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Fracture behavior of Metallic multilayers

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On plasticity and fracture of nanostructured Cu/X (X =Au,Cr)multilayers:The e?ects of length scale and interface/boundary

Y.P.Li,G.P.Zhang *

Shenyang National Laboratory for Materials Science,Institute of Metal Research,Chinese Academy of Sciences,72Wenhua Road,

Shenyang 110016,People’s Republic of China

Received 19December 2009;accepted 24March 2010

Available online 17April 2010

Abstract

Plastic deformation and fracture behavior of two di?erent types of Cu/X (X =Au,Cr)multilayers subjected to tensile stress were investigated via three-point bending experiments.It was found that the plastic deformation ability and fracture mode depended on layer thickness and interface/boundary.The Cu/Au multilayer showed signi?cant features of plastic ?ow before fracture,and such plasticity was gradually suppressed by premature unstable shearing across the layer interface with decreasing layer thickness.In comparison,Cu/Cr multilayers were prone to a quasi-brittle normal fracture with decreasing layer thickness.Both experimental observations and theo-retical analyses revealed di?erences in plasticity and fracture mode between the two types of metallic multilayers and the relevant physical mechanism transition due to length scale constraint and interface/boundary blocking of dislocation motion.ó2010Acta Materialia Inc.Published by Elsevier Ltd.All rights reserved.

Keywords:Multilayers;Plastic deformation;Fracture;Length scale;Interface

1.Introduction

Conventional methods of strengthening metallic materi-als involve enhancing resistance to dislocation motion by re?ning length scales of intrinsic microstructures,e.g.grain or particle size and spacing between solute atoms,second phases or particles,etc.[1].However,continuous re?ne-ment of the microstructural length scale (especially to the submicrometer scale)will lead to a gradual loss of plasticity [2,3].To address this problem,a potential alternative way is to design a multilayered composite by such that there are suitable matches of constituent layer,layer scale and heterogeneous layer interface.Such a multilayer composed of ordinary metals exhibits a signi?cant increase in strength as the layer thickness is decreased from the micrometer to the nanometer scale [4–6].

Recently,attention has shifted from length-scale-depen-dent strength to plasticity/ductility of nanostructured

metallic multilayers [7–18].Most experimental results have indicated that the ductility of metallic multilayers becomes very limited with reducing layer thickness to a critical value (normally <100nm)[8–13].Elongation for Al/Ti multilay-ers with a layer thickness of 45nm is not more than 2%[8].Through tensile testing of free-standing Cu/Ag multilayers,Huang and Spaepen [9]found that fracture forestalled gen-eral yield and the specimens were macroscopically brittle when the layer thickness was less than 40nm.When inves-tigating the fracture behavior of sputter-deposited Ni/Ni 3Al multilayers with layer thicknesses of 20and 120nm,Banerjee et al.[10]found that the fracture mode was related to crystal orientation,i.e.the h 111i -oriented multilayer was more brittle than the h 001i -oriented one.Uniform tensile elongation of free-standing 60nm layer thick Cu/Nb multilayers with a total thickness of 15l m was less than 5%at room temperature,in spite of a 1.2GPa fracture strength [11].Meanwhile,Misra et al.found that the rolling strain to fracture of Cu/Nb multilay-ers at room temperature decreased rapidly when the layer thickness was less than about 30nm [12].They attributed

Corresponding author.Tel./fax:+862423971938.E-mail address:gpzhang@https://www.doczj.com/doc/5e2859707.html, (G.P.Zhang).

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Acta Materialia 58(2010)

3877–3887

this to relative variations in yield strength and fracture stress,and subsequently proposed a dislocation mechanism transition from Orowan bowing to interface crossing[14]. The elongation of Cu/304stainless steel multilayers with layer thickness of25nm was also observed to be less than 2%[13].On the other hand,Zhang et al.[15]and Wen et al.

[16]showed an increasing tendency for shear banding of nanometer-scale Cu/Au and Cu/Ag multilayers under indentation,which was attributed to the potential occurrence of a grain boundary sliding mechanism.In gen-eral,the limited plasticity of conventional metallic multi-layers is strongly dependent on the type of constituent layer,layer thickness and layer-to-layer interface/grain boundary.

Several recent studies have shown potential improve-ments in the ductility of metallic multilayers through adjusting the constituent layers and interfaces.Wang et al.reported that both ultrahigh(1.09±0.02GPa) strength and exceptional ductility(13.8±1.7%)could be obtained for a35/5nm crystalline/amorphous type Cu/ Cu–Zr laminate[13].This was attributed to the nanoscale amorphous layer,with a high sink capacity for disloca-tions,and interplay between the crystalline and amorphous layers.Homogeneous and large plastic deformation with up to75%thickness reduction of crystalline/amorphous type Cu/Pd0.77Si0.23multilayers has been observed by Don-ohue et al.under cold rolling and bending,but it was found to require certain thickness conditions[17].In addition, Mara et al.[18]reported that a micropillar made of a5/ 5nm Cu/Nb multilayer exhibited surprising deformability in excess of25%true strain under compressive load.All these experimental results further imply that interface/ boundary structure and length scale of the constituent lay-ers are the most important factors in improving the plastic-ity of metallic multilayers.Thus,a careful examination of the plastic deformation and fracture behavior of various multilayered systems at di?erent length scales is helpful to better understand the toughening mechanism of multilayers.

