A Finite Strain Constitutive Model for Martensitic Transformation in Shape Memory Alloys Based on Logarithmic Strain

Abstract

Shape Memory Alloys (SMAs) are materials with the ability to recover apparently permanent deformation under specific thermomechanical loading. The majority of constitutive models for SMAs are developed based on the infinitesimal strain theory. However, such assumption may not be proper in the presence of geometric discontinuities, such as cracks, and repeated cycling loading that has been reported to induce irrecoverable strains up to 20% due to transformation induced plasticity. In addition to finite strains, SMA-based devices may also undergo large rotations. Thus, it is indispensable to develop a constitutive model based on the finite strain to provide accurate predictions of these actuators response. A three-dimensional phenomenological constitutive model for SMAs considering finite strains and finite rotations is proposed in this work. This model utilizes the logarithmic strain as the strain measure that is the strain measure whose logarithmic rate in a corotating material frame is equal to the rate of deformation tensor. In the proposed model, the martensitic volume fraction and the second-order logarithmic transformation strain tensor are chosen as the internal state variables associated with the inelastic transformation process. Numerical simulations considering basic SMAs component geometries such as a bar, a beam, and a torque tube are performed to test the capabilities of the proposed model under both mechanically and thermally induced phase transformation.For numerical examples in which the SMA components exhibits finite strains along with finite rotations, discrepancies are observed between the responses predicted by the present model and its infinitesimal counterpart. Also, the spurious accumulated residual stress observed in infinitesimal strain model is eliminated by the proposed model. This shows that the infinitesimal strain assumption is not applicable in such cases and the proposed model considering large strains and rotations is needed to provide accurate predictions. The presented model formulation will be extended in future work for the incorporation of transformation-induced plasticity.

Crack Growth Behavior in NiTi Shape Memory Alloys Under Mode-I Isothermal Loading: Effect of Stress State

“…Implementing various constitutive models [7][8][9][10][11], fracture of SMAs has been studied numerically in the presence of stationary cracks [12][13][14][15][16][17][18][19]. It is shown that stress concentration at the crack tip causes forward transformation (i.e.…”

Phase Transformation Characteristics of High-Temperature Shape Memory Alloy under Tension, Compression, and Bending Actuation Cycling

“…There has been a lot of constitutive modeling efforts been made during recent decades to predict the intrinsic material response of SMAs, a through review can be found from elsewhere. [24][25][26][27] As the motivation of this research is to facilitate the development of a phenomenological model that is able to capture the tensioncompression asymmetry and TRIP during cyclic thermo-mechanical actuation loading, the results obtained from previously performed tension/compression and bending experiments are used for the formulation and validation of the SMA constitutive model capturing the anisotropic phase transformation characteristics. In order to achieve the desired modeling capability, modifications on the transformation functions are needed.…”

Finite strain constitutive modeling for shape memory alloys considering transformation-induced plasticity and two-way shape memory effect

“…A three-dimensional constitutive model at finite strain regime for SMAs incorporating TRIP is proposed in this work. The adopted logarithmic strain measure and rate [20,21,22,23] enables the model to effectively capture the material response under finite strains with rotations, and attribute modeling advantages in the presence of large accumulated plastic strain under cyclic thermo-mechanical loading for SMAs. The martensitic volume fraction, transformation strain, and TRIP strain are used to characterize material nonlinear behavior while back stress tensor and a drag stress term are used to introduce the effects of the kinematic and isotropic hardening in the model.…”