Multiscale finite element modeling of superelasticity in Nitinol polycrystals

Abstract

An efficient method is proposed for modeling superelastic polycrystalline NiTi by solving a two-scale problem. The RVE size of the fine scale is determined using a statistics-based approach. Both problems are discretized in space using the finite element method and their communication is effected using MPI. Representative simulations illustrate the modeling capabilities of the proposed approach.

Constitutive modeling and finite element approximation of B2-R-B19′ phase transformations in Nitinol polycrystals

“…In the tension problem, this leads to a representative volume element of 4 3 (=64) crystals at each Gauss point of the coarse scale. As in [10], a higher value of the critical driving force is chosen for the martensitic nucleation regime opposed to the propagation regime. Specifically, the critical driving force during nucleation of martensite was chosen as F c;M ¼ 9:0 MPa, while that during propagation of martensite phase boundary was taken to be F c;M ¼ 6:2 MPa.…”

“…Texture data for the tube were collected from several tube specimens and processed using the Berkeley Texture Package (BEAR-TEX) [21]. For the polycrystalline case, the numerical implementation involved a multi-scale approach, in which both the coarse and the fine scale were spatially resolved using the finite element method, see [10] for details. All numerical simulations were conducted using FEAP, a general-purpose finite element program partially documented in [22].…”

“…All other parameters are chosen as in Section 5.1. To further reduce the computational expense, and adopting the approach taken in [10], a relatively coarse mesh with 220 eight-node brick elements is employed to model the tube in the continuum scale and a one-point integration method with stabilization is adopted [23].…”

“…This formulation employs finite element discretizations for both the coarse (continuum) and fine (microstructure) scales with periodic boundary conditions for the latter. The size of the fine-scale volume is determined so as to guarantee statistical representation of all dominant crystal orientations, see [10] for a detailed discussion. In the tension problem, this leads to a representative volume element of 4 3 (=64) crystals at each Gauss point of the coarse scale.…”

“…In fact, it is demonstrated that this procedure leads to a well-posed optimization problem. The proposed methodology is subsequently extended to textured 0045 polycrystals through homogenization of the response of periodic Representative Volume Elements (RVE) defined at Gauss points of each macro-scale finite element, following earlier work in [10].…”