Determination of residual stress and thermal history

Determination of residual stress and thermal historyfor IM7/977-2composite laminatesWilliam A.Schulz 1,Donald G.Myers,Tom N.Singer,Peter G.Ifju *,Raphael T.HaftkaDepartment of Mechanical and Aerospace Engineering,University of Florida,Gainesville,FL 32611,USAReceived 14September 2004;received in revised form 5April 2005;accepted 14April 2005Available online 13June 2005AbstractAs graphite/epoxy composites become more popular in advanced structural design,there is a need to better understand their mechanical behavior in extreme temperature posites offer many advantages over traditionally used materials;however,they tend to be susceptible to residual stress-induced failure.Residual strains,residual stresses,and thermal history of a composite panel are determined over a broad temperature range by using a combination of strain gages and an optical technique called the Cure Reference Method (CRM).CRM is an accurate,full field,method used to determine the strain on the surface of acomposite via Moire´Interferometry.CRM also enables the accurate determination of the chemical shrinkage of the epoxy matrix during cure.Classical Laminate Theory (CLT)is widely used to predict stress and strain in composite panels,yet it does not account for the chemical shrinkage of the epoxy.The paper describes a method to characterize multidirectional laminate behavior based on a few tests carried out on a unidirectional laminate.The purpose is to eliminate testing of each desired lay-up,by modifying CLT to predict the behavior of a multidirectional laminate based solely on the behavior of a unidirectional sample of the same material system.Testing various lay-ups and comparing analytical to experimental results is used to validate the model.Ó2005Elsevier Ltd.All rights reserved.Keywords:A.Polymer–matrix composites;B.Thermal properties;C.Residual stress;minate theory;D.Moire techniques1.IntroductionFor the next generation reusable launch vehicle to be viable,it is necessary to minimize airframe weight in or-der to increase the ability to carry more fuel.By reduc-ing the weight of the fuel tank as well as using it as a structural member,the relative percentage of fuel weight can be increased.In order to accomplish this goal,ad-vanced composite technology must be utilized.How-ever,the operating environment of the liquid hydrogen (LH 2)fuel tanks presents a serious challenge for theapplication of laminated composite materials.In order to safely utilize laminated composites in the cryogenic environment,there is a need to fully understand and measure the mechanisms that cause thermal stresses.Thermal stresses arise because of the mismatch in coefficient of thermal expansion (CTE)between the fi-bers and the epoxy matrix in laminates.These stresses can be quite large (up to or exceeding the failure strength of the matrix).In testing of the X-33LH 2fuel tanks [1],failure occurred as a result of thermal stress-induced micro-cracks,which led to hydrogen leakage through the face sheet and into the sandwich core.Dur-ing the transition back to room temperature,the hydro-gen trapped in the core expanded,and catastrophic delamination of the face sheets occurred.Chemical shrinkage of the epoxy during cure can also induce significant stresses in laminated composites [2,3],0266-3538/$-see front matter Ó2005Elsevier Ltd.All rights reserved.doi:10.1016/pscitech.2005.04.017*Corresponding author.Tel.:+13523926744;fax:+13523927303.E-mail addresses:wytshark@ufl.edu (W.A.Schulz),pgi@mae.ufl.edu (P.G.Ifju).1Tel.:+13525142376;fax:+1352392posites Science and Technology 65(2005)2014–2024/locate/compscitechCOMPOSITES SCIENCE AND TECHNOLOGYas much as15%of the thermal stresses.Chemical shrinkage is a permanent one-time phenomenon,in ther-moset polymers,that occurs during the initial cure pro-cess.The‘‘shrinkage’’is induced by the polymerization of the epoxy matrix during the cure cycle.The chemical shrinkage contribution is often neglected in analysis,as it is currently not an easy quantity to obtain.For the same reason,this contribution is rarely considered in experimental work on polymer matrix composites. Neglecting the chemical shrinkage contribution can lead to a less than accurate interpretation of the true physical behavior of the composite specimen.It is commonly as-sumed that at the cure temperature the composite is in a stress free state.While it is true that returning a speci-men to its cure temperature will remove the thermal stresses,the chemical shrinkage contribution remains. Through our experiments,it has been shown that the chemical shrinkage can be as high as0.2%strain,which is a significant quantity,and consequently should not be neglected.Taken