Ph.D. / Please refer to full text to view abstract

Crystal plasticity has been an active research field for several decades. The crystal plasticity of the bulk materials has its key relevance in the industrial process. Besides, the plasticity of nano-sized materials becomes a topic attracting a lot of interest recently. In the Part I of the thesis, molecular dynamics (MD) simulations were used to study the plasticity of small nanoparticles. Firstly, the coalescence process of Cu nanoparticles was explored. It was found that a peculiar type of five-fold twins in the sintered products were formed via an unseen before dislocation-free process involving a series of shear waves and rigid-body rotations. Secondly, a similar study on the heating of a single nanoparticle was conducted. The same dislocation-free shear wave mechanism was spotted again. In this mechanism, a cluster of atoms rearranges in a highly coordinated way between different geometrical configurations (e.g. fcc, decahedral, icosahedral) without involving dislocations. Thirdly, simulations on the sintering of many nanoparticles were performed, and the governing processes during the consolidation were discussed. The findings in this part of the thesis can provide some guidance for controlling the motifs of nanoparticles. In Part II of the thesis, the emphasis was switched to the crystal plasticity at larger spatial and temporal scales. A dislocation density-based model was developed in our research group. This model employs a dynamics formulation in which the force on each group of dislocation density is calculated with the Taylor and mutual elastic interactions taken into account. The motion of the dislocation densities is then predicted using a conservative law, with annihilation and generation considered. The new dislocation density-based model was used in this work to simulate the plastic deformation of single crystals under ultrasonic irradiation. Softening during vibrations as well as enhanced cell formation was predicted. This is the first simulation effort to successfully predict the cell formation phenomenon under vibratory loadings. / published_or_final_version / Mechanical Engineering / Master / Master of Philosophy

This PhD thesis consists of five complementary chapters. Chapters 2 through 4 constitute the basis of research papers to be published subsequently. These three chapters summarize the state of a single crystal undergoing elastoplastic deformation. The studies presented in this thesis primarily deal with experimental and computational concepts that enable the calculation, measurement and extraction of the spatially resolved net Burgers density vector and the geometrically necessary dislocation densities (GNDs), which reveal the small scale continuum characteristics of a single crystal in the elastoplastic state. The calculation methodology of a new validation parameter, β, which is the orientation of the net Burgers density vector, is given in chapter 2. This new parameter, β, enables us to validate the elastic-plastic constitutive relations. Since the existing methods used for validation cannot give direct information about the state of the material, the β-variable is introduced for elastic- plastic constitutive models. β-fields, which are essentially contour maps of β-variables on two dimensional spatial coordinates, are used to monitor the activity regions of effective slip systems. Chapters 2 through 4 present a comprehensive analysis of the spatially resolved net Burgers density vector, along with the length scale characterization of dislocation structures and validation of constitutive relations. The studies presented in this work are the outcome of experimental and computational research. The experimental work consists of the indentation of a nickel single crystal deformed through a quasi-statically applied line load parallel to the [110] crystallographic orientation. The line load was applied onto (001) surface of the single crystal by a tungsten carbide wedge indenter with a 90◦ included angle. A two-dimensional deformation field on an indented single crystal, in which the only non-zero lattice rotation occurs in the plane of deformation and only three effective in-plane slip systems are activated, was investigated. The mid-section of the deformed single crystal was exposed by EDM and polished electrochemically. The in-plane lattice rotations were measured by high-resolution electron backscattered diffraction (HR-EBSD). The Nye's dislocation density components, lattice curvatures, GNDs and net Burgers density vectors were calculated. Therefore, the β- variable and the β-fields are calculated both experimentally, analytically and numerically in Chapter 2. A qualitative comparison of the three methods showed that the β-field obtained from experimental measurements agrees with those obtained from analytical and numerical methods. The directions of the net Burgers density vector, which are used to determine the boundaries of the slip activity regions, are also given in Chapter 2. Chapter 3 mainly deals with the hardening parameters associated with strain hardening rules utilized in finite element simulations, and investigates the sensitivity of the β-variable to parameters such as latent hardening ratio, initial hardening modulus and saturation strength. The study revealed that a change in the saturation strength has a significant effect on both magnitude of the β-variable and the boundary of the slip activity regions. Chapter 4 presents a length scale analysis associated with dislocation structures such as cell size and cell wall width. The methods presented in this chapter employ the SEM- based continuum method and Fourier Analysis. As-measured GNDs are extracted along the local crystallographic traces, and a quasi-periodic arrangement of dislocation structures is obtained. The extracted GND functions are truncated, interpolated, and filtered. Finally, Fourier Transform is applied to obtain a relationship between cell size and cell wall width of the dislocation structures. The results are compared with those obtained by TEM micrographs. Whereas TEM micrographs characterize the dislocation structures in small scale, the method that is presented in this chapter provides multi scale characterization, which is an order of magnitude larger. Concluding remarks and recommendations for future studies are given in Chapter 5.

