The operative deformation mechanisms which include both dislocation slip and twinning have a significant impact on the mechanical response of hexagonal close-packed (HCP) metals. Twinning plays an important role in accommodating plastic deformation due to the limited number of independent slip systems in HCP metals. The objective of this research is to study the deformation mechanisms associated with twinning in HCP metals (magnesium and zirconium alloys). Heat treatments are often involved in the manufacturing of zirconium alloys. These alloys exhibit a strong thermal anisotropy with a thermal expansion coefficient along the c-axis nearly two times of that along a-direction. Therefore, residual stresses/strains are generated during the heat treatment process which influences the mechanical response (e.g. lattice evolution) under subsequent loading. The elastic viscoplastic self-consistent (EVPSC) model has been improved which includes thermal strain to study the behavior of a Zircaloy-2 slab under moderately large strains. Various self-consistent schemes (SCSs) of the EVPSC model are evaluated in terms of the deformation behavior of the material under different uniaxial strain paths. Numerical results show that the Affine and Meff=0.1 self-consistent models give much better performance for the Zircaloy-2 slab than the Secant and Tangent models. The EVPSC-TDT model has been employed to mimic the twinning and detwinning behavior of extruded Mg alloy ZK60A under monotonic and cyclic loading. The model differentiates between the stress required to initiate twinning and that required to grow (thicken) existing twins. This enables the model to simulate the unusual sharp yielding behavior during twinning as well as the gradual yielding associated with detwinning. It is demonstrated that this model gives a good prediction of the strength anisotropy, strength asymmetry, and strain hardening behavior along different directions, for cases in which the contribution of twinning is large, small and intermediate. For the first time, the lattice strain evolution is well predicted in an extruded magnesium alloy under cyclic loading which involves twinning and detwinning. In all polycrystal models, an empirical equation for the termination of twinning in a grain is required. A new physics-based empirical equation for describing this phenomenon in magnesium alloys has been proposed in this study. It should be noted that the popular empirical equation currently used in all polycrystal models is applied at the grain level, while the new empirical equation is introduced at the twinning system level. The new description is represented by a single parameter while the commonly used empirical equation depends on two parameters. It is demonstrated that the proposed empirical equation is easily calibrated with the single parameter and is able to accurately simulate the experimentally observed rapid hardening associated with twinning exhaustion. / Thesis / Doctor of Philosophy (PhD)

The aim of this PhD thesis is to incorporate deformation twinning in a fullield viscoplastic crystal plasticity model based on fast Fourier transform in an effort to gain insights into its role on strain localization. This work is motivated by current experimental evidences on the important role that dislocation reactions at the twin interface play on damage initiation in materials during plastic deformation. We began first by investigating the role of slip on stress localization. To this end, we simulated the effect of macroscopic deformation path, which dictates a macroscopic stress state, as well as pre-existing microstructure in typical ferritic steel, where plastic deformation is accommodated by slip mechanism. The results show that the width of localized strain rate regions near grain boundaries is a function of the deformation path, and there is a positive correlation between local Taylor factor and local stress field, which slightly depends on deformation path. For the incorporation of mechanical twinning in twinning-induced plasticity (TWIP) steel, we implemented predominant reorientation scheme (PTR) in vpFFT, which was implemented previously in the mean field VPSC. The comparison between experimental and simulation results indicates that twin volume fraction, final texture, and stress-strain curve were satisfactorily predicted. Despite that predominant twin reorientation scheme was not suitable to capture lamellar shape of twins in the microstructure, twin domains were predicted to form and grow at or close to grain boundary regions. Finally, we surveyed current literature, which aimed at capturing the characteristic lamellar morphology of twins. Literature review shows several unsuccessful crystal plasticity simulations in capturing twin nucleation and twin lamellar shape at measocale. These inabilities can be attributed to i) twin nucleation that is controlled by local atomistic configurations and stress fluctuations at the grain boundaries, and ii) the random or stochastic nature of twin nucleation, which has been proved by EBSD observation. Based on the EBSD observations, twin nucleation depends on both microstructural (e.g, grain size, dislocation density) and loading conditions ( e.g, stress, strain). Furthermore, the propensity, frequency, and morphology of deformation twins are different among grain with the same orientation and applied boundary conditions.