together,thermal stress and chemical shrink-age comprise the residual stress in a composite.On the ply-scale it is possible to minimize the residual stresses by varying the ply angles.For instance,a uni-directional laminate has no residual stresses on the ply-scale,whereas a cross-ply represents the extreme case.A unidirectional composite,however,is a poor choice for carrying non-axial mechanical loads.There-fore,there is a tradeoffbetween load carrying strength and thermal strength,the latter referring to the ability for a material to avoid micro-cracking at low temper-atures.Trying to obtain the best orientation of plies for a specific task lends itself to a necessity for optimi-zation studies.The results obtained from this research are intended to be used as inputs in optimization studies.This paper describes the use of the Cure Reference Method(CRM)[4,5],combined with the coupling of Moire´Interferometry[6]and conventional strain gage measurements to characterize the thermal history and expansion as a function of temperature for a given com-posite material system.These thermal properties,as well as measured elastic properties,will be used as inputs for a Classical Laminate Theory(CLT)analysis,which is a commonly used analytical tool for predicting strains and stresses in composite laminates.A comparison will then be shown between the analytical prediction and our experimental results.Nomenclaturex–y coordinate system aligned with laminate0°(x)and90°(y)directions1–2coordinate system aligned with laminafiber(1)and transverse(2)directionsA1st quadrant of laminate stiffness matrix,3·3 CTE x coefficient of thermal expansion in the x-directionCTE y coefficient of thermal expansion in the y-directionE1lamina elastic modulus infiber directionE2lamina elastic modulus in transverse direction G12lamina shear modulusN x number of fringes in x-directionN y number of fringes in y-directionN applied force per unit length vector,3·1N M mechanical force per unit length vector,3·1 N T thermal force per unit length vector,3·1N C chemical force per unit length vector,3·1 NL number of layers in laminateQ ply stiffness matrixR reuter transformation matrix between engi-neering and tensorial strains,3·3T temperatureT test specific temperature of test/predictionT cure peak temperature of composite cure cycleD T temperature difference of(T testÀT cure)U horizontal displacementV vertical displacementa experimentally measured CTEa ave average laminate CTEc cos he x strain in the x-directione y strain in the y-directione chem chemical shrinkage vector of a unidirectionalpanel,3·1e lam laminate strain vector in x–y system,3·1 e res laminate residual strain vector in1–2system,3·1e uni strain vector on a unidirectional panel in thex–y system,3·1e CLT Classical Laminate Theory predicted strain e0laminate strain vector in x–y system mea-sured at midplane,3·1f frequency of reference diffraction gratingk ply indexs transformation matrix,3·3h angle between x–y and1–2coordinate systems r res residual stress vector in the1–2coordinate system,3·1s sin ht ply thicknessm12lamina PoissonÕs ratioW.A.Schulz et al./Composites Science and Technology65(2005)2014–202420152.Experimental purposeDue to the increase in desire to use composites,there are many methods to predict,characterize,and measure residual stress and strains in laminated composites. These methods consist of both computational and experimental techniques.Many experimental techniques are destructive[7–9]in nature and once a specimen has been tested it is no longer viable for use or further eval-uation,which is highly undesirable.For this reason, many non-destructive techniques have been developed and implemented.These include sensor-embedding [10,11],X-ray diffraction[12],and the Cure Reference Method[5].The goal of this research was to accurately determine the residual stress and thermal expansion coefficients as functions of temperature in a non-destructive manner via CRM and conventional strain gage technology. These thermal properties and behaviors are then to be used to improve optimization studies.A secondary goal was to improve the predictions generated with Classical Lamination Theory(CLT).This technique is used to predict stresses,strains,and curvatures for arbitrary stacking sequences,while the laminates experience mechanical,moisture,and thermal loads.Several samples of each of three prepreg laminates of the IM7/977-2material system shown in Fig.1were produced for analysis:(a)13layer unidirectional lay-up[013];(b)‘‘Quasi-isotropic’’lay-up½45=903=À45= O3s ;(c)optimized angle ply,[(±25)]3s.The‘‘quasi-isotropic’’lay-up is taken from the design of the LH2tank used in the NASA X-33project.We note that the lay-up is not a true quasi-isotropic lami-nate as the number of plies is not equivalent in all direc-tions,however,it will be referred to as such.The lay-up of the optimized angle ply sample stems from a reliabil-ity optimization performed by Qu et al.