeened specimen is also studied.Crack growth vs.load cycles for specimen without shot peening effect is shown in Fig.6.For both load cases,the crack growth speed increases after crack initiation and becomes steady rapidly.The numerically predicted crack growth for shot-peened mate-rial reveals that fatigue crack growth may not only start from the pre-existing initial crack tip as in the case of unpeened specimen,but also start from the position deeper than the initial crack tip,as shown in Fig.7.The conventional deﬁnition of the cracklengthFig.7.Scheme showing the fatigue crack growth for shot-peenedmaterial.Fig.8.The crack growth with the number of load cycles under different loading forces.Shot peening intensity is 0.12mmA.measured from initial crack tip is no longer suitable in the shot peening case.Here,the crack tip position measured from free sur-face is used for describing the fatigue crack growth of shot-peened material.Crack growth vs.load cycles in a specimen with 0.12mmA shot peening is depicted in Fig.8. K ,based on calculation of speci-men without shot peening but under the same load,is used as an indicator of the loading intensity for shot peening par-ing the ﬁgures,it can be found,besides that shot peening greatly retards the crack initiation for both load intensities,the location where the crack growth starts is also changed by shot peening.For the 0.12mmA shot peening intensity,the crack growth starts at the position that is 0.15mm away from the initial pre-existing crack tip.This position is where the initial residual stress reaches its maximum positive value while the initial existing crack is within compressive stress zone.Once a crack initiates,it grows in two directions,i.e.toward the center of the specimen and toward the surface of the specimen.The crack growth speed toward the cen-ter is a little faster than that in the unpeened specimen.However,the crack growth speed toward the surface is much slower than that in the unpeened specimen because this area has the strong compressive residual stress.After a certain load cycles,besides the two newly formed crack tips,the crack also begins to grow from the initial crack tip.Thus,in specimen the crack growth occurs on three crack tips simultaneously.The crack growth in the compres-sive stress zone is very slow.The last cracking position in this zone is where the residual stress reaches its maximum negative value.The results indicate that the tensile residual stress can accelerate crack growth.Thus,the overall effect of shot peening seems to acceler-ate crack growth in two-dimensional case once the crack begins to grow,even though the compressive residual stress will decelerate crack growth.For the two load intensities shown in the ﬁgure,the characteristics of the crack initiation and growth are the same.Fig.9presents crack growth vs.load cycles in the specimen with the 0.25mmA shot peening.The 0.25mmA shot peening delays the crack initiation more than the 0.12mmA shot peening pared with the 0.12mmA shot peening,the position where crack growth starts is not 0.15mm but 0.3mm away from initial pre-existing crack tip,which corresponds to the maximum tensile stress area of the 0.25mmA shot peening.The reason for the differ-ences of crack growth is that the 0.25mmA shot peening creates a deeper compressive zone and larger maximum compressive resid-ual stress.Except for above mentioned differences,the shapes of the curves are basically the same for both shot peening intensities.In general,introduction of residual stress through shot peening is intended to extend fatigue life via the delay of crack initiation.Fig.10summarizes the effect of shot peening on the delay of crack5966J.Liu et al./Materials Science and Engineering A527 (2010) 5962–5968Fig.9.The crack growth with the number of load cycles under different loading forces.Shot peening intensity is 0.25mmA.initiation,although the positions of crack initiation can be different.For all cases,i.e.unpeened,0.12and 0.25mmA shot peening,with increasing load intensity,the number of load cycles to crack initi-ation decreases nonlinearly.Shot peening increases the number of load cycles to crack initiation when specimens are exposed to the same load intensities.The delay of crack initiation caused by shot peening is much longer at lower load than that at higher load.In addition,higher shot peening intensity results in a larger number of load cycles for crack initiation.4.Relaxation of residual stressThe residual stress,caused by shot peening,can be relaxed by cyclic loads.For specimens without initial cracks,the stress relaxation has been extensively studied.For specimens with initial cracks,the interaction between a growing fatigue crack and resid-ual stress ﬁeld is not well understood.The lack of understanding has sometimes led to confusions and possibly inaccurate methods being employed in fatigue life prediction.In the study of the two-dimensional case,the initial crack is in the area with initial compressive stress and far away from the ini-tial tensile stress.Fig.11shows the relaxation of residual stress before the crack starts to propagate.The computational condition is that the shot peening intensity is 0.12mmA and the load intensityis 34.3MPa √m.As load cycle increases,the relaxation of residual stress is increased even without crack growth.At the same time,the cyclic load introduces a little compressive stress inside the specimen in areas where they previously do not exist.ThestressFig.10.The effect of shot peening on the number of load cycles to start crack growth in 2Dcomputations.Fig.11.Redistribution of residual stress under cyclic load before crack initiation.Shot peening intensity is 0.12mmA,and load is K =34.3MPa √m.relaxation is not linear with load cycles.In the ﬁgure,the increment of loading cycles for every curve is 100load cycles.It can be seen that the stress relaxation in the ﬁrst 100load cycles is much larger than that in the following cycles until 400load cycles.In fact,the stress relaxation in this stage is mainly caused by the redistribution of the residual stress under the ﬁrst load cycle.After the ﬁrst loading cycle,the residual stress is relatively stable due to relatively small damage accumulation and small change in stiffness of the cohe-sive zone until a certain load cycles,here,400load cycles.Beyond 400load cycles,the damage accumulation becomes larger and thus results in the decreases of stiffness of the cohesive zone,and load-bearing capacity.Consequently,a