This is the seminar I will present at WCCM conference highlighting our latest research work on incorporating genetic programming to obtain data-driven strength models for complex materials.
Heterogenous materials under shock compression can be expected to reach different shock states throughout the material according to local differences in microstructure and the history of wave propagation. Here, a compact, multiple-beam focusing optic assembly is used with high-speed velocimetry to interrogate the shock response of porous tantalum films prepared through thermal-spray deposition. The distribution of particle velocities across a shocked interface is compared to results obtained using a set of defocused interferometric beams that sampled the shock response over larger areas. The two methods produced velocity distributions along the shock plateau with the same mean, while a larger variance was measured with narrower beams. The finding was replicated using three-dimensional, mesoscopically resolved hydrodynamics simulations of solid tantalum with a pore structure mimicking statistical attributes of the material and accounting for radial divergence of the beams, with agreement across several impact velocities. Accounting for pore morphology in the simulations was found to be necessary for replicating the rise time of the shock plateau. The validated simulations were then used to show that while the average velocity along the shock plateau could be determined accurately with only a few interferometric beams, accurately determining the width of the velocity distribution, which here was approximately Gaussian, required a beam dimension much smaller than the spatial correlation lengthscale of the velocity field, here by a factor of ∼30×, with implications for the study of other porous materials.
SPPARKS is an open-source parallel simulation code for developing and running various kinds of on-lattice Monte Carlo models at the atomic or meso scales. It can be used to study the properties of solid-state materials as well as model their dynamic evolution during processing. The modular nature of the code allows new models and diagnostic computations to be added without modification to its core functionality, including its parallel algorithms. A variety of models for microstructural evolution (grain growth), solid-state diffusion, thin film deposition, and additive manufacturing (AM) processes are included in the code. SPPARKS can also be used to implement grid-based algorithms such as phase field or cellular automata models, to run either in tandem with a Monte Carlo method or independently. For very large systems such as AM applications, the Stitch I/O library is included, which enables only a small portion of a huge system to be resident in memory. In this paper we describe SPPARKS and its parallel algorithms and performance, explain how new Monte Carlo models can be added, and highlight a variety of applications which have been developed within the code.
This report documents details of the microstructure and mechanical properties of -tin (Sn), that is used in the Tri-lab (Los Alamos National Laboratory (LANL), Lawrence Livermore National Laboratory (LLNL), Sandia National Laboratories (SNL)) collaboration project on Multi-phase Tin Strength. We report microstructural features detailing the crystallographic texture and grain morphology of as-received -tin from electron back scatter diffraction (EBSD). Temperature and strain rate dependent mechanical behavior was investigated by multiple compression tests at temperatures of 200K to 400K and strain rates of 0.0001 /s to 100 /s. Tri-lab tin showed significant temperature and strain rate dependent strength with no significant plastic anisotropy. A sample to sample material variation was observed from duplicate compression tests and texture measurements. Compression data was used to calibrate model parameters for temperature and rate dependent strength models, Johnson-Cook (JC), Zerilli-Armstrong (ZA) and Preston-Tonks-Wallace (PTW) strength models.
Crystal plasticity-finite element method (CP-FEM) is now widely used to understand the mechanical response of polycrystalline materials. However, quantitative mesh convergence tests and verification of the necessary size of polycrystalline representative volume elements (RVE) are often overlooked in CP-FEM simulations. Mesh convergence studies in CP-FEM models are more challenging compared to conventional finite element analysis (FEA) as they are not only computationally expensive but also require explicit discretization of individual grains using many finite elements. Resolving each grains within a polycrystalline domain complicates mesh convergence study since mesh convergence is strongly affected by the initial crystal orientations of grains and local loading conditions. In this work, large-scale CP-FEM simulations of single crystals and polycrystals are conducted to study mesh sensitivity in CP-FEM models. Various factors that may affect the mesh convergence in CP-FEM simulations, such as initial textures, hardening models and boundary conditions are investigated. In addition, the total number of grains required to obtain adequate RVE is investigated. This work provides a list of guidelines for mesh convergence and RVE generation in CP-FEM modeling.
