Phase field-finite element approach to study the effects of plasticity on thermal- and stress-induced martensite in shape memory alloys

Numerous experimental studies have shown that evolution of the martensite microstructure in shape memory alloys can lead to plastic deformation. This results in poor functional fatigue in many commercial applications, whereby strain incrementally advances with repeated thermal cycling under stress. This can also affect structural fatigue, whereby repeated cycling initiates and grows fatigue cracks. Conventional strategies to improve fatigue life include increasing fl ow strength as to decrease plastic zone size, but binary Ni–Ti alloys do not always follow this trend and there is evidence that a stress-induced phase transformation may not improve fatigue life. Thus, functional and structural fatigue performances are coupled to the underlying interaction between phase transformation and plasticity. This interaction is studied using a unique phase fi eld-fi nite element approach that incorporates fi nite deformation. It models the austenite-to-martensite phase transformation at the fi nest (nm) scale and includes the kinetics of nucleation and growth of correspondence variants. Like spectral methods, it includes the driving forces from chemical, mechanical, and interfacial energies. However, the fi nite deformation approach also captures the rotation and deformation of material elements during transformation and plasticity. The latter is modeled using a rate-dependent crystal plasticity fl ow law in the austenite phase. The formalism also includes anisotropic elasticity and thermal expansion, thus capturing texture development and local internal stress during arbitrary thermo-mechanical histories. We examine three hypotheses associated with transformation and plasticity. The fi rst is that plasticity can affect the microstructure of thermally induced martensite and the critical temperature at which it forms. This is explored by varying the rate of cooling, which is expected to moderate the amount of rate-dependent plasticity during transformation. We also study cases where the cooling rate is the same but the plastic yield strength is varied. The second hypothesis is that plasticity can affect the microstructure of stress-induced martensite and the critical applied stress at which it forms. This is explored by simulating uniaxial compression tests of single austenite crystals of varying orientation. The change in orientation moderates the relative Schmid factors for transformation vs. plasticity and the large deformation simulations highlight the complex bending and macrostress state during the test. The third hypothesis is that plasticity can affect the microstructure of stress-induced martensite at crack tips. This is explored through Mode I loading in cracked austenite single crystals. Different crack orientations are considered, thus moderating the relative Schmid factors for transformation and plasticity. The crack tip fi elds can be contrasted with those from conventional elasticity and crystal-plasticity solutions. The effects of plasticity on microstructure in shape memory alloys connect to transmission electron microscope observations of defect and texture evolution during thermal and stress cycling. These microstructural changes affect the performance and ratcheting measured in macroscopic tests. The phase fi eld-fi nite element approach presented here can explore such microstructure-property-performance relationships in shape memory alloys.