Comparative Study of Two Multiscale Thermomechanical Models of Polycrystalline Shape Memory alloys: Application to a Representative volUme Element of Titanium–Niobium

Abstract

This paper presents a comparative study between two micro-macro modeling approaches to simulate stress-induced martensitic transformation in shape memory alloys (SMA). One model is a crystal plasticity based model and the other describes the evolution of the microstructure with a Boltzmann-type statistical approach.Both models consider a self-consistent scheme to perform the scale transition from the local thermomechanical behavior to the global one. The way the two modeling approaches describe the local behavior is analyzed.Similarities and differences are pointed out. Numerical simulations of the thermo-mechanical behavior of an isotropic titanium-niobium SMA are performed. These alloys have known a growing interest of scientific community given their high potential for application in the biomedical field. Stress-strain curves obtained from the two simulations are compared with experimental results. Evolutions of volume fractions of martensite variants predicted by the two approaches are compared for <100>, <110> and <111> tensile directions. Due to the absence of comparative studies between multiscale models dedicated for SMA, this paper fills a gap in the state of the art in this field and provides a significant step toward the definition of an efficient numerical tool for the analysis of SMA behavior under multiaxial loadings.KEYWORDS SHAPE MEMORY ALLOYS (SMA). MARTENSITIC TRANSFORMATION. MICRO -MACRO MODELING.

Stochastic multiscale modeling of the thermomechanical behavior of polycrystalline shape memory alloys

“…This deformation level may appear too high. This is a common defect when a homogeneous stress assumption is used [13]. Value reached is however in accordance with the parameters of the Bain matrices.…”

“…Despite these strong hypotheses, a pretty good prediction of the transformation threshold of Ni-Ti SMA alloy under multiaxial stress condition was obtained; a good qualitative estimation of phase composition under thermal loading was obtained too [27] [13]. However, due to the thermodynamic equilibrium assumption, the thermomechanical behavior is reversible.…”

“…The same quantities can be calculated at the RVE scale by averaging over the grains. It must be noticed that no strain localization is required since homogeneous stress assumption [13] is retained for all calculations.…”