In this paper Cu/Au and Cu/Cr multilayers with two typical layer interface structures,i.e.miscible fcc Cu/fcc Au and immiscible fcc Cu/bcc Cr interfaces(fcc=face-centered cubic;bcc=body-centered cubic),were selected.Plastic deformation behavior and fracture mode of the multilayers with individual layer thicknesses ranging from25to 250nm were systematically investigated by means of three-point bending tests.The e?ects of the constituent layer scales,layer interfaces and grain boundaries on plas-ticity and fracture of the multilayers were examined exper-imentally and evaluated theoretically.2.Experimental

2.1.Materials selection and preparation

Multilayers with two typical constituents and interface microstructures,i.e.fcc Cu/fcc Au and fcc Cu/bcc Cr,were selected for the present experiments.The Cu layer thickness (h)in both multilayers ranged from25to250nm,and layer thickness ratios of1:1and2:1were chosen for the Cu/Au and Cu/Cr multilayers,respectively.The total thicknesses of the multilayers were1and0.75l m for the Cu/Au and Cu/Cr multilayers(see Table1),respectively.One reason for such a choice is that Cu/Au can be considered miscible while Cu/Cr can be regarded as immiscible[19].The max-imum solubility of Cu in bcc Cr is less than0.2at.%and the maximum solubility of Cr in fcc Cu is0.89at.%at 1350K,while there is no intermetallic phase reported in the phase diagram[19].Thus,no extra e?ect can be intro-duced at the layer interface.Both multilayers were depos-ited onto a525l m thick single-crystal Si(001)substrate under ultrahigh vacuum(base pressure<10à7Torr,work-ing pressure0.4Pa)using a radiofrequency magnetron sputtering system.The target purities of Cu,Au and Cr were99.999%,99.95%and99.95%,respectively.The whole deposition process was performed at a speed of0.3nm s–1 for both multilayers,with the substrate kept at room temperature.

2.2.Microstructure characterization

Both multilayers were observed to have good surface quality by optical and electron microscopy.Here,Fig.1a and b show typical three-dimensional(3D)surface mor-phology of the h=50nm Cu/Au and Cu/Cr multilayers determined by atomic force microscopy,from which uni-form surface grains can be identi?ed.Subsequent measure-ment indicated that the surface grain size of the Cu/Au multilayer increased from79to116nm with increasing h from25to250nm,while there was a slight increase from 70to82nm for that of the Cu/Cr multilayer(Fig.1c). X-ray texture measurements were performed on the as-deposited multilayer with Cu K a radiation.Preferential out-of-plane orientations of Cu h111i,Au h111i and Cr h110i have been found in multilayers with di?erent h, which implies a{111}Cu//{111}Au interface in the Cu/ Au multilayer and a{111}Cu//{110}Cr interface in the Cu/Cr multilayer.As demonstrated in Fig.2,such textures were very strong and the di?usion angle was no more than $10–12°.Finally,microstructures of two kinds of the as-deposited multilayers were characterized by transmission

Table1

Structure and length scale parameters for Cu/X(X=Au,Cr)multilayers.

Multilayer Type of lattice Layer thickness ratio Cu layer thickness h(nm)Total thickness(l m)Substrate t(l m) Cu/Au fcc/fcc1:125,50,100,2501Si(100)

Cu/Cr fcc/bcc2:125,50,100,2500.75Si(100)

3878Y.P.Li,G.P.Zhang/Acta Materialia58(2010)3877–3887

electron microscopy (TEM)cross-sectional observations.It can be seen from Fig.3that all multilayer samples consist of regular columnar grains.The sizes of the interior colum-nar grains basically agreed well with that of the surface grains,except that the grains in the Cr layer were slightly smaller than those of the Cu layer due to layer thickness constraints.In addition to the silk texture identi?ed by

X-ray di?raction,the results of TEM observation con-?rmed that the grains in the di?erent constituent layers of the multilayers may have exact orientation relationships,as indicated in the insets to Fig.3,i.e.{111}fcc//{111}fcc,h 110i fcc//h 110i fcc in the Cu/Au multilayer and {111}fcc//{110}bcc,h 110i fcc//h 111i bcc (the so-called Kurdjumov–Sachs orientation relationship)in the Cu/Cr multilayer.

2.3.Localized fracture experiments

Although tensile testing of free-standing ?lms is thought to be a direct and e?ective way of determining the intrinsic mechanical properties of various metal ?lms,owing to dif-?culties with the experiments,indentation is usually uti-lized instead of tensile testing [20].However,one problem is that the actual mechanical properties and/or

the

Fig.1.AFM observation of typical 3D morphology of the multilayer surface:(a)the h =50nm Cu/Au multilayer;(b)the h =50nm Cu/Cr multilayer;(c)in-plane surface grain size of both multilayers plotted as a function of modulation

wavelength.

Fig. 2.Representative X-ray di?raction pole ?gures showing:(a)the Cu h 111i texture in the h =25nm Cu/Au multilayer and (b)the Cr h 110i texture in the h =25nm Cu/Cr multilayer.

Y.P.Li,G.P.Zhang /Acta Materialia 58(2010)3877–38873879

processes of deformation and fracture are di?cult to deter-mine from indentation experiments due to the non-uniform stress–strain ?eld beneath the indent and strong constraints of the substrate on the ?lm [21].Here we propose a hypoth-esis by which the plasticity and fracture mode of a local free-standing multilayer may be examined through three-point bending a relatively brittle substrate coated with a metallic multilayer,as illustrated in Fig.4.To ensure sub-

strate cracking prior to multilayer fracture,a brittle 525l m thick Si(100)single crystal was selected as the substrate and the bending span was set as 6mm.The width of all specimens was 1.2mm.Static bending tests were conducted using an Instron òElectroplus E1000testing machine.The velocity of the loading head was 0.1mm min –1,corre-sponding to a nominal strain rate of 1.46?10à4s –1in the maximum strained region.By simultaneously inspect-ing the fracture points in the substrate and multilayer with a force sensor and a digital multimeter,respectively,during the loading process,we found that the substrate indeed cracked before the multilayer.Finally,it should be noted that the multilayer must be thin enough relative to the sub-strate in order to eliminate the e?ects of stress non-homo-geneity at the crack tip.In the present work this was completely satis?ed because the multilayer/substrate thick-ness ratio is less than 1/525.3.Results

As expected,a crack preferentially initiated in the mid-dle of the Si substrate,close to the ?lm/substrate interface due to the maximum tensile stress,and then a local free-standing multilayer was produced ahead of the opening crack.Thus,plastic deformation of the free-standing mul-tilayer subject to tensile stress continued with substrate crack opening until ?nal rupture of the multilayer/sub-strate system.In what follows we will focus on observa-tions of the deformation and fracture behavior of the two types of local free-standing

multilayers.

