Uncertainty quantification (UQ) plays a major role in verification and validation for computational engineering models and simulations, and establishes trust in the predictive capability of computational models. In the materials science and engineering context, where the process-structure-property-performance linkage is well known to be the only road mapping from manufacturing to engineering performance, numerous integrated computational materials engineering (ICME) models have been developed across a wide spectrum of length-scales and time-scales to relieve the burden of resource-intensive experiments. Within the structure-property linkage, crystal plasticity finite element method (CPFEM) models have been widely used since they are one of a few ICME toolboxes that allows numerical predictions, providing the bridge from microstructure to materials properties and performances. Several constitutive models have been proposed in the last few decades to capture the mechanics and plasticity behavior of materials. While some UQ studies have been performed, the robustness and uncertainty of these constitutive models have not been rigorously established. In this work, we apply a stochastic collocation (SC) method, which is mathematically rigorous and has been widely used in the field of UQ, to quantify the uncertainty of three most commonly used constitutive models in CPFEM, namely phenomenological models (with and without twinning), and dislocation-density-based constitutive models, for three different types of crystal structures, namely face-centered cubic (fcc) copper (Cu), body-centered cubic (bcc) tungsten (W), and hexagonal close packing (hcp) magnesium (Mg). Our numerical results not only quantify the uncertainty of these constitutive models in stress-strain curve, but also analyze the global sensitivity of the underlying constitutive parameters with respect to the initial yield behavior, which may be helpful for robust constitutive model calibration works in the future.
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.
Low friction is demonstrated with pure polycrystalline tantalum sliding contacts in both molecular dynamics simulations and ultrahigh vacuum experiments. This phenomenon is shown to be correlated with deformation occurring primarily through grain boundary sliding and can be explained using a recently developed predictive model for the shear strength of metals. Specifically, low friction is associated with grain sizes at the interface being smaller than a critical, material-dependent value, where a crossover from dislocation mediated plasticity to grain-boundary sliding occurs. Low friction is therefore associated with inverse Hall-Petch behavior and softening of the interface. Direct quantitative comparisons between experiments and atomistic calculations are used to illustrate the accuracy of the predictions.
Metal additive manufacturing (AM) allows for the freeform creation of complex parts. However, AM microstructures are highly sensitive to the process parameters used. Resulting microstructures vary significantly from typical metal alloys in grain morphology distributions, defect populations and crystallographic texture. AM microstructures are often anisotropic and possess three-dimensional features. These microstructural features determine the mechanical properties of AM parts. Here, we reproduce three “canonical” AM microstructures from the literature and investigate their mechanical responses. Stochastic volume elements are generated with a kinetic Monte Carlo process simulation. A crystal plasticity-finite element model is then used to simulate plastic deformation of the AM microstructures and a reference equiaxed microstructure. Results demonstrate that AM microstructures possess significant variability in strength and plastic anisotropy compared with conventional equiaxed microstructures.
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.
In this study, a multiscale electron microscopy-based approach is applied to understanding how different aspects of the microstructure in a notched AA6061-T6, including grain boundaries, triple junctions, and intermetallic particles, promote localized dislocation accumulation as a function of applied tensile strain and depth from the sample surface. Experimental measurements and crystal plasticity simulations of dislocation distributions as a function of distance from specified microstructural features both showed preferential dislocation accumulation near intermetallic particles relative to grain boundaries and triple junctions. High resolution electron backscatter diffraction and site-specific transmission electron microscopy characterization showed that high levels of dislocation accumulation near intermetallic particles led to the development of an ultrafine sub-grain microstructure, indicative of a much higher level of local plasticity than predicted from the coarser measurements and simulations. In addition, high resolution measurements in front of a crack tip suggested a compounding influence of intermetallic particles and grain boundaries in dictating crack propagation pathways.
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.
Material strength and moduli can be determined from dynamic high-pressure ramp-release experiments using an indirect method of Lagrangian wave profile analysis of surface velocities. This method, termed self-consistent Lagrangian analysis (SCLA), has been difficult to calibrate and corroborate with other experimental methods. Using nonequilibrium molecular dynamics, we validate the SCLA technique by demonstrating that it accurately predicts the same bulk modulus, shear modulus, and strength as those calculated from the full stress tensor data, especially where strain rate induced relaxation effects and wave attenuation are small. We show here that introducing a hold in the loading profile at peak pressure gives improved accuracy in the shear moduli and relaxation-adjusted strength by reducing the effect of wave attenuation. When rate-dependent effects coupled with wave attenuation are large, we find that Lagrangian analysis overpredicts the maximum unload wavespeed, leading to increased error in the measured dynamic shear modulus. These simulations provide insight into the definition of dynamic strength, as well as a plausible explanation for experimental disagreement in reported dynamic strength values.
