Constitutive modelling and numerical simulation of multivariant phase transformation in superelastic shape‐memory alloys

Abstract

SUMMARYThis work concerns the micromechanical constitutive modelling, algorithmic implementation and numerical simulation of polycrystalline superelastic alloys under multiaxial loading. The model is formulated in finite deformations and incorporates the effect of texture. The numerical implementation is based on the constrained minimization of the Helmholtz free energy with dissipation. Simulations are conducted for thin tubes of Nitinol under tension-torsion, as well as for a simplified model of a biomedical stent.

Contributions on the theory and computation of mono‐ and poly‐crystalline cyclic martensitic phase transformations

“…These assumptions are in line with the work of Huang, Gao, and Brinson [47]. Furthermore, the total number of martensitic variants depends on the crystalline structure, Jung, Papadopoulos, and Ritchie [48], and it is reported in Brinson, Lammering, and Schmidt [22] that the active variants in each grain are the same in each load-unload cycle according to the type of alloy. This has been illustrated in the micrograph of activated variants at 2% strain in one set of grains at different cycle numbers for NiTi alloy, [22].…”

“…Lu and Weng [56,57] proposed a self-consistent model where the variants are interacting within crystals. The model proposed by Jung et al [48] considers the coupling between variants and neglects the interaction between grains. In the presented polycrystalline model too, the interaction between the variants (of equivalent monocrystal) is considered via quasi-convex relaxation which is intimately connected to the notion of homogenization of optimal microstructure (at minimum energy).…”

“…(47) - (50); n is the total number of phases, and m is the number of constraints for the active set. The global unknowns are stored in the vector X := {f , γ B , Δλ, δ} and the global residuals in the vector R := {(47), (48), (49), (50)}. The iteration tangent matrix reads (see also [38])…”

“…3. Based on these kinematic assumptions, theories and computations of monocrystalline PTs have been treated in, e.g., [38,41,46,76,77], and polycrystalline research results can be found in, e.g., [22,40,47,48,60,72]. Naturally, mono-and polycrystalline PTs are treated separately in these cited papers.…”

“…as applied in [48]. In this article a simple habit plane-based multi-variant model has been proposed as extension of the earlier work [72], and the macroscopic Lagrangian transformation strains were computed as in monocrystal.…”