Almost compatible microstructures in shape memory alloys

Coherent stress-free (CSF) microstructures with specific morphologies are favored in shape memory alloys (SMAs) when special relations are satisfied by the lattice parameters. Experimentally observed microstructures are, however, also formed at non-exact CSF conditions. Here we propose a framework for the investigation of almost compatible (i.e. non-perfectly CSF) twinned wedges in SMAs, and make a systematic study of these microstructures for two types of symmetry-breaking martensitic transformations. We determine the domains in lattice-parameter space wherein there exist, and coexist, different families of almost compatible wedges with low overall stress. We find these to be wide regions largely unrelated to the existence of special CSF relations, if any even exist, giving stress-free configurations. We propose SMA improvement can be obtained by targeting domains in lattice-parameter space wherein, besides satisfying other suitable properties, a maximum number of almost compatible microstructures can also form in the material. We develop this approach for wedges in SMAs undergoing the cubic-to-orthorhombic transformation.