Mechanical Properties of Engineered Materials 2008 Part 13 ppt

12 Mechanisms of Fracture 12.1 INTRODUCTION Fracture occurs by the separation of bonds. However, it is often preceded by plastic deformation. Hence, it is generally difficult to understand the physi- cal basis of fracture without a careful consideration of the deformation phenomena that precede it. Nevertheless, at one extreme, one may consider the case of brittle fracture with limited or no plasticity. This represents an important industrial problem that can be overcome largely by the under- standing of the factors that contribute to brittle fracture. However, ab initio models for the prediction of brittle fracture are yet to emerge. On the other hand, ductile fracture mechanisms represent another class of important fracture modes in engineering structures and components. They are somewhat more complex to analyze due to the nonlinear nature of the underying plasticity phenomena. However, a significant amount of scientific understanding of ductile fracture processes has facilitated the safe use of metals and their alloys in a large number of structural applications. Most recently, there have been significant efforts to develop novel composite materials and engineered materials with improved fracture resis- tance. These efforts have led to an improved understanding of how to tailor the microstructure/architecture of a material for improved fracture tough- ness. The research that has been performed in the past 25–35 years has also Copyright © 2003 Marcel Dekker, Inc. ledtoidentificationoftougheningmechanismsthatcanbeusedtoengineer improvedfracturetoughnessinallclassesofmaterials.Thesewillbedis- cussedindetailinChap.13. Thischapterpresentsanintroductiontothemicromechanismsoffrac- tureindifferentclassesofmaterials.Followinganinitialreviewofbrittle andductilefracturemechanisms,themechanismsoffractureindifferent classesofmaterialsarediscussedalongwithmechanicsmodelsthatprovide someadditionalinsightsintothemechanismsoffracture.Quantitativeand qualitativeapproachesarealsopresentedforthecharacterizationoffracture modesbeforeconcludingwithasectiononthethermalshockresponseof materials. 12.2FRACTOGRAPHICANALYSIS Tomostpeople,thereisanaturaltendencytoassumethatmacroscopic ductilityisaclearindicationofductilefracture,e.g.,duringtensilefracture ofsmooth‘‘dog-bone’’specimens.However,althoughthismaybetruefor manysolids,evidenceofmacroscopicductilityisgenerallyinsufficientin fractureanalysis.Instead,weareusuallycompelledtoperformdetailed analysesofthefracturesurface(s)usingscanningortransmissionelectron microscopytechniques.Theseprovidethelocalevidenceofmicroscopically ductileorbrittlefractures. Inthecaseofscanningelectronmicroscopy(Fig.12.1),electronsare accelerated from an electron gun (cathode). The electron beam is collimated by a series of lenses and coils until it hits the specimen surface (fracture surface). The electrons are then reflected from the specimen surface after interacting with a small volume of material around the surface. The two types of electrons that are reflected back from the surface are secondary electrons and back-scattered electron. These are detected by detectors that are rastered to form a TV image. The second electron images usually pro- vide good depth of field and clear images of surface topography, while the back-scattered electron images have the advantage of providing atomic number contrast that can be used to identify different phases (due to differ- ences in chemical composition). The fracture surfaces of conducting materials (mostly metals/interme- tallics) can generally be viewed directly with little or no surface preparation prior to scanning electron microscopy. However, the fracture surfaces of nonconducting materials are generally coated with a thin (a few nanometers) layer of conducting material, e.g, gold, to facilitate fractographic examina- tion in a scanning electron microscope (SEM). The SEM can be used to obtain images over a wide range of magnifications (100–100,000). Copyright © 2003 Marcel Dekker, Inc. Mostelaboratefracturesurfacepreparationisneededfortheexam- inationoffracturesurfacesinthetransmissionelectronmicroscope.These involvethepreparationofreplicasofthefracturesurface.Thecentersofthe replicasmustalsobethinnedtofacilitatethetransmissionofelectrons.In