Thermal effects in the superelasticity of crystalline shape-memory materials

By L. Anand, M. Gurtin. 2003

202 citations recorded by the source corpus.

Abstract This paper develops a three-dimensional theory for the superelastic response of single-crystal shape-memory materials. Since energetic considerations play a major role in the phase transformations associated with the superelastic response, we have developed the theory within a framework that accounts for the laws of thermodynamics. We have implemented a special set of constitutive equations resulting from the general theory in a finite-element computer program, and using this program have simulated the superelastic response of a single crystal Ti–Ni shape-memory alloy under both isothermal and thermo-mechanically coupled situations. Both manifestations of superelasticity—stress–strain response at fixed temperature and strain–temperature response at fixed stress—are explored. The single-crystal constitutive-model is also used to discuss the superelastic response of a polycrystalline aggregate with a random initial crystallographic texture. The overall features of the results from the numerical simulations are found to be qualitatively similar to existing experimental results on Ti–Ni.

Subfields: Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/378f49458c26bb6f7a612438c7db59905579bcee

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Materials Chemistry

In Mechanics of Materials

Citations in the corpus

Shape memory alloys, Part II: Modeling of polycrystals (2006, background): “Anand and Gurtin (2003) for example, use a model for single crystal SMA and perform representative numerical calculations for the response of polycrystals with random orientation of the single crystals.”
Crystal Plasticity Finite Element Methods: in Materials Science and Engineering (2010, background): “…and Sabar (1998), Cherkaoui, Berveiller, and Lemoine (2000), Thamburaja and Anand (2001), Tomita and Iwamoto (2001), Govindjee and Miehe (2001), Anand and Gurtin (2003), Turteltaub and Suiker (2005), Thamburaja (2005), Lan et al. (2005), Turteltaub and Suiker (2006b), Tjahjanto, Turteltaub,…”
A review of constitutive models and modeling techniques for shape memory alloys (2016, methodology): “In FSM, the right and left Cauchy Green deformation tensors, C and b, are derived from the deformation gradient as follows (Anand and Gurtin, 2003; Jung et al., 2004; Pan et al., 2007; Christ and Reese, 2009; Arghavani et al., 2011b; Stupkiewicz and Petryk, 2013): C = FF and b = FF.”
Constitutive equations for martensitic reorientation and detwinning in shape-memory alloys (2005, methodology): “Guided by the work of Anand and Gurtin (2003) and neglecting martensite– martensite interaction the Helmholtz free energy per unit reference volume is taken to be in the separable form cðEe;y;x Þ¼ ceðEe;y Þþ cpðx;y Þþ cyðyÞ; (23)”
Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications (2010, background): “Tomita and Iwamoto [75], Govindjee and Miehe [76], Anand and Gurtin [77], Turteltaub and Suiker”
Thermodynamics of Shape Memory Alloy Wire: Modeling, Experiments, and Application (2006, methodology): “Here, we note just a few recent modeling efforts and categorize them into those which are intended to capture continuum–level behavior based on volume fractions of martensite variants [ 3 ,16], explicit polycrystalline microstructural models [28], Ginzburg–Landau models to simulate microstructure ev”
Constitutive modeling and structural analysis considering simultaneous phase transformation and plastic yield in shape memory alloys (2009, background): “Past modelers have made the assumption that a strict inequality is enforced [45] and further that some materials satisfy an even stronger form of (2.”
A 3-D constitutive model for shape memory alloys incorporating pseudoelasticity and detwinning of self-accommodated martensite (2007, background): “Examples of SMA models formulated in terms of finite strains can be found, for example, in Auricchio and Taylor (1997); Qidwai and Lagoudas (2000b); Anand and Gurtin (2003).”
Transformation-induced plasticity in ferrous alloys (2005, methodology): “(1953) and further developed by Ball and James (1987) and others (Bhattacharya, 1993; Hane and Shield, 1998, 1999; James and Hane, 2000).”