To better understand consequences of classical assumptions regarding deformation mechanisms at the mesoscale, experimental observations of mesoscale deformation are presented. In light of actual micrographics of deformed polycrystals, the Von Mises criterion which states that 5 independent plastic deformation sources are needed at each material point to satisfy compatibility is studied, and the consequences of violating this assumption are presented through comprehensive parametric studies. From these studies, it can be concluded that not only are 5 independent plastic deformation sources not needed or observed at each point, but if less than 5 sources are allowed to be active a new physical understanding of a mechanism for kinematic hardening emerges. Furthermore, for enhanced subgrain rotation and evolution the Von Mises criterion must be violated. The second focus of this work is looking at studies, experiments, and models of mesoscale deformation in order to better understand controlling deformation length scales, so that they can be fed into a combined top-down, bottom-up, non-uniform crystal plasticity model that captures the variability provided by the mesoscale during deformation. This can in turn be used to more accurately model the heterogeneity provided by the response of each grain. The length scale intuited from insight into mesoscale deformation mechanisms through observation of experiments and analytical models is the free slip line length of each slip system, which informs non-uniform material parameters in a crystal plasticity model that control the yielding, hardening, and subsequent softening of each individual slip system. The usefulness of this non-uniform multiscale crystal plasticity model is then explored with respect to its ability to reproduce experimentally measured responses at different strain levels for different size grains. Furthermore, a "Mantle-Core" type model which combines both the non-uniform material parameter model and the limited slip model is created, in which the majority of plastic deformation is accommodated near the grain boundary under multi-slip, and uniform plastic deformation occurs in the bulk dominated by double or triple slip. These models are compared for similar levels of hardening, and the pole figures that result from their deformation are compared to experimental pole figures. While there are other models that can capture the heterogeneity introduced by mesoscale deformation at the grain scale, this combined top-down, bottom-up multiscale crystal plasticity model is by far one of the most computationally efficient as the heterogeneity of the mesoscale is does not emerge by introducing higher order terms, but rather by incorporating the heterogeneity into a simple crystal plasticity formulation. Therefore, as computational power increases, this approach will be among the first that will be able to perform accurate polycrystal level modeling while retaining the heterogeneity introduced by non-local mesoscale deformation mechanisms at the sub-grain scale.