thecaseoftransmissionelectronmicroscopy,thecollimatedelectronbeams aretransmittedthroughthinnedspecimens(Fig.12.2).Thetransmitted electronbeamsmaythenbeviewedinthediffractionmode[Fig. 12.29(a)],orintheimagingmode[Fig.12.2(b)].Someoftheearlystudies offractureweredoneusingtransmissionelectronmicroscopyanalysesof thereplicasoffracturesurfacesinthe1950sand1960s.However,withthe adventoftheSEM,ithasbecomeincreasinglyeasiertoperformfracto- graphicanalyses.Mostoftheimagesoffracturesurfacespresentedinthis chapterwill,therefore,beimagesobtainedfromSEMs.Thesehavegood depthoffocus,andcanproduceimageswithresolutionsof510nm. FIGURE12.1Schematicillustrationoftheoperationofascanningelectron microscope. (From Reed-Hill and Abbaschian, 1991—reprinted with permis- sion from PWS Publishing Co.) Copyright © 2003 Marcel Dekker, Inc. 12.3TOUGHNESSANDFRACTUREPROCESSZONES Fractureexperimentsareusuallypeformedonsmoothornotchedspeci- mens.Theexperimentsonsmoothspecimensgenerallyinvolvethe measurementofstress–straincurves,asdiscussedinChap.3.The smoothspecimensareloadedcontinuouslytofailureatcontrolledstrain rates,inaccordancewithvarioustestingcodes,e.g.,theASTME-8 specification. Theareaunderthegenericstress–straincurveisrepresentativeofthe energyperunitvolumerequiredforthefracture.Thisisoftendescribedas thetoughnessofthematerial.Hence,intherepresentativestress–strain curvesshowninFig.12.3,materialBisthetoughest,whilematerialsA andCarenotastough.However,materialAisstrongandbrittle,while materialCisweakandductile. FIGURE12.2Schematicraydiagramsfor(a)thediffractionmodeand(b)the imaging mode of a transmission electron microscope. Most microscopes have more lenses than those shown here. (From Hull and Bacon, 1984— adapted from Loretto and Smallman, 1975—reprinted with permission from Pergamon Press.) Copyright © 2003 Marcel Dekker, Inc. Thetoughnessorenergyperunitvolume,W,isgivenby W¼ ð " f 0 d"ð12:1Þ where" f isthefracturestrain,andistheappliedstress,expressedasa functionofstrain,".Thetoughnessmustbedistinguishedfromthefracture toughness,whichmaybeconsideredasameasureoftheresistanceofa materialtocrackgrowth. Materialswithhightoughnessorfracturetoughnessgenerallyrequire asignificantamountofplasticworkpriortofailure.Incontrast,thefracture toughnessofpurelybrittlematerialsiscontrolledlargelybythesurface energy, s ,whichisameasureoftheenergyperunitarearequiredforthe creatingofnewsurfacesaheadofthecracktip.However,thereisastrong couplingbetweenthesurfaceenergy, s ,andplasticenergyterm, p .This couplingissuchthatsmallchangesin s canresultinlargechangesin p , andtheoveralltoughnessorfracturetoughness. Finallyinthissection,itisimportanttonotethatthedeformation associatedwiththefractureoftoughmaterialsgenerallyresultsinthe creationofadeformationprocesszonearoundthedominantcrack. ThisisillustratedschematicallyinFig.12.4Thesurfaceenergytermis associatedwiththeruptureofbondsatthecracktip,whiletheplastic worktermisusedpartlyinthecreationofthedeformationprocesszone. Detailsofthephenomenathatoccurinthedeformationprocesszonesare presentedinthenextfewsectionsonfractureinthedifferentcasesof materials. FIGURE12.3Illustrationoftoughnessastheareaunderthestress–strain curves for materials A, B, and C. Copyright © 2003 Marcel Dekker, Inc. 12.4MECHANISMSOFFRACTUREINMETALSAND THEIRALLOYS 12.4.1Introduction Fractureinmetalsandtheiralloysoccursbynominallybrittleorductile fractureprocesses.Incaseswherebrittlefractureoccurswithoutlocalplas- ticityalonglowindexcrystallographicplanes,thefailureisdescribedasa cleavagefracture.Cleavagefractureusuallyoccursbybondruptureacross gains.Itis,therefore,oftenreferredtoastransgranularcleavage.However, bondrupturemayalsooccurbetweengrains,givingrisetoaformoffrac- turethatisknownasintergranularfailure. Inthecaseofductilefailure,fractureisusuallyprecededbylocal plasticityanddebondingofthematrixfromrigidinclusions.Thisdebond- ing,whichoccursasaresultofthelocalplasticflowoftheductilematrix,is followedbylocalizedneckingbetweenvoids,andthesubsequentcoales- cenceofvoidstoformdominantcracks.Itresultsinductiledimpledfracture modesthatarecharacteristicofductilefailureincrystallinemetalsandtheir alloys. Incontrast,thefractureofamorphousmetalstypicallyoccursbythe propagationofshearbands,andthepropagationofmicrocracksaheadof dominantcracks.Thesedifferentfracturemechanismsarediscussedbriefly inthissectionformetalsandtheiralloys. 