PSI - Issue 60

B.P. Kashyap et al. / Procedia Structural Integrity 60 (2024) 494–509 B.P. Kashyap et al. / Structural Integrity Procedia 00 (2023) 000 – 000

497

4

Grain boundary sliding by grain boundary diffusion controlled

2

3

Courtney 2000; Cao et al., 2013)

Q gb

Mechanisms for superplastic deformation Ashby-Verrall Diffusional accommodation (rate controlling) 1

2

Q gb to Q L by considering effective diffusion coefficient

(Ashby and Verrall, 1973)

for relation between effective stress ( σ e = σ - σ TH ) and strain rate, but increases to higher values (2-3) with strain rate

Mukherjee model

2

2

(Mukherjee, 1971)

Q gb

Gifkins core-mantle model

2 2

2 1

(Gifkins, 1976) (Langdon, 1970)

Q gb

Langdon model

Q L

Gittus model for two phase materials

2

2

(Gittus, 1977)

Q IPB

In fine grained materials, below 10 μm grain size, superplastic deformation involves a number of deformation processes. For example, the dominant mechanism is known to be grain boundary sliding (GBS), but by itself, it is also responsible for being a source of damage in materials, like cavities or crack nucleation. However, its accommodation by diffusion in the form of grain boundary migrationand intra-granular slip, grain rotation, and grain switching eliminates or minimizes the probability of damage occurring. Figure 1 summarizes the major mechanisms for deformation along with the parameters of constitutive relationship and the effects on flow and damage that can result depending on strain rate/stress level, temperature and grain size of material.

Fig. 1. Log-log plot of stress as a function of strain rate showing the superplastic region II along with the lower strain rate region I and the higher strain rate region III, the secondary mechanisms of deformation and the extent of associated changes and the values of parameters ( m, p, Q ) of constitutive relationship (Kashyap and Mukherjee, 1985). 2.2. Constitutive relationships for cavitation during high temperature deformation Deformation processes in polycrystalline materials with or without the presence of a second phase and/or particles provide sufficient sites of heterogeneity in deformation, causing local stress concentration exceeding the limit of resistance to cavity nucleation. Just like the nucleation of a new phase in the phase transformation study, the cavity nucleation is considered to have a critical nucleus size to be stable and grow further. The free energy associated with cavity nucleation comprises of surface energy increment due to the formation of the cavity by agglomeration of vacancies, decrease in interface energy due to the disappearance of