Micromechanical modeling of polycrystalline shape-memory alloys including thermo-mechanical coupling

The main objective of this paper is to derive a simple, engineering model for a NiTi-based shape memory alloy (SMA) that can be used as a first-step, inexpensive computational tool in designing components including SMAs. The model is based on a Reuss approximation in which the stress in every grain is considered the same. A random and a simple texture distribution for the grain orientations as well as a normal distribution for the transformation force are used in the calculations so that a round shape of stress–strain curve and transformation start and finish temperatures can be considered. A new algorithm based on minimizing the energy at each transformation step is provided that is simple, fast and accurate. Thermo-mechanical coupling is taken into account, therefore various strain-rate regimes can be modeled. Both superelastic and shape memory effect (SME) are analyzed. The model can also replicate complex behavior encountered in real materials such as small strain–amplitude hysteresis cycles, ratio of lateral to longitudinal strain during transformation and asymmetric behavior in tension compared with compression, while keeping the number of modeling parameters small. Numerical simulations show excellent agreement with available experimental results by applying the adequate grain orientation and the transformation force distribution.

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