Task II Modeling: Crystal Plasticity Simulations
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International Materials Review
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Proposed for publication in International Journal of Plasticity.
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Acta Materialia
After sliding contact of a hard spherical counterface on a metal surface, the resulting wear scar possesses a complex microstructure consisting of dislocations, dislocation cells, ultrafine or nanocrystalline grains, and material that has undergone dynamic recovery. There remains a controversy as to the mechanical properties of the tribolayer formed in this wear scar. To investigate the properties of this thin layer of damaged material in single crystal nickel, we employed two complementary techniques: pillar compression and nanoindentation. In both techniques, the tests were tailored to characterize the near surface properties associated with the top 500 nm of material, where the wear-induced damage was most extensive. Pillar compression indicated that the worn material was substantially softer than neighboring unworn base metal. However, nanoindentation showed that the wear track was substantially harder than the base metal. These apparently contradictory results are explained on the basis of source limited deformation. The worn pillars are softer than unworn pillars due to a pre-straining effect: undefected pillars are nearly free of dislocations, whereas worn pillars have pre-existing dislocations built in. Nanoindentation in worn material behaves harder than unworn single crystal nickel due to source length reduction from the fine-grained wear structure. © 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
International Journal of Plasticity
Despite the technological importance of body-centered cubic (BCC) metals, models of their plastic deformation are less common than those of face-centered cubic (FCC) metals, due in part to the complexity of slip in BCC crystals caused by the thermal activation of screw dislocation motion. This paper presents a physically based crystal plasticity model that incorporates atomistic models and experimental measurements of the thermally activated nature of screw dislocation motion. This model, therefore, reproduces the temperature, stress, and strain rate dependence of flow in BCC metals in a simple formulation that will allow for large, grain-scale simulations. Furthermore, the results illustrate the importance of correctly representing mechanistic transitions in materials with high lattice friction. © 2012 Elsevier Ltd. All rights reserved.
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JOM
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Scripta Materialia
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Recently, molecular dynamics simulations (e.g. Groger et al. Acta Mat. vol.56) have uncovered new insights into dislocation motion associated with plastic deformation of BCC metals. Those results indicate that stress necessary for glide along 110[111] crystallographic systems plus additional shear stresses along non-glide directions may accurately characterize plastic flow in BCC crystals. Further, they are readily adaptable to micromechanical formulations used in crystal plasticity models. This presentation will discuss an adaptation into a classical mechanics framework for use in a large scale rate-dependent crystal plasticity model. The effects of incorporating the non-glide influences on an otherwise associative flow model are profound. Comparisons will be presented that show the effect of the non-glide stress components on tension-compression yield stress asymmetry and the evolution of texture in BCC crystals.
Metallic materials in sliding contact typically undergo dislocation-mediated plasticity, which results in stick-slip frictional behavior associated with high coefficients of friction ({mu} > 0.8). Our recent work on two electroplated nanocrystalline Ni alloys reveal that under combined conditions of low stress and low sliding velocity, these metals have very low friction ({mu} < 0.3). The observed frictional behavior is consistent with the transition from dislocation-mediated plasticity to an alternative mechanism such as grain boundary sliding. Focused ion beam cross-sections viewed in the TEM reveal the formation of a subsurface tribological bilayer at the contact surface, where the parent nanocrystalline material has evolved in structure to accommodate the frictional contact. Grain growth at a critical distance below the contact surface appears to promote a shear-accomodation layer. We will discuss these results in the context of a grain-size dependent transition from conventional microcrystalline wear behavior to this unusual wear behavior in nanocrystalline FCC metals.
