The capability to predict the impact tolerance of next generation lightweight metallic materials for protective armor application requires fundamental understanding of the deformation and failure behavior of these materials under dynamic loading conditions. Loading conditions of impact/shock result in complex stress states that range from uniaxial compression to tension at high strain rates ranging from 105 s-1 to 1010s-1. The deformation response of these materials is determined by the capability of the microstructures to nucleate dislocations and failure response is determined by the creation of weak sites for void nucleation during uniaxial expansion. A critical challenge in the understanding of mechanisms of plastic deformation and onset of dynamic failure (spallation) is the short time scales associated with these phenomena that limit the capabilities of experimental characterization methods to investigate these mechanisms. As a result, this dissertation focuses on investigation of micromechanisms of interaction, evolution and accumulation of defects and damage during shock compression and spall failure at atomic scale using molecular dynamics (MD) simulations. The MD simulations, due to their high computational cost, are limited to system sizes that are upto a few hundred nanometers and timescales of tens of picoseconds. These limitations result in strain rates of ~1010 s-1 under shock loading conditions using reasonable computing resources. The dissertation demonstrates the capability of newly developed quasi-coarse-grained dynamics (QCGD) method to retain atomistic mechanisms of evolution of microstructure during shock compression and spall failure at time and length scales which are beyond the capability of MD simulations i.e at mesoscales.
Characterization and modeling of deformation and failure in metallic materials under extreme conditions, such as the high loads and strain rates found under shock loading due to explosive detonation and high velocity-impacts, are extremely important for a wide variety of military and industrial applications. When a shock wave causes stress in a material that exceeds the elastic limit, plasticity and eventually spallation occur in the material. The process of spall fracture, which in ductile materials stems from strain localization, void nucleation, growth and coalescence, can be caused by microstructural heterogeneity. The analysis of void nucleation performed from a microstructurally explicit simulation of a spall damage evolution in a multicrystalline copper indicated triple junctions as the preferred sites for incipient damage nucleation revealing 75% of them with at least two grain boundaries with misorientation angle between 20-55°. The analysis suggested the nature of the boundaries connecting at a triple junction is an indicator of their tendency to localize spall damage. The results also showed that damage propagated preferentially into one of the high angle boundaries after voids nucleate at triple junctions. Recently the Rayleigh-Taylor Instability (RTI) and the Richtmyer-Meshkov Instability (RMI) have been used to deduce dynamic material strength at very high pressures and strain rates. The RMI is used in this work since it allows using precise diagnostics such as Transient Imaging Displacement Interferometry (TIDI) due to its slower linear growth rate. The Preston-Tonks-Wallace (PTW) model is used to study the effects of dynamic strength on the behavior of samples with a fed-thru RMI, induced via direct laser drive on a perturbed surface, on stability of the shock front and the dynamic evolution of the amplitudes and velocities of the perturbation imprinted on the back (flat) surface by the perturbed shock front. Simulation results clearly showed that the amplitude of the hydrodynamic instability increases with a decrease in strength and vice versa and that the amplitude of the perturbed shock front produced by the fed-thru RMI is also affected by strength in the same way, which provides an alternative to amplitude measurements to study strength effects under dynamic conditions. Simulation results also indicate the presence of second harmonics in the surface perturbation after a certain time, which were also affected by the material strength.
Orientation-imaging microscopy offers unique capabilities to quantify the defects and damage evolution occurring in metals following dynamic and shock loading. Examples of the quantification of the types of deformation twins activated, volume fraction of twinning, and damage evolution as a function of shock loading in Ta are presented. Electron back-scatter diffraction (EBSD) examination of the damage evolution in sweeping-detonation-wave shock loading to study spallation in Cu is also presented.
Design of next-generation high strength metallic materials for damage-resistant applications relies on a fundamental understanding of the deformation mechanisms and failure behavior of these materials under dynamic loading conditions. The dynamic strength of metals is typically characterized based on the "spall strength" defined as the peak tensile pressure the metal can withstand prior to failure. For pure FCC metals, the capability to increase the spall strength is limited due to insufficient microstructural features that can be used to tailor/modify the deformation and failure behavior under dynamic loading conditions. The current understanding of the role of grain boundaries and deformation twinning in BCC metals, however, is still in its infancy. Another promising strategy to design high strength microstructures is the engineering of nanoscale interfaces in alloy microstructures that may alter the nucleation and evolution of defects/damage. Such strategies have been successfully demonstrated experimentally in FCC/BCC alloy microstructures. A critical challenge in engineering these microstructures, however, is the lack of understanding on the role of interfaces on the spall failure behavior. Such an understanding is particularly challenging using experimental techniques due to the short time and length scales of the processes of nucleation and evolution of defects/damage. Therefore, the goal of this dissertation is to carry out a systematic study using classical molecular dynamics (MD) simulations to investigate the role of structure and energies of grain boundaries in BCC microstructures as well as the structure, size and distribution of FCC/BCC interfaces on the twinning/de-twinning behavior as well as the damage nucleation (void nucleation and growth) behavior under shock loading conditions. Such understanding will enable to identify key microstructural descriptors of the interfaces that determine the spall strength, and aid in the design of nanocrystalline Ta and Cu/Ta microstructures with enhanced spall strengths for damage-tolerant applications.