A parallel, adaptive overlay grid procedure is proposed for use in generating all-hex meshes for stochastic (SVE) and representative (RVE) volume elements in computational materials modeling. The mesh generation process is outlined including several new advancements such as data filtering to improve mesh quality from voxelated and 3D image sources, improvements to the primal contouring method for constructing material interfaces and pillowing to improve mesh quality at boundaries. We show specific examples in crystal plasticity and syntactic foam modeling that have benefitted from the proposed mesh generation procedure and illustrate results of the procedure with several practical mesh examples.
Crystal plasticity-finite element method (CP-FEM) is now widely used to understand the mechanical response of polycrystalline materials. However, quantitative mesh convergence tests and verification of the necessary size of polycrystalline representative volume elements (RVE) are often overlooked in CP-FEM simulations. Mesh convergence studies in CP-FEM models are more challenging compared to conventional finite element analysis (FEA) as they are not only computationally expensive but also require explicit discretization of individual grains using many finite elements. Resolving each grains within a polycrystalline domain complicates mesh convergence study since mesh convergence is strongly affected by the initial crystal orientations of grains and local loading conditions. In this work, large-scale CP-FEM simulations of single crystals and polycrystals are conducted to study mesh sensitivity in CP-FEM models. Various factors that may affect the mesh convergence in CP-FEM simulations, such as initial textures, hardening models and boundary conditions are investigated. In addition, the total number of grains required to obtain adequate RVE is investigated. Furthermore, this work provides a list of guidelines for mesh convergence and RVE generation in CP-FEM modeling.
When a material that contains precipitates is deformed, the precipitates and the matrix may strain plastically by different amounts causing stresses to build up at the precipitate-matrix interfaces. If premature failure is to be avoided, it is therefore essential to reduce the difference in the plastic strain between the two phases. Here, we conduct nanoscale digital image correlation to measure a new variable that quantifies this plastic strain difference and show how its value can be used to estimate the associated interfacial stresses, which are found to be approximately three times greater in an Fe-Ni2AlTi steel than in the more ductile Ni-based superalloy CMSX-4®. It is then demonstrated that decreasing these stresses significantly improves the ability of the Fe-Ni2AlTi microstructure to deform under tensile loads without loss in strength.
Deformation mechanisms in bcc metals, especially in dynamic regimes, show unusual complexity, which complicates their use in high-reliability applications. Here, we employ novel, high-velocity cylinder impact experiments to explore plastic anisotropy in single crystal specimens under high-rate loading. The bcc tantalum single crystals exhibit unusually high deformation localization and strong plastic anisotropy when compared to polycrystalline samples. Several impact orientations - [100], [110], [111] and [149] -Are characterized over a range of impact velocities to examine orientation-dependent mechanical behavior versus strain rate. Moreover, the anisotropy and localized plastic strain seen in the recovered cylinders exhibit strong axial symmetries which differed according to lattice orientation. Two-, three-, and four-fold symmetries are observed. We propose a simple crystallographic argument, based on the Schmid law, to understand the observed symmetries. These tests are the first to explore the role of single-crystal orientation in Taylor impact tests and they clearly demonstrate the importance of crystallography in high strain rate and temperature deformation regimes. These results provide critical data to allow dramatically improved high-rate crystal plasticity models and will spur renewed interest in the role of crystallography to deformation in dynamics regimes.
Mattsson, Thomas; Flicker, Dawn; Foulk, James W.; Battaile, Corbett C.; Brown, Justin L.; Lane, James M.D.; Lim, Hojun; Arsenlis, Thomas A.; Barton, Nathan R.; Park, Hye-Sook; Swift, Damian C.; Prisbrey, Shon T.; Austin, Ryan; Mcnabb, Dennis P.; Remington, Bruce A.; Prime, Michael B.; III Gray, George T.; Bronkhorst, Curt A.; Shen, Shuh-Rong; Luscher, D.J.; Scharff, Robert J.; Fensin, Sayu J.; Schraad, Mark W.; Dattelbaum, Dana M.; Brown, Staci L.
