Mechanical Properties of Engineered Materials 2008 Part 13 ppt

On the other hand, ductile fracture mechanisms represent another classof important fracture modes in engineering structures and components.They are somewhat more complex to analyze due t

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 ofscientific understanding of ductile fracture processes has facilitated the safeuse of metals and their alloys in a large number of structural applications.Most recently, there have been significant efforts to develop novelcomposite materials and engineered materials with improved fracture resis-tance These efforts have led to an improved understanding of how to tailorthe microstructure/architecture of a material for improved fracture tough-ness The research that has been performed in the past 25–35 years has also

led to identification of toughening mechanisms that can be used to engineerimproved fracture toughness in all classes of materials These will be dis-cussed in detail inChap 13.

This chapter presents an introduction to the micromechanisms of ture in different classes of materials Following an initial review of brittleand ductile fracture mechanisms, the mechanisms of fracture in differentclasses of materials are discussed along with mechanics models that providesome additional insights into the mechanisms of fracture Quantitative andqualitative approaches are also presented for the characterization of fracturemodes before concluding with a section on the thermal shock response ofmaterials

In the case of scanning electron microscopy (Fig 12.1),electrons areaccelerated from an electron gun (cathode) The electron beam is collimated

by a series of lenses and coils until it hits the specimen surface (fracturesurface) The electrons are then reflected from the specimen surface afterinteracting with a small volume of material around the surface The twotypes of electrons that are reflected back from the surface are secondaryelectrons and back-scattered electron These are detected by detectors thatare rastered to form a TV image The second electron images usually pro-vide good depth of field and clear images of surface topography, while theback-scattered electron images have the advantage of providing atomicnumber contrast that can be used to identify different phases (due to differ-ences in chemical composition)

The fracture surfaces of conducting materials (mostly tallics) can generally be viewed directly with little or no surface preparationprior to scanning electron microscopy However, the fracture surfaces ofnonconducting 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 toobtain images over a wide range of magnifications (100–100,000
)

metals/interme-Most elaborate fracture surface preparation is needed for the ination of fracture surfaces in the transmission electron microscope Theseinvolve the preparation of replicas of the fracture surface The centers of thereplicas must also be thinned to facilitate the transmission of electrons Inthe case of transmission electron microscopy, the collimated electron beamsare transmitted through thinned specimens (Fig 12.2) The transmittedelectron beams may then be viewed in the diffraction mode [Fig.12.29(a)], or in the imaging mode [Fig 12.2(b)] Some of the early studies

exam-of fracture were done using transmission electron microscopy analyses exam-ofthe replicas of fracture surfaces in the 1950s and 1960s However, with theadvent of the SEM, it has become increasingly easier to perform fracto-graphic analyses Most of the images of fracture surfaces presented in thischapter will, therefore, be images obtained from SEMs These have gooddepth of focus, and can produce images with resolutions of  510 nm

FIGURE 12.1 Schematic illustration of the operation of a scanning electronmicroscope (From Reed-Hill and Abbaschian, 1991—reprinted with permis-sion from PWS Publishing Co.)

12.3 TOUGHNESS AND FRACTURE PROCESS ZONES

Fracture experiments are usually peformed on smooth or notched mens The experiments on smooth specimens generally involve themeasurement of stress–strain curves, as discussed in Chap 3 Thesmooth specimens are loaded continuously to failure at controlled strainrates, in accordance with various testing codes, e.g., the ASTM E-8specification

speci-The area under the generic stress–strain curve is representative of theenergy per unit volume required for the fracture This is often described asthe toughness of the material Hence, in the representative stress–straincurves shown in Fig 12.3, material B is the toughest, while materials Aand C are not as tough However, material A is strong and brittle, whilematerial C is weak and ductile

FIGURE12.2 Schematic ray diagrams for (a) the diffraction mode and (b) theimaging mode of a transmission electron microscope Most microscopeshave more lenses than those shown here (From Hull and Bacon, 1984—adapted from Loretto and Smallman, 1975—reprinted with permission fromPergamon Press.)

