Scale-Free Modeling of Coupled Evolution of Discrete Dislocation Bands and Multivariant Martensitic Microstructure

A scale-free model for the coupled evolution of discrete dislocation bands and multivariant martensitic microstructure is developed. In contrast to previous phase field models, which are limited to nanoscale specimens, this model allows for treating the nucleation and evolution of martensite at evolving dislocation pileups, twin tips, and shear bands in a sample of an arbitrary size. The model is applied for finite element simulations of plastic strain-induced phase transformations (PTs) in a polycrystalline sample under compression and shear. The solution explains the one to two orders of magnitude reduction in PT pressure by plastic shear, the existence of incompletely transformed stationary state, and optimal shear strain for the strain-induced synthesis of high pressure phases.

Figure 1

Distribution of normalized sliding displacements $u_s/L$ along the slip system in the left grain vs normalized distance $x/L$. Results for $L=25\mathrm{nm}$ and $L$ increased by factors of 10, $10^2$, and $10^3$ coincide; i.e., solutions for stress, strain, and PT are independent of scale. Inset: Geometry, loading conditions, and stationary solutions for a volume fraction of HPP $c$ and dislocations in a bicrystal under fixed compression ${\sigma }_n=3.05\mathrm{GPa}$ and shear $\gamma =0.2$. Dislocation signs are placed at points corresponding to the integer values of the number of dislocations $n=u_s/b$.

Figure 2

Nucleation and evolution of the HPP in the right grain at fixed $\gamma =0.2$ and ${\sigma }_n=3.05\mathrm{GPa}$ (a) without plasticity for ${\phi }_1=69.7°$ and (b) for ${\phi }_1=89.7°$, as well as (c) with plasticity for ${\phi }_1=89.7°$. White isolines for the stationary solutions correspond to the local phase equilibrium condition, $\mathbf{\sigma }:{\mathbf{ϵ}}_t=\mathrm{\Delta }{G}^{\theta }=1.0\mathrm{GPa}$.

Figure 3

(a) The grain structure of the polycrystal with shown ${\phi }_1$ angles loaded by fixed ${\sigma }_n=6.05$ and shear strain rate of $0.004{\mathrm{s}}^{-1}$, (b) evolution of the averaged volume fraction of the HPP, $\tilde{c}$, in each grain, and (c) evolution of pressure, shear stress, and volume fraction of the HPP $\overline{c}$, as well as each of the martensitic variants ${\overline{c}}_i$ averaged over the sample vs the macroscopic shear strain.

Figure 4

Evolution of dislocations, the HPP (a), and two martensitic variants (b and c) under stress fixed ${\sigma }_n=6.05$ and shear strain rate of $0.004{\mathrm{s}}^{-1}$.