Fig.3.TEM cross-sectional images of microstructures of multilayers at di?erent length scales,with the inset showing typical selected-area di?raction:(a)the h =25nm Cu/Au multilayer;(b)the h =25nm Cu/Cr multilayer;(c)the h =250nm Cu/Au multilayer;(d)the h =250nm Cu/Cr

multilayer.

Fig.4.Schematic illustration of three-point bending apparatus used for localized fracture experiment.

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3.1.Deformation and fracture behavior of Cu/Au multilayers Fractography (Fig.5)of the Cu/Au multilayer subjected to tensile stress showed distinct deformation and fracture behaviors at di?erent length scales.A general trend was that with increasing h the fracture mode of the multilayer varied from brittle to ductile.For the h =25nm Cu/Au multilayer (Fig.5a)direct intragranular shearing (Type A)across the layer interface took place,with some dimples left on the upper layer,indicated by open arrows.The size of the dimples ($83nm)was slightly larger than the origi-nal grain size.Obviously,these dimples are evidence of pulling-out deformation of grains.In comparison,inter-granular brittle shearing (Type B)in the h =50nm multi-layer occurred preferentially along columnar grain boundaries with some dimples left in the bottom layer,indicated by open arrows in Fig.5b.Both of the nanome-ter-scale multilayers exhibited macroscopic brittleness,with almost no plasticity.A similar fracture behavior has been observed in Cu/Nb multilayers subject to cold rolling,but the layer thickness (4nm)was much less than in the present case [12].Furthermore,ductile shear fracture (Type C)occurred in the h =100nm and h =250nm Cu/Au mul-tilayers,as shown in Fig.5c and d.Notable plastic ?ow and localized necking before ultimate shear fracture showed the evident plasticity of the submicron scale multilayers.In general,we observed three types of fracture modes in the Cu/Au multilayers,which correspond to di?erent layer scales,i.e.intragranular brittle shear fracture (Type A)of the h =25nm multilayer,intergranular brittle shear frac-ture (Type B)of the h =50nm multilayer and ductile shear fracture (Type C)of the h =100and 250nm multilayers.

The corresponding schematic illustrations are presented in Fig.6a–c,respectively.

At the same time,we found that the Cu/Au multilayers with di?erent layer thicknesses exhibited di?erent micro-scopic deformation characteristics.At thin layer thick-nesses (nanometer scale)the extent of deformation of the surface grains close to the fracture was too small to be resolved.Grain boundaries tended to become loosened and grain pulling-out can be identi?ed near the

fracture,

Fig.5.Fractography of Cu/Au multilayer specimens with di?erent layer thicknesses:(a)h =25nm;(b)h =50nm;(c)h =100nm;(d)h =250nm.The shearing direction is indicated by white

arrows.

Fig.6.Schematic illustration of three types of fracture modes observed in Cu/Au multilayers with di?erent layer scales:(a)intragranular brittle shear fracture (Type A)for the nanometer-scale multilayers;(b)inter-granular brittle shear fracture (Type B)for the nanometer-scale multilay-ers;(c)ductile shear fracture (Type C)of the submicron scale multilayers.

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indicated by arrows in Fig.7a.At thicker layer thicknesses (submicron scale)a remarkable plastic?ow-related mor-phology(especially extensive slip lines)of the surface grains could be observed near the fracture,indicated by the arrows in Fig.7b.Due to plastic deformation and rota-tion of surface grains,the deformed surface became rougher than originally.For all multilayer samples the width of the deformation region was about2l m from the fracture.These phenomena indirectly re?ect a decrease in dislocation mobility as well as an increase in plastic deformation instability of the multilayer with reducing length scale.

3.2.Deformation and fracture behavior of Cu/Cr multilayers

Compared with the Cu/Au multilayer,the Cu/Cr multi-layer exhibited a completely di?erent deformation and fracture behavior.Firstly,all Cu/Cr multilayers exhibit a macroscopically brittle normal fracture with extremely lim-ited plasticity(Fig.8).Secondly,at the microscopic level normal fracture initially occurred in the Cr layers along columnar grain boundaries,with local necking of the Cu layer then appearing between cracks until fracture.As shown by the arrows in Fig.8,a large number of grain scale steps and cavities or hillocks can be identi?ed as evi-dence of crack propagation along columnar grain bound-aries.Generally,the Cu/Cr multilayers with four di?erent h values show a similar fracture mode,i.e.the Cr layer frac-tured by normal mode while the Cu layer fractured by local necking,even if the Cu layer with various h values had dif-ferent plasticity.The corresponding deformation and frac-ture modes,namely Type D,are depicted in Fig.9a and b, i.e.brittle normal fracture.Fractography of the multilayers indicated that the extent of deformation near the fracture of the Cu/Cr multilayer was much smaller than that for the Cu/Au multilayer.As indicated by the arrows

in Fig.7.SEM observations of deformation behavior near the fracture of(a)h=25nm and(b)h=250nm Cu/Au

multilayers.

