Session: 12-21-02: General: Mechanics of Solids, Structures and Fluids

Paper Number: 99442

99442 - A New Crystal Plasticity Modeling Framework for Fully Implicit Time Integration of Coupled Phase Transformation and Slip in Shape Memory Alloys 

A crystal-plasticity based rate-dependent framework is developed for capturing the coupled phase transformation-slip deformation modes at the crystal-scale in NiTi shape memory alloy using a fully-implicit time integration scheme. The computational procedures developed in this work have been successfully incorporated as a user material subroutine (UMAT) in the commercial finite element code ABAQUS Standard. They have been demonstrated for both habit plane variants (HPVs) and lattice correspondence variants (LCVs). Previous literature that proposed a finite strain model using LCVs have employed a flow rule where the velocity gradient was calculated using directly the stretch component of the inelastic deformation gradient for martensitic phase transformation. This formulation mainly ignores the rotation components of the phase transformation. In the current approach, a new flow rule is derived for the LCV model that incorporates the entire deformation gradient (including the rotational component) for the phase transformation. The predictions from our new model are compared with those from previous literature to illustrate the differences that rise in the stress-strain response and variant selection in Ni-Ti single crystals from the inclusion of the rotational components. The predictions from our simulations are also compared against previously published experimental data in literature for single and polycrystalline representative volume elements (RVE) at various temperatures. The effect of temperature and texture on phase transformation and residual strain is investigated systematically. The computational benefits of the current numerical implementation of the model is demonstrated and compared against previously reported models. All prior coupled phase transformation-plasticity finite-deformation modeling and simulations efforts have employed explicit or semi-implicit time-integration schemes. Specifically, the currently used rate-independent formulation for phase transformation does not lend itself to easy implementation of fully-implicit time-integration schemes. Although shape memory alloys do not exhibit significant rate-dependence, the incorporation of a slight rate-dependence can help regularize the crystal plasticity constitutive equations. One of the known benefits of including a slight rate-dependence is that it resolves the non-uniqueness in the solutions obtained using rate-independent models for systems with more than the minimum requisite independent deformation modes. Although the use of singular value decomposition successfully resolves the non-uniqueness issues for rate-independent models, they still do not allow for the implementation of an efficient fully-implicit time integration scheme. Another benefit of incorporating a slight rate-dependence is that it allows for the derivation of an analytical Jacobian needed to drive efficiently the global equilibrium iterations in CPFEM. It is emphasized that the incorporation of phase transformation in a rate-dependent crystal plasticity framework holds tremendous potential for improving the computational efficiency of the CPFEM formulations in shape memory alloys at both the grain-scale (e.g., indentations in individual grains) as well as the polycrystal scale (e.g., simulations of representative volume elements of polycrystalline aggregates).

Presenting Author: Rupesh Kumar Mahendran Georgia Institute of Technology

Presenting Author Biography: Rupesh Kumar Mahendran is a 2nd year PhD student in the George W. Woodruff School of Mechanical Engineering at Georgia Institute of Technology, working with Professor Surya Kalidindi and Professor Aaron Stebner. He got his Masters degree from the University of Illinois at Urbana-Champaign, USA and his Bachelors degree from Indian Institute of Technology, Madras, India. Rupesh’s research is focussed on physics-based and data-driven model development for Shape Memory Alloy (SMA), manufacturing, and part design, including developing high throughput methodology and surrogate models to accelerate SMA developments.

Authors:

Rupesh Kumar Mahendran Georgia Institute of Technology
Surya R Kalidindi Georgia Institute of Technology
Aaron Stebner Georgia Institute of Technology
Aditya Venkatraman Georgia Institute of Technology