Voiding and fracture at elevated temperatures

7.4.9 Voiding and fracture at elevated temperatures

Creep usually takes place above 0.3T m with a rate given by ˙ε = Bσ n , where B and n are material parameters, as discussed in Chapter 6. Under such conditions ductile failure of a transgranular nature,

similar to the ductile failure found commonly at low temperatures, may occur, when voids nucleated at inclusions within the grains grow during creep deformation and coalesce to produce fracture.

Mechanical properties II – Strengthening and toughening 437

(a)

(b)

Figure 7.36 Schematic representation of rupture with dynamic recrystallization (after Ashby et al., 1979).

However, because these three processes are occurring at T ≈ 0.3T m , local recovery is taking place, and this delays both the onset of void nucleation and void coalescence. More commonly at lower stresses and longer times to fracture, intergranular rather than transgranular fracture is observed. In this situation, grain boundary sliding leads to the formation of either wedge cracks or voids on those boundaries normal to the tensile axis, as shown schematically in Figure 7.37b. This arises because grain boundary sliding produces a higher local strain rate on an inclusion in the boundary than in the body of the grain, i.e. ˙ε local ≈ ˙ε( fd/2r), where f ≈ 0.3 is the fraction of the overall strain due to sliding.

The local strain therefore reaches the critical nucleation strain ε n much earlier than inside the grain. The time to fracture t f is observed to be ∝ (1/˙ε ss ), which confirms that fracture is controlled by power-law creep even though the rounded shape of grain boundary voids indicates that local diffusion must contribute to the growth of the voids. One possibility is that the void nucleation, even in the

boundary, occupies a major fraction of the lifetime t f , but a more likely general explanation is that the nucleated voids or cracks grow by local diffusion controlled by creep in the surrounding grains. Figure 7.37c shows the voids growing by diffusion, but between the voids the material is deforming by power-law creep, since the diffusion fields of neighboring voids do not overlap. Void growth therefore depends on coupled diffusion and power-law creep, with the creep deformation controlling the rate of cavity growth. It is now believed that most intergranular creep fractures are governed by this type of mechanism.

At very low stresses and high temperatures where diffusion is rapid and power-law creep negligible, the diffusion fields of the growing voids overlap. Under these conditions, the grain boundary voids are able to grow entirely by boundary diffusion; void coalescence then leads to fracture by a process of creep cavitation (Figure 7.38). In uniaxial tension the driving force arises from the process of taking atoms from the void surface and depositing them on the face of the grain that is almost perpendicular to the tensile axis, so that the specimen elongates in the direction of the stress and work is done. The

vacancy concentration near the tensile boundary is c 0 exp(σ /kT ) and near the void of radius r is

c 0 exp(2γ /rkT ), as discussed previously in Chapter 6, where is the atomic volume and γ the surface energy per unit area of the void. Thus, vacancies flow usually by grain boundary diffusion from the boundaries to the voids when σ ≥ 2γ/r, i.e. when the chemical potential difference (σ − 2γ /r) between the two sites is negative. For a void r ≈ 10 −6 m and γ ≈1Jm −2 the minimum stress for

438 Physical Metallurgy and Advanced Materials s n

Power-law creeping cage

d Void d

u Sliding

Zones unloaded Diffusion

displacements

by diffusion from voids

(c) Figure 7.37 Intergranular, creep-controlled, fracture. Voids nucleated by grain boundary sliding

(a)

(b)

(a and b) and growth by diffusion (c) (after Ashby et al., 1979).

Voids grow by boundary diffusion

l Surface diffusion

maintains void shape

(a)

(b)

Figure 7.38 Voids lying on ‘tensile’ grain boundaries (a) grown by grain boundary diffusion (b) (after Ashby et al., 1979).

hole growth is ≈2 MN m −2 . In spite of being pure diffusional controlled growth, the voids may not always maintain their equilibrium near-spherical shape. Rapid surface diffusion is required to keep the balance between growth rate and surface redistribution, and with increasing stress the voids become somewhat flattened.