Ductile rupture in metals is generally a multi-step process of void nucleation, growth, and coalescence. Particle decohesion and particle fracture are generally invoked as the primary microstructural mechanisms for room-temperature void nucleation. However, because high-purity materials also fail by void nucleation and coalescence, other microstructural features must also act as sites for void nucleation. Early studies of void initiation in high-purity materials, which included post-mortem fracture surface characterization using scanning electron microscopy (SEM) and high-voltage electron microscopy (HVEM) and in-situ HVEM observations of fracture, established the presence of dislocation cell walls as void initiation sites in high-purity materials. Direct experimental evidence for this contention was obtained during in-situ HVEM tensile tests of Be single crystals. Voids between 0.2 and 1 μm long appeared suddenly along dislocation cell walls during tensile straining. However, subsequent attempts to replicate these results in other materials, particularly α -Fe single crystals, were unsuccessful because of the small size of the dislocation cells, and these remain the only published in-situ HVEM observations of void nucleation at dislocation cell walls in the absence of a growing macrocrack. Despite this challenge, other approaches to studying void nucleation in high-purity metals also indicate that dislocation cell walls are nucleation sites for voids.
Traditional singularity-based fracture mechanics theories rely on their ability to infer the crack tip driving force (local field) by surveying macroscopic physical magnitudes far from the crack tip (far field). This key capability allows engineers to employ nominal forces or displacements to estimate the potential for stable or unstable crack growth. In the case of heterogeneous or anisotropic materials, traditional fracture approaches are not fully theoretically sound and applications rely on extrapolating methodologies with ad-hoc corrections. This Express Laboratory Directed Research and Development (ELDRD) program employed mesoscale-sensitive finite element simulations to assess the impact of grain size and texture on the crack tip behavior. A dislocation-based crystal plasticity model conveys grain size effects by computing the constraint on dislocation cell structures. We assessed the effects of microstructural variability on multiple displacement-based measurements of the fracture driving forces for crack opening (Mode I) and sliding (Mode II). We also consider multiple microstructural realizations of single phase metals undergoing ductile failure. The results show that grain size and texture affect the applied fracture driving force and can induce a significant Mode II deformation under force and displacement control, which is completely neglected in homogeneous models. A large variability in driving forces upon identical far field applied conditions is attributed to a buffering effects of the microstructure. Furthermore, crack mouth opening displacement is almost insensitive to microstructure, which suggests that experimental measurements using such a magnitude (e.g., plastic hinge model) may underestimate local crack tip driving force variability.
In this work, we develop a tantalum strength model that incorporates effects of temperature, strain rate and pressure. Dislocation kink-pair theory is used to incorporate temperature and strain rate effects while the pressure dependent yield is obtained through the pressure dependent shear modulus. Material constants used in the model are parameterized from tantalum single crystal tests and polycrystalline ramp compression experiments. It is shown that the proposed strength model agrees well with the temperature and strain rate dependent yield obtained from polycrystalline tantalum experiments. Furthermore, the model accurately reproduces the pressure dependent yield stresses up to 250 GPa. The proposed strength model is then used to conduct simulations of a Taylor cylinder impact test and validated with experiments. This approach provides a physically-based multi-scale strength model that is able to predict the plastic deformation of polycrystalline tantalum through a wide range of temperature, strain and pressure regimes.
In this work, a crystal plasticity-finite element (CP-FE) model is used to investigate the effects of microstructural variability at a notch tip in tantalum single crystals and polycrystals. It is shown that at the macroscopic scale, the mechanical response of single crystals is sensitive to the crystallographic orientation while the response of polycrystals shows relatively small susceptibility to it. However, at the microscopic scale, the local stress and strain fields in the vicinity of the crack tip are completely determined by the local crystallographic orientation at the crack tip for both single and polycrystalline specimens with similar mechanical field distributions. Variability in the local metrics used (maximum von Mises stress and equivalent plastic strain at 3% deformation) for 100 different realizations of polycrystals fluctuates by up to a factor of 2-7 depending on the local crystallographic texture. Comparison with experimental data shows that the CP model captures variability in stress-strain response of polycrystals that can be attributed to the grain-scale microstructural variability. This work provides a convenient approach to investigate fluctuations in the mechanical behavior of polycrystalline materials induced by grain morphology and crystallographic orientations.