Damage detection in heterogeneous material systems is a complex problem and requires an in-depth understanding of the material characteristics and response under varying load and environmental conditions. A significant amount of research has been conducted in this field to enhance the fidelity of damage assessment methodologies, using a wide range of sensors and detection techniques, for both metallic materials and composites. However, detecting damage at the microscale is not possible with commercially available sensors. A probable way to approach this problem is through accurate and efficient multiscale modeling techniques, which are capable of tracking damage initiation at the microscale and propagation across the length scales. The output from these models will provide an improved understanding of damage initiation; the knowledge can be used in conjunction with information from physical sensors to improve the size of detectable damage. In this research, effort has been dedicated to develop multiscale modeling approaches and associated damage criteria for the estimation of damage evolution across the relevant length scales. Important issues such as length and time scales, anisotropy and variability in material properties at the microscale, and response under mechanical and thermal loading are addressed. Two different material systems have been studied: metallic material and a novel stress-sensitive epoxy polymer. For metallic material (Al 2024-T351), the methodology initiates at the microscale where extensive material characterization is conducted to capture the microstructural variability. A statistical volume element (SVE) model is constructed to represent the material properties. Geometric and crystallographic features including grain orientation, misorientation, size, shape, principal axis direction and aspect ratio are captured. This SVE model provides a computationally efficient alternative to traditional techniques using representative volume element (RVE) models while maintaining statistical accuracy. A physics based multiscale damage criterion is developed to simulate the fatigue crack initiation. The crack growth rate and probable directions are estimated simultaneously. Mechanically sensitive materials that exhibit specific chemical reactions upon external loading are currently being investigated for self-sensing applications. The "smart" polymer modeled in this research consists of epoxy resin, hardener, and a stress-sensitive material called mechanophore The mechanophore activation is based on covalent bond-breaking induced by external stimuli; this feature can be used for material-level damage detections. In this work Tris-(Cinnamoyl oxymethyl)-Ethane (TCE) is used as the cyclobutane-based mechanophore (stress-sensitive) material in the polymer matrix. The TCE embedded polymers have shown promising results in early damage detection through mechanically induced fluorescence. A spring-bead based network model, which bridges nanoscale information to higher length scales, has been developed to model this material system. The material is partitioned into discrete mass beads which are linked using linear springs at the microscale. A series of MD simulations were performed to define the spring stiffness in the statistical network model. By integrating multiple spring-bead models a network model has been developed to represent the material properties at the mesoscale. The model captures the statistical distribution of crosslinking degree of the polymer to represent the heterogeneous material properties at the microscale. The developed multiscale methodology is computationally efficient and provides a possible means to bridge multiple length scales (from 10 nm in MD simulation to 10 mm in FE model) without significant loss of accuracy. Parametric studies have been conducted to investigate the influence of the crosslinking degree on the material behavior. The developed methodology has been used to evaluate damage evolution in the self-sensing polymer.
Understanding the mechanical strength of metals and alloys under different temperatures is essential in materials design for modern technology applications. Predicting temperature-dependent mechanical properties requires detailed knowledge of the elementary thermally activated defect processes governing plasticity. These microstructural mechanisms contribute to the plastic flow stress through (a) the 'intrinsic energy barrier' due to unfavorable atomic structures; (b) the long-range elastic interactions between these defects and other obstacles. Both aspects provide crucial inputs to mesoscale modeling methods for plasticity, such as dislocation dynamics (DD). This thesis includes three major projects. The first two focus mainly on (a), in which we combine atomistic simulation with statistical mechanical analysis to develop predictive kinetic theories of defect dynamics under stress. The third project focuses on (b), in which we develop a fast elasticity solver for solving long-range dislocation-void interactions. The first part of the thesis discusses the cross slip of screw dislocations in fcc metals, an essential mechanism for the temperature-dependent stage-III strain hardening. Cross slip of screw dislocations in crystalline solids is a stress-driven thermally activated process essential to many phenomena during plastic deformation, including dislocation pattern formation, strain hardening, and dynamic recovery. Molecular dynamics (MD) simulation has played an important role in determining the microscopic mechanisms of cross slip, but due to its limited timescale, predicting cross slip rate from MD is only possible at high-stress or high-temperature conditions. The transition state theory (TST) can predict the cross-slip rate over a wide range of stress and temperature conditions, but its predictions have been found to be several orders of magnitude too low in comparison to MD results. This discrepancy can be expressed by a large activation entropy whose physical origin remains unclear. Here we resolve this discrepancy by showing that the large activation entropy results from anharmonic effects, including thermal softening, thermal expansion, and soft vibrational modes of the dislocation. We expect these anharmonic effects to be significant when