An efficient implementation for a model of martensite reorientation in martensitic shape memory alloys under multiaxial nonproportional loading

作者：Zaki Wael^*

来源：International Journal of Plasticity, 2012, 37: 72-94.

DOI：10.1016/j.ijplas.2012.04.002

• Shape memory alloys
• Detwinning
• Reorientation
• Constitutive modeling
• Finite elements

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 multiaxial 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 finite element software. For this purpose, the evolution equations are solved implicitly using a Newton-Raphson scheme and the consistent tangent stiffness matrix of the material is determined in closed form. Examples are given that show the ability of the model to effectively simulate the response of martensitic shape memory alloy structures to complex loading. The model is then validated using experimental data taken from the literature.

• 出版日期2012-10