Modeling and simulation of the mechanical response of martensitic shape memory alloys

The process of detwinning of martensite in shape memory alloys involves the deformation of the crystalline lattice of the material by twin boundary motion. The amount of maximum deformation that can be achieved this way is known to saturate at some point, beyond which further loading will eventually lead to permanent deformation of the material. We present an algorithm for the simulation of martensite reorientation in shape memory materials subjected to multi-axial loading that may exceed the saturation threshold. If the applied load is still nonproportional beyond this threshold, the reorientation strain tensor may continue to evolve while its magnitude remains constant. Such evolution can be simulated using a simple strain-based criterion. The complete process of martensite reorientation can thus be modeled using a set of two yield functions, the first of which is stress-based and governs the detwinning process prior to saturation, and the second is strain-based and governs the reorientation of variants at maximum equivalent reorientation strain. The model is implemented in a numerical analysis code. For this purpose, the evolution equations are solved implicitly using a Newton-Raphson scheme and the tangent stiffness matrix of the material is determined using a combination of analytical and numerical techniques.