A Multiscale Computational Model Combining a Single Crystal Plasticity Constitutive Model with the Generalized Method of Cells (GMC) for Metallic Polycrystals.

Masoud Ghorbani Moghaddam,Steven Arnold,Ajit Achuthan,Brett Bednarcyk,Evan Pineda

doi:10.3390/ma9050335

Masoud Ghorbani Moghaddam, Steven Arnold + Show 3 more

Open Access

https://doi.org/10.3390/ma9050335

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Journal: Materials	Publication Date: May 4, 2016
Citations: 9	License type: CC BY 4.0

Affiliation: Clarkson University, Glenn Research Center

Abstract

A multiscale computational model is developed for determining the elasto-plastic behavior of polycrystal metals by employing a single crystal plasticity constitutive model that can capture the microstructural scale stress field on a finite element analysis (FEA) framework. The generalized method of cells (GMC) micromechanics model is used for homogenizing the local field quantities. At first, the stand-alone GMC is applied for studying simple material microstructures such as a repeating unit cell (RUC) containing single grain or two grains under uniaxial loading conditions. For verification, the results obtained by the stand-alone GMC are compared to those from an analogous FEA model incorporating the same single crystal plasticity constitutive model. This verification is then extended to samples containing tens to hundreds of grains. The results demonstrate that the GMC homogenization combined with the crystal plasticity constitutive framework is a promising approach for failure analysis of structures as it allows for properly predicting the von Mises stress in the entire RUC, in an average sense, as well as in the local microstructural level, i.e., each individual grain. Two–three orders of saving in computational cost, at the expense of some accuracy in prediction, especially in the prediction of the components of local tensor field quantities and the quantities near the grain boundaries, was obtained with GMC. Finally, the capability of the developed multiscale model linking FEA and GMC to solve real-life-sized structures is demonstrated by successfully analyzing an engine disc component and determining the microstructural scale details of the field quantities.

Highlights

Engine fan blades and discs are subjected to extreme temperatures and mechanical stresses during their operation
A multiscale computational model was developed by employing the single crystal plasticity constitutive model at the microscale, in conjunction with generalized method of cells (GMC) for homogenization, coupled to an finite element analysis (FEA) framework at the macroscale
In order to verify the effectiveness of GMC as a homogenization tool, the microscale behavior of single and polycrystalline samples were determined using the

Summary

Introduction

Engine fan blades and discs are subjected to extreme temperatures and mechanical stresses during their operation. The prediction of damage initiation and propagation is important in these engine components, to avoid potential catastrophic mission failures, but for developing optimal and economical designs as well. Developing such prediction capabilities requires development of stress analysis models that can incorporate the interaction of various microstructural features, such as grain boundaries and dislocations. In the single crystal plasticity models, the dislocation motion is implemented as permanent shear strain in the various slip systems (slip plane and slip direction) with the aid of a set of state variables [1,2]. The strain hardening property that defines the strength of the slip systems is implemented in terms of another set of state variables

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