Fig.8.Fractography of Cu/Cr multilayer specimen with di?erent layer thicknesses:(a)h=25nm;(b)h=50nm;(c)h=100nm;(d)h=250nm. 3882Y.P.Li,G.P.Zhang/Acta Materialia58(2010)3877–3887

Fig.10a,multiple microcracks initiated and propagated along grain boundaries in the h =25nm Cu/Cr multilayer,while in the h =250nm multilayer (Fig.10b)the surface grains became deformable.As indicated by the arrows,local grain deformation and grain pulling-out can be clearly identi?ed.4.Discussion

A comparison of the plastic deformation behaviors and fracture modes of Cu/Au and Cu/Cr multilayers clearly revealed that plasticity and fracture mode of the multilay-ers was strongly dependent on length scale and the inter-face/boundary of the multilayers.To understand the physical mechanism,a detailed analysis will next be given based on the following,as well as coupling e?ects between them:(1)the crystallographic orientation relationship

between the two constituent layers,which determines the activation of slip systems,the interface barrier strength and deformation accommodation between constitute lay-ers;(2)the constraints of layer thickness and layer interface on dislocation motion;(3)the columnar grain boundary e?ect on fracture mode.4.1.Activation of the slip system

The number of activated slip systems and the slip conti-nuity of dislocations crossing the layer interface may have an important role in accommodating plastic deformation of the constituent layers.As shown in Fig.11a,projected traces of a force axis can be represented by an orientation triangle according to the symmetry of cubic crystal,i.e.an arc ABC for an fcc crystal and a line DEF for a bcc crystal.Here we assume that the preferred out-of-plane orientation for fcc and bcc crystals is h 111i and h 110i ,

respectively,

Fig.9.Sketches of typical deformation and fracture behavior found in Cu/Cr multilayer with:(a)small layer thickness;(b)large layer thickness.Both of them belong to the same fracture mode (Type D),i.e.brittle normal

fracture.

Fig.10.SEM observations of deformation behavior near fracture of the Cu/Cr multilayer with:(a)h =25nm;(b)h =250

nm.

Fig.11.Schematic illustration of activation and continuity of slip system:(a)projected traces of force axis within standard cubic projection considering preferred out-of-plane orientation of h 111i and h 110i for fcc and bcc crystals,respectively;(b)continuous con?guration of slip system ({111}h 110i )in Cu/Au multilayer,i.e.Thompson tetrahedron;(c)discontinuous con?guration of slip system ({111}h 110i in Cu and {110}h 111i in Cr)in Cu/Cr multilayer.

Y.P.Li,G.P.Zhang /Acta Materialia 58(2010)3877–38873883

to which the tensile stress direction is perpendicular.The maximum Schmid factor (m )of the two slip systems in bcc crystals was calculated to be 0.45at point E when the projection trace of the force axis moved from point D to point F,while that of the single slip system in fcc crystals was 0.47at point B when the force axis was oriented along the arc ABC.Meanwhile,owing to crystal symmetry,dou-ble slip systems at point A with m =0.41and four slip sys-tems at point C with m =0.41were more possibly activated for an fcc crystal,but for bcc it was more di?cult for six slip systems at point F with m =0.27and eight slip systems at point D with m =0.41to be activated.Thus,it is easier for the fcc/fcc Cu/Au multilayer to deform than the fcc/bcc Cu/Cr multilayer.

Furthermore,the slip system between the Cu and the Au layers was continuous across the Cu/Au interface (Fig.11b),while that between the Cu and the Cr layers was discontinuous (Fig.11c),i.e.the Cu/Au interface was transparent while the Cu/Cr interface was opaque to dislo-cation transmission.In general,an opaque interface is more resistant to dislocations crossing the layer interface [22].This is also why the plasticity of the Cu/Au multilayer was better than that of the Cu/Cr multilayer.4.2.E?ects of length scale and layer interface

Experimental observations indicated that the fracture mode of the Cu/Au multilayers subject to tensile stress changed from ductile shearing to brittle shearing with decreasing h (Fig.5).Obviously,such a transition in defor-mation and fracture mode may be associated with length scale and layer interface structure.

At large length scales plastic deformation was accom-modated by dislocation multiplication and piling up at the layer interfaces.Macroscopic yielding took place when gliding dislocation transmitted the layer interface or plastic deformation spreads from one layer to the adjacent one.The shear stress at which the leading dislocation in the pile-up overcame the interface was [23]:

D s H àP ?

??????????????????????????????????

Gb sin u p e1àm TVf eh Ts ?

h s e1Twhere G =E /2(1+m )is the e?ective shear modulus.The e?ective elastic modulus E and the e?ective Poisson’s ratio m can be calculated by E =E 1E 2/(E 1V 2+E 2V 1)and m =m 1m 2/(m 1V 2+m 2V 1),respectively.Here E i ,m i and V i are the elastic modulus,Possion’s ratio and volume fraction of a constituent layer.b is the magnitude of the Burger’s vector,u is the angle between the slip plane and the inter-face,which can be taken as 70.5°here,s ?is the shear strength of the interface barrier for gliding dislocation transmission,V is the volume fraction of the layers in which the pile-up is included,h is the individual layer thick-ness and f (h )represents a discrete dislocation correction factor for the Liebfried formula,which ranges from 1(at large length scales)to 4(at small length scales)[24].It

can be seen from Fig.12that the size dependence of strength/hardness obtained through nanoindentation in-deed obeys the Hall–Petch relation at h >50nm by letting f (h )=1.This con?rms that there is enough dislocation storage capability at such length scales.Therefore,within the h =100and 250nm Cu/Au multilayers a signi?cant number of gliding dislocations were created and interacted with interfaces,resulting in considerable strain https://www.doczj.com/doc/5e2859707.html,rge plastic deformation can be accommodated through such a dislocation multiplication and gliding mechanism until the layer interface was overcome by stress concentra-tion produced by dislocations piling up.As a result,evident plasticity was produced before ultimate shear fracture,as depicted in Fig.13a.Moreover,the interface barrier strengths of the Cu/Au and Cu/Cr multilayers were

found

Fig.12.Length-scale-dependent strength/hardness of Cu/Au and Cu/Cr multilayers demonstrating transition of the deformation mechanism.Here k and M represent a coe?cient proportionality ($2.5–3)and the Taylor factor ($3),

respectively.