Polycrystal models, beginning with the work of Sachs (1928) and Taylor (1938), have been used to predict very complex material behavior. The basis of these models is single crystal plasticity theory, which is then extended to model an actual (polycrystalline) material composed of a large number of single crystals or grains. Crystal plasticity models are formulated at the scale of the individual grain, which is viewed as a fundamental material element. To first order this is a reasonable approximation, and results in qualitatively good predictions. However, it is also well known that the grain is not a uniform entity, and that a great deal of non-uniform activity, including the development of well-defined dislocation structures, occurs within individual grains. The goals of this research are to complete an experimental data set for validation of material modeling, and to then improve the physical basis of predictive polycrystal plasticity models. Preferred orientations (textures) of oxygen free high conductivity (OFHC) copper were measured using reflection x-ray diffraction techniques. Monotonic strain paths included a variety of strain levels for both compression and torsion. One of the significant contributions of this research was the measurement of textures resulting from non-monotonic deformation histories, specifically compressive prestrain (to two different levels) followed by torsion to an effective plastic strain of 1.00. We also concluded synchrotron radiation experiments to map Laue images to examine subgrain microtexture formation at various stages of finite deformation. The second major contribution is to polycrystal plasticity modeling. Improvements to the plasticity model were achieved by including the effects of gradually developing, sub-grain scale microstructures, without explicitly modeling the structures, in terms of both crystallographic texture formation and work hardening. The effects of these microstructures were incorporated through the use of new internal state variables. They result in a broadening of the peaks of the macroscopic texture and a reduction of the rate of texture formation. Predictions of crystallographic orientation distributions were verified by plotting stereographs, which were shown to match measured crystallographic textures. The microstructural hardening law was introduced through a new form of latent hardening, which was shown to match experimental stress-strain behavior more closely than the basic model of Pierce, Asaro, and Needleman (1982). This latent hardening form augmented a Taylor-type term, which reflected statistically stored dislocations in the slip system hardness. Significantly, this improvement was also noted in the case of non-monotonic loading, which the standard model could not predict even to first order. Also, in the course of this research a planar double slip model was used as a precursor to the full three-dimensional modeling. The objective was to use the planar model to test various formulations, at least qualitatively, since it is a simpler model. As a result of comparisons between the three-dimensional simulations and the planar ones, the planar model was shown to be an insufficient tool for developing new texture and hardening evolution schemes as compared to the three-dimensional models. The planar model was unsuitable for modeling any but the most basic crystal plasticity relations and most simple deformation paths in a qualitative manner.

Thesis (Ph. D.)--Mechanical Engineering, Georgia Institute of Technology, 2008. / Committee Chair: David. L. McDowell; Committee Member: Min Zhou; Committee Member: Naresh N. Thadhani; Committee Member: Rami M. Haj-Ali; Committee Member: Richard W. Neu.

Crystallographic texture and its evolution are known to be major sources of anisotropy in polycrystalline metals. Highly simplified phenomenological models cannot usually provide reliable predictions of the materials anisotropy under complex deformation paths, and lack the fidelity needed to optimize the microstructure and mechanical properties during the production process. On the other hand, physics-based models such as crystal plasticity theories have demonstrated remarkable success in predicting the anisotropic mechanical response in polycrystalline metals and the evolution of underlying texture in finite plastic deformation. However, the integration of crystal plasticity models with finite element (FE) simulations tools (called CPFEM) is extremely computationally expensive, and has not been adopted broadly by the advanced materials development community. The current dissertation has mainly focused on addressing the challenges associated with integrating the recently developed spectral database approach with a commercial FE tool to permit computationally efficient simulations of heterogeneous deformations using crystal plasticity theories. More specifically, the spectral database approach to crystal plasticity solutions was successfully integrated with the implicit version of the FE package ABAQUS through a user materials subroutine, UMAT, to conduct more efficient CPFEM simulations on both fcc and bcc polycrystalline materials. It is observed that implementing the crystal plasticity spectral database in a FE code produced excellent predictions similar to the classical CPFEM, but at a significantly faster computational speed. Furthermore, an important application of the CPFEM for the extraction of crystal level plasticity parameters in multiphase materials has been demonstrated in this dissertation. More specifically, CPFEM along with a recently developed data analysis approach for spherical nanoindentation and Orientation Imaging Microscopy (OIM) have been used to extract the critical resolved shear stress of the ferrite phase in dual phase steels. This new methodology offers a novel efficient tool for the extraction of crystal level hardening parameters in any single or multiphase materials.