[13],of a LH2 fuel tank constructed from a graphite–epoxy system. The stacking sequence for the tank was[±h/±h]s.Opti-mal designs had ply angles h and h which were near+25°andÀ25°,and nearly equal;the stacking sequence was thus simplified to[±h]s.It should be noted that this opti-mized ply sequence was developed for a different mate-rial system,but it was used as a starting point to accrue statistical data on typical lay-ups.Variability is also an extremely important quantity to obtain.Our current research aims at being able to re-duce weight by reducing the variability of input proper-ties into reliability-based optimization studies.Current deterministic design practices employ safety factors in order to ensure reliability.This method,although effec-tive,results in the addition of extra material and conse-quently weight.Probabilistic designs,which are based on probability of failure,allow you to set target func-tions,such as minimizing the weight.The previous LH2tank optimization study showed that the skin thick-ness was highly affected by the variability in certain in-put material properties.Fig.2shows the importance of variability in optimization studies.The solid curve represents the initial analysis of the study while the dashed curve represents the same study when the vari-ability in the ultimate transverse tensile strengthðe ult2Þwas reduced by10%.What this shows is that a variabil-ity reduction of10%in that single property resulted in a 15%reduction in thickness,more importantly weight, for the same probability of failure of10À6.Fig.1.Prepreg laminates.2016W.A.Schulz et al./Composites Science and Technology65(2005)2014–20243.Experimental techniques3.1.Cure Reference Method and Moire´InterferometryResidual and thermal stresses can be determined by using the Cure Reference Method to measure the resid-ual strain in unidirectional or multidirectional compos-ite laminates.CRM uses the full-field laser based optical method of Moire´Interferometry to document strains on the surface of laminates that initiate during the high temperature curing process.The method in-volves replicating a high frequency diffraction grating on the specimen while in the autoclave.The grating acts as a reference to the stress free condition just prior to re-sin solidification.Since the grating is cured with the composite,it carries the same thermal strain and chem-ical shrinkage information as the composite cools.Sub-sequent strains result from two mechanisms,the chemical shrinkage of the polymer matrix and the ther-mal mismatch between the resin and matrix.Strain due to the chemical shrinkage of the epoxy is a one-time event which develops during the curing process,while the thermal mismatch contribution is dependent on the temperature of the specimen,and the cure temperature.The process by which a diffraction grating is pro-duced for application to a composite laminate involves several steps which are outlined in[5].Thefinal stage is production of the autoclave tool that consists of an aluminized grating on a500Â500Â100piece of astrositall Fig.3.Astrositall is an ultra low expansion(ULE)glass with a coefficient of thermal expansion(CTE)of 0.3·10À7mm/mm/°C.The low expansion of the tool is necessary so that the tool does not transfer any ther-mally induced strain to the panel during the transfer process in the autoclave.Most high performance composite laminates are pro-duced with the use of an autoclave.The autoclave is a pressure oven that has vacuum line connections within the pressurized chamber.Once the stacking sequence for the specific laminate is chosen,one can begin to pro-cess the laminate in the following steps:y-up:Assemble the laminate in the specific stackingsequence that has been prescribed.2.Vacuum bagging:Fig.4shows a schematic of the vac-uum bag assembly.The ULE tool with the grating side up is placed at the base of the assembly and the surface is then covered with a non-porous release film.A hole of%1.500diameter is cut into the release film,which allows for the grating to be exposed to the composite surface during the cure cycle.It is crit-ical that thefilm thickness is as minimal as possible so that it will not indent the surface of the composite during the cure process as the resin begins to poly-merize.The prepreg laminate is then placed on top of the releasefilm,centered over the ULE tool,and aligned with the grating.The non-porous releasefilm placed between the tool and the laminate prevents the epoxy from curing to