The toughness or energy per unit volume, W, is given by

Materials with high toughness or fracture toughness generally require

a significant amount of plastic work prior to failure In contrast, the fracturetoughness of purely brittle materials is controlled largely by the surfaceenergy,s, which is a measure of the energy per unit area required for thecreating of new surfaces ahead of the crack tip However, there is a strongcoupling between the surface energy,s, and plastic energy term,p Thiscoupling is such that small changes ins can result in large changes in p,and the overall toughness or fracture toughness

Finally in this section, it is important to note that the deformationassociated with the fracture of tough materials generally results in thecreation of a deformation process zone around the dominant crack.This is illustrated schematically in Fig 12.4 The surface energy term isassociated with the rupture of bonds at the crack tip, while the plasticwork term is used partly in the creation of the deformation process zone.Details of the phenomena that occur in the deformation process zones arepresented in the next few sections on fracture in the different cases ofmaterials

FIGURE 12.3 Illustration of toughness as the area under the stress–straincurves for materials A, B, and C

12.4 MECHANISMS OF FRACTURE IN METALS AND

THEIR ALLOYS

12.4.1 Introduction

Fracture in metals and their alloys occurs by nominally brittle or ductilefracture processes In cases where brittle fracture occurs without local plas-ticity along low index crystallographic planes, the failure is described as acleavage fracture Cleavage fracture usually occurs by bond rupture acrossgains It is, therefore, often referred to as transgranular cleavage However,bond rupture may also occur between grains, giving rise to a form of frac-ture that is known as intergranular failure

In the case of ductile failure, fracture is usually preceded by localplasticity and debonding of the matrix from rigid inclusions This debond-ing, which occurs as a result of the local plastic flow of the ductile matrix, isfollowed by localized necking between voids, and the subsequent coales-cence of voids to form dominant cracks It results in ductile dimpled fracturemodes that are characteristic of ductile failure in crystalline metals and theiralloys

In contrast, the fracture of amorphous metals typically occurs by thepropagation of shear bands, and the propagation of microcracks ahead ofdominant cracks These different fracture mechanisms are discussed briefly

in this section for metals and their alloys

FIGURE12.4 Schematic of the fracture process zone

fracture is preceded by some local plasticity Under such conditions, fracture

is preceded by some local plasticity and the mirror halves of the two fracturesurfaces do not match This gives rise to a form of brittle fracture that isknown as ‘‘quasi-cleavage’’ (Thompson, 1993)

Cleavage fracture is often obseved in metals at lower temperatures.Furthermore, a transition from brittle to ductile fracture is generallyobserved to occur with increasing temperature in body-centered cubic(b.c.c.) metals and their alloys, e.g., steels This transition has been studiedextensively, but is still not fully understood

The first explanation of the so-called brittle-to-ductile transition(BDT) was offered by Orowan (1945) who considered the variations inthe temperature dependence of the stresses required for yielding and clea-vage (Fig 12.6) He showed that the cleavage fracture stress exhibits aweak dependence on temperature, while the yield stress generally increasessignificantly with decreasing temperature This is illustrated schematically

in Fig 12.6 The stresses required for yielding are, therefore, lower thanthose required for cleavage fracture at higher temperatures Hence, failureabove the BDT regime should occur by ductile fracture In contrast, sincethe cleavage fracture stresses are less than the yield stresses below theBDT regime, cleavage fracture would be expected to occur below thisregime

Following the work of Orowan (1945), other researchers recognizedthe critical role that defects play in the nucleation of cleavage fracture Strohsuggested that cleavage fracture occurs in a polycrystal when a critical value

of tensile stress, is reached in an unyielded grain

FIGURE 12.5 Cleavage fracture in niobium aluminide intermetallics: (a) Nb–15Al–10Ti, (b) Nb–15Al-25Ti (From Ye et al., 1999.)

Using similar arguments to those employed in the Hall–Petch model(Chap 8),Stroh (1954, 1957) derived the following relationship between thecleavage fracture stress, c, and the grain size, d:

where kf is the local tensile stress required to induce fracture in an adjacentgrain under nucleation-controlled conditions This theory correctly predictsthe inverse dependence of the cleavage fracture stress on grain size, but itsuggests a constant value of ky that is not true for finer grain sizes.Subsequent work by Cottrell (1958) showed that if the tensile stress isthe key parameter, as suggested by experimental results, then cleavage frac-ture must be growth controlled Cottrell suggested that cleavage fracture iniron occurs by the intersection ofa

2h11111i dislocations gliding on {101} slipplanes This results in the following dislocation reaction (Fig 13.7):a

2h 11111ið101Þþ1

2h111ið 1101Þ ! a½001 ð12:3ÞSince the resulting a[001] dislocation is sessile, this provides the first stage ofcrack nucleation that occurs due to the relative motion of material aboveand below 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

