Theoretical modelling of the effect of plasticity on reverse transformation in superelastic shape memory alloys

Abstract

Stimulated by recent experimental results on superelastic NiTi shape memory alloy, a theoretical study is carried out to quantify the effect of plasticity on stress-induced martensite transformation, using a constitutive model that combines phase transformation and plasticity. A constraint equation is introduced to quantify the phenomenon of the stabilization of plasticity on stress-induced martensite. The stabilized martensite volume fraction is determined by the equivalent plastic strain. The transformation constitutive model is adopted from a generalized plastic model with Drucker-Prager type phase transformation functions, which are pressure sensitive, while the plasticity is described by the von Mises isotropic hardening model.The martensite volume fraction is chosen as the internal variable to represent the transformation state and it is determined by the consistency transformation condition. An approach to calibrate model parameters from uniaxial tensile tests is explored, as well as the issue of elastic mismatch between austenite and martensite is discussed. Based on the proposed constitutive model, the influence of hydrostatic stress on transformation is examined. As an example of application, this new constitutive model is employed to numerically study the transformation field and the plastic deformation field near a crack tip.

Spherical indentation hardness of shape memory alloys

“…The coupling behavior between transformation deformation and plastic deformation is quite complicated and unclear, which is one of the focuses of our experimental studies. Some experimental observations and simple theoretical modeling can be found respectively in [22,23].…”

Micromechanical modelling of the effect of plastic deformation on the mechanical behaviour in pseudoelastic shape memory alloys

“…In both models, the development of the plastic strain is connected to the detwinned martensitic volume fraction and is induced by cyclic loading conditions. Savi et al (2002), Yan et al (2003) and Paiva et al (2005) considered the plasticity after the stress induced phase transformation in their models, respectively. In the model of Yan et al (2003), plasticity is described by the von Mises isotropic hardening model.…”

“…Savi et al (2002), Yan et al (2003) and Paiva et al (2005) considered the plasticity after the stress induced phase transformation in their models, respectively. In the model of Yan et al (2003), plasticity is described by the von Mises isotropic hardening model. Plastic strain is included by a combination of the kinematic and isotropic hardening model by Savi et al (2002) and Paiva et al (2005).…”

Finite element analysis of a superelastic shape memory alloy considering the effect of plasticity

“…Lazghab (2001) carried out a theoretical study to SMAs with plastic deformation of martensite, although it was not available to implement into a commercial finite element software. Yan et al (2003) developed a constitutive model to quantify the effect of plasticity on the reverse transformation and examined the influence of hydrostatic stress on the transformation. Bo and Lagoudas (1999) proposed several constitutive models considering the evolution of plastic strain under cyclic thermal induced transformation cycles with micromechanical analyses by a representative volume element.…”

“…However, that model cannot describe plasticity of the martensite. In a more recent work, Kan et al (2010) and Yan et al (2003) developed a temperature-dependent three-dimensional phenomenological constitutive model considering the local plastic yield of martensite under a high stress, and successfully implemented into the finite element package ABAQUS. Moreover, the nonlinear problem was solved within a framework of the updated Lagrangian formulation using a return mapping algorithm (Lagoudas et al, 1996;Cisse et al, 2016) to update the stress value according to the current strain.…”