Ductile fracture simulations using a multi-surface coupled damage-plasticity model

In this paper, an isotropic porous metal plasticity model accounting for both void growth by diffuse plastic deformation and void ‘coalescence’ by localization of plastic flow in the inter-void ligaments is presented. Predictions for the effective stress-strain response, evolution of damage and the strains to failure are obtained by integrating the model numerically under triaxial proportional loading conditions. The model predictions are compared with results from micromechanical finite element simulations of the average response of voided unit cells under similar loading conditions. It is shown that the model predictions for the failure strains as a function of the loading path are in good qualitative agreement with the results of the cell model simulations

A micromechanics based ductile damage model for anisotropic titanium alloys

The hot-workability of Titanium (Ti) alloys is of current interest to the aerospace industry due to its widespread application in the design of strong and light-weight aircraft structural components and engine parts. Motivated by the need for accurate simulation of large scale plastic deformation in metals that exhibit macroscopic plastic anisotropy, such as Ti, a constitutive model is developed for anisotropic materials undergoing plastic deformation coupled with ductile damage in the form of internal cavitation. The model is developed from a rigorous micromechanical basis, following well-known previous works in the field. The model incorporates the porosity and void aspect ratio as internal damage variables, and seeks to provide a more accurate prediction of damage growth compared to previous existing models. A closed form expression for the macroscopic yield locus is derived using a Hill-Mandel homogenization and limit analysis of a porous representative volume element. Analytical expressions are also developed for the evolution of the internal variables, porosity and void shape. The developed yield criterion is validated by comparison to numerically determined yield loci for specific anisotropic materials, using a numerical limit analysis technique developed herein. The evolution laws for the internal variables are validated by comparison with direct finite element simulations of porous unit cells. Comparison with previously published results in the literature indicates that the new model yields better agreement with the numerically determined yield loci for a wide range of loading paths. Use of the new model in continuum finite element simulations of ductile fracture may be expected to lead to improved predictions for damage evolution and fracture modes in plastically anisotropic materials

A Contribution to the Modeling of Metal Plasticity and Fracture: From Continuum to Discrete Descriptions

The objective of this dissertation is to further the understanding of inelastic behavior in metallic materials. Despite the increasing use of polymeric composites in aircraft structures, high specific strength metals continue to be used in key components such as airframe, fuselage, wings, landing gear and hot engine parts. Design of metallic structures subjected to thermomechanical extremes in aerospace, automotive and nuclear applications requires consideration of the plasticity, creep and fracture behavior of these materials. Consideration of inelasticity and damage processes is also important in the design of metallic components used in functional applications such as thin films, flexible electronics and micro electro mechanical systems. Fracture mechanics has been largely successful in modeling damage and failure phenomena in a host of engineering materials. In the context of ductile metals, the Gurson void growth model remains one of the most successful and widely used models. However, some well documented limitations of the model in quantitative prediction of the fracture strains and failure modes at low triaxialities may be traceable to the limited representation of the damage microstructure in the model. In the first part of this dissertation, we develop an extended continuum model of void growth that takes into account details of the material microstructure such as the texture of the plastically deforming matrix and the evolution of the void shape. The need for such an extension is motivated by a detailed investigation of the effects of the two types of anisotropy on the materials' effective response using finite element analysis. The model is derived using the Hill-Mandel homogenization theory and an approximate limit analysis of a porous representative volume element. Comparisons with several numerical studies are presented towards a partial validation of the analytical model. Inelastic phenomena such as plasticity and creep result from the collective behavior of a large number of nano and micro scale defects such as dislocations, vacancies and grain boundaries. Continuum models relate macroscopically observable quantities such as stress and strain by coarse graining the discrete defect microstructure. While continuum models provide a good approximation for the effective behavior of bulk materials, several deviations have been observed in experiments at small scales such as an intrinsic size dependence of the material strength. Discrete dislocation dynamics (DD) is a mesoscale method for obtaining the mechanical response of a material by direct simulation of the motion and interactions of dislocations. The model incorporates an intrinsic length scale in the dislocation Burgers vector and potentially allows for size dependent mechanical behavior to emerge naturally from the dynamics of the dislocation ensemble. In the second part of this dissertation, a simplified two dimensional DD model is employed to study several phenomena of practical interest such as strain hardening under homogeneous deformation, growth of microvoids in a crystalline matrix and creep of single crystals at elevated temperatures. These studies have been enabled by several recent enhancements to the existing two-dimensional DD framework described in Chapter V. The main contributions from this research are: (i) development of a fully anisotropic continuum model of void growth for use in ductile fracture simulations and (ii) enhancing the capabilities of an existing two-dimensional DD framework for large scale simulations in complex domains and at elevated temperatures

Strain hardening in 2D discrete dislocation dynamics simulations: A new '2.5D' algorithm

The two-dimensional discrete dislocation dynamics (2D DD) method, consisting of parallel straight edge dislocations gliding on independent slip systems in a plane strain model of a crystal, is often used to study complicated boundary value problems in crystal plasticity. However, the absence of truly three dimensional mechanisms such as junction formation means that forest hardening cannot be modeled, unless additional so-called '2.5D' constitutive rules are prescribed for short-range dislocation interactions. Here, results from three dimensional dislocation dynamics (3D DD) simulations in an FCC material are used to define new constitutive rules for short-range interactions and junction formation between dislocations on intersecting slip systems in 2D. The mutual strengthening effect of junctions on preexisting obstacles, such as precipitates or grain boundaries, is also accounted for in the model. The new '2.5D' DD model, with no arbitrary adjustable parameters beyond those obtained from lower scale simulation methods, is shown to predict athermal hardening rates, differences in flow behavior for single and multiple slip, and latent hardening ratios. All these phenomena are well-established in the plasticity of crystals and quantitative results predicted by the model are in good agreement with experimental observations. (C) 2016 Elsevier Ltd. All rights reserved

Interfacial diffusion in high-temperature deformation of composites: A discrete dislocation plasticity investigation

© 2016 Elsevier Ltd We present a discrete dislocation plasticity (DDP) framework to analyse the high temperature deformation of multi-phase materials (composites) comprising a matrix and inclusions. Deformation of the phases is by climb-assisted glide of the dislocations while the particles can also deform due to stress-driven interfacial diffusion. The general framework is used to analyse the uniaxial tensile deformation of a composite comprising elastic particles with dislocation plasticity only present in the matrix phase. When dislocation motion is restricted to only glide within the matrix a strong size effect of the composite strength is predicted with the strength increasing with decreasing unit cell size due to dislocations forming pile-ups against the matrix/particle interface. Interfacial diffusion decreases the composite strength as it enhances the elongation of the elastic particles along the loading direction. When dislocation motion occurs by climb-assisted glide within the matrix the size effect of the strength is reduced as dislocations no longer arrange high energy pile-up structures but rather form lower energy dislocation cell networks. While interfacial diffusion again reduces the composite strength, in contrast to continuum plasticity predictions, the elongation of the particles is almost independent of the interfacial diffusion constant. Rather, in DDP the reduction in composite strength due to interfacial diffusion is a result of changes in the dislocation structures within the matrix and the associated enhanced dislocation climb rates in the matrix.Support from ONR under grant number N62909-14-1N242 on Multi-scale methods for creep resistant alloys (program manager Dr. David Shifler) is gratefully acknowledged