FIGURE 12.6 Schematic of Orowan ductile-to-brittle transition (From Knott,1973—reprinted with permission from Butterworth-Heinemann

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:

U1¼p2ð1  2Þ

E

c2

 2

ð12:4aÞ(for a crack of length 2a ¼ cÞ

2 The work done by the stress in forming the nucleus:

 

ð12:4dÞwhere R is the distance over which the strain field is significant,  isthe shear modulus, and c=2 is the radius of the dislocation score of thecracked dislocation The equilibrium crack lengths are found from @=@c

FIGURE12.7 Cottrell’s model of brittle fracture (From Knott 1973—reprintedwith permission from Butterworth-Heinemann.)

ðU1þ U2þ U3þ U4Þ ¼ 0 This gives a quadratic function with two possiblesolutions for the crack lengths Alternatively, there may be no real roots, inwhich case the total energy decreases spontaneously The transition point isthus given by

However, for grains coarser than d inFig 12.8, the fracture is not growthcontrolled This is because it is necessary to first form the dislocations before

a nucleus can be produced The fracture stress is thus simply equal to theyield stress However, for grains larger than d, yielding occurs prior tofracture, and the nucleus will spread when

 1

i eff

Work by Hull (1960) also recognized that cleavage fracture can benucleated by interactions between dislocations twins Similar results werelater reported by Knott and Cottrell (1963) for fracture in polycrystallinemild steel In the case of b.c.c metals, twinning occurs by the movement

of a=6h1111i dislocations on {211} planes The twinning shear is 0.707.This can produce significant displacements normal to the cleavageplane Estimates of  associated with these displacements are  20 J/m2

.These are approximately one order of magnitude greater than the surfaceenergies

Since the early work on cleavage fracture, subsequent research hasshown that cleavage fracture is most likely to occur under conditions ofhigh-stress triaxiality In most cases, the so-called triaxiality factor, T.F.,

is expressed as a ratio of the hydrostatic stress to the Von Mises stress:

The critical role of crack-tip/notch-tip stress distributions in thenucleation of brittle cleavage fracture was first examined in detail byRitchie, Knott, and Rice (1973) By considering the results of finite ele-ment calculations of the notch-tip fields of Griffith and Owens (1972),

FIGURE12.9 Schematic of cleavage fracture nucleation from carbides (FromKnott, 1973—reprinted with permission from Butterworth-Heinemann.)

Ritchie et al (1973) postulated that cleavage-fracture nucleation is mostlikely to occur at a distance of 2–3 CTODs ahead of the notch-tip, Fig.12.10(a) The so-called Ritchie–Knott–Rice (RKR) theory recognized theneed for local tensile stresses to exceed the local fracture stress over amicrostructurally significant distance ahead of a notch/crack tip, asshown in Fig 12.10(a).

Subsequent work by Lin et al (1986) resulted in the development of astatistical model for the prediction of brittle fracture by transgranular clea-vage Using weakest link statistics to characterize the strength distributions

of the inclusions ahead of the notch tip/crack tip, they showed that thefailure probability associated with the element of material in the plasticzone is given by

 ¼ 1  exp½bfN"K4

1 2ðn2Þ

0 S0mð 0 SuÞm ð2nþ3Þd  ð12:9Þwhere b is the characteristic dimension along the crack tip, f is the frac-tion 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 isthe yield or flow stress, S0 is the Weibull scale parameter, Su is the lowerbound strength (of the largest feasible cracked particle), m is the shapefactor, n is the work hardening exponent ð1 < n < 1Þ, is the local stresswithin plastic zone, and " is a strain term that is given by Lin et al 1986

K1 0

 2 0

Su

 nþ1

~ nþ1 ð12:11aÞoccurring at the stress:

A number of other researchers have made significant contributions tothe modeling of cleavage fracture within a statistical framework Theseinclude Curry (1980), Evans (1983), Beremin (1983), Mudry (1987),

FIGURE12.10 Stress distributions ahead of blunt notches: (a) Ritchie–Knott–Rice (RKR) model; (b) Lin–Evans–Ritchie model (From Lin et al., 1986—rep-rinted with permission from Elsevier Science.)