the tool.A layer of porous releasefilm is placed on the upper surface of the lam-inate,which provides two functions,allowing excess resin to be drawn offthe laminate and into the bleeder cloth,as well as for separation from the bleeder cloth.The bleeder cloth is a porous material that absorbs excess resin drawn out of the laminate via vacuum, which allows an appropriatefiber volume fraction to be achieved.The breather cloth,which can be the same material as the bleeder cloth,is used to dis-tribute the vacuum throughout the entire bag.Another layer of non-porous releasefilm is placed between the bleeder and the breather cloths sothatFig.4.Vacuum bagschematic.Fig.3.Astrositall autoclave tool.W.A.Schulz et al./Composites Science and Technology65(2005)2014–20242017excess resin is not transferred into the breather mate-rial resulting in resin being drawn into the vacuum line or clogging the breather cloth which would pre-vent an even vacuum distribution on the laminate during cure.Finally,the ULE and laminate assembly are placed into a vacuum bag;sealed with a sealant tape,and placed in the autoclave for curing.3.Cure preparation:The vacuum bag is connected to thevacuum line.Vacuum is applied and a leak check is performed.It is imperative that the vacuum integrity is maintained,throughout the necessary portions of the curing process,as a poor vacuum can lead to a resin rich laminate.4.Cure:Execute the appropriate cure cycle for theepoxy matrix material.After the composite has cured,the specimen is then ready to be analyzed.A panel with a transferred grating can be seen in Fig.5.The basis of the Cure Reference Method is the tech-nique of Moire´Interferometry.Moire´Interferometry is an optical technique that can be used to determine in-plane displacements.Moire´is characterized by high dis-placement and strain sensitivity,high spatial resolution, and a high signal-to-noise ratio[14].It is a non-contact-ing,full-field method capable of measuring both normal and shear strain.A schematic of the Moire´Interferome-try setup can be seen in Fig.6.The technique is based on the principal of the destructive and constructive interfer-ence of light.The result of the interference is a very char-acteristic pattern of light and dark fringes as seen in Fig.7.These fringe patterns can be used to directly determine the in-plane displacements and residual strains,which lead to residual stresses in each ply.The analysis of the images will be covered in the following section.3.2.Strain gage techniqueOnce strains have been recorded with CRM on each of the panels,they are then sectioned into two pieces. One piece will retain the original grating,while the other will be prepared for strain gage application.The strain gages are applied at room temperature(24°C),and thus room temperature will be our reference point for all strain gage measurements.Vishay Measurements Group WK-13-250BG-350 gages were applied to each specimen with MBond610. These gages and the adhesive were selected for their per-formance ability in the desired temperature range of cryogenic(À190°C)to the cure temperature oftheFig.6.Four beam Moire´interferometerschematic.Fig.5.Cured compositespecimen.Fig.7.Typical fringe patterns(scribed circle is100in diameter). 2018W.A.Schulz et al./Composites Science and Technology65(2005)2014–2024epoxy (182°C).There are a total of four gages applied to each specimen,two of which are on the front of the panel in the corresponding x and y directions (Fig.8),while the other two are on the reverse of the panel in the same location as the gages on the front.The gages were also medium sized gages (0.2500·0.1200).The place-ment of gages on the front and back of the specimens,in addition to the gage size,allows an average of the strain in the x and y directions of the panel to be determined.As strain gages are made of metal alloys,they tend to expand and contract according to changes in tempera-ture.Each alloy type of strain gage is designed to be most accurate over a specific temperature range.Cur-rently no gages exist that are accurate over a broad tem-perature range,such as ours,without implementing temperature compensation.Through our experiments,the measured strain solely due to a gage Õs own expansion at extreme temperatures was as high as 0.2%strain.Gages from the same lot were applied to astrositall and a titanium alloy (Ti6–4Al–4V)which were used as reference materials to compensate for temperature ef-fects.The strain as a function of temperature was known for each of the reference materials.The strain on the ref-erence material was measured at the same time and tem-perature as the gages on the composite specimens.Taking the difference between the measured strain on the reference