Intergranular fracture

8.4.6 Intergranular fracture

Intergranular brittle failures are often regarded as a special class of fracture. In many alloys, however, there is a delicate balance between the stress required to cause a crack to propagate by cleavage and that needed to cause brittle separation along grain bound- aries. Although the energy absorbed in crack propa- gation may be low compared to cleavage fractures,

292 Modern Physical Metallurgy and Materials Engineering much of the analysis of cleavage is still applica-

8.4.7 Ductile failure

ble if it is considered that chemical segregation to Ductile failure was introduced in Chapter 4 because grain boundaries or crack faces lowers the surface

of the role played by voids in the failure processes, energy of the material. Fractures at low stresses are

which occurs by void nucleation, growth and coa- observed in austenitic chromium–nickel steels, due to

lescence. The nucleation of voids often takes place the embrittling effect of intergranular carbide precipi-

at inclusions. The dislocation structure around parti- tation at grain boundaries. High transition temperatures

cle inclusions leads to a local rate of work-hardening and low fracture stresses are also common in tungsten

higher than the average and the local stress on reach- and molybdenum as a result of the formation of thin

c will cause fracture of the second-phase films due to small amounts of oxygen,

inclusion or decohesion of the particle/matrix inter- nitrogen or carbon. Similar behaviour is observed in

face, thereby nucleating a void. The critical nucleation the embrittlement of copper by antimony and iron by

strain ε n can be estimated and lies between 0.1 and oxygen, although in some cases the second-phase films

1.0 depending on the model. For dispersion-hardening cannot be detected.

materials where dislocation loops are generated the

A special intergranular failure, known as temper stress on the interface due to the nearest prismatic embrittlement, occurs in some alloy steels when tem- pered in the range 500–600 °

ration of the interface when it reaches the theoretical associated with the segregation of certain elements or

C. This phenomenon is

strength of the interface, of order w /b . The param- combinations of elements to the grain boundaries. The

eter r is given in terms of the applied shear strain amount segregated is very small (¾ a monolayer) but

ε , the particle diameter d and the length k equal to the species and amount has been identified by AES on

half the mean particle spacing as r D 4kb/εd. Hence, specimens fractured intergranularly within the ultra-

void nucleation occurs on a particle of diameter d after high vacuum of the Auger system. Group VIB ele-

a strain ε, given by ε D 4k w . Any stress con- ments are known to be the most surface-active in iron

centration effect from other loops will increase with but, fortunately, they combine readily with Mn and Cr

particle size, thus enhancing the particle size depen- thereby effectively reducing their solubility. Elements

dence of strain to voiding.

Once nucleated, the voids grow until they coalesce in Groups IVB and VB are less surface-active but often

to provide an easy fracture path. A spherical-shaped co-segregate in the boundaries with Ni and Mn. In

void concentrates stress under tensile conditions and, Ni –Cr steels, the co-segregation of Ni –P and Ni –Sb

as a result, elongates initially at about C⊲³2⊳ times occurs, but Mo additions can reduce the tendency for

the rate of the specimen, but as it becomes ellipsoidal temper embrittlement. Since carbides are often present

the growth-rate slows until finally the elongated void in the grain boundaries, these can provide the crack

grows at about the same rate as the specimen. At nucleus under the stress concentration from disloca-

some critical strain, the plasticity becomes localized tion pile-ups either by cracking or by decohesion of

and the voids rapidly coalesce and fracture occurs. The the ferrite/carbide interface, particularly if the interfa-

localization of the plasticity is thought to take place cial energy has been lowered by segregation.

when the voids reach a critical distance of approach,

Figure 8.35 Schematic representation of ductile fracture. (a) Voids nucleate at inclusions, (b) voids elongate as the specimen extends, (c) voids coalesce to cause fracture when their length 2h is about equal to their separation (after Ashby et al., 1979) .

Strengthening and toughening 293 given when the void length 2h is approximately equal

to the separation, as shown in Figure 8.35. The true strain for coalescence is then

v ⊳/ 2r v ] ' ⊲ 1/C⊳ ln[˛⊲1/f 1/2 v

where ˛ ³ 1 and f v is the volume fraction of inclu- sions.

Void growth leading to failure will be much more rapid in the necked portion of a tensile sample follow- ing instability than during stable deformation, since the stress system changes in the neck from uniaxial tension to approximately plane strain tension. Thus the over- all ductility of a specimen will depend strongly on the macroscopic features of the stress–strain curves which (from Consid`ere’s criterion) determines the extent of stable deformation, as well as on the ductile rupture process of void nucleation and growth. Nevertheless, an equation of the form of (8.30) reasonably describes the fracture strain for cup and cone failures.

