Simulations of multivariant Si I to Si II phase transformation in polycrystalline silicon with finite-strain scale-free phase-field approach

Scale-free phase-field approach (PFA) at large strains and corresponding finite element method (FEM) simulations for multivariant martensitic phase transformation (PT) from cubic Si I to tetragonal Si II in a polycrystalline aggregate are presented. Important features of the model are large and very anisotropic transformation strain tensor $\varepsilon_{t}=\{0.1753;0.1753; -0.447\}$ and stress-tensor dependent athermal dissipative threshold for PT, which produce essential challenges for computations. 3D polycrystals with 55 and 910 stochastically oriented grains are subjected to uniaxial strain- and stress-controlled loadings under periodic boundary conditions and zero averaged lateral strains. Coupled evolution of discrete martensitic microstructure, volume fractions of martensitic variants and Si II, stress and transformation strain tensors, and texture are presented and analyzed. Macroscopic variables effectively representing multivariant transformational behavior are introduced. Macroscopic stress-strain and transformational behavior for 55 and 910 grains are close (less than 10% difference). This allows the determination of macroscopic constitutive equations by treating aggregate with a small number of grains. Large transformation strains and grain boundaries lead to huge internal stresses of tens GPa, which affect microstructure evolution and macroscopic behavior. In contrast to a single crystal, the local mechanical instabilities due to PT and negative local tangent modulus are stabilized at the macroscale by arresting/slowing the growth of Si II regions by the grain boundaries and generating the internal back stresses. This leads to increasing stress during PT. The developed methodology can be used for studying similar PTs with large transformation strains and for further development by including plastic strain and strain-induced PTs.