Fig.13.Schematic diagram of two representative deformation and fracture mechanisms in Cu/Au multilayers:(a)ductile shear fracture at large layer scale;(b)brittle shear fracture at small layer scale.

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to be,by Hall–Petch ?tting,0.53and 1.35GPa,respec-tively.As indicated by the red line in Fig.12,the peak strengths/hardnesses corresponding to such interface bar-rier strength values were slightly higher than the experi-mental results,which may suggest an e?ect of interface structure at di?erent length scales.

As h decreased the dependence of strength/hardness on the length scale gradually deviated from the traditional Hall–Petch relation.Discrete dislocation gliding will dom-inate the plastic deformation process due to limited disloca-tion capacity on the nanometer scale [25,26].Based on the classical Orowan model [4,25],plastic yielding occurs when a dislocation can be curved into a semicircle within a softer constituent layer (Fig.14).The required shear stress is approximately (Gb /2h )ln(h /b )in the constituent layer,with Burger’s vector b ,shear modulus G and layer thickness h .However,this formula cannot accurately describe the data either from this work or in the literature [27,28].Regarding dislocation core spreading,residual interface stress and interaction between gliding dislocations and mis?t disloca-tion arrays deposited at the interface,Misra et al.re?ned the previous Orowan model [27].The modi?ed shear stress required to mobilize a channeling dislocation can be writ-ten as:s RCLS

?Gb sin u 2p e1àm Th ln a h b sin u àa 0Gb 2h tG e M e1àm T

e2T

where a is a coe?cient representing extension of the dislo-cation core,a 0%0.5and M %3are Saada’s constant and Taylor’s factor,respectively [27],e =b /D is equivalent to the in-plane plastic strain expressed by the in-plane Bur-ger’s vector component b and the spacing D between mis?t dislocations deposited at the interface [27].Other symbols in Eq.(2)have the same meaning as before.It can be seen from Fig.12that the strength/hardness obtained here and in the literature [28]can be quite well ?tted to the modi?ed

formula in the range 10–50nm.This is an indirect re?ec-tion of the mechanism controlling con?ned layer slip at

such length scales.Based on the calculations and analysis,it may be speculated that the multilayer would exhibit good uniform plasticity if the channeling dislocation could be e?ectively con?ned within the layer by the layer interfaces.Although this was corroborated by good plasticity in a cold-rolled Cu/Nb multilayer and a strong resistance to shear banding of an indented Cu/Cr multilayer [12,29],similar behavior was not observed under tensile loading.In fact,with decreasing h there was inevitable competi-tion between the con?ned layer slip mechanism and the interface crossing mechanism,as shown in Fig.14a.Con-sidering blocking of gliding dislocation due to the existence of modulus mismatch and mis?t dislocation resulting from lattice mismatch,the barrier shear strength of the interface for dislocation transmission can be expressed as [30–32]:

s ??

G 1eG 2àG 1Tsin u 8p eG 2tG 1Tta 0

G d àb 2p e1àm 2Th ln h b

e3Twhere G 1and G 2are the shear moduli of the softer and stif-fer constituent layers (i.e.G 1

Other symbols have the same meaning as before.The inter-face barrier strength gradually decreased with decreasing h ,but it decreased rapidly when h was less than $10–20nm [31].Therefore,once the shear stress required for con?ned layer slip increased to exceed the interface barrier strength,this would favor dislocation transmission across the layer interface to accommodate plastic deformation,as depicted in Fig.13b.The consequence of such a transition in defor-mation mechanism would be expected to cause brittle shear fracture,as observed in Fig.5a.

Based on theoretical calculations using Eqs.(2)and (3),we found that the Cu/Cr interface barrier strength decreased from 1.36GPa at h =100nm to 0.95GPa at h =10nm,which is in good agreement with with the exper-imental results.The Cu/Au interface barrier strength decreased from 2.3GPa at h =100nm to 2GPa at h =10nm,which was about three times greater than exper-imentally measured values.This may be due to the e?ect of the solubility of the constituent layers.For the miscible Cu/Au multilayer the signi?cant e?ect of lattice mismatch would be largely eliminated by interfacial interdi?usion.This would lead to a notable reduction in the interface bar-rier strength,although we are unable to estimate this accu-rately at present.The Cu/Cr interface barrier strength was not in?uenced by interdi?usion because of immiscibility of the Cu and Cr elements.Thus,interdi?usion between the two layers would render interface crossing much easier than usual,which could play an important role in facilitat-ing the transition in fracture mode.4.3.In?uence of columnar grain boundary

So far all the above discussions assumed that the colum-nar grain boundaries were strong,but this may not

Fig.14.Two possible single-dislocation slip mechanisms in Cu/Au multilayers:(a)con?ned layer slip (or bowing out)on the left side and interface crossing slip on the right side;(b)single-dislocation bowing out within the softer layer in the case of two di?erent types of discontinuity of slip systems in Cu/Cr multilayers.

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always the case.When the layer interface was su?ciently strong,tensile fracture was inclined to initiate ?rst within the sti?er layers.If the cohesive strength of the columnar grain boundary was relatively weak,then the columnar grain boundaries became natural sources of cracking.