12.4.2CleavageFracture Asdiscussedearlier,cleavagefractureoccursbybondrupturealonglow indexcrystallographicplanes.Itisusuallycharacterizedbythepresenceof ‘‘riverlines’’(Fig.12.5)thatareformedasaresultofthelinkageofledges producedbycrackingalongdifferentcrystallographicplanes(Tipper,1949). Theriverlinesoftenresembleriverlinesonamap,andarerelativelyeasyto identify.However,thepresenceofriverlinesalonemaynotbesufficient evidencetoinfertheoccurrenceof‘‘pure’’cleavagefractureincaseswhere FIGURE12.4Schematicofthefractureprocesszone. Copyright © 2003 Marcel Dekker, Inc. fractureisprecededbysomelocalplasticity.Undersuchconditions,fracture isprecededbysomelocalplasticityandthemirrorhalvesofthetwofracture surfacesdonotmatch.Thisgivesrisetoaformofbrittlefracturethatis knownas‘‘quasi-cleavage’’(Thompson,1993). Cleavagefractureisoftenobsevedinmetalsatlowertemperatures. Furthermore,atransitionfrombrittletoductilefractureisgenerally observedtooccurwithincreasingtemperatureinbody-centeredcubic (b.c.c.)metalsandtheiralloys,e.g.,steels.Thistransitionhasbeenstudied extensively,butisstillnotfullyunderstood. Thefirstexplanationoftheso-calledbrittle-to-ductiletransition (BDT)wasofferedbyOrowan(1945)whoconsideredthevariationsin thetemperaturedependenceofthestressesrequiredforyieldingandclea- vage(Fig.12.6).Heshowedthatthecleavagefracturestressexhibitsa weakdependenceontemperature,whiletheyieldstressgenerallyincreases significantlywithdecreasingtemperature.Thisisillustratedschematically inFig.12.6.Thestressesrequiredforyieldingare,therefore,lowerthan thoserequiredforcleavagefractureathighertemperatures.Hence,failure abovetheBDTregimeshouldoccurbyductilefracture.Incontrast,since thecleavagefracturestressesarelessthantheyieldstressesbelowthe BDTregime,cleavagefracturewouldbeexpectedtooccurbelowthis regime. FollowingtheworkofOrowan(1945),otherresearchersrecognized thecriticalrolethatdefectsplayinthenucleationofcleavagefracture.Stroh suggestedthatcleavagefractureoccursinapolycrystalwhenacriticalvalue oftensilestress,  isreachedinanunyieldedgrain. FIGURE12.5Cleavagefractureinniobiumaluminideintermetallics:(a)Nb– 15Al–10Ti, (b) Nb–15Al-25Ti. (From Ye et al., 1999.) Copyright © 2003 Marcel Dekker, Inc. UsingsimilarargumentstothoseemployedintheHall–Petchmodel (Chap.8),Stroh(1954,1957)derivedthefollowingrelationshipbetweenthe cleavagefracture stress, c ,and thegrainsize,d:  c ¼  i þ k f d  1 2 ð12:2Þ where k f isthelocaltensilestressrequiredtoinducefractureinanadjacent grain undernucleation-controlledconditions.Thistheorycorrectlypredicts theinversedependenceof thecleavagefracturestresson grainsize,butit suggestsaconstantvalueofk y thatisnottrueforfinergrainsizes. Subsequent work by Cottrell (1958) showed that if the tensile stress is the key parameter, as suggested by experimental results, then cleavage frac- ture must be growth controlled. Cottrell suggested that cleavage fracture in iron occurs by the intersection of a 2 h " 11 " 111idislocationsglidingon{101}slip planes.Thisresultsinthefollowingdislocationreaction(Fig.13.7): a 2 h " 11 " 111i ð101Þ þ 1 2 h111i ð " 1101Þ !a½001ð12:3Þ Sincetheresultinga[001]dislocationissessile,thisprovidesthefirststageof cracknucleationthatoccursduetotherelativemotionofmaterialabove andbelow the slip plane. Furthermore, the pumping of n pairs of disloca- tions into the wedge results in a displacement nb of length c. The total FIGURE12.6SchematicofOrowan ductile-to-brittletransition.(From Knott, 1973—reprinted with permission from Butterworth-Heinemann. Copyright © 2003 Marcel Dekker, Inc. energy per unit thickness now consists of the following four components (Knott, 1973). 1. The Griffith energy of a crack of length, c, under tensile stress, p: U 1 ¼ p 2 ð1  2 Þ E c 2  2 ð12:4aÞ (for a crack of length 2a ¼ cÞ 2. The work done by the stress in forming the nucleus: U 2 ¼ 1 2 pnbc ð12:4bÞ 3. The surface energy: U 3 ¼ 2c ð12:4cÞ 4. The strain energy of the cracked edge dislocation of Burgers vector nb: U v ¼ ðnbÞ 2 4ð1 Þ ln 2R c  ð12:4dÞ where R is the distance over which the strain field is significant,  is the shear modulus, and c=2 is the radius of the dislocation score of the cracked dislocation. The equilibrium crack lengths are found from @=@c FIGURE 12.7 Cottrell’s model of brittle fracture. (From Knott 