Constitutive Modeling of the Thermomechanical and Cyclic Behavior of Shape Memory Alloys in Finite Deformations

Abstract : Shape Memory Alloys (SMAs) are a class of smart materials that possess two salient features known as pseudoelasticity (PE) and shape memory effect(SME). In industrial applications, SMA structures are typically subjected to complex service conditions, such as large deformations, thermomechanically coupled boundaries and loadings, and cyclic loadings. The reliability and durability analysis of these SMA structures requires a good understanding of constitutive behavior in SMAs. To this end, this work develops a comprehensive constitutive modeling approach to investigate thermomechanical and cyclic behavior of SMAs in fi nite deformations. The work is generally divided into three steps. First, to improve accuracy of SMA model infinite deformation regime, the ZM model proposed by Zaki and Moumni (2007b) is extended within a fi nite-strain thermodynamic framework. Moreover, the transformation strain is decomposed into phase transformation and martensite reorientation components to capture multi-axial non-proportional response. Secondly, in addition to the fi nite deformation, thermomechanical coupling effect is taken into account by developing a new fi nite-strain thermomechanical constitutive model. A more straightforward approach is obtained by using the fi nite Hencky strain. This model incorporates three important thermomechanical characteristics, namely the coexistence effect between austenite and two distinct martensite variants, the variation with temperature of hysteresis size, and the smooth transition at initiation and completion of phase transformation. Finally, with a view to studying SMA behavior under cyclic loading, the model developed in the second step is generalized to describe cyclic pseudoelasticity of polycrystalline SMAs. The generalized model captures four fundamental characteristics related to the cyclic behavior of SMAs: large accumulated residual strain, degeneration of pseudoelasticity and hysteresis loop, rate dependence, and evolution of phase transformation from abrupt to smooth transition. Numerical implementation of these models are realized by introducing proper integration algorithms. Finite element simulations, including orthodontic archwire, helical and torsion spring actuators, are carried out using the proposed models. The future directions of this work mainly involve plasticity and fatigue analysis of SMA structures.
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Jun Wang. Constitutive Modeling of the Thermomechanical and Cyclic Behavior of Shape Memory Alloys in Finite Deformations. Mechanics of materials [physics.class-ph]. Université Paris-Saclay, 2017. English. ⟨NNT : 2017SACLY013⟩. ⟨tel-01617607⟩

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