As shown in Fig.14b for the Cu/Cr multilayer,a discon-tinuous slip system between two constituent layers (e.g.b P 5°or 10°)made it very di?cult for a gliding disloca-tion to cross the layer interface.Moreover,in comparison with the Cu layer,the sti?er Cr layer with a thinner layer thickness and smaller grain size was more di?cult to deform by dislocation gliding.It can be seen from Fig.8that cracking occurred at the weak bonded columnar grain boundaries,thus the Cu layer became the only link bridg-ing cracks in the Cr layer.Due to stress concentration and a loss of the interface barrier at the crack tip,the free-standing Cu layer in front of the opening crack could be easily deformed via dislocation gliding across the whole layer (Fig.15a).Therefore,deformation of the Cu layers was con?ned to the local area,which seriously a?ected the plasticity of the Cu layers,as well as that of the whole multilayer.With decreasing h the sites of crack initiation became random,because of an inhomogeneous distribu-tion of the cohesive strength of the columnar grain bound-aries.This led to the formation of grain sized steps or cavities at the fracture surface (Fig.8).

In addition,the shape and size of the columnar grains may also a?ect the fracture mode.With decreasing h the deformation mechanism tended to transition from a con-?ned layer slip to an interface crossing mechanism.None-theless,if the shear strength of the columnar grain boundaries was low,then brittle shear fracture along

columnar grain boundaries rather than interface crossing would take place for certain boundary con?gurations,as depicted in Fig.15b.It is suggested that such fracture behavior only appeared in the h =50nm Cu/Au multilayer due to the combined e?ects of grain size and shape.Simi-larly to other nanostructured metals [33],a shear fracture behavior was expected to be favored in small equiaxial grained metals,which may have a low grain boundary shear resistance.Among all Cu/Au multilayers the ratio of grain size to layer thickness was closest to unity for the h =50nm multilayer,making it easier to produce inter-granular shearing.5.Conclusions

The systematic investigation of the local plastic defor-mation and fracture behavior of Cu/Au and Cu/Cr multi-layers with di?erent layer thicknesses has provided new insights into the in?uence of length scale and interface on the mechanisms of plasticity and fracture.The ?ndings can be summarized as follows.

(1)With decreasing layer thickness the Cu/Au multilayer

showed an evident transition of fracture mode from ductile shear to brittle shear with less plasticity,while the Cu/Cr multilayer exhibited brittle normal fracture at all length scales.

(2)A series of plastic deformation behaviors in the nano-meter/submicron scale multilayers,such as local necking,dislocation slip lines,dimples and grain pull-ing-out,were clearly identi?ed.Firstly,the plasticity of the multilayer correlated with e?ective match of the constituent metals,which are able to provide active slip systems.Secondly,the theoretical analysis indicated a preferred transition from ductile shear fracture to brittle shear fracture behavior with decreasing layer thickness,in response to a transition of the plastic deformation mechanism from disloca-tion piling up to con?ned layer slip,and even to inter-face crossing.

(3)The plasticity and fracture mode were also modulated

by grain size and shape and the cohesive strength of the columnar grain boundary.The Cu/Cr multilayer typically failed due to premature cracking along the Cr columnar grain boundaries,and the h =50nm Cu/Au multilayer failed due to columnar grain boundary sliding/shearing.In general,our ?ndings reveal that the ability for plastic deformation and the fracture behavior of a metallic multi-layer strongly depend on competition between various physical mechanisms associated with dislocation activity in the con?ned volume,which are controlled by the length scale and interface/boundary.The present study further provides a clue that a proper combination of constituent layer scale and layer interface/grain boundary,as well as the intrinsic properties of the constituents,may result

Fig.15.Two representative fracture mechanisms modulated by columnar grain boundaries:(a)limited ductile fracture of Cu layers induced by premature fracture of the Cr layer along columnar grain boundaries;(b)brittle shear fracture of a Cu/Au multilayer along columnar grain boundaries.

3886Y.P.Li,G.P.Zhang /Acta Materialia 58(2010)3877–3887

the optimum balance between high strength and good plas-ticity.This would seem to be achievable,as shown by sev-eral recent novel?ndings[13,17].

Acknowledgements

This work was supported by the National Natural Sci-ence Foundation of China(Grant Nos.50971125and 50890173)and the National Basic Research Program of China(Grant No.2010CB631003).

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股骨颈骨折(transcervical fracture)