determining the rate of a wide range of stress-driven thermally activated processes in solids. The second part investigates how shear-transformation (ST) events respond to applied stress and thermal activation in CuZr metallic glasses. Understanding how shear transformation (ST) events respond to applied stress and thermal activation remains challenging for glassy materials due to their amorphous structure. Using MD simulation of early-stage deformation of CuZr metallic glasses, we find an anomalous temperature dependence of the elastic limit. We present the energy-strain landscape (ESL) based on high-throughput NEB calculations to probe the strain dependence on activation energies of multiple competitive ST events. A quantitative description is obtained from ESL analyses for the ST dynamics in metallic glasses, which reveals that the reversibility of ST events governs the elastic limit. We discover a strain-independent quantity eigen barrier that characterizes the reversibility of ST events and thus predicts the elastic limit of metallic glasses. We believe that the ESL picture brings a new perspective to understanding ST events' dynamics in glassy materials under external loading. Finally, we introduce a fast numerical methods we developed based on spherical harmonics for solving elasticity problems with any arbitrary boundary conditions defined on a sphere. We develop an efficient numerical method for calculating the image stress field induced by spherical voids in materials, and applied the method to dislocation-void interactions. The method is constructed based on a complete set of basis functions for the displacement potential of the elastic boundary value problem for a spherical hole, as well as the corresponding displacement, stress, and traction fields, all in terms of linear combinations of spherical harmonics. Using the fast transformation between the real and spherical-harmonics spaces provided by the {\it SHTOOLS} package, the method is more efficient than other image stress solvers such as the finite-element method. This method can be readily extended for solving elasticity problems involving inclusions and inhomogeneities, as well as contact between spheres. The tools developed here can also be useful for fast solution of differential equations with spherical boundaries beyond elasticity. The method is applied to long-range elastic interactions between dislocations and voids in crystalline solids and a biomechanical application in the force microscope for measuring immune cell-target interactions.
This book is the standard text book for elastoplasticity/viscoplasticity which is explained comprehensively covering the rate-independent to -dependent finite deformations of metals, soils, polymers, crystal plasticity, etc. and the friction phenomenon. Concise explanations on vector-tensor analysis and continuum mechanics are provided first, covering the underlying physical concepts, e.g. various time-derivatives, pull-back and push-forward operations, work-conjugacy and multiplicative decomposition of deformation gradient tensor. Then, the rigorous elastoplastic/viscoplastic model, called the subloading surface model, is explained comprehensively, which is based on the subloading surface concept to describe the continuous development of the plastic/viscoplastic strain rate as the stress approaches to the yield surface, while it can never be described by the other plasticity models, e.g. the Chaboche-Ohno and the Dafalias-Yoshida models assuming the purely-elastic domain. The main features of the subloading surface model are as follows: 1) The subloading surface concept underling the cyclic plasticity is introduced, which insists that the plastic deformation develops as the stress approaches the yield surface. Thus, the smooth elastic-plastic transition leading to the continuous variation of the tangent stiffness modulus is described always. 2) The subloading-overstress model is formulated by which the elastoplastic deformation during the quasi-static loading and the viscoplastic deformation during the dynamic and impact loading can be described by the unified equation. Then, only this model can be used to describe the deformation in the general rate of deformation, disusing the elastoplastic constitutive equation. 3) The hyperelastic-based (visco)plasticity based on the multiplicative decomposition of deformation gradient tensor and the subloading surface model is formulated for the exact descriptions of the finite elastic and (visco)plastic deformations. 4) The subloading-friction model is formulated for the exact description of the dry and the fluid (lubricated) frictions at the general rate of sliding from the static to the impact sliding. Thus, all the elastic and inelastic deformation/sliding phenomena of solids can be described accurately in the unified equation by the subloading-overstress model. The subloading surface model will be engraved as the governing law of irreversible deformation of solids in the history of solid mechanics.
This book presents the state-of-the-art in multiscale modeling and simulation techniques for composite materials and structures. It focuses on the structural and functional properties of engineering composites and the sustainable high performance of components and structures. The multiscale techniques can be also applied to nanocomposites which are important application areas in nanotechnology. There are few books available on this topic.
Summary: A Generalized Multiscale Analysis Approach brings together comprehensive background information on the multiscale nature of the composite, constituent material behaviour, damage models and key techniques for multiscale modelling, as well as presenting the findings and methods, developed over a lifetime's research, of three leading experts in the field. The unified approach presented in the book for conducting multiscale analysis and design of conventional and smart composite materials is also applicable for structures with complete linear and nonlinear material behavior, with numerous applications provided to illustrate use. Modeling composite behaviour is a key challenge in research and industry; when done efficiently and reliably it can save money, decrease time to market with new innovations and prevent component failure.