1973—reprinted with permission from Butterworth-Heinemann.) Copyright © 2003 Marcel Dekker, Inc. ðU 1 þ U 2 þ U 3 þ U 4 Þ¼0. This gives a quadratic function with two possible solutions for the crack lengths. Alternatively, there may be no real roots, in which case the total energy decreases spontaneously. The transition point is thus given by pnb ¼ 2 ð12:5aÞ or for b ¼ 2½001: pna ¼ 2 ð12:5bÞ The tensile stress that is needed to propagate a nucleus is thus given by p  2 k y  d  1 2 ð12:5cÞ Cottrell (1958) used the above expression to explain the results of Low (1954) for mild steel that was tested at 77 K (Fig. 12.8). By substituting p ¼  y ¼ 2 y into the above expression, he obtained the following expres- sions for the stress to propagate an existing nucleus:  y   k y  d  1 2 ð12:5dÞ or  y  2 k y  d  1 2 ð12:5eÞ FIGURE 12.8 Yield and fracture stress in mild steel as functions of grain size. (From Low, 1954—reprinted with permission from ASM International.) Copyright © 2003 Marcel Dekker, Inc. [...]... characteristic dimension along the crack tip, f is the fraction of particles that participate in the fraction initiation, N is the number of particles per unit volume, K1 is the Mode I stress intensity factor, 0 is the yield or flow stress, S0 is the Weibull scale parameter, Su is the lower bound strength (of the largest feasible cracked particle), m is the shape factor, n is the work hardening exponent... QUANTITATIVE FRACTOGRAPHY So far, our discussion of fracture modes has provided only qualitative descriptions of the failure mechanisms in the different types of materials However, it is sometimes useful to obtain quantitative estimates of the features such as asperities on the fracture surfaces Quantitative measurements of such features may be obtained by the use of stereo microscopes, profilometers (Talysurf... right-hand side of Eq (12.19) In many cases, Rs is often greater than 2 A great deal of caution is, therefore, needed in the measurement of linear profiles/area parameters on fracture surfaces Finally, in this section, it is of interest to define a fractal framework that can be used to analyze fracture surface features Fractals recognize that the length of an irregular profile depends on the size scale of the... (1960), who was one of the first to explore the use of ductile phase reinforcement in the toughening of cermets Nakayama and Ishizuka (1969) later tested five brands of commercial refractory firebricks They were identically thermally shocked until a weight loss of 5% was reached They concluded that the R0000 term correctly predicted the relative thermal shock resistance of the five types of bricks Hasselman... ahead of a notch/crack tip, as shown in Fig 12.10(a) Subsequent work by Lin et al (1986) resulted in the development of a statistical model for the prediction of brittle fracture by transgranular cleavage Using weakest link statistics to characterize the strength distributions of the inclusions ahead of the notch tip/crack tip, they showed that the failure probability associated with the element of material... Equation (12.33) indicates that the final crack length of an initially short crack, except for Poisson’s ratio, is independent of material properties Longer cracks will not attain kinetic energy, and propagate in a quasistatic manner This leads to a gradual decrease in strength after thermal shock, instead of the instantaneous decrease often seen in materials with small initial flaw sizes Hasselman suggested... FIGURE 12.19 Dependence of fracture stress on mist–hackle radius (From Mecholsky et al., 1976—reprinted with permission from Materials Research Society.) Three stages of cracking are typically observed as a crack advances through an amorphous polymers The first stage (Stage A in Fig 12.20) involves crazing through the midplane This results in the formation of a mirror area by the growth of voids along the... microscope A single color reflects the presence of a single craze of uniform thickness, FIGURE 12.21 Band hackle markings in fast fracture region in poly(aryl ether ether ketone) Copyright © 2003 Marcel Dekker, Inc while multicolor fringes are formed by the reflection of light from multiple craze layers, or a single craze of variable thickness During the final stages of crack growth in amorphous polymers, crack... FIGURE 12.23 Schematics of (a) possible crack growth associated with spherulites in crystalline polymers and (b) orientations of crystal lamellae (From Hertzberg, 1996—reprinted with permission from John Wiley.) 