Viscoplastic self-consistent formulation as generalized material model for solid mechanics applications
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42 ENGINEERING↗
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Results for “Crystal Plasticity Finite Element”
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A cycle-jump acceleration method for the crystal plasticity simulation of high cycle fatigue of the metallic microstructure
For metallic materials, high-cycle fatigue life is sensitive to underlying microstructure features including secondary phases, textures, grains morphology, etc. The traditional, data-based safe-life approaches for modeling fatigue don’t explicitly consider the microstructure and can’t guide study in microstructure modification for improved fatigue property. Crystal plasticity-based simulation provides increased model fidelity at the expense of immense computation time, making it inapplicable for high cycle fatigue. In this work, an acceleration method based on cycle-jump approach (Lesne and Savalle, 1989) was developed for microstructure-based high-cycle FE simulation using crystal plasticity constitutive-model. We report this method demonstrated high efficiency in benchmark tests of various conditions.
36 MATERIALS SCIENCE↗
Modeling Ti–6Al–4V using crystal plasticity, calibrated with multi-scale experiments, to understand the effect of the orientation and morphology of the α and β phases on time dependent cyclic loading
Classically, crystal plasticity modeling has used a range of constitutive equations, in which the incorporation of additional physics-based relationships typically results in additional model parameters. These additional parameters need to be reliably calibrated, which often necessitates the use of a range of experimental data acquired at multiple length scales. In this work, a crystal plasticity based finite element (CPFE) model for a dual-phase Titanium alloy, Ti–6Al–4V, is developed. The α and β phases of the microstructure are explicitly modeled. The model is calibrated using a systematic optimization routine and experimental data that consist of macroscopic stress-strain curves coupled with lattice strains on different crystallographic planes for the two phases. These experimental data were obtained from in situ high energy X-ray diffraction experiments for multiple material pedigrees, with varying crystallographic orientation distribution and β volume fractions. Depending on the thermomechanical-processing route and the heat treatment used to manufacture the alloy, Ti–6Al–4V can exist in a wide number of microstructural forms, which often results in the α and β phases either having well aligned slip systems (following the Burgers orientation relationship (BOR)) or possessing no alignment of the slip systems across the interphase boundary (not following the BOR). In this study, the fully-calibrated CPFE model is used to gain a comprehensive understanding of the deformation behavior of Ti–6Al–4V, specifically, the effect of microstructures that follow the BOR (or not) on time-dependent cyclic loading (including the effects of dwell hold times).
36 MATERIALS SCIENCE↗
Effects of Zn and Ca on the deformation texture evolution of Mg–Zn–Ca alloys at elevated temperatures
This work utilized crystal plasticity simulations and experimental thermo-mechanical processing to examine how Zn and Ca content affects texture evolution in Mg–Zn–Ca alloys during simulated hot rolling. Four different compositions were studied: unalloyed Mg and three Mg alloys of ZX0p50 (Mg- 0.5 wt% Zn- 0.1 wt% Ca), ZX30 (Mg-3 wt% Zn- 0.1 wt% Ca), and ZX31 (Mg-3 wt% Zn- 0.3 wt% Ca). Multi-pass Gleeble experiments simulated hot rolling using plane strain conditions. Unalloyed Mg developed a strong basal texture, while the addition of Zn and Ca significantly weakened the texture in ZX30 and ZX31; this reduction was not seen in ZX0p50. Notably, ZX31 exhibited a split basal texture aligned with the rolling direction. Crystal plasticity simulations revealed that the weaker basal texture in ZX30 and ZX31 resulted from reduced activation of basal and twinning modes compared to unalloyed Mg and Zx0p50. Increased Zn and Ca content raised the ratios of basal to pyramidal critical resolved sheer stress (CRSS) and twin to pyramidal CRSS, enhancing pyramidal slip activity and weakening the basal texture. Extension twinning played a critical role in texture development during the first deformation pass. In unalloyed Mg and ZX0p50, twinning led to a strong basal texture, while ZX30 and ZX31 had weak basal textures that increased only slightly with further deformation. The split basal poles simulated in ZX31 were consistent with the experimental findings, highlighting the interplay between alloy composition and texture evolution.