Two fundamental approximations in macroscale solid-mechanics modeling are (1) the assumption of scale separation in homogenization theory and (2) the use of a macroscopic plasticity material model that represents, in a mean sense, the multitude of inelastic processes occurring at the microscale. With the goal of quantifying the errors induced by these approximations on engineering quantities of interest, we perform a set of direct numerical simulations (DNS) in which polycrystalline microstructures are embedded throughout a macroscale structure. The largest simulations model over 50,000 grains. The microstructure is idealized using a randomly close-packed Voronoi tessellation in which each polyhedral Voronoi cell represents a grain. An face centered cubic crystal-plasticity model is used to model the mechanical response of each grain. The overall grain structure is equiaxed, and each grain is randomly oriented with no overall texture. The detailed results from the DNS simulations are compared to results obtained from conventional macroscale simulations that use homogeneous isotropic plasticity models. The macroscale plasticity models are calibrated using a representative volume element of the idealized microstructure. Ultimately, we envision that DNS modeling will be used to gain new insights into the mechanics of material deformation and failure.
The mechanical properties of materials systems are highly influenced by various features at the microstructural level. The ability to capture these heterogeneities and incorporate them into continuum-scale frameworks of the deformation behavior is considered a key step in the development of complex non-local models of failure. In this study, we present a modeling framework that incorporates physically-based realizations of polycrystalline aggregates from a phase field (PF) model into a crystal plasticity finite element (CP-FE) framework. Simulated annealing via the PF model yields ensembles of materials microstructures with various grain sizes and shapes. With the aid of a novel FE meshing technique, FE discretizations of these microstructures are generated, where several key features, such as conformity to interfaces, and triple junction angles, are preserved. The discretizations are then used in the CP-FE framework to simulate the mechanical response of polycrystalline α-iron. It is shown that the conformal discretization across interfaces reduces artificial stress localization commonly observed in non-conformal FE discretizations. The work presented herein is a first step towards incorporating physically-based microstructures in lieu of the overly simplified representations that are commonly used. In broader terms, the proposed framework provides future avenues to explore bridging models of materials processes, e.g. additive manufacturing and microstructure evolution of multi-phase multi-component systems, into continuum-scale frameworks of the mechanical properties.
The formation of He bubbles in erbium tritides is a significant process in the aging of these materials. Due to the long-standing uncertainty about the initial nucleation process of these bubbles, there is interest in mechanisms that can lead to the localization of He in erbium hydrides. Previous work has been unable to identify nucleation sites in homogeneous erbium hydride. This work builds on the experimental observation that erbium hydrides have nano- scale erbium oxide precipitates due to the high thermodynamic stability of erbium oxide and the ubiquitous presence of oxygen during materials processing. Fundamental DFT calculations indicate that the He is energetically favored in the oxide relative to the bulk hydride. Activation energies for the motion of He in the oxide and at the oxide-hydride interface indicate that trapping is kinetically feasible. A simple kinetic Monte Carlo model is developed that demonstrates the degree of trapping of He as a function of temperature and oxide fraction.
In this report, we present a multi-scale computational model to simulate plastic deformation of tantalum and validating experiments. In atomistic/ dislocation level, dislocation kink- pair theory is used to formulate temperature and strain rate dependent constitutive equations. The kink-pair theory is calibrated to available data from single crystal experiments to produce accurate and convenient constitutive laws. The model is then implemented into a BCC crystal plasticity finite element method (CP-FEM) model to predict temperature and strain rate dependent yield stresses of single and polycrystalline tantalum and compared with existing experimental data from the literature. Furthermore, classical continuum constitutive models describing temperature and strain rate dependent flow behaviors are fit to the yield stresses obtained from the CP-FEM polycrystal predictions. The model is then used to conduct hydro- dynamic simulations of Taylor cylinder impact test and compared with experiments. In order to validate the proposed tantalum CP-FEM model with experiments, we introduce a method for quantitative comparison of CP-FEM models with various experimental techniques. To mitigate the effects of unknown subsurface microstructure, tantalum tensile specimens with a pseudo-two-dimensional grain structure and grain sizes on the order of millimeters are used. A technique combining an electron back scatter diffraction (EBSD) and high resolution digital image correlation (HR-DIC) is used to measure the texture and sub-grain strain fields upon uniaxial tensile loading at various applied strains. Deformed specimens are also analyzed with optical profilometry measurements to obtain out-of- plane strain fields. These high resolution measurements are directly compared with large-scale CP-FEM predictions. This computational method directly links fundamental dislocation physics to plastic deformations in the grain-scale and to the engineering-scale applications. Furthermore, direct and quantitative comparisons between experimental measurements and simulation show that the proposed model accurately captures plasticity in deformation of polycrystalline tantalum.