Figure 8.36 Schematic representation of rupture with The work of decohesion influences the progress of

dynamic recrystallization (after Ashby et al., 1979) . voiding and is effective in determining the overall ductility in a simple tension test in two ways. The onset of voiding during uniform deformation depresses the

8.4.8 Rupture

rate of work-hardening which leads to a reduction in If the ductile failure mechanisms outlined above are the uniform strain, and the void density and size at the

inhibited then ductile rupture occurs (see Figure 8.36). onset of necking determines the amount of void growth

Specimens deformed in tension ultimately reach a required to cause ductile rupture. Thus for matrices

stage of mechanical instability when the deformation is having similar work-hardening properties, the one with

localized either in a neck or in a shear band. With con- the least tendency to ‘wet’ the second phase will show

tinued straining the cross-section reduces to zero and both lower uniform strain and lower necking strain.

the specimen ruptures, the strain-to-rupture depending For matrices with different work-hardening potential

on the amount of strain before and after localization. but similar work of decohesion the matrix having

These strains are influenced by the work-hardening the lower work-hardening rate will show the lower

behaviour and strain-rate sensitivity. Clearly, rupture reduction prior to necking but the greater reduction

is favoured when void nucleation and/or growth is during necking, although two materials will show

inhibited. This will occur if (1) second-phase particles similar total reductions to failure.

are removed by zone-refining or dissolution at high The degree of bonding between particle and matrix

temperatures, (2) the matrix/particle interface is strong may be determined from voids on particles annealed

and ε n is high, (3) the stress state minimizes plas- to produce an equilibrium configuration by measuring

tic constraint and plane strain conditions (e.g. single crystals and thin sheets), (4) the work-hardening rate

surface. Resolving surface forces tangential to the and strain-rate sensitivity is high as for superplastic

materials (in some superplastic materials voids do not approximately in terms of the matrix surface energy

particle, then the specific interface energy I is given

form but in many others they do and it is the growth

and coalescence processes which are suppressed), and m

m and the particle surface energy P as I D P

(5) there is stress relief at particles by recovery or then given by

w is

dynamic recrystallization. Rupture is observed in most w D P C m

fcc materials, usually associated with dynamic recrys- tallization.

Measurements show that the interfacial energy of TD nickel is low and hence exhibits excellent ductility

8.4.9 Voiding and fracture at elevated

at room temperature. Specific additions (e.g. Zr to

TD nickel, and Co to Ni –Al 2 O 3 alloys) are also

temperatures

effective in lowering the interfacial energy, thereby Creep usually takes place above 0.3T m with a rate causing the matrix to ‘wet’ the particle and increase the

n , where B and n are material param-

eters, as discussed in Chapter 7. Under such condi- materials have superior mechanical properties at high

ductility. Because of their low I , dispersion-hardened

tions ductile failure of a transgranular nature, sim- temperatures compared with conventional hardened

ilar to the ductile failure found commonly at low alloys.

temperatures, may occur, when voids nucleated at

294 Modern Physical Metallurgy and Materials Engineering inclusions within the grains grow during creep defor-

that most intergranular creep fractures are governed by mation and coalesce to produce fracture. However,

this type of mechanism.

because these three processes are occurring at T ³ At very low stresses and high temperatures where 0.3T m , local recovery is taking place and this delays

diffusion is rapid and power-law creep negligible, the both the onset of void nucleation and void coales-

diffusion fields of the growing voids overlap. Under cence. More commonly at lower stresses and longer

these conditions, the grain boundary voids are able to times-to-fracture, intergranular rather than transgranu-

grow entirely by boundary diffusion; void coalescence lar fracture is observed. In this situation, grain bound-

then leads to fracture by a process of creep cavita- ary sliding leads to the formation of either wedge

tion (Figure 8.38). In uniaxial tension the driving force cracks or voids on those boundaries normal to the

arises from the process of taking atoms from the void tensile axis, as shown schematically in Figure 8.37b.

surface and depositing them on the face of the grain This arises because grain boundary sliding produces a

that is almost perpendicular to the tensile axis, so that higher local strain-rate on an inclusion in the bound-

the specimen elongates in the direction of the stress ary than in the body of the grain, i.e. Pε local ' Pε⊲fd/ 2r⊳

and work is done. The vacancy concentration near the where f ³ 0.3 is the fraction of the overall strain due

tensile boundary is c 0

to sliding. The local strain therefore reaches the crit- radius r is c 0 exp⊲2 /rkT⊳, as discussed previously ical nucleation strain ε n much earlier than inside the

in Chapter 7, where  is the atomic volume and the grain.

surface energy per unit area of the void. Thus vacan- The time-to-fracture t f is observed to be / ⊲1/Pε ss ⊳ ,

cies flow usually by grain boundary diffusion from the which confirms that fracture is controlled by power-

law creep even though the rounded-shape of grain the two sites is negative. For a void r ' 10 6 m and boundary voids indicates that local diffusion must con-

tribute to the growth of the voids. One possibility is ³ 1 J/m the minimum stress for hole growth is 2 that the void nucleation, even in the boundary, occu-

³2 MN/m . In spite of being pure diffusional con-

trolled growth, the voids may not always maintain their likely general explanation is that the nucleated voids

pies a major fraction of the lifetime t f , but a more

equilibrium near-spherical shape. Rapid surface diffu- or cracks grow by local diffusion controlled by creep in

sion is required to keep the balance between growth the surrounding grains. Figure 8.37c shows the voids

rate and surface redistribution and with increasing growing by diffusion, but between the voids the mate-

stress the voids become somewhat flattened. rial is deforming by power-law creep, since the dif-

fusion fields of neighbouring voids do not overlap.

