Surface layer effect on high pressure phase growth in a bicrystal: phase field model and simulations

Effect of the external surface layer on the phase transition (PT) between the low pressure phase and high pressure phase (HPP) in a NiAl bicrystal is investigated. Using a phase field model, the external surface layer is included, within which the elastic properties and surface energy are properly distributed. After resolving a stationary layer, the coupled phase field and elasticity equations are solved to capture the HPP evolution. Residual stress concentrator is included as a shear band representing an inelastic shear strain. Due to the small grain size, the surface layer can influence the stress distribution and consequently, the critical inelastic shear strain \(\gamma _{cr}\) ${\gamma }_{\mathit{cr}}$ for the HPP growth. Above a certain applied pressure, the surface layer width \({\Delta }_{{\xi }}\) ${\mathrm{\Delta }}_{\xi }$ shows no effect on \(\gamma _{cr}\) ${\gamma }_{\mathit{cr}}$ , e.g., \(P=10\) $P=10$  GPa for the grain size of L \(=\) $=$ 20 nm. For lower pressures, \(\gamma _{cr}\) ${\gamma }_{\mathit{cr}}$ increases as pressure reduces. Due to the interplay of size addition by the surface layer and size reduction by the transformation strain, \(\gamma _{cr}\) ${\gamma }_{\mathit{cr}}$ reduces versus \({\Delta }_{{\xi }}\) ${\mathrm{\Delta }}_{\xi }$ and then increases for larger \({\Delta }_{{\xi }}\) ${\mathrm{\Delta }}_{\xi }$ . For smaller grain sizes, the surface layer effect is promoted as it is imposed to a larger transformation work. The lowest \(\gamma _{cr}\) ${\gamma }_{\mathit{cr}}$ is obtained for \(P=19\) $P=19$ GPa, in good agreement with the theoretical pressure of 20 GPa. Combining the external shear on pressure adds an extra shear term to the transformation work, which allows for the relaxation of the shear band and results in a nonlinear reduction of the PT pressure versus applied shear.