In ductile metals, sliding contact is often accompanied by severe plastic deformation localized to a small volume of material adjacent to the wear surface. During the initial run-in period, hardness, grain structure and crystallographic texture of the surfaces that come into sliding contact undergo significant changes, culminating in the evolution of subsurface layers with their own characteristic features. Here, a brief overview of our ongoing research on the fundamental phenomena governing the friction-induced recrystallization in single crystal metals, and how these recrystallized structures with nanometer-size grains would in turn influence metallic friction will be presented. We have employed a novel combination of experimental tools (FIB, EBSD and TEM) and an analysis of the critical resolved shear stress (RSS) on the twelve slip systems of the FCC lattice to understand the evolution of these friction-induced structures in single crystal nickel. The later part of the talk deals with the mechanisms of friction in nanocrystalline Ni films. Analyses of friction-induced subsurfaces seem to confirm that the formation of stable ultrafine nanocrystalline layers with 2-10 nm grains changes the deformation mechanism from the traditional dislocation mediated one to that is predominantly controlled by grain boundaries, resulting in significant reductions in the coefficient friction.
The kinetic Monte Carlo method and its variants are powerful tools for modeling materials at the mesoscale, meaning at length and time scales in between the atomic and continuum. We have completed a 3 year LDRD project with the goal of developing a parallel kinetic Monte Carlo capability and applying it to materials modeling problems of interest to Sandia. In this report we give an overview of the methods and algorithms developed, and describe our new open-source code called SPPARKS, for Stochastic Parallel PARticle Kinetic Simulator. We also highlight the development of several Monte Carlo models in SPPARKS for specific materials modeling applications, including grain growth, bubble formation, diffusion in nanoporous materials, defect formation in erbium hydrides, and surface growth and evolution.
Most engineering materials are inherently inhomogeneous in their processing, internal structure, properties, and performance. Their properties are therefore statistical rather than deterministic. These inhomogeneities manifest across multiple length and time scales, leading to variabilities, i.e. statistical distributions, that are necessary to accurately describe each stage in the process-structure-properties hierarchy, and are ultimately the primary source of uncertainty in performance of the material and component. When localized events are responsible for component failure, or when component dimensions are on the order of microstructural features, this uncertainty is particularly important. For ultra-high reliability applications, the uncertainty is compounded by a lack of data describing the extremely rare events. Hands-on testing alone cannot supply sufficient data for this purpose. To date, there is no robust or coherent method to quantify this uncertainty so that it can be used in a predictive manner at the component length scale. The research presented in this report begins to address this lack of capability through a systematic study of the effects of microstructure on the strain concentration at a hole. To achieve the strain concentration, small circular holes (approximately 100 {micro}m in diameter) were machined into brass tensile specimens using a femto-second laser. The brass was annealed at 450 C, 600 C, and 800 C to produce three hole-to-grain size ratios of approximately 7, 1, and 1/7. Electron backscatter diffraction experiments were used to guide the construction of digital microstructures for finite element simulations of uniaxial tension. Digital image correlation experiments were used to qualitatively validate the numerical simulations. The simulations were performed iteratively to generate statistics describing the distribution of plastic strain at the hole in varying microstructural environments. In both the experiments and simulations, the deformation behavior was found to depend strongly on the character of the nearby microstructure.
Fatigue cracking in metals has been and is an area of great importance to the science and technology of structural materials for quite some time. The earliest stages of fatigue crack nucleation and growth are dominated by the microstructure and yet few models are able to predict the fatigue behavior during these stages because of a lack of microstructural physics in the models. This program has developed several new simulation tools to increase the microstructural physics available for fatigue prediction. In addition, this program has extended and developed microscale experimental methods to allow the validation of new microstructural models for deformation in metals. We have applied these developments to fatigue experiments in metals where the microstructure has been intentionally varied.
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Proposed for publication in the International Journal of Plasticity.
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The goal of this study is to model the electrical response of gold plated copper electrical contacts exposed to a mixed flowing gas stream consisting of air containing 10 ppb H{sub 2}S at 30 C and a relative humidity of 70%. This environment accelerates the attack normally observed in a light industrial environment (essentially a simplified version of the Battelle Class 2 environment). Corrosion rates were quantified by measuring the corrosion site density, size distribution, and the macroscopic electrical resistance of the aged surface as a function of exposure time. A pore corrosion numerical model was used to predict both the growth of copper sulfide corrosion product which blooms through defects in the gold layer and the resulting electrical contact resistance of the aged surface. Assumptions about the distribution of defects in the noble metal plating and the mechanism for how corrosion blooms affect electrical contact resistance were needed to complete the numerical model. Comparisons are made to the experimentally observed number density of corrosion sites, the size distribution of corrosion product blooms, and the cumulative probability distribution of the electrical contact resistance. Experimentally, the bloom site density increases as a function of time, whereas the bloom size distribution remains relatively independent of time. These two effects are included in the numerical model by adding a corrosion initiation probability proportional to the surface area along with a probability for bloom-growth extinction proportional to the corrosion product bloom volume. The cumulative probability distribution of electrical resistance becomes skewed as exposure time increases. While the electrical contact resistance increases as a function of time for a fraction of the bloom population, the median value remains relatively unchanged. In order to model this behavior, the resistance calculated for large blooms has been weighted more heavily.