概述髋关节是躯干与下肢的重要连接装置与承重结构，主要由股骨头、颈与髋臼共同构成。股骨颈的长轴线与股骨干纵轴线之间形成颈干角，为110°-140°，平均为127°儿童颈干角大于成人。成人股骨头的血液供应有多种来源：①股骨头圆韧带内的小凹动脉，提供股骨头凹部的血液循环；②股骨干滋养动脉升支，沿股骨颈进入股骨头；③旋股内、外侧动脉的分支，是股骨头、颈的重要营养动脉。股骨颈骨折（fracture of the fenoral neck）常发生于老年人，随着人的寿命延长，其发病率日渐增高。其临床治疗中存在骨折不愈合和股骨头缺血坏死两个主要问题。病因和发病机制中老年人发生骨折有两个基本因素，一是骨强度下降，二是老年人髋周肌群退变，不能有效地抵消髋部有害应力。而青壮年股骨颈骨折，往往由于严重损伤所致，且多见于不稳定型。一、按骨折部位分类 1、股骨头下骨折骨折线在股骨头下，损伤旋股内、外侧动脉发出的营养血管支，使股骨头的血液供应中断，仅有股骨头圆韧带内的小凹动脉提供是少量供血，导致股骨头缺血严重，发生股骨头缺血性坏死。2、经股骨颈骨折骨折线在股骨颈中部，呈斜形，多有一三角形骨块与股骨头相连。骨折损伤股骨干滋养动脉升支，导致股骨头供血不足，易发生股骨头缺血性坏死和骨折不愈合。3、股骨颈基底骨折骨折线位于股骨颈大、小转子之间连线处。旋股内、外侧动脉的分支提供血液循环，故对骨折部的血液供应影响不大，骨折容易愈合。二、按X线表现分类 1、内收骨折远端骨折线与两侧髂嵴连线的夹角（Pauwells角）大于50°，为内收骨折，属于不稳定型骨折，因为其骨折面接触较少，容易移位。Pauwells角越大，骨折端所遭受的剪切力越大，骨折越不稳定。2、外展骨折远端骨折线与两侧髂嵴连线的夹角小于30°，为外展骨折，属于稳定性骨折。若处理不当，如过度牵引，外旋、内收，或过早负重等，也可发生移位，成为不稳定性骨折。三、按移位程度分类 1、不完全骨折仅有部分骨完整性破坏，股骨颈的一部分出现裂纹，类似于骨折的裂纹骨折。2、完全性骨折骨折线贯穿股骨颈，骨结构完全破坏。可分为：（1）无移位的完全性骨折；（2）部分移位的完全骨折；（3）完全移位的完全骨折。临床表现一、畸形患肢多有轻度屈髋屈膝及外旋畸形，一般在45°-60°之间。二、疼痛移动患肢时髋部疼痛明显。在患肢足跟部或大粗隆部叩击时，髋部感疼痛。三、功能障碍移位骨折病人在伤后不能坐起或站立。有时伤后并不立即出现功能障碍，仍能行走，数天后髋部疼痛逐渐加重，才出现不能行走。实验室及其他检查一、肢体测量通过检查可发现患肢缩短。在平卧位，由髂前上嵴向水平划垂线，再由大转子与髂前上嵴的垂线画水平线，构成Bryant三角，股骨颈骨折时，此三角底边较健侧缩短。在平卧位，由髂前上嵴与坐骨结节之间画线，为Nélaton线。正常情况下，大转子在此线上，若大转子超过此线，表明大转子有向上移位。二、X线检查X线检查可同时发现骨折的部位、类型、移位情况，是选择治疗方法的重要依据。疾病概述病因病理临床表现检查检验诊断鉴别并发症治疗预后预防诊断和鉴别诊断根据中老年患者摔倒后出现髋部疼痛，下肢活动受限，不能站立和行走，应怀疑病人有股骨颈骨折。结合X线检查、肢体测量可明确骨折部位、类型和移位。一般诊断明确，不需要鉴别。并发症一、骨折不愈合。二、股骨头缺血性坏死是股骨颈骨折晚期最常见的并发症，发生率为20%-40%.当患者已恢复正常活动后患髋出现疼痛时应复查，若X线显示股骨变白、囊性变活股骨头塌陷，可认为是股骨头缺血性坏死的表现，但往往难以预测其发病趋势。治疗一、治疗时机早期治疗有利于尽快恢复骨折后血管受压或痉挛。股骨颈骨折手术原则上不超过2周。二、骨折复位准确良好的复位是骨愈合重要的条件。牵引患肢，同时在大腿根部加反牵引，待肢体原长度恢复后，行内旋外展复位。三、内固定目前内固定器材主要四类：①单钉类：三翼钉为代表，三刃钉内固定为众所熟悉的传统疗法。这种单根钉在骨的力学效能上不能持久，另外，此钉也不适于青少年及颈部粉碎性骨折者。②多钉固定类：包括史氏针、三角针和多根螺纹钉。此类固定对骨的损伤较小，利用多钉的布局在生物力学上的优势，疗效较好，缺点是钉退出后骨不愈合。③滑移式钉板固定装置

股骨粗隆间骨折(intertrochanteric fracture)

?股骨粗隆间骨折(intertrochanteric fracture) ?2009年03月04日电力医院骨科 ? 股骨近端解剖定义：股骨粗隆间骨折系指股骨颈基底至小粗隆（小转子）下缘之间的骨折。概述：股骨粗隆间骨折多见于老年人，男性多于女性，约为1．5：1，属于关节囊外骨折。美国每年发生超过25万例髋部骨折，总的的治疗费用估计超过80亿美元，其中股骨粗隆间骨折约占1/2,我国统计股骨粗隆间骨折患病年龄平均为70岁，比股骨颈骨折患者高5~6岁，高龄患者长期卧床引起并发症（肺炎；褥疮；泌尿系感染）较多，病死率为15~20%。股骨粗隆部有许多肌肉附着，所以局部的血液供给丰富，加以骨折的接触面积大，因此，骨折后愈合连接一般不成问题。主要问题是有发生髋内翻的趋势，形成畸形连接，造成跛行，并由于承重线的改变，可能在后期引起患肢创伤性关节炎。病因及危险因素： 1.直接暴力：大粗隆受到直接打击。 2.间接暴力：下肢突然扭转、跌倒时强力内收或外展。 3.骨质疏松：骨质疏松本身不是单独的危险因素，但绝经后妇女增加锻炼、激素替代治疗并摄入足够的钙质能够降低股骨粗隆间骨折（髋部骨折）的发生率。分类及分型： 1.按骨折线方向分型：此分型目的在于表示其稳定性。

