Stress–strain relation of CuAlNi SMA single crystal under biaxial loading—constitutive model and experiments

Abstract In the previous work of two of the authors, a generalized micromechanics constitutive model was developed to describe thermoelastic martensitic transformation. In order to verify the theory and to investigate basic properties of thermoelastic martensitic transformation in shape memory alloys (SMA), uniaxial and biaxial loading tests under different combined loads at a constant temperature were performed on cruciform specimens of a SMA CuAlNi single crystal. The crystallographic theory for martensitic transformation has been employed to calculate the orientations of martensite variants and the transformation plastic strain. Experimental data were compared with theoretical calculation by the generalized constitutive model based on micromechanics. The results show that the constitutive theory can describe the complex thermodynamic processes, such as the forward transformation, reverse transformation and reorientation happening simultaneously, and the theoretical predictions consist well with experiments.

[1]  J. Mackenzie,et al.  The crystallography of martensite transformations II , 1954 .

[2]  J. Boehler,et al.  Optimal design of biaxial tensile cruciform specimens , 1993 .

[3]  Kaushik Bhattacharya,et al.  Wedge-like microstructure in martensites , 1991 .

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

[5]  George J. Weng,et al.  Martensitic transformation and stress-strain relations of shape-memory alloys , 1997 .

[6]  C. Liang,et al.  A multi-dimensional constitutive model for shape memory alloys , 1992 .

[7]  K. Hwang,et al.  A continuum analysis of transformation plastic localization in ceramics , 1997 .

[8]  Franz Dieter Fischer,et al.  Transformation-Induced Plasticity (TRIP) , 1996 .

[9]  Huibin Xu,et al.  On the pseudo-elastic hysteresis , 1991 .

[10]  J. Ball,et al.  Fine phase mixtures as minimizers of energy , 1987 .

[11]  J. Christian.  Deformation by moving interfaces , 1982 .

[12]  K. Tanaka,et al.  The Influence of Transformation Kinetics on Stress-Strain Relations of Shape Memory Alloys in Thermomechanical Processes , 1994 .

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

[14]  F. Falk.  Model free energy, mechanics, and thermodynamics of shape memory alloys , 1980 .

[15]  Daining Fang,et al.  Micromechanics simulation of ferroelectric polarization switching , 1997 .

[16]  K. Tanaka,et al.  Average stress in matrix and average elastic energy of materials with misfitting inclusions , 1973 .

[17]  Toshio Mura,et al.  Micromechanics of defects in solids , 1982 .

[18]  Masataka Tokuda,et al.  Experimental study on the thermoelastic martensitic transformation in shape memory alloy polycrystal induced by combined external forces , 1995 .

[19]  T. Shield.  Orientation dependence of the pseudoelastic behavior of single crystals of CuAlNi in tension , 1995 .

[20]  K. Shimizu,et al.  Crystallography of β1 → γ′1 stress-induced martensitic transformation in a CuAlNi alloy , 1986 .

[21]  M. Wechsler.  O the Theory of the Formation of Martensite. , 1953 .

[22]  J. Rice.  Inelastic constitutive relations for solids: An internal-variable theory and its application to metal plasticity , 1971 .

[23]  E. Patoor,et al.  Thermomechanical behaviour of shape memory alloys , 1988 .

[24]  R. James.  Displacive phase transformations in solids , 1986 .

[25]  Lucas Delaey,et al.  Thermoelasticity, pseudoelasticity and the memory effects associated with martensitic transformations: Part 1 Structural and microstructural changes associated with the transformations , 1974 .

[26]  Shuichi Miyazaki,et al.  Orientation dependence of β1 → β1′ stress-induced martensitic transformation in a Cu-AI-Ni alloy , 1988 .

[27]  K. Hwang,et al.  Micromechanics Constitutive Description of Thermoelastic Martensitic Transformations , 1994 .

[28]  P. Meijers,et al.  EFFECT OF TRANSFORMATION-INDUCED SHEAR STRAINS ON CRACK GROWTH IN ZIRCONIA- CONTAINING CERAMICS , 1994 .

[29]  D. Fang,et al.  A mesoscopic model of the constitutive behaviour of monocrystalline ferroelectrics , 1997 .

[30]  J. P. Boehler,et al.  A new direct biaxial testing machine for anisotropic materials , 1994 .