12.8 FRACTURE OF COMPOSITES Since composite damage mechanisms may occur in the matrix, interface(s)/ interphase(s), and reinforcement(s) in composite materials, a wide range of complex damage modes... such materials under monotonic loading Depending on the relative ductility of the matrix and reinforcement materials, and the interfacial strength levels, damage in composite materials may occur by: 1 2 3 4 5 Matrix or fiber cracking (single or multiple cracks) Interfacial or interphase cracking or debonding Fiber pull-out or fiber cracking Delamination between piles Tunneling cracks between layers of . Inc. ledtoidentificationoftougheningmechanismsthatcanbeusedtoengineer improvedfracturetoughnessinallclassesofmaterials.Thesewillbedis- cussedindetailinChap .13. Thischapterpresentsanintroductiontothemicromechanismsoffrac- tureindifferentclassesofmaterials.Followinganinitialreviewofbrittle andductilefracturemechanisms,themechanismsoffractureindifferent classesofmaterialsarediscussedalongwithmechanicsmodelsthatprovide someadditionalinsightsintothemechanismsoffracture.Quantitativeand qualitativeapproachesarealsopresentedforthecharacterizationoffracture modesbeforeconcludingwithasectiononthethermalshockresponseof materials. 12.2FRACTOGRAPHICANALYSIS Tomostpeople,thereisanaturaltendencytoassumethatmacroscopic ductilityisaclearindicationofductilefracture,e.g.,duringtensilefracture ofsmooth‘‘dog-bone’’specimens.However,althoughthismaybetruefor manysolids,evidenceofmacroscopicductilityisgenerallyinsufficientin fractureanalysis.Instead,weareusuallycompelledtoperformdetailed analysesofthefracturesurface(s)usingscanningortransmissionelectron microscopytechniques.Theseprovidethelocalevidenceofmicroscopically ductileorbrittlefractures. Inthecaseofscanningelectronmicroscopy(Fig.12.1),electronsare accelerated. Inc. Mostelaboratefracturesurfacepreparationisneededfortheexam- inationoffracturesurfacesinthetransmissionelectronmicroscope.These involvethepreparationofreplicasofthefracturesurface.Thecentersofthe replicasmustalsobethinnedtofacilitatethetransmissionofelectrons.In thecaseoftransmissionelectronmicroscopy,thecollimatedelectronbeams aretransmittedthroughthinnedspecimens(Fig.12.2).Thetransmitted electronbeamsmaythenbeviewedinthediffractionmode[Fig. 12.29(a)],orintheimagingmode[Fig.12.2(b)].Someoftheearlystudies offractureweredoneusingtransmissionelectronmicroscopyanalysesof thereplicasoffracturesurfacesinthe1950sand1960s.However,withthe adventoftheSEM,ithasbecomeincreasinglyeasiertoperformfracto- graphicanalyses.Mostoftheimagesoffracturesurfacespresentedinthis chapterwill,therefore,beimagesobtainedfromSEMs.Thesehavegood depthoffocus,andcanproduceimageswithresolutionsof510nm. FIGURE12.1Schematicillustrationoftheoperationofascanningelectron microscope Inc. Thetoughnessorenergyperunitvolume,W,isgivenby W¼ ð " f 0 d"ð12:1Þ where" f isthefracturestrain,andistheappliedstress,expressedasa functionofstrain,".Thetoughnessmustbedistinguishedfromthefracture toughness,whichmaybeconsideredasameasureoftheresistanceofa materialtocrackgrowth. Materialswithhightoughnessorfracturetoughnessgenerallyrequire asignificantamountofplasticworkpriortofailure.Incontrast,thefracture toughnessofpurelybrittlematerialsiscontrolledlargelybythesurface energy, s ,whichisameasureoftheenergyperunitarearequiredforthe creatingofnewsurfacesaheadofthecracktip.However,thereisastrong couplingbetweenthesurfaceenergy, s ,andplasticenergyterm, p .This couplingissuchthatsmallchangesin s canresultinlargechangesin p , andtheoveralltoughnessorfracturetoughness. Finallyinthissection,itisimportanttonotethatthedeformation associatedwiththefractureoftoughmaterialsgenerallyresultsinthe creationofadeformationprocesszonearoundthedominantcrack. ThisisillustratedschematicallyinFig.12.4Thesurfaceenergytermis associatedwiththeruptureofbondsatthecracktip,whiletheplastic worktermisusedpartlyinthecreationofthedeformationprocesszone. Detailsofthephenomenathatoccurinthedeformationprocesszonesare presentedinthenextfewsectionsonfractureinthedifferentcasesof materials. FIGURE12.3Illustrationoftoughnessastheareaunderthestress–strain curves