Crystal plasticity finite element↗
Predicting Failure Using Deep Learning SAND Report
Accurate prediction of ductile failure is critical to Sandia’s NW mission, but the models are computationally heavy. The costs of including high-fidelity physics and mechanics that are germane to the failure mechanisms are often too burdensome for analysts either because of the person-hours it requires to input them or because of the additional computational time, or both. In an effort to deliver analysts a tool for representing these phenomena with minimal impact to their existing workflow, our project sought to develop modern data-driven methods that would add microstructural information to business-as-usual calculations and expedite failure predictions. The goal is a tool that receives as input a structural model with stress and strain fields, as well as a machine-learned model, and output predictions of structural response in time, including failure. As such, our project spent substantial time performing high-fidelity, three-dimensional experiments to elucidate materials mechanisms of void nucleation and evolution. We developed crystal-plasticity finite-element models from the experimental observations to enrich the findings with fields not readily measured. We developed engineering length-scale simulations of replicated test specimens to understand how the engineering fields evolve in the presence of fine-scale defects. Finally, we developed deep learning convolutional neural networks, and graph-based neural networks to encode the findings of the experiments and simulations and make forward predictions in time for structural performance. This project demonstrated the power of data-driven methods for model development, which have the potential to vastly increase both the accuracy and speed of failure predictions. These benefits and the methods necessary to develop them are highlighted in this report. However, many challenges remain to implementing these in real applications, and these are discussed along with potential methods for overcoming them.
97 MATHEMATICS AND COMPUTING↗
Nanoindentation Stress Relaxation to Quantify Dislocation Velocity–Stress Exponent
This work reports a new methodology using indentation stress relaxation to characterize the dislocation velocity–stress exponent. Through the indentation stress relaxation process, the dislocation structure builds up at the rate governed by dislocation velocity, which is a function of the externally applied stress. The relationship between the dislocation velocity and stress can thus be derived from the indentation stress relaxation data of the stress as a function of time. In this study, instrumented nanoindentation stress relaxation experiments were performed on pure aluminum samples, following three different initial displacement rates of 100, 400, and 800 nm/s. Based on the scaling properties of dislocation kinetics, the data were interpreted to derive a dislocation velocity–stress exponent of 2.5 ± 0.5 for room-temperature aluminum. Crystal plasticity finite-element simulations were performed to illustrate the sensitivity of the proposed nanoindentation stress relaxation methodology to the dislocation velocity–stress exponent value.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Thermodynamic theory of crystal plasticity: Formulation and application to polycrystal fcc copper
We present a thermodynamic description of crystal plasticity. Our formulation is based on the Langer-Bouchbinder-Lookman thermodynamic dislocation theory (TDT), which asserts the fundamental importance of an effective temperature that describes the state of configurational disorder and therefore the dislocation density of the crystalline material. We extend the TDT description from isotropic plasticity to crystal plasticity with many slip systems. Finite-element simulations show favourable comparison with experiments on polycrystal fcc copper under uniaxial compression, tension, and simple shear. Here, the thermodynamic theory of crystal plasticity thus provides a thermodynamically consistent and physically rigorous description of dislocation motion in crystals. We also discuss new insights about the interaction of dislocations belonging to different slip systems.