large relaxation of residual stress can be observed after 400load cycles.Because the damage accumu-lation is in an accelerated relation with the increasing of load cycles,the relaxation of residual stress becomes faster and faster.With load cycle increasing,the separation of potential fracture surfaces,i.e.cohesive zone,is increasing once damage begins to accumu-late.The increasing separation in fact weakens the crack closure effect in the initial crack area caused by the compressive residual stress.When the crack closure effect ﬁnally vanishes,the resid-ual stress in initial crack area disappears totally.Under the same computational condition,the relaxation of residual stress after the crack growing is given in Fig.12.It can be seen in the ﬁgure that during the crack growth the residual stress in newly cracked area vanishes eventually.Meanwhile,in order to keep in stress equi-librium,the compressive residual stress increases in areas where crack propagation has not reached yet.After a certain load cycle,the compressive residual stress will stop increasing and begins to decrease due to weakened stiffness in its correspondingcohesiveFig.12.Redistribution of residual stress under cyclic load after crack initiation.Shotpeening intensity is 0.12mmA,and load is K =34.3MPa √m.J.Liu et al./Materials Science and Engineering A 527 (2010) 5962–59685967Fig.13.Redistribution of residual stress under cyclic load before crack initiation.Shot peening intensity is 0.12mmA,and load is K =37.7MPa √m.zone.Once the crack growth is completed in the cohesive zone,the residual stress becomes zero on the whole fracture surface.Figs.13and 14show the relaxation of residual stress before and after the crack growth.The shot peening intensity is the same as in Figs.11and 12,but the load intensity has a larger value of37.7MPa √paring the results of the two load intensities,it is observed that higher load intensity leads to larger relaxation of residual stress for the same load cycles.Consequently,higher load intensity reduces the number of load cycles to eliminate the resid-ual stress in the initial crack area.Except for this difference,the stress relaxations,before and after the crack growth,have the same trends for both load intensities.The relaxation of residual stress,for the studied case of 0.25mmA shot peening intensity and 34.3MPa √m load amplitude,is plotted in Figs.15and 16,before and after the crack growth,respec-tively.It can be seen from the ﬁgures that,similar to the 0.12mmA shot peening intensity,the stress relaxation in the ﬁrst 100cycles is much larger than that in the following cycle increment before crack begins to propagate.Different from the 0.12mmA shot peen-ing intensity,however,the residual stress in the initial crack area does not release totally before crack begins to propagate for the 0.25mmA shot peening intensity.The reason is that the crack closure effect of the residual stress for 0.25mmA shot peening intensity is stronger than the 0.12mmA shot peening intensity andcan not be overcome under 34.3MPa √m load intensity.The stress relaxation behavior after crack begins to propagate,has the same characteristics for 0.25and 0.12mmA shot peening intensities.Figs.17and 18show the relaxation of residual stress under thecondition of the 0.25mmA shot peening intensity and 37.7MPa √mFig.14.Redistribution of residual stress under cyclic load after crack initiation.Shotpeening intensity is 0.12mmA,and load is K =37.7MPa √m.Fig.15.Redistribution of residual stress under cyclic load before crack initiation.Shot peening intensity is 0.25mmA,and load is K =34.3MPa √m.Fig.16.Redistribution of residual stress under cyclic load after crack initiation.Shotpeening intensity is 0.25mmA,and load is K =34.3MPa √m.load amplitude before and after the crack growth,respectively.The trends of the stress relaxation are observed to be the same as the 0.12mmA shot peening intensity,both before and after crack growth.The residual stress in the initial crack area releases completely before crack begins to grow.This means whether the residual stress will release totally in the initial crack area before crack growth depends not only on the shot peening intensity but also on the load amplitude.Furthermore,the residual stress releases to zero on newly formed surface for all cases,and this is independent of the shot peening intensity and loadingampli-Fig.17.Redistribution of residual stress under cyclic load before crack initiation.Shot peening intensity is 0.25mmA,and load is K =37.7MPa √m.5968J.Liu et al./Materials Science and Engineering A527 (2010) 5962–5968Fig.18.Redistribution of residual stress under cyclic load after crack initiation.Shotpeening intensity is 0.25mmA,and load is K =37.7MPa √m.tude.It should be noted that the material ahead of the crack tip is not described by conventional elastic–plastic constitutive rela-tion but traction–separation equation of cohesive zone model.The response of material closely adjacent to cohesive zone is also strongly affected by the properties of cohesive zone.The results of residual stress relaxation are very sensitive to cohesive zone model.It is not easy to quantitatively give the inﬂuence of plasticity on the residual stress state.5.ConclusionsThe application of the cohesive zone model in the study pro-vides a detailed understanding of the fatigue crack growth in shot-peened specimens.This model provides a reasonable crack initiation and propagation in 2D simulation.The current investigation predicts that the crack initiation posi-tion and time depend not only on shot peening intensity but also on cyclic load amplitude.The crack can be started from the position deeper than the initial crack tip for shot-peened specimen,as pre-dicted by the computations.Retardation of fatigue crack growth is more remarkable for higher shot peening intensity.The relaxation of residual stress is increased with increasing load cycles,even without crack growing.The stress relaxation isnot linear with load rger residual stress relaxation can be observed before and when crack begins to propagate.Gener-ally speaking,the residual stress relaxation is induced by material damage in the crack growth direction which is modeled by the cohesive zone model.Cyclic loads lead to decrease of cohesive zone stiffness.And when crack grows,restrain condition for residual stress is changed.These two factors result in redistribution and relaxation of residual stress.The 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