A micromechanical model for martensitic phase‐transformations in shape‐memory alloys based on energy‐relaxation

Abstract

We develop a micromechanical model for single-crystalline materials undergoing diffusionless solid-to-solid phase transitions. It is based on the specification of laminated microstructures on the materials' microscale and hence is designed to approximate the rank-1-convex hull of the underlying energy-density for the phase-mixture. In order to capture the hysteretic behavior of such materials like shape-memory-alloys we also account for dissipation by means of evolution equations for the inelastic internal variables. In this context, we derive different evolution-laws from inelastic potentials via least-action principles. Several material-point computations emphasize the characteristics of the presented model.

Partially relaxed energy potentials for the modelling of microstructures – application to shape memory alloys

“…However, laminates of first order serve as a basis for further enhancements. In this subsection we briefly recall the main aspects of the model presented in [19,26], where the aforementioned procedure has been extended to higher order laminates and the consideration of arbitrarily many material phases in the context of phase transformations in shape memory alloys (SMA). More precisely, laminates of first order are used therein to distinguish between austenite and martensite in general.…”

“…These laminates are aligned in different directions characterised by unit vectors n A and n M . The specifically chosen perturbation field introduced in this work includes the maximum valuesb A as well asb i (denoted by different symbols in [19]) with i = 1, . .…”

“…As shown in, e.g., [34,[38][39][40], the continuous evolution of inelastic processes and microstructure evolution can be modeled by approximations for the dissipation distance. In contrast to this approach, an alternative formulation is suggested in [19,26] which leads to the relaxed problem via a partial relaxation. To this end, a distinction is made between elastic and dissipative internal variables according to…”

“…In this work we focus on two different concepts for the derivation: The first method is based on the aforementioned laminate approach where the focal point will be laid on the microscopic material model presented in [19]. The second framework to approximate the quasiconvex energy hull is achieved by the discretisation of the displacement perturbation field by means of the finite element method.…”

A Thermodynamically Consistent Finite Strain Micro-Sphere Framework for Phase-Transformation

“…Taking into account complex interactions at the micro-scale-such as specific microstructure arrangements and twin formations-leads to reliable micromechanical material models, such as the ones presented in, e.g., [6,7,8,9,10,11,12,13,14]. However, a possible disadvantage of such precise modelling approaches might be the high computational costs that usually accompany the detailed capturing of microstructural material effects.…”