In order to better incorporate microstructures in continuum scale models, we use a novel finite element (FE) meshing technique to generate three-dimensional polycrystalline aggregates from a phase field grain growth model of grain microstructures. The proposed meshing technique creates hexahedral FE meshes that capture smooth interfaces between adjacent grains. Three dimensional realizations of grain microstructures from the phase field model are used in crystal plasticity-finite element (CP-FE) simulations of polycrystalline a -iron. We show that the interface conformal meshes significantly reduce artificial stress localizations in voxelated meshes that exhibit the so-called "wedding cake" interfaces. This framework provides a direct link between two mesoscale models - phase field and crystal plasticity - and for the first time allows mechanics simulations of polycrystalline materials using three-dimensional hexahedral finite element meshes with realistic topological features.
Abstract In this work, we develop an atomistically informed crystal plasticity finite element (CP-FE) model for body-centered-cubic (BCC) α-Fe that incorporates non-Schmid stress dependent slip with temperature and strain rate effects. Based on recent insights obtained from atomistic simulations, we propose a new constitutive model that combines a generalized non-Schmid yield law with aspects from a line tension (LT) model for describing activation enthalpy required for the motion of dislocation kinks. Atomistic calculations are conducted to quantify the non-Schmid effects while both experimental data and atomistic simulations are used to assess the temperature and strain rate effects. The parameterized constitutive equation is implemented into a BCC CP-FE model to simulate plastic deformation of single and polycrystalline Fe which is compared with experimental data from the literature. This direct comparison demonstrates that the atomistically informed model accurately captures the effects of crystal orientation, temperature and strain rate on the flow behavior of siangle crystal Fe. Furthermore, our proposed CP-FE model exhibits temperature and strain rate dependent flow and yield surfaces in polycrystalline Fe that deviate from conventional CP-FE models based on Schmid's law.
We use insights gained from atomistic simulation to develop an activation enthalpy model for dislocation slip in body-centered cubic iron. Using a classical potential that predicts dislocation core stabilities consistent with ab initio predictions, we quantify the non-Schmid stress-dependent effects of slip. The kink-pair activation enthalpy is evaluated and a model is identified as a function of the general stress state. Our model enlarges the applicability of the classic Kocks activation enthalpy model to materials with non-Schmid behavior.
This report summarizes a project in which the authors sought to develop and deploy: (i) experimental techniques to elucidate the complex, multiscale nature of thermal transport in particle-based materials; and (ii) modeling approaches to address current challenges in predicting performance variability of materials (e.g., identifying and characterizing physical- chemical processes and their couplings across multiple length and time scales, modeling information transfer between scales, and statically and dynamically resolving material structure and its evolution during manufacturing and device performance). Experimentally, several capabilities were successfully advanced. As discussed in Chapter 2 a flash diffusivity capability for measuring homogeneous thermal conductivity of pyrotechnic powders (and beyond) was advanced; leading to enhanced characterization of pyrotechnic materials and properties impacting component development. Chapter 4 describes success for the first time, although preliminary, in resolving thermal fields at speeds and spatial scales relevant to energetic components. Chapter 7 summarizes the first ever (as far as the authors know) application of TDTR to actual pyrotechnic materials. This is the first attempt to actually characterize these materials at the interfacial scale. On the modeling side, new capabilities in image processing of experimental microstructures and direct numerical simulation on complicated structures were advanced (see Chapters 3 and 5). In addition, modeling work described in Chapter 8 led to improved prediction of interface thermal conductance from first principles calculations. Toward the second point, for a model system of packed particles, significant headway was made in implementing numerical algorithms and collecting data to justify the approach in terms of highlighting the phenomena at play and pointing the way forward in developing and informing the kind of modeling approach originally envisioned (see Chapter 6). In both cases much more remains to be accomplished.