8.4.10 Fracture mechanism maps

Void growth therefore depends on coupled diffusion The fracture behaviour of a metal or alloy in different and power-law creep, with the creep deformation con-

stress and temperature regimes can be summarized trolling the rate of cavity growth. It is now believed

conveniently by displaying the dominant mechanisms

Figure 8.37 Intergranular, creep-controlled, fracture. Voids nucleated by grain boundary sliding (a) and (b) growth by diffusion in (c) (after Ashby et al., 1979) .

Strengthening and toughening 295

a cleavage or brittle boundary failure after general yield and with measurable strain-to-failure is called either cleavage 3 or BIF3. In many cases, mixed transgranular and intergranular fractures are observed, as a result of small changes in impurity content, texture or temperature which cause the crack to deviate from one path to another, no distinction is then made in the regime between cleavage and BIF. While maps for only two structures are shown in Figure 8.39 it is evident that as the bonding changes from metallic to ionic and covalent the fracture-mechanism fields will move from left to right: refractory oxides and silicates, for example, exhibit only the three brittle regimes and intergranular creep fracture.

Figure 8.38 Voids lying on ‘tensile’ grain boundaries (a) grow by grain boundary diffusion (b) (after Ashby et al.,

8.4.11 Crack growth under fatigue conditions

1979) . Engineering structures such as bridges, pressure ves- sels and oil rigs all contain cracks and it is necessary

on a fracture mechanism map. Seven mechanisms have to assess the safe life of the structure, i.e. the num- been identified, three for brittle behaviour including

ber of stress cycles the structure will sustain before a cleavage and intergranular brittle fracture, and four

crack grows to a critical length and propagates catas- ductile processes. Figure 8.39 shows schematic maps

trophically. The most effective approach to this prob- for fcc and bcc materials, respectively. Not all the frac-

lem is by the use of fracture mechanics. Under static ture regimes are exhibited by fcc materials, and even

stress conditions, the state of stress near a crack tip is some of the ductile processes can be inhibited by alter-

described by K, the stress intensity factor, but in cyclic ing the metallurgical variables. For example, intergran-

loading K varies over a range K⊲D K max min ⊳ . ular creep fracture is absent in high-purity aluminium

The cyclic stress intensity K increases with time at but occurs in commercial-purity material, and because

constant load, as shown in Figure 8.40a, because the the dispersoid suppresses dynamic recrystallization in

crack grows. Moreover, for a crack of length a the rate TD nickel, rupture does not take place whereas it does

K according to the Paris–Erdogan equation carbides dissolve.

in Nimonic alloys at temperatures where the 0 and

(8.32) In the bcc metals, brittle behaviour is separated into

da/dN D C⊲K⊳ m

three fields; a brittle failure from a pre-existing crack, where C and m are constants, with m between 2 and well below general yield, is called either cleavage

4. A typical crack growth rate curve is shown in

1 or brittle intergranular fracture BIF1, depending Figure 8.40b and exhibits the expected linear relation- on the fracture path. An almost totally brittle failure

ship over part of the range. The upper limit corre- from a crack nucleated by slip or twinning, below

sponds to K Ic , the fracture toughness of the material, general yield, is called either cleavage 2 or BIF2, and

and the lower limit of K is called the threshold for

Figure 8.39 Schematic fracture mechanism maps for (a) fcc and (b) bcc materials .

296 Modern Physical Metallurgy and Materials Engineering

Figure 8.40 (a) Increase in stress intensity K during fatigue; (b) variation of crack growth rate with increasing K . crack growth ⊲K th ⊳ . Clearly, when the stress intensity

little effect. At higher growth rate exhibited in regime factor is less than K th the crack will not propagate at

C, the growth rates become extremely sensitive to both that particular stress and temperature, and hence K th

microstructure and mean stress, with a change from is of significance in design criteria. If the initial crack

striation formation to fracture modes normally asso-

ciated with noncyclic deformation, including cleavage of cycles to catastrophic failure will be given by

length is a 0 and the critical length a c , then the number

and intergranular fracture.

N D da/C⊲K⊳ f m

a c Further reading

a 0 Ashby, M. F. and Jones, D. R. H. (1980). Engineering Mate- rials—An Introduction to their properties and applications . The mean stress level is known to affect the fatigue

Pergamon.

life and therefore da/dN. If the mean stress level Bilby, B. A. and Christian, J. W. (1956) The Mechanism of is increased for a constant value of K, K max will

Phase Transformations in Metals , Institute of Metals.

Bowles and Barrett. Progress in Metal Physics, 3, 195. Perg- of da/dN increases rapidly in practice, despite the