material and the theoretical strain the material should experience allowed the calculation of the gage expansion.This quantity was then removed from all of the gages on the composite specimens yield-ing the true strain of the specimen at that temperature.The gages were conditioned and read by the use of National Instruments data acquisition hardware and the strains were recorded from the cure temperature of 182°C down to the temperatures of LN 2(À190°C).4.Data analysis 4.1.StrainOnce the fringe patterns on the specimens have been photographed,the resulting strain field images need to be analyzed.As was seen in Fig.7,the resulting images are a pattern of light and dark bands,where each darkband is referred to as a fringe.The fringe order,or num-ber of fringes,(N )is directly related to the displacement of the composite panel.The relationship between the fringe order and the displacement are shown in Eqs.(1)and (2)for the horizontal and vertical displacement fields,respectively:U ¼N xf ;ð1ÞV ¼N yf;ð2Þwhere f is the frequency of the virtual reference grating that is created inside the interferometer,in this case the frequency is 2400lines/mm,and N x and N y are the number of fringes in the vertical and horizontal images.Now that a relationship between displacements and the number of fringes have been established the absolute strains can then be determined by taking the derivative of the displacements as shown in Eqs.(3)and (4):e x ¼o U o x ¼1f o N x o x !ffi1f D N xD x!;ð3Þe y ¼o V o x ¼1f o N y o y !ffi1f D N yD y !;ð4Þwhere D N x and D N y represent the number of fringes that are seen over a given gage length of D x or D y on the respective image.With these measurements,a room temperature refer-ence point of the surface strain on each panel is able to be attained.This room temperature measurement is the keystone to obtaining an accurate relationship of the strain and thermal contraction as a function of temper-ature for the composite specimens.As mentioned previ-ously,strain gages were used to measure the strains over the desired temperature range of cure to cryogenic,and room temperature was chosen as the reference tempera-ture point.Strain measurements were zeroed out at room temperature and then recorded over the entire temperature range.The measured strain was the relative change in strain from the reference point to the specific temperature at which the measurement was taken.Since the reference point was chosen as room temperature,we were then able to superimpose the room temperature measurement from CRM with the strain gage measure-ments.This allowed the generation of the strain as a pure function of temperature in the composite panels.Figs.9–11show the strain as a function of temperature for all the tested panels in each of the different lay-ups.One can see good agreement between test runs,as evi-denced by the overlap of the experimental data.Also evident is the chemical shrinkage contribution to the to-tal strain on the composite.Looking at the strain versus temperature plots,one can see that the strains do not go to zero at the cure temperature.The strain difference that exists at the cure temperature is the chemical shrinkage contribution.Also noteworthy is thattheFig.8.Specimen with strain gages.W.A.Schulz et al./Composites Science and Technology 65(2005)2014–20242019‘‘quasi-isotropic’’lay-up experiences strain values an or-der of magnitude smaller than the other two lay-ups.This is due to the fact that the lay-up is highly con-strained by having plys in many directions.4.2.Coefficient of thermal expansionThe strain as a function of temperature data can then be transformed into a linear coefficient of thermal expansion (CTE)from cure to the testing temperature.Dividing Eqs.(3)and (4)by the change in temperature gives:CTE x ¼e x D T ¼1f ðT test ÀT cure ÞD N xD x!;ð5ÞCTE y ¼e y D T ¼1f ðT test ÀT cure ÞD N yD y !.ð6ÞFig.12shows CTE as a function of temperature in the x and y directions for the three specimens tested.4.3.Residual stressThe residual stress within a ply can be obtained by analyzing the strain state that the ply would be in if the stresses bonding its neighboring plies together were liberated.This liberated strain we define as the residual strain in the composite,and it is calculated based on the same assumptions as Classical Laminate Theory.The most important assumptions of CLT are that plane sec-tions remain plane and the strain at the surface matches the strain at any point in the interior.The residual strain was calculated for each ply orientation as seen in Eq.(7)by taking the difference between a ply Õs unidirectional behavior and its behavior inside a laminate transformed into the material 1–2coordinate systemf e resg k ¼f e uni g À½s k Áf e lam g .