Nanocrystalline copper lms were created by both repetitive high-energy pulsed power, to produce material without internal nanotwins; and pulsed laser deposition, to produce nan- otwins. Samples of these lms were indented at ambient (298K) and cryogenic temperatures by immersion in liquid nitrogen (77K) and helium (4K). The indented samples were sectioned through the indented regions and imaged in a scanning electron microscope. Extensive grain growth was observed in the lms that contained nanotwins and were indented cryogenically. The lms that either lacked twins, or were indented under ambient conditions, were found to exhibit no substantial grain growth by visual inspection. Precession transmission elec- tron microscopy was used to con rm these ndings quantitatively, and show that 3 and 7 boundaries proliferate during grain growth, implying that these interface types play a key role in governing the extensive grain growth observed here. Molecular dynamics sim- ulations of the motion of individual grain boundaries demonstrate that speci c classes of boundaries - notably 3 and 7 - exhibit anti- or a-thermal migration, meaning that their mobilities either increase or do not change signi cantly with decreasing temperature. An in-situ cryogenic indentation capability was developed and implemented in a transmission electron microscope. Preliminary results do not show extensive cryogenic grain growth in indented copper lms. This discrepancy could arise from the signi cant di erences in con g- uration and loading of the specimen between the two approaches, and further research and development of this capability is needed.
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.
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.
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.
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.
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.
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.
Thermionic energy conversion in a miniature format shows potential as a viable, high efficiency, micro to macro-scale power source. A microminiature thermionic converter (MTC) with inter-electrode spacings on the order of microns has been prototyped and evaluated at Sandia. The remaining enabling technology is the development of low work function materials and processes that can be integrated into these converters to increase power production at modest temperatures (800 - 1300 K). The electrode materials are not well understood and the electrode thermionic properties are highly sensitive to manufacturing processes. Advanced theoretical, modeling, and fabrication capabilities are required to achieve optimum performance for MTC diodes. This report describes the modeling and fabrication efforts performed to develop micro dispenser cathodes for use in the MTC.
The purpose of microstructural control is to optimize materials properties. To that end, they have developed sophisticated and successful computational models of both microstructural evolution and mechanical response. However, coupling these models to quantitatively predict the properties of a given microstructure poses a challenge. This problem arises because most continuum response models, such as finite element, finite volume, or material point methods, do not incorporate a real length scale. Thus, two self-similar polycrystals have identical mechanical properties regardless of grain size, in conflict with theory and observations. In this project, they took a tiered risk approach to incorporate microstructure and its resultant length scales in mechanical response simulations. Techniques considered include low-risk, low-benefit methods, as well as higher-payoff, higher-risk methods. Methods studied include a constitutive response model with a local length-scale parameter, a power-law hardening rate gradient near grain boundaries, a local Voce hardening law, and strain-gradient polycrystal plasticity. These techniques were validated on a variety of systems for which theoretical analyses and/or experimental data exist. The results may be used to generate improved constitutive models that explicitly depend upon microstructure and to provide insight into microstructural deformation and failure processes. Furthermore, because mechanical state drives microstructural evolution, a strain-enhanced grain growth model was coupled with the mechanical response simulations. The coupled model predicts both properties as a function of microstructure and microstructural development as a function of processing conditions.
