Thesis Defense: Ahmad Shahba, “Crystal Plasticity Finite Element Simulation of Deformation and Fracture in Polycrystalline Microstructures”
THE DEPARTMENT OF CIVIL ENGINEERING
ADVISOR, SOMNATH GHOSH, PROFESSOR
ANNOUNCE THE THESIS DEFENSE OF
Tuesday, September 4, 2018
“Crystal Plasticity Finite Element Simulation of Deformation and Fracture in Polycrystalline Microstructures”
The mechanical response of metals and their alloys are governed by the deformation mechanisms in the underlying microstructure. High-fidelity modeling of deformation in metals requires development of proper constitutive laws at single crystal scale. Image-based crystal plasticity FE framework is regarded as one of the most powerful tools for deformation simulations, allowing the modelers to explicitly represent the elastic and plastic anisotropy of the material using physics-based laws in a computational domain which statistically represents the morphological and crystallographic properties of the microstructure.
In this work, a thermodynamically-consistent coupled crystal plasticity-crack phase field framework is derived to model fracture process in polycrystalline microstructures. The governing differential equations for the displacement and crack phase field are coupled via the Helmholtz free energy density (HFED). Using the volumetric-deviatoric decomposition of the elastic deformation gradient, a new HFED formulation is proposed which respects the unilateral damage conditions (tension-compression asymmetry of material response in the presence of cracks) and can be used for modeling fracture in anisotropic media under finite deformation conditions.
Numerical modeling of fracture is computationally daunting, partly due to the frequent convergence issues and occurrence of instabilities. Recognizing that the instabilities take place due to an excess energy, three viscous stabilization methods are proposed in this work to dissipate this excess energy and effectively overcome the instabilities. Unlike arc-length methods, the viscous stabilization is applicable for rate-dependent constitutive models and its implementation into any existing FE code is straightforward.
Crystal plasticity simulations of polycrystalline are generally carried out with linear tetrahedral elements due to their capability in conforming to complex geometries. These elements are known to suffer from volumetric locking in modeling (nearly-) incompressible materials, leading to numerical artifacts such as underestimation of displacements and overestimation of pressure levels. A modified F-bar-patch technique is developed in this work to alleviate volumetric locking in phase field modeling of ductile fracture.
In the course of plastic deformation, the local strain rate experienced by different material points in the microstructure could be orders of magnitude different from the applied macroscopic strain rate. It is of paramount significance to develop a unified crystal plasticity law which could be applied for a wide range of strain rates. Using the dislocation glide mechanisms in hcp metals, a unified flow rule is developed by combining the thermally-activated and drag-dominated processes. This unified law can be employed to model deformation over a wide range of strain rates and its explicit dependence of temperature makes it suitable for modeling high rate deformation of metals where adiabatic heating is significant.
Thesis Committee: Somnath Ghosh, James Guest, Jaafar El-Awady