An isotropic-plasticity-based constitutive model for martensitic reorientation and shape-memory effect in shape-memory alloys

Abstract In this work, we develop an isotropic-plasticity-based constitutive model for initially martensitic shape-memory alloys (SMA) which exhibit martensitic reorientation and the shape-memory effect. The constitutive model is then implemented in the [Abaqus reference manuals. 2006. Providence, R.I.] finite-element program by writing a user-material subroutine. The results from the constitutive model and numerical procedure are then compared to representative physical experiments conducted on polycrystalline rod and sheet Ti–Ni. The constitutive model and the numerical simulations are able to reproduce the stress–strain responses from these physical experiments to good accuracy. Finally, two different boundary value problems utilizing the one-way shape-memory effect are studied: (a) the deformation of an arterial stent, and (b) a micro-clamper. We show that our constitutive model can be used to model the response of the aforementioned boundary value examples.

[1]  F. D. Fischer,et al.  Modelling the mechanical behavior of shape memory alloys under variant coalescence , 1996 .

[2]  Lucas Delaey,et al.  Asymmetry of stress–strain curves under tension and compression for NiTi shape memory alloys , 1998 .

[3]  S. Miura,et al.  Pseudoelasticity in Au-Cd thermoelastic martensite , 1973 .

[4]  Lallit Anand,et al.  An implicit time-integration procedure for a set of internal variable constitutive equations for isotropic elasto-viscoplasticity , 1989 .

[5]  T. P. G. Thamburaja.  Constitutive equations for martensitic reorientation and detwinning in shape-memory alloys , 2005 .

[6]  Lallit Anand,et al.  An objective time-integration procedure for isotropic rate-independent and rate-dependent elastic-plastic constitutive equations , 1990 .

[7]  E. Schnack,et al.  Macroscopic Modeling of Shape Memory Alloys Under Non-Proportional Thermo-Mechanical Loadings , 2002 .

[8]  Panayiotis Papadopoulos,et al.  Constitutive modelling and numerical simulation of multivariant phase transformation in superelastic shape‐memory alloys , 2004 .

[9]  Qingping Sun,et al.  Micromechanics modelling for the constitutive behavior of polycrystalline shape memory alloys. I: Derivation of general relations , 1993 .

[10]  T Prakash G. Thamburaja,et al.  Multi-axial behavior of shape-memory alloys undergoing martensitic reorientation and detwinning , 2007 .

[11]  James K. Knowles,et al.  A continuum model of a thermoelastic solid capable of undergoing phase transitions , 1993 .

[12]  T Prakash G. Thamburaja,et al.  Polycrystalline shape-memory materials: effect of crystallographic texture , 2001 .

[13]  George J. Weng,et al.  A self-consistent model for the stress-strain behavior of shape-memory alloy polycrystals , 1998 .

[14]  Dirk Helm,et al.  Shape memory behaviour: modelling within continuum thermomechanics , 2003 .

[15]  T Prakash G. Thamburaja,et al.  Martensitic reorientation and shape-memory effect in initially textured polycrystalline Ti–Ni sheet , 2005 .

[16]  L. Brinson.  One-Dimensional Constitutive Behavior of Shape Memory Alloys: Thermomechanical Derivation with Non-Constant Material Functions and Redefined Martensite Internal Variable , 1993 .

[17]  Etienne Patoor,et al.  Constitutive equations for polycrystalline thermoelastic shape memory alloys.: Part I. Intragranular interactions and behavior of the grain , 1999 .

[18]  P. Prendergast,et al.  Cardiovascular stent design and vessel stresses: a finite element analysis. , 2005, Journal of biomechanics.

[19]  D. Lagoudas,et al.  A thermodynamical constitutive model for shape memory materials. Part I. The monolithic shape memory alloy , 1996 .

[20]  J. K. Knowles,et al.  A One-Dimensional Continuum Model for Shape-Memory Alloys , 1994 .

[21]  Ferdinando Auricchio,et al.  Shape-memory alloys: modelling and numerical simulations of the finite-strain superelastic behavior , 1997 .

[22]  Etienne Patoor,et al.  Micromechanical Modelling of Superelasticity in Shape Memory Alloys , 1996 .

[23]  Ken Gall,et al.  The role of texture in tension–compression asymmetry in polycrystalline NiTi , 1999 .

[24]  Lallit Anand,et al.  On modeling the micro-indentation response of an amorphous polymer , 2006 .

[25]  Stefan Seelecke,et al.  Shape memory alloy actuators in smart structures: Modeling and simulation , 2004 .

[26]  Toru Inoue,et al.  Stress–strain relation of CuAlNi SMA single crystal under biaxial loading—constitutive model and experiments , 1998 .

[27]  L G Machado,et al.  Medical applications of shape memory alloys. , 2003, Brazilian journal of medical and biological research = Revista brasileira de pesquisas medicas e biologicas.

[28]  Craig A. Rogers,et al.  One-Dimensional Thermomechanical Constitutive Relations for Shape Memory Materials , 1990 .

[29]  Lallit Anand,et al.  A theory of amorphous solids undergoing large deformations, with application to polymeric glasses , 2003 .

[30]  James G. Boyd,et al.  Thermodynamical constitutive model for the shape memory effect due to transformation and reorientation , 1994, Smart Structures.