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 5

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prior grain boundary, and relaxation of elastic strain energy in the system (Zhang, 2010). The critical cavity radius at nucleation, r c , is given by = 2 (10) wh ere γ is the cavity surface energy, σ n the normal stress acting on the grain boundary. Cavity growth occurs by different mechanisms, viz.  grain boundary diffusion cavity growth , whereby the exchange of atoms from the cavity surface migration occurs through the interconnectinggrain boundary region by stress directed vacancy flux (Beere and Speight, 1978);  Superplastic diffusion cavity growth , where owing to smaller grain size, diffusion is facilitated by a large number of grain boundaries getting connected to a cavity surface (Chokshi, 1986);  Power-law cavity growth is based on the development of a higher plastic strain rate adjacent to the cavity site, as promoted by local stress gradient causing the movement of atoms in the loading direction (Hancock, 1976);  Lattice diffusion cavity growth could occur under the condition where lattice diffusion is dominant over grain boundary diffusion at a homologous temperature closer to the melting point of the material (Hull and Rimmer, 1959; Beere and Speight, 1978).

The constitutive growth rates according to the above theories are presented in Table 2.

Table 2. The mechanisms for cavity growth rate for high temperature deformation of superplastic material.

Cavity growth mechanism

Equation for cavity growth rate

Eqns.

= Ω 5 1 2 ( −2 ⁄ ) ̇ (Beere and Speight, 1978) = 45Ω 1 2 ̇ (Chokshi, 1986)

Grain boundary diffusion

(11)

Superplastic diffusion

(12)

Power-law/plasticity-controlled growth = − 3 2

(13)

(Hancock, 1976)

Lattice diffusion (14) ⁄ is the cavity growth rate where r is the cavity radius, ε is the true strain, Ω is the atomic volume, δ is the grain boundary width, D gb is the grain boundary diffusivity, k iB is Boltzmann constant, T is the absolute temperature, σ is the flow stress, γ is the surface energy, ̇ is the strain rate and α is the cavity size-spacing parameter. 3. Experimental aspects of deformation and damage behavior 3.1. Materials and experimental procedures Materials which were investigated for their high temperature deformation and microstructure characterization in the past by Kashyap and co-workers are summarized in Table 3. The materials listed include examples of single phase, quasi-single phase and two-phase alloys. They were subjected to tensile tests at true constant strain rate or initial constant strain rate (cross-head speed) tests. Samples were mechanically polished and chemically etched, except the type 316L stainless steel which was electrolytically polished and etched. The microstructures were examined as detailed in the original papers. = Ωλ 5 1 2 ( −2 ⁄ ) ̇ (Hull and Rimmer, 1959; Beere and Speight, 1978)