ð7ÞFig.12.Coefficient of thermal expansion as a function oftemperature.Fig.9.Unidirectional strain as a f (T).Fig.10.Optimized angle ply strain as a f (T).Fig.11.‘‘Quasi-isotropic’’strain as a f (T ).2020W.A.Schulz et al./Composites Science and Technology 65(2005)2014–2024After the residual strain has been determined,the resid-ual stress can be defined by a constitutive relation Eq.(8)that relates stress to strain through the use of the stiffness matrix of the composite[Q]f r res gk ¼½Qkf e res gk.ð8ÞThe residual stress in the direction transverse to thefibers is shown in Fig.13for the three different ply orientations within the‘‘quasi-isotropic’’lay-up,as well as the opti-mized panel.Note that the‘‘quasi-isotropic’’lay-up has reached the failure strength(dashed horizontal line)of the matrix at LN2(À196°C)temperatures,a full57°C above its intended operating LH2(À253°C)tempera-ture.Stresses of this magnitude-induced micro-cracking within the matrix and ultimately were the root cause of the failure of the X-33fuel tank.Whereas the residual stress in the optimized configuration is only half of the ultimate matrix strength at the extreme cryogenic tem-peratures.It should also be noted,that the residual stres-ses do not return to zero at the cure temperature of the laminate.This is in fact due to the chemical shrinkage contribution to the residual stresses within the compos-ite.Neglecting the chemical contribution would produce the same curves as presented in Fig.13only they would be shifted down by the amount present at the cure tem-perature($17MPa).If this were the case it can be seen that the predicted residual stresses would now fall below the matrix ultimate strength;yielding a false sense of security about the behavior of the laminate.5.Analytical method5.1.PurposePhysical testing of graphite/epoxy material systems is currently a time intensive process.Each combination of fiber and epoxy behaves differently from any other com-bination.Specific combinations are chosen for a partic-ular task that needs to be accomplished.In order to choose the correct material combination,designers need to be able to fully understand the physical behavior of the combination that they chose.Material behavior in-cludes elastic properties such as YoungÕs Modulus in thefiber and transverse directions,Shear Modulus, and PoissonÕs Ratio,as well as thermal expansion behavior.Obtaining these elastic properties is consid-ered a trivial task compared to quantifying properties such as the coefficient of thermal expansion(CTE)in thefiber and transverse directions or the chemical shrinkage imposed on the material due to polymeriza-tion.All of these properties are important in validating a chosen material system as a viable material to use.In order to obtain the behavior of a specific lay-up, one must construct that lay-up and run it through a ser-ies of tests to obtain its CTE and its mechanical behav-ior.An entirely new test must be conducted for each lay-up of interest of a specific material system.This can be a time consuming and expensive process.Thus, there is a need for a method that can predict material behavior and characteristics of any lay-up in a short time and small cost.The analytical method presented here is proposed as a method to predict the process-induced strains on a composite panel based on a few simple tests carried out on unidirectional samples of the given material sys-tem.This means that the process of testing individual lay-ups of a given material system to determine its behavior can be eliminated.The behavior of a laminate with any ply orientation can be predicted with the infor-mation collected from the tests carried out on the unidi-rectional specimens.5.2.Classical Lamination TheoryCLT is a commonly used predictive tool that makes it possible to analyze complex coupling effects that may oc-cur in composite laminates[15].It is able to predict strains,displacements,and curvatures that develop in a laminate as it is mechanically and thermally loaded.The method is derived from several common assumptions, the most basic of which are that plane sections remain plane,and that there is perfect bonding between layers.A program implementing CLT was written in MAT-LAB to calculate the strains in the given laminates as a function of temperature for comparison with our exper-imental results.Inputs such as:•combined material properties of the lamina for the fiber and matrix(E1,E2,G12,m12,a1(T),a2(T));•stacking sequence and ply thickness;•temperature difference from cure;•chemical shrinkage contributions;•loadingconditions.Fig.13.Residual stress as a function of temperature.W.A.Schulz et al./Composites Science and Technology65(2005)2014–20242021。