Analysis of the deformation paths and thermomechanical parameter identification of a shape memory alloy using digital image correlation over heterogeneous tests

Abstract

With the design of new devices with complex geometry and to take advantage of their large recoverable strains, shape memory alloys components (SMA) are increasingly subjected to multiaxial loadings. The development process of SMA devices requires the prediction of their thermomechanical response, for which the calibration of the material parameters for the numerical model is an important step. In this work, the parameters of a phenomenological model are extracted from tests performed on specimens with non-uniform geometry, which induce heterogeneous strain fields carried out on specimens with the same thermomechanical loading history. The digital image correlation technique is employed to measure the strain fields on the surface of the specimen and to analyze the strain paths of chosen points. Finite element analysis enables the computation of numerical strain fields using a thermodynamicalconstitutive model for shape memory alloys previously implemented in a finite element code. The strain fields computed numerically are compared with experimental ones obtained by DIC to find the model parameters which best match experimental measurements using a newly developed parallelized mixed genetic/gradient-based optimization algorithm. These numerical simulations are carried out in parallel using a supercomputer to reduce the time necessary to identify the set of model parameters. The major features of this new algorithm is its ability to identify the material parameters which describe the thermomechanical behavior of shape memory alloys from full-field measurements for various loading conditions (different temperatures, multiaxial behavior, heterogeneous test configurations). It is demonstrated that model parameters for the simulation of SMA structures are thus obtained based on a reduced number of heterogeneous tests at different temperatures.International audienceWith the design of new devices with complex geometry and to take advantage of their large recoverable strains, shape memory alloys components (SMA) are increasingly subjected to multiaxial loadings. The development process of SMA devices requires the prediction of their thermomechanical response, for which the calibration of the material parameters for the numerical model is an important step. In this work, the parameters of a phenomenological model are extracted from tests performed on specimens with non-uniform geometry, which induce heterogeneous strain fields carried out on specimens with the same thermomechanical loading history. The digital image correlation technique is employed to measure the strain fields on the surface of the specimen and to analyze the strain paths of chosen points. Finite element analysis enables the computation of numerical strain fields using a thermodynamicalconstitutive model for shape memory alloys previously implemented in a finite element code. The strain fields computed numerically are compared with experimental ones obtained by DIC to find the model parameters which best match experimental measurements using a newly devel...

Modeling of coupled phase transformation and reorientation in shape memory alloys under non-proportional thermomechanical loading

“…A last set of experiment is complex tension/torsion and tension compression on NiTi tube Grabe and Bruhns (2009). Parameter identication was carried out using a proven method reliable in identifying complex modeling parameters for SMAs using inverse identication methods developed by Meraghni et al (2014) and extended for heterogeneous conguration in 340 Chemisky et al (2015). Table 4: Material constants for equiatomic NiTi utilized in loading simulations of experiments presented in (Sittner et al, 2009).…”

“…This form is chosen to accommodate experimental data demonstrating lower transformation strains under compression than under tension (Bouvet et al, 2004;Grolleau et al, 2011;Chemisky et al, 2015). H cur is considered the same as in (Hartl et al, 2010).…”

Comparative study of the direct and inverse finite element methods for pricing American options

“…The approach involves the use of simulated finite elements to inversely predict desired quantities that are spatially varying with time. Any assumptions included in the finite element model and in the whole simulation of the experiment determine the quality of the inverse solution (Chemisky et al, 2015). In quantitative finance, iFEM is employed by craving the boundaries of the finite elements to remain on "isotherms" of the asset price, whereas, the option value is specified a priori everywhere in the domain.…”

“…Nevertheless, FEM can be made more efficient by considering its inverse formulation (inverse finite elements). The inverse finite element method (iFEM) is a numerical approach in which an optimization algorithm is coupled with finite element method to find optimal values for a set of target parameters which enter the finite element simulation (Chemisky et al, 2015). A user defined objective function serves to measure the optimality of the parameters.…”

Multi-scale investigation of highly anisotropic zinc alloys using crystal plasticity and inverse analysis

“…This is accomplished by finding the set of micro-scale material parameters that produces the macro-scale tensile curves that are closest to the experimental tensile curves, using inverse analysis [55][56][57].…”