Three-dimensional constitutive model considering transformation-induced damage and resulting fatigue failure in shape memory alloys

In this work, a constitutive model is developed that describe the behavior of shape memory alloys undergoing a large number of cycles, developing internal damage, and eventually failing. Physical mechanisms associated with martensitic phase transformation occurring during cyclic loadings such as transformation strain generation and recovery, transformation-induced plasticity, and fatigue damage are all taken into account within a thermo-dynamically consistent framework. Fatigue damage is described utilizing a continuum theory of damage. The damage growth rate has been formulated as a function of both the stress state and also the magnitude of the transformation strain, while the complete or partial nature of the transformation cycles is also considered as per experimental observations. Simulation results from the model developed are compared to uniaxial actuation fatigue tests at different stress levels. It is shown that both lifetime and the evolution irrecoverable strain can be accurately simulated.

[1]  Victor Birman,et al.  Review of Mechanics of Shape Memory Alloy Structures , 1997 .

[2]  J. Chaboche,et al.  Mechanics of Solid Materials , 1990 .

[3]  L. Brinson,et al.  Shape memory alloys, Part I: General properties and modeling of single crystals , 2006 .

[4]  Wael Zaki,et al.  An extension of the ZM model for shape memory alloys accounting for plastic deformation , 2010 .

[5]  Dimitris C. Lagoudas,et al.  Modeling of transformation-induced plasticity and its effect on the behavior of porous shape memory alloys. Part I: constitutive model for fully dense SMAs , 2004 .

[6]  Sylvain Calloch,et al.  A 3D super-elastic model for shape memory alloys taking into account progressive strain under cyclic loadings , 2009 .

[7]  Dimitris C. Lagoudas,et al.  On thermomechanics and transformation surfaces of polycrystalline NiTi shape memory alloy material , 2000 .

[8]  Dimitris C. Lagoudas,et al.  Thermomechanical transformation fatigue of SMA actuators , 2000, Smart Structures.

[9]  Marcelo A. Savi,et al.  An overview of constitutive models for shape memory alloys , 2006 .

[10]  L. G. Machado,et al.  Thermomechanical Constitutive Modeling of SMAs , 2008 .

[11]  Walter Noll,et al.  Material symmetry and thermostatic inequalities in finite elastic deformations , 1964 .

[12]  Ireneusz Lapczyk,et al.  Continuum Damage Mechanics , 2012 .

[13]  D. Lagoudas,et al.  Constitutive modeling and structural analysis considering simultaneous phase transformation and plastic yield in shape memory alloys , 2009 .

[14]  Dimitris C. Lagoudas,et al.  Thermomechanical modeling of polycrystalline SMAs under cyclic loading, Part II : material characterization and experimental results for a stable transformation cycle , 1999 .

[15]  Jean-Louis Chaboche,et al.  Continuous damage mechanics — A tool to describe phenomena before crack initiation☆ , 1981 .

[16]  Alain Mikolajczak,et al.  A constitutive model for Fe-based shape memory alloy considering martensitic transformation and plastic sliding coupling: Application to a finite element structural analysis , 2012 .

[17]  D. Lagoudas,et al.  Three-dimensional modeling and numerical analysis of rate-dependent irrecoverable deformation in shape memory alloys , 2010 .

[18]  Dimitris C. Lagoudas,et al.  Thermomechanical transformation fatigue of TiNiCu SMA actuators under a corrosive environment – Part I: Experimental results , 2009 .

[19]  Dimitris C. Lagoudas,et al.  A Study of Actuation Fatigue of Shape Memory Alloy , 2012 .

[20]  L. G. Machado,et al.  Constitutive model for the numerical analysis of phase transformation in polycrystalline shape memory alloys , 2012 .

[21]  Dimitris C. Lagoudas,et al.  Modeling and Experimental Study of Simultaneous Creep and Transformation in Polycrystalline High-Temperature Shape Memory Alloys , 2009 .

[22]  Dimitris C. Lagoudas,et al.  A constitutive model for cyclic actuation of high-temperature shape memory alloys , 2014 .

[23]  M. Gurtin,et al.  Thermodynamics with Internal State Variables , 1967 .

[24]  Dimitris C. Lagoudas,et al.  Shape memory alloys, Part II: Modeling of polycrystals , 2006 .