PARAMETRICALLY HOMOGENIZED CONSTITUTIVE MODELS FOR TITANIUM ALLOYS
Embargo until
2022-05-01
Date
2020-12-21
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Publisher
Johns Hopkins University
Abstract
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 such as elastic stiffness and yield stress are calibrated to match PHCM stress-strain response with that obtained from CPFE analysis. These constitutive parameters are related to corresponding RAMPs using functional forms determined using 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 in predicting microstructure-sensitive response.
Finally, a coupled elasto-plastic-damage model is formulated by extending the PHCM constitutive equations to include the effect of damage on microstructure dependent
elasto-plastic response. The anisotropic elasticity, plasticity and damage are coupled via a Helmholtz free energy density function that is proposed based on homogenized stress-strain responses and crack propagation behaviors observed from coupled crystal plasticity-phase field simulations of polycrystalline SERVEs. The proposed elasto-plastic-damage model is thermodynamically consistent and accounts for anisotropy, tension-compression asymmetry and strain rate dependency of damage. Numerical results that demonstrate different aspects of the coupled elasto-plastic-damage model are discussed at the end.
The PHCM model developed in this thesis combines physics-based modeling with machine learning to capture relevant mechanical behaviors in constitutive relations. These models are necessary in the multi-scale modeling of fatigue in Titanium alloys which requires material microstructure dependent models such as PHCM to better understand and predict fatigue behaviors. For example, PHCMs provide useful insights into the fatigue behavior of structural components for which full-scale experimental testing may be impractical. Parametric studies using PHCMs also help designers gain insights into the role of critical microstructural features that influence the mechanical response and subsequently determine the optimal material properties for a given structural performance requirement. Thus, PHCMs provide a connection to microstructure and enable material design which is an important part of Integrated Computational Materials Engineering (ICME).
Description
Keywords
Titanium Alloys, Parametric Homogenization, Crystal Plasticity, Machine Learning, Damage Model, Phase Field