A new crystal plasticity scheme for explicit time integration codes is developed based on a forward Euler algorithm in the first part of this paper. The new numerical model is incorporated in the UMAT subroutine for implementing rate dependent crystal plasticity model in LS-DYNA/Explicit. The material is modeled as a Face centered cubic (FCC) polycrystalline aggregate, and a finite element analysis based on rate-dependent crystal plasticity is developed to simulate large strain behaviour. Accordingly, an element or a number of elements of the finite element mesh is considered to represent a single crystal within the polycrystal aggregate and the constitutive response at a material point is given by the single crystal constitutive model. The second part of this thesis presents two applications of the crystal plasticity scheme used in conjunction with numerical modeling of three-dimensional (3D) real microstructures. First, finite element meshes containing both particle and texture data are created with solid elements. Particle size, location and orientation are represented by 3D ellipsoids and the elements within these ellipsoids are given rigid properties. Simulations of in-plane plane strain with different combinations of texture and particle location are performed. The effect on texture development, strain magnitudes, and strain localizations is investigated. Second, the three dimensional (3D) polycrystalline microstructure of the aluminum alloy AA5754 is modeled and subjected to three different strain rates for each strain path. The effect of strain paths, strain rates and thermal softening on the formation of localized deformation is investigated. Simulations show that strain path is the most dominant factor in localized deformation and texture evolution.

A new crystal plasticity scheme for explicit time integration codes is developed based on a forward Euler algorithm in the first part of this paper. The new numerical model is incorporated in the UMAT subroutine for implementing rate dependent crystal plasticity model in LS-DYNA/Explicit. The material is modeled as a Face centered cubic (FCC) polycrystalline aggregate, and a finite element analysis based on rate-dependent crystal plasticity is developed to simulate large strain behaviour. Accordingly, an element or a number of elements of the finite element mesh is considered to represent a single crystal within the polycrystal aggregate and the constitutive response at a material point is given by the single crystal constitutive model. The second part of this thesis presents two applications of the crystal plasticity scheme used in conjunction with numerical modeling of three-dimensional (3D) real microstructures. First, finite element meshes containing both particle and texture data are created with solid elements. Particle size, location and orientation are represented by 3D ellipsoids and the elements within these ellipsoids are given rigid properties. Simulations of in-plane plane strain with different combinations of texture and particle location are performed. The effect on texture development, strain magnitudes, and strain localizations is investigated. Second, the three dimensional (3D) polycrystalline microstructure of the aluminum alloy AA5754 is modeled and subjected to three different strain rates for each strain path. The effect of strain paths, strain rates and thermal softening on the formation of localized deformation is investigated. Simulations show that strain path is the most dominant factor in localized deformation and texture evolution.

Fatigue of metals is a problem that affects almost all sectors of industry, from energy to transportation, and failures to account for fatigue or incorrect estimations of service life have cost many lives. To mitigate such fatigue failures, engineers must be able to reliably predict the fatigue life of components under service conditions. Great progress has been made in this regard in the past 40 years; however one aspect of fatigue that is still being actively researched is the behavior of microstructurally small cracks (MSCs), which can diverge significantly from that of long cracks. The portion of life spent nucleating and growing a MSC over the first few grains/phases can consume over 90% of the total fatigue life under High Cycle Fatigue (HCF) conditions and is the primary source of the scatter in fatigue lives. Therefore, the development of robust fatigue design methodologies requires that the MSC regime of crack growth can be adequately modeled. The growth of microstructurally small cracks is dominated by influence of the local heterogeneity of the microstructure and is a highly complex process. In order to successfully model the growth of these microstructurally small cracks (MSCs), two computational frameworks are necessary. First, the local behavior of the material must be modeled, necessitating a constitutive relation with resolution on the scale of grain size. Second, a physically based model for the nucleation and growth of microstructurally small fatigue cracks is needed. The overall objective of this thesis is best summarized as the introduction these two computational frameworks, a crystal plasticity constitutive model and fatigue model, specifically for aluminum alloy 7075-T6, a high-strength, low density, precipitation hardened alloy used extensively in aerospace applications. Results are presented from simulations conducted to study the predicted crack growth under a variety of loading conditions and applied strain ratios, including uniaxial tension-compression and simple shear at a range of applied strain amplitudes. Results from the model are compared to experimental results obtained by other researchers under similar loading conditions. A modified fatigue crack growth algorithm that captures the early transition to Stage II growth in this alloy will also be presented.

