  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.