The increasing use of alpha/beta Ti-Al alloys in critical aircraft gas turbine engine and airframe applications necessitates the further development of physically-based constitutive models that account for their complex microdeformation mechanisms. Alpha/beta Ti-Al alloys are dual-phase in nature consisting of a mixture of hcp (alpha) and bcc (beta) crystal structures, which through variation in alloying elements and/or processing techniques can be produced in a wide range of microstructural compositions and morphologies. A constitutive model for these materials should address the various sources of material anisotropy and heterogeneity at both the micro and macroscales. The main sources of anisotropy in these materials are the low symmetry of the hcp phase, the texture, the relative strengths of different slip systems, non-planar dislocation core structures, phase distributions, and dislocation substructure evolution. The focus of this work is the development of a 3-D crystal plasticity model for duplex Ti-6Al-4V (Ti-64), an (alpha+beta) alloy. The model is used to study the process of attachment fatigue. Attachment fatigue is a boundary layer phenomenon in which most of the plastic deformation and damage accumulation occurs at depths on the order of tens of microns and encompasses regions of only a few grains into the depth of the material. The use of computational micromechanics-based crystal plasticity models to study attachment fatigue is a relatively new approach. This approach has the potential to offer additional insight to classical homogeneous plasticity models, since the length scales over which relative slip and crack initiation occur during this process is on the order of microstructural dimensions. Emphasis is placed on understanding the effects that texture, slip strength anisotropy, and phase distribution have on the surface and subsurface deformation fields during attachment fatigue. The deformation fields are quantified in terms of cumulative effective plastic strain distributions, plastic strain maps, and plastic strain-based critical plane multiaxial fatigue parameters.

Ti-6Al-4V, known for high strength-to-weight ratio and good resistance to corrosion, has been widely used in aerospace, biomedical, and high-performance sports applications. A wide range of physical and mechanical properties of Ti-6Al-4V can be achieved by varying the microstructures via deformation and recrystallization processes. The aim of this thesis is to establish a microstructure-sensitive fatigue analysis approach that can be applied in engineering applications such as fretting fatigue to permit explicit assessment of the influence of microstructure. In this thesis, crystal plasticity constitutive relations are developed to model the cyclic deformation -TiAl has beenabehavior of Ti-6Al-4V. The development of the slip bands within widely reported and has been found to play an important role in deformation and fatigue behaviors of Ti-6Al-4V. The shear enhanced model is used to simulate the formation and evolution of slip bands triggered by planar slip under static or quasi-static loading at room temperature. Fatigue Indicator Parameters (FIPs) are introduced to reflect driving force for the different crack formation mechanisms in Ti-6Al-4V. The cyclic stress-strain behavior and fretting fatigue sensitivity to microstructure and loading parameters in dual phase Ti-6Al-4V are investigated.

The mechanical behavior of structural materials used in nuclear applications is significantly degraded as a result of irradiation, typically characterized by an increase in yield stress, localization of inelastic deformation along narrow dislocation channels, and considerably reduced strains to failure. Further, creep rates are accelerated under irradiation. These changes in mechanical properties can be traced back to the irradiated microstructure which shows the formation of a large number of material defects, e.g., point defect clusters, dislocation loops, and complex dislocation networks. Interaction of dislocations with the irradiation-induced defects governs the mechanical behavior of irradiated metals. However, the mechanical properties are seldom systematically correlated to the underlying irradiated microstructure. Further, the current state of modeling of deformation behavior is mostly phenomenological and typically does not incorporate the effects of microstructure or defect densities. The present research develops a continuum constitutive crystal plasticity framework to model the mechanical behavior and deformed microstructure of bcc ferritic/martensitic steels exposed to irradiation. Physically-based constitutive models for various plasticity-induced dislocation migration processes such as climb and cross-slip are developed. We have also developed models for the interaction of dislocations with the irradiation-induced defects. A rate theory based approach is used to model the evolution of point defects generated due to irradiation, and coupled to the mechanical behavior. A void nucleation and growth based damage framework is also developed to model failure initiation in these irradiated materials. The framework is used to simulate the following major features of inelastic deformation in bcc ferritic/martensitic steels: irradiation hardening, flow localization due to dislocation channel formation, failure initiation at the interfaces of these dislocation channels and grain boundaries, irradiation creep deformation, and temperature-dependent non-Schmid yield behavior. Model results are compared to available experimental data. This framework represents the state-of-the-art in constitutive modeling of the deformation behavior of irradiated materials.