Thesis Defense: Shravan Kumar Reddy Kotha, “Parametrically Homogenized Constitutive Models for Titanium Alloys ”

December 1, 2020





Doctoral Candidate


Monday, December 14, 2020

3 PM

Contact Elena Shichkova for access to this presentation.

“Parametrically Homogenized Constitutive Models for Titanium Alloys”

            Structural analysis of heterogeneous materials using phenomenological constitutive models, is often faced with inaccuracies stemming from the lack of connection with the material microstructure and underlying physics. Pure micromechanical analysis, on the other hand, is computationally prohibitive on account of the large degrees of freedom needed to represent the entire structure. Hierarchical multiscale models based on computational homogenization, have been proposed to determine the homogenized material response for heterogeneous materials that can be used in component-scale analysis. However, for nonlinear problems involving history-dependent constitutive relations, many multiscale methods incur prohibitive computational costs from solving the micromechanical problem for every macroscopic point in the computational domain.

To overcome these shortcomings, this thesis develops a computationally efficient, Parametrically Homogenized Constitutive Model (PHCM) for dual-phase α/β Titanium alloys such as Ti6242S. PHCMs incorporate characteristic microstructural features as well as underlying physical mechanisms of deformation in macro-scale constitutive models. A size, rate and temperature dependent Crystal Plasticity Finite Element Model (CPFE) has been used to characterize the micro-mechanisms of deformation in dual-phase Titanium alloys. Statistically Equivalent Representative Volume Elements (SERVEs) are constructed to study the influence of different microstructural morphological and crystallographic distributions such as crystallographic orientation distribution, misorientation distribution, grain size distribution etc. on homogenized response. A detailed sensitivity analysis is performed to identify important microstructural distributions that govern the macroscopic material response and Representative Aggregated Microstructural Parameters (RAMPs) that quantify these distributions are defined. The constitutive equations in PHCM are then chosen to represent different homogenized mechanical behaviors observed from CPFE analysis such as elasto-plastic anisotropy, tension-compression asymmetry, grain size, strain rate and temperature dependency etc.. A database of SERVEs with different morphology and crystallographic distributions is created and CPFE simulations are performed under a variety of loading cases. The constitutive parameters of PHCM equations are calibrated to match its response with that obtained from CPFE analysis. These constitutive parameters are related to corresponding RAMPs using functional forms obtained from machine learning. A finite deformation formulation of PHCM constitutive equations is implemented in Abaqus as a user material subroutine. Using PHCM, microstructure-sensitive structural simulations of a representative ortho-grid panel are performed to demonstrate the microstructural dependency of structural response and the computational efficiency of PHCM. Moreover, the PHCM based predictions are compared with those obtained from isotropic elasticity and J2 plasticity models to demonstrate their deficiency.

Finally, the PHCM model for dual-phase Titanium alloys is extended to include the effects of damage. An anisotropic, coupled plasticity-damage model is formulated in which plasticity and damage are coupled via a Helmholtz free energy density function. Based on homogenized stress-strain response and crack propagation behaviors observed from coupled crystal plasticity-phase field simulations, an anisotropic damage surface and damage evolution equations are proposed. The proposed plasticity-damage model accounts for tension-compression asymmetry and strain rate dependency of damage and its thermodynamic consistency is established. Numerical results that demonstrate different aspects of the coupled plasticity-damage model are discussed at the end.

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