This report summarizes materials issues associated with advanced micromachines development at Sandia. The intent of this report is to provide a perspective on the scope of the issues and suggest future technical directions, with a focus on computational materials science. Materials issues in surface micromachining (SMM), Lithographic-Galvanoformung-Abformung (LIGA: lithography, electrodeposition, and molding), and meso-machining technologies were identified. Each individual issue was assessed in four categories: degree of basic understanding; amount of existing experimental data capability of existing models; and, based on the perspective of component developers, the importance of the issue to be resolved. Three broad requirements for micromachines emerged from this process. They are: (1) tribological behavior, including stiction, friction, wear, and the use of surface treatments to control these, (2) mechanical behavior at microscale, including elasticity, plasticity, and the effect of microstructural features on mechanical strength, and (3) degradation of tribological and mechanical properties in normal (including aging), abnormal and hostile environments. Resolving all the identified critical issues requires a significant cooperative and complementary effort between computational and experimental programs. The breadth of this work is greater than any single program is likely to support. This report should serve as a guide to plan micromachines development at Sandia.
Computational materials simulations have traditionally focused on individual phenomena: grain growth, crack propagation, plastic flow, etc. However, real materials behavior results from a complex interplay between phenomena. In this project, the authors explored methods for coupling mesoscale simulations of microstructural evolution and micromechanical response. In one case, massively parallel (MP) simulations for grain evolution and microcracking in alumina stronglink materials were dynamically coupled. In the other, codes for domain coarsening and plastic deformation in CuSi braze alloys were iteratively linked. this program provided the first comparison of two promising ways to integrate mesoscale computer codes. Coupled microstructural/micromechanical codes were applied to experimentally observed microstructures for the first time. In addition to the coupled codes, this project developed a suite of new computational capabilities (PARGRAIN, GLAD, OOF, MPM, polycrystal plasticity, front tracking). The problem of plasticity length scale in continuum calculations was recognized and a solution strategy was developed. The simulations were experimentally validated on stockpile materials.
The incorporation of vacancies, H atoms, and sp{sup 2} bond defects into single-crystal homoepitaxial (100)(2x1)- and(111)-oriented CVD diamond was simulated by atomic-scale kinetic Monte Carlo. Simulations were performed for substrate temperatures from 600 C to 1200 C with 0.4% CH{sub 4} in the feed gas, and for 0.4% to 7% CH{sub 4} feeds with a substrate temperature of 800 C. The concentrations of incorporated H atoms increase with increasing substrate temperature and feed gas composition, and sp{sup 2} bond trapping increases with increasing feed gas composition. Vacancy concentrations are low under all conditions. The ratio of growth rate to H atom concentration is highest around 800-900 C, and the growth rate to sp{sup 2} ratio is maximum around 1% CH{sub 4}, suggesting that these conditions are ideal for economical diamond growth under the simulated conditions.
The microstructural evolution of heavily deformed polycrystalline Cu is simulated by coupling a constitutive model for polycrystal plasticity with the Monte Carlo Potts model for grain growth. The effects of deformation on boundary topology and grain growth kinetics are presented. Heavy deformation leads to dramatic strain-induced boundary migration and subsequent grain fragmentation. Grain growth is accelerated in heavily deformed microstructures. The implications of these results for the thermomechanical fatigue failure of eutectic solder joints are discussed.
Diamond films were grown by chemical deposition of hydrocarbon species in a vapor composed predominantly of hydrogen. The rate constants of the surface reactions and the concentrations of the gas-phase species were used as input to a variable time step Monte Carlo algorithm, which simulates the evolution of the diamond growth surface by tracking the occupancies of surface sites. The results of the combined tight binding and density functional theory quantum mechanical calculations are presented, suggesting that the etching of isolated, monomolecular moieties occurred at an appreciable rate, while etching from larger carbon islands was nor favorable.
Grain growth experiments and simulations exhibit self-similar grain size distributions quite different from that derived via a mean field approach by Hillert [ 1]. To test whether this discrepancy is due to insufficient anneal times, two different two-dimensional grain structures with realistic topologies and Hillert grain size distributions are generated and subjected to grain growth via the Monte Carlo Potts Model (MCPM). In both cases, the observed self-similar grain size distributions deviate from the initial Hillert form and conform instead to that observed in MCPM grain growth simulations that start from a random microstructure. This suggests that the Hillert grain size distribution is not an attractor.