(1)顺粗隆间线型（骨折），即骨折线由大粗隆向内下至小粗隆，其走行与粗隆间线平行，称为稳定型。 (2)逆粗隆间线型（骨折）：即骨折线由大粗隆下方向内上达小粗隆的上方，称为不稳定型。有时骨折线难以分辨走向，呈粉碎骨折，其稳定性亦差。临床实践表现，以骨折的原始状态来判断其稳定性似乎更为重要。凡伤后髋内翻越严重，骨折越不稳定，反之，原始髋内翻越轻或无内翻者，骨折越趋稳定。因此，骨折的稳定性似与骨折走向方向无关。 A图为顺粗隆间线型（骨折） B图为逆粗隆间线型（骨折） 2. 改良Evans或Evans-Jensen分型系统： Jensen对于Evans分型进行了改进，基于大小粗隆是否受累及复位后骨折是否稳定而分为五型。Ⅰa型：两骨折片段，骨折无移位。Ⅰb型：两骨折片段，骨折有移位。Ⅱa型：三骨折片段，累及大粗隆，因为移位的大粗隆片段而缺乏后外侧支持。Ⅱb型：3骨折片段，累及小粗隆，由于小粗隆或股骨矩骨折缺乏后内侧支持。Ⅲ型：四骨折片段，骨折累及两个粗隆，缺乏内侧和外侧的支持，为Ⅱa型和Ⅱb型的结合。Jensen研究发现Ⅰa、Ⅰb型骨折94％复位后稳定；Ⅱa型骨折33％复位后稳定；Ⅱb 型骨折21％复位后稳定；Ⅲ型骨折8％复位后稳定。Jensen指出大小粗隆的粉碎程度与复位后骨折的稳定性成反比，改良的Evans分型为判断复位后的稳定性和骨折再次移位的风险提供了最为可靠的预测。

【创伤骨科常用汉英词汇】

【创伤骨科常用汉英词汇】 A 凹陷骨折depressed fracture B 半脱位subluxation 半月板meniscus 闭合性骨折closed fracture 髌骨patella 髌骨骨折fracture of patella 髌骨脱位dislocation of patella 髌上囊suprapatellar bursa 髌下脂肪垫subpatellar fat pad 髌韧带patellar ligament 病理性骨折pathological fracture 爆裂骨折bursting fracture 鼻骨骨折fracture of nasal bone 不完全骨折no-complete fracture C 尺骨ulnar 尺骨茎突styloid process of ulna

尺骨鹰嘴骨折olecranon fracture of ulna 创伤性脱位traumatic dislocation 创伤性关节炎traumatic arthritis 创伤性滑膜炎traumatic synovitis 耻骨pubis 耻骨联合pubic symphysis 耻骨上支superior ramus of pubis 耻骨下支inferior ramus of pubis 陈旧性骨折old fracture 垂直压迫损伤vertical compression injuries 齿状突odontoid process 错位displacement D 骶骨sacrum 骶椎sacral vertebrae 骶髂关节cacroiliac joint 骶髂关节分离separation of cacroiliac joint 大多角骨trapezium bone 大结节greater tubercle 大转子greater trochanter 对位paratope 对线alignment

骨科专业英语

骨科相关词汇 abduction 外展 abrasion 擦伤 abscess 脓肿 acromegaly 肢端肥大症 adenoma 腺瘤 adolescent 青少年的 adduction 内收 afferent neuron 传入神经 ankylosing spondylitis 强直性脊柱炎 achilles tendon 跟腱 arthritis 关节炎 arthrogryposis 关节屈曲 Aseptic Necrosis 无菌坏死 Avascular necrosis of femoral head 股骨头坏死 axillary nerve 腋神经 bone 骨 brachial plexus 臂丛 Bunion拇囊炎 bursitis 粘液囊炎 calcaneus 跟骨 callus 胼胝 Cellulitis 蜂窝组织炎 cervical 颈椎的 bone cement 骨水泥 chiropody 足科 clubfoot 马蹄内翻足 corn 鸡眼 crescent 新月形 cubital 尺侧的 cyst 囊 cystic 囊性变 débridement 清创术 dislocation 脱位 dysplasia 发育不良 effusion 渗出 erosion 侵蚀 extension 伸展 flexion 屈曲 fracture 骨折 fungal 真菌的 fusion 融合 humeral 肱骨的 humerus 肱骨 hyperostosis 骨肥厚 hypertrophy 肥大 lumbar 腰椎的 idiopathic 特发的 Ingrown toenail 嵌甲

Fracture toughness 断裂韧度

Fracture Toughness Fracture toughness is an indication of the amount of stress required to propagate(繁殖) a preexisting(先前的) flaw. It is a very important material property since the occurrence of flaws is not completely avoidable in the processing, fabrication, or service of a material/component. Flaws may appear as cracks, voids, metallurgical inclusions, weld defects, design discontinuities, or some combination thereof. Since engineers can never be totally sure that a material is flaw free, it is common practice to assume that a flaw of some chosen size will be present in some number of components and use the linear elastic fracture mechanics (LEFM) approach to design critical components. This approach uses the flaw size and features, component geometry, loading conditions and the material property called fracture toughness to evaluate the ability of a component containing a flaw to resist fracture. A parameter called the stress-intensity factor (K) is used to determine the fracture toughness of most materials. A Roman numeral subscript indicates the mode of fracture and the three modes of fracture are illustrated in the image to the right. Mode I fracture is the condition in which the crack plane is normal to the direction of largest tensile loading. This is the most commonly encountered mode and, therefore, for the remainder of the material we will consider K I The stress intensity factor is a function of loading, crack size, and structural geometry. The stress intensity factor may be represented by the following equation: Where:K I is the fracture toughness in s is the applied stress in MPa or psi a i s the crack length in meters or inches B is a crack length and component geometry factor that is different for each specimen and is dimensionless.

骨折愈合(Fracture healing)

骨折愈合（Fracture healing） General fracture healing schedule: Fracture site healing time (week), fracture site healing time (unit: week) Phalanx (metacarpal bone) 4-8 Pelvic 6-10 Phalanx (metatarsus) 6-8 Femoral neck 12-24 Common fracture healing time unit: Week Fracture type - spiral or long oblique: upper limb clinical healing 3, firm heal 6 Lower limb clinical healing 6, firm healing 12 Fracture type transverse section: upper limb clinical healing 6, firm union 12 Lower limb clinical healing 12, firm healing 24 Note: suitable for tubular bone; children heal half time How long is the fracture healing time? In order to promote fracture healing faster and better, fracture healing time is faster.