At low temperatures, glide twinning activates in HCP structures easier than non-close packed slip necessary to accommodate strain along the c-axis. In contrast to slip, twinning occurs as an accumulation of successive stacking faults that properly report reconstruction of the stacking sequence in a new crystal-reorientated lenticular lamella. These faults are spread by partial dislocations known as twinning dislocations, forcing atoms to switch positions by shear into new crystal planes. As the twinning dislocations thread the faults, the new crystal lamella grows at the expense of the parent. Grain texture changes upon strain, and a strong non-linear trend marks the strain hardening rate. The strain hardening rate changes to a point where it switches sign upon strain. Since activation of these twinning dislocations obey Schmid’s law, twinning could be precluded or exhaustively promoted in sharp textures upon slight changes in loading orientations, so strong anisotropy arises. Moreover, a twinning shear can only reproduce the stacking sequence in one direction, unless the twin mode changes or the c/a ratio crosses a certain ratio. When a twin mode arises with reversed sign, the reorientation is different and more importantly, the strength is different and also the growth rate. Therefore, in addition to strain anisotropy, twin polarity induces a strong asymmetry in textured HCP structures, e.g. wrought HCP metals. This anisotropy/asymmetry is still a barrier to the great economic gain expected from the industrialization of low density, high specific strength and stiffness, HCP Magnesium. This barrier has stimulated efforts to identify the missing links in current scientific knowledge to proper prediction of Magnesium anisotropy. The effect of twinninginduced texture change on the mechanical response is of a major concern. Mesoscale modelers still struggle, without success to predict simultaneously twinning and strain hardening rates upon arbitrary loading directions. We propose a new mechanism that relies on admitting dislocation populations of the twin by dislocations transmuted from the parent when they intersect twinning disconnections. These dislocations interact with original dislocations created in the twin to cause hardening able to faithfully capture anisotropy upon any loading orientation and any initial texture.

Historically, the ability of crystal plasticity to incorporate the Schmid’s law at each integration point has been a powerful tool to simulate and predict the slip behavior at the grain level and the succeeding heterogeneous stress/strain localization and texture evolution at the macroscopic level. Unfortunately, this remarkable capability has not been replicated for materials where twinning becomes a noticeable deformation mechanism, namely in the case of low-stacking fault energy cubic, orthorhombic, and hexagonal close packed structures. This dissertation is an attempt to gain understanding on the heterogeneous deformation due to twinning through various techniques including micromechanics, discrete dislocation dipole loops, and digital image correlation (DIC) analyses, and then bring the collected small scale information up to the fullield crystal plasticity scale using fast Fourier Trans- forms. Results indicate that the twin spacing depends primarily upon the height of the twin, and the stress relaxation from the twinning depends upon the thickness of the twin. Furthermore, in a homogenous stress state, discrete dislocation dipole loop-based twinning model showed that the lenticular shape has the minimum stable energy rather than the lamellar or ellipsoidal twin morphology. Our study on the evolution of twinning under three-point bending condition in strongly basal textured magnesium alloy allowed us to build a strategy to incorporate characteristic twin spacing parameter in the crystal plasticity framework. Inspired by results from molecular dynamics (MD) simulations stressing the effect of shuffles on twin nucleation and disconnection core width, we developed an explicit twinning nucleation criterion based on hydrostatic stress gradient and volume fraction of twin inside a grain. Characteristic twin spacing parameter is used as a function of twin height to determine site specific nucleation points in case of multiple twinnings. This ap- proach offered a good reproduction of the microstructure evolution as affected by twinning in a tri-crystal system.

In this work, a crystal elasto-viscoplastic model was modified to account for the anisotropic mechanical response of magnesium aluminum alloys. Crystal plasticity may offer new understanding of these alloys by explicitly modeling the texture development that profoundly affects the properties of magnesium. The model is able to account for the individual slip systems of both the cubic and hexagonal phases. The constants of the model were determined from published experimental AZ31 data, and the plastic hardening response is shown to match these results well using a modification to the hardening rule to approximate the kinetics of twinning. Model aggregates were created with aluminum compositions representative of common magnesium structural alloys. This approach allows the effect of varying percentage of cubic phase on the hexagonal magnesium alloy aggregate to be studied both in terms of macroscopic response and the crystallographic changes occurring within the system.

No description available.

The objective of this work is to provide various improvements to the modeling and uncertainty quantification of fatigue lives of materials as understood via simulation of crystal plasticity models applied to synthetically reconstructed microstructures. A computational framework has been developed to automate standardized analysis of crystal plasticity models in the high cycle fatigue regime. This framework incorporates synthetic microstructure generation, simulation preparation, execution and post-processing to analysis statistical distributions related to fatigue properties. Additionally, an improved crack nucleation and propagation approach has been applied to Al 7075-T6 to improve predictive capabilities of the crystal plasticity model for fatigue in various loading regimes. Finally, sensitivities of fatigue response to simulation and synthetic microstructure properties have been explored to provide future guidance for the study of fatigue quantification based on crystal plasticity models.