The heterogeneity in mechanical fields introduced by microstructure plays a critical role in the localization of deformation. To resolve this incipient stage of failure, it is therefore necessary to incorporate microstructure with sufficient resolution. On the other hand, computational limitations make it infeasible to represent the microstructure in the entire domain at the component scale. In this study, the authors demonstrate the use of concurrent multiscale modeling to incorporate explicit, finely resolved microstructure in a critical region while resolving the smoother mechanical fields outside this region with a coarser discretization to limit computational cost. The microstructural physics is modeled with a high-fidelity model that incorporates anisotropic crystal elasticity and rate-dependent crystal plasticity to simulate the behavior of a stainless steel alloy. The component-scale material behavior is treated with a lower fidelity model incorporating isotropic linear elasticity and rate-independent J2 plasticity. The microstructural and component scale subdomains are modeled concurrently, with coupling via the Schwarz alternating method, which solves boundary-value problems in each subdomain separately and transfers solution information between subdomains via Dirichlet boundary conditions. In this study, the framework is applied to model incipient localization in tensile specimens during necking.
Mattsson, Thomas M.; Flicker, Dawn G.; Benage, John F.; Battaile, Corbett C.; Brown, Justin L.; Lane, James M.; Lim, Hojun L.; Arsenlis, Thomas A.; Barton, Nathan R.; Park, Hye-Sook P.; Swift, Damian C.; Prisbrey, Shon T.; Austin, Ryan A.; McNabb, Dennis P.; Remington, Bruce A.; Prime, Michael B.; Gray, George T.; Bronkhorst, Curt B.; Shen, Shuh-Rong S.; Luscher, D.J.L.; Scharff, Robert J.; Fensin, Sayu J.; Schraad, Mark W.; Dattelbaum, Dana M.; Brown, Staci L.
The heterogeneity in mechanical fields introduced by microstructure plays a critical role in the localization of deformation. To resolve this incipient stage of failure, it is therefore necessary to incorporate microstructure with sufficient resolution. On the other hand, computational limitations make it infeasible to represent the microstructure in the entire domain at the component scale. In this study, the authors demonstrate the use of concurrent multi- scale modeling to incorporate explicit, finely resolved microstructure in a critical region while resolving the smoother mechanical fields outside this region with a coarser discretization to limit computational cost. The microstructural physics is modeled with a high-fidelity model that incorporates anisotropic crystal elasticity and rate-dependent crystal plasticity to simulate the behavior of a stainless steel alloy. The component-scale material behavior is treated with a lower fidelity model incorporating isotropic linear elasticity and rate-independent J 2 plas- ticity. The microstructural and component scale subdomains are modeled concurrently, with coupling via the Schwarz alternating method, which solves boundary-value problems in each subdomain separately and transfers solution information between subdomains via Dirichlet boundary conditions. Beyond cases studies in concurrent multiscale, we explore progress in crystal plastic- ity through modular designs, solution methodologies, model verification, and extensions to Sierra/SM and manycore applications. Advances in conformal microstructures having both hexahedral and tetrahedral workflows in Sculpt and Cubit are highlighted. A structure-property case study in two-phase metallic composites applies the Materials Knowledge System to local metrics for void evolution. Discussion includes lessons learned, future work, and a summary of funded efforts and proposed work. Finally, an appendix illustrates the need for two-way coupling through a single degree of freedom.
Wrought Al-Ge-Si alloys were designed and produced to ensure dislocation bypass strengthening (“hard pin” precipitates) without significant precipitate cutting/shearing (“soft pin” precipitates). These unusual alloys were processed from the melt, solution heat treated and aged. Aging curves at temperatures of 120, 160, 200 and 240 °C were established and the corresponding precipitate spacings, sizes, and morphologies were measured using TEM. The role of non-shearable precipitates in determining the magnitude of Bauschinger was revealed using large-strain compression/tension tests. The effect of precipitates on the Bauschinger response was stronger than that of grain boundaries, even for these dilute alloys. The Bauschinger effect increases dramatically from the under-aged to the peak aged condition and remains constant or decreases slowly through over-aging. This is consistent with reported behavior for Al-Cu alloys (maximum effect at peak aging) and for other Al alloys (increasing through over-aging) such as Al-Cu-Li, Al 6111, Al 2524, and Al 6013. The Al-Ge-Si alloy response was simulated with three microstructural models, including a novel SD (SuperDislocation) model, to reveal the origins of the Bauschinger effect in dilute precipitation-hardened / bypass alloys. The dominant mechanism is related to the elastic interaction of polarized dislocation arrays (generalized pile-up or bow-out model) at precipitate obstacles. Such effects are ignored in continuum and crystal plasticity models.
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.
We have conducted molecular dynamics (MD) simulations of quasi-isentropic ramp-wave compression to very high pressures over a range of strain rates from 1011 down to 108 1/s. Using scaling methods, we collapse wave profiles from various strain rates to a master profile curve, which shows deviations when material response is strain-rate dependent. Thus, we can show with precision where, and how, strain-rate dependence affects the ramp wave. We find that strain rate affects the stress-strain material response most dramatically at strains below 20%, and that above 30% strain the material response is largely independent of strain rate. We show good overall agreement with experimental stress-strain curves up to approximately 30% strain, above which simulated response is somewhat too stiff. We postulate that this could be due to our interatomic potential or to differences in grain structure and/or size between simulation and experiment. Strength is directly measured from per-atom stress tensor and shows significantly enhanced elastic response at the highest strain rates. This enhanced elastic response is less pronounced at higher pressures and at lower strain rates.
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.
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.
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.