Rousselier (1987), Fontaine et al (1987), Rosenfield and Majumdar (1987),and Thompson and Knott (1993) All of these studies have suggested refine-ments to the approach of Lin et al (1986) In general, however, the trendspredicted by the different models are generally consistent However, the sizeeffect predicted by the Beremin (1983) and Evans (1983) theories are not thesame.

12.4.3 Ductile Fracture

Ductile fracture in metals and their alloys is generally associated with thenucleation of voids around rigid inclusions Since plastic flow of the matrixcan occur around the inclusions, the matrix may become debonded fromthe rigid inclusions during plastic flow, Figs 12.11(a) and 12.11(b).Subsequent localized void growth [Fig 12.11(c)] and deformation andnecking [Figs 12.11(d) and 12.11(e)] may then occur prior to the coales-cence of microvoids and final fracture, Fig 12.11(f) This gives rise to theformation of larger dominant cracks that may propagate in a ‘‘stable’’manner until catastrophic failure occurs Not surprisingly, the fracturesurfaces will contain dimples (Fig 12.12) associated with the microvoidnucleation and propagation processes The inclusions associated withnucleation and propagation may also be seen in some of the microvoids(Fig 12.12)

Considerable experimental work has also been done to provideinsights into the mechanisms of ductile fracture The pioneering work inthis area has been done by Knott and co-workers (1973, 1987) Other experi-mental researchers that have made significant contributions to the under-standing of ductile fracture include Thompson and Knott (1993) andEbrahimi and Seo (1996)

The studies by Ebrahimi and Seo (1996) explored the sional nature of crack initiation in ferritic and bainitic steels They con-cluded that crack initiation occurs by the formation of disconnectedcracks along the crack front Inclusions and highly strained regions werefound to be the sites for crack nucleation in ferritic–pearlitic steels, whilegeometrical inhomogenities associated with fatigue provided the sites forcrack nucleation in bainitic steels

three-dimen-In general, however, the dominant viewpoint is that voids nucleate atparticles (Rice and Tracey, 1969) These include primary and secondaryparticles formed by phase transformations, and inclusions that are intro-duced largely during processing, e.g., during casting or powder processing.The pioneering theoretical work on void growth was done byMcClintock (1968), who analyzed the effects of stress rate on the growth

of a long cylindrical void Subsequent work by Rice and Tracey (1969)

proposed the well-known Rice–Tracey (RT) model for the characterization

of the growth rate of an isolated spherical void (Fig 12.13) The void growthrate predicted under continuum plasticity conditions in which( ffiffiffi

R ¼R1þ R2þ R3

FIGURE 12.11 Schematics of ductile fracture processes in metals and theiralloys: (a) onset of deformation; (b) microvoid nucleation; (c) void growth;(d) strain localization between voids; (e) necking between voids; (f) knife-edgeseparation (From Thomason, 1990—reprinted with permission fromPergamon Press.)

However, in rear materials, more than one void nucleates almost at the sametime, and there are interactions between the different growing voids Also,although the RT model does not consider the interactions between voids, it

is generally used to predict void growth behavior in ductile fracture cesses

pro-Several modifications have been made to develop the RT model Byconsidering the nucleation and propagation of dislocation in the matrixbetween voids, Kameda (1989) deduced that the relationships between thevoid growth rate and the hydrostatic tensile stress and the void fracture is afunction of the thermally activated shear stress and the activation volumefor dislocation motiton in the matrix triaxility

Idealizing the process of ductile fracture by confining void growthand coalescence to a material layer of initial thickness, D, ahead of theinitial crack tip, Xia and Shih (1996) developed a mechanism-based cellmodel for the characterization of ductile tearing, and the transition fromductile-to-brittle fracture The most important fracture process parametersare the initial void volume fracture in the cell, f0, and the characteristiclength of a cell, D, which should be interpreted as the mean spacingbetween the voids nucleated from the large inclusions Microvoidsnucleated from small inclusions assist with the process of hole link-upwith the crack tip during the coalescence phase The current void volumefraction, f , and the current flow stress of the matrix ... characteristic dimension along the crack tip, f is the frac-tion of particles that participate in the fraction initiation, N is the number

of particles per unit volume, K1 is the Mode... class="text_page_counter">Trang 13< /span>

Ritchie et al (1973) postulated that cleavage-fracture nucleation is mostlikely to occur at a distance of 2–3 CTODs ahead of the... this provides the first stage ofcrack nucleation that occurs due to the relative motion of material aboveand below the slip plane Furthermore, the pumping of n pairs of disloca-tions into the wedge