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International Journal of Plasticity
Many conventional continuum approaches to solid mechanics do not address the size sensitivity of deformation to microstructural features like grain boundaries, and are therefore unable to capture much of the experimentally observed behavior of polycrystal deformation. We propose a non-local crystal plasticity model, in which the geometrically necessary dislocation (GND) density is calculated using a non-local integral approach. The model is based on augmented FeFp kinematics, which account for the initial microstructure (primarily grain boundaries) present in the polycrystal. With the augmented kinematics, the initial GND and the evolving GND state are determined in a consistent manner. The expanded kinematics and the non-local crystal plasticity model are used to simulate the tensile behavior in copper polycrystals with different grain sizes ranging from 14 μm to 244 μm. The simulation results show a grain size dependence on the polycrystal's yield strength, which are in good agreement with the experimental data. © 2007 Elsevier Ltd. All rights reserved.
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Proposed for publication in International Journal of Solids and Structures.
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Frictional contact results in surface and subsurface damage that could influence the performance, aging, and reliability of moving mechanical assemblies. Changes in surface roughness, hardness, grain size and texture often occur during the initial run-in period, resulting in the evolution of subsurface layers with characteristic microstructural features that are different from those of the bulk. The objective of this LDRD funded research was to model friction-induced microstructures. In order to accomplish this objective, novel experimental techniques were developed to make friction measurements on single crystal surfaces along specific crystallographic surfaces. Focused ion beam techniques were used to prepare cross-sections of wear scars, and electron backscattered diffraction (EBSD) and TEM to understand the deformation, orientation changes, and recrystallization that are associated with sliding wear. The extent of subsurface deformation and the coefficient of friction were strongly dependent on the crystal orientation. These experimental observations and insights were used to develop and validate phenomenological models. A phenomenological model was developed to elucidate the relationships between deformation, microstructure formation, and friction during wear. The contact mechanics problem was described by well-known mathematical solutions for the stresses during sliding friction. Crystal plasticity theory was used to describe the evolution of dislocation content in the worn material, which in turn provided an estimate of the characteristic microstructural feature size as a function of the imposed strain. An analysis of grain boundary sliding in ultra-fine-grained material provided a mechanism for lubrication, and model predictions of the contribution of grain boundary sliding (relative to plastic deformation) to lubrication were in good qualitative agreement with experimental evidence. A nanomechanics-based approach has been developed for characterizing the mechanical response of wear surfaces. Coatings are often required to mitigate friction and wear. Amongst other factors, plastic deformation of the substrate determines the coating-substrate interface reliability. Finite element modeling has been applied to predict the plastic deformation for the specific case of diamond-like carbon (DLC) coated Ni alloy substrates.
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This report summarizes the work performed as part of a one-year LDRD project, 'Evolutionary Complexity for Protection of Critical Assets.' A brief introduction is given to the topics of genetic algorithms and genetic programming, followed by a discussion of relevant results obtained during the project's research, and finally the conclusions drawn from those results. The focus is on using genetic programming to evolve solutions for relatively simple algebraic equations as a prototype application for evolving complexity in computer codes. The results were obtained using the lil-gp genetic program, a C code for evolving solutions to user-defined problems and functions. These results suggest that genetic programs are not well-suited to evolving complexity for critical asset protection because they cannot efficiently evolve solutions to complex problems, and introduce unacceptable performance penalties into solutions for simple ones.
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