36 MATERIALS SCIENCE↗
Multi-Scale Computational Modeling of Two-Phased Metal Using GMC Method
A multi-scale computational model for determining plastic behavior in two-phased CMSX-4 Ni-based superalloys is developed on a finite element analysis (FEA) framework employing crystal plasticity constitutive model that can capture the microstructural scale stress field. The generalized method of cells (GMC) micromechanics model is used for homogenizing the local field quantities. At first, GMC as stand-alone is validated by analyzing a repeating unit cell (RUC) as a two-phased sample with 72.9% volume fraction of gamma'-precipitate in the gamma-matrix phase and comparing the results with those predicted by finite element analysis (FEA) models incorporating the same crystal plasticity constitutive model. The global stress-strain behavior and the local field quantity distributions predicted by GMC demonstrated good agreement with FEA. High computational saving, at the expense of some accuracy in the components of local tensor field quantities, was obtained with GMC. Finally, the capability of the developed multi-scale model linking FEA and GMC to solve real life sized structures is demonstrated by analyzing an engine disc component and determining the microstructural scale details of the field quantities.
nickel alloys↗
Modeling the non-Schmid crystallographic slip in MAX phases
We present a crystal plasticity constitutive relation for the description of experimentally observed non-Schmid crystallographic slip in a class of ternary carbides and nitrides commonly referred to as MAX phases. In the constitutive relation, we assume that the evolution of the slip system strength in MAX phases has two components – a classical component that depends on the Taylor cumulative shear strain and a non-Schmid component that depends on the stress normal to the slip plane. The non-Schmid crystal plasticity constitutive relation is then used to carry out finite element simulations of micropillar compression of single crystals of two MAX phases, Ti 2 AlC and Ti 3 AlC 2 . The finite element simulations not only quantitatively predict the stress – strain response of a wide range of crystallographic orientations of the micropillars but also rationalize the non-uniform deformation and the deformed shape of the micropillars observed in the experiments for the two materials. As a result, parametric studies are also carried out to quantify the role of the non-Schmid effect and understand the effects of key experimental parameters on the stress – strain response of the micropillars of the two MAX phases.
36 MATERIALS SCIENCE↗
Deformation heterogeneity and intragrain lattice misorientation in high strength contrast, dual-phase bridgmanite/periclase
A bridgmanite/periclase aggregate is investigated due to its prevalence in the Earth’s lower mantle and its importance for understanding geodynamic processes. In dual-phase polycrystalline aggregates, both strength contrast between phases and single crystal elastic and plastic anisotropy are known to influence the development of intragrain misorientation, and the evolution of crystallographic texture. In this study, full-field crystal plasticity simulations are performed with a finite element solution method, and applied to an aggregate of a mechanically strong orthorhombic phase with perovskite structure (bridgmanite, MgSiO 3 ), and a relatively weaker cubic phase (periclase, MgO). The relative strengths of the phases are parameterized to elucidate the effect that strength contrast has on texture evolution and single-phase simulations are performed for comparison. Altogether, results indicate that the relative strength between the two phases influences the development of plasticity, and the overall texture evolution. Results are discussed in light of trends related to the evolution of plasticity and misorientation in the aggregate, and their dependence on both the strength contrast between phases as well as the spatial distribution of grains and phases.
36 MATERIALS SCIENCE↗
Predicting extreme anisotropy and shape variations in impact testing of tantalum single crystals
We report recent Taylor cylinder impact tests carried out for Ta single crystals showed strong variations in dimensional changes for different crystallographic directions aligned with the cylindrical axis. In order to capture the effect of crystallography on the deformation characteristics and final shapes of the impacted cylinders, a single crystal material subroutine is adapted and embedded in the solid mechanics/dynamics Finite Element solver Abaqus to simulate the aforementioned single crystal Ta Taylor impact experiments. Details of the coupled model implementation, and insights on the role played by single crystal anisotropic flow on the deformation behavior across a broad range of strain rates and temperatures for different single crystal orientations are presented and discussed. We demonstrate the predictive capability of the adopted crystal plasticity model to capture the significant role played by crystal orientation-induced anisotropy, as well as strain hardening and adiabatic heating, on the dynamic deformation response of crystalline materials. This re-emphasizes the need of microstructure-aware models to improve the accuracy of simulations for high-consequence engineering design.
36 MATERIALS SCIENCE↗
Coupled phase field damage and crystal plasticity analysis of intragranular fracture: The role of crystallographic orientation and voids
Damage evolution in engineering metal alloys at the grain scale exhibits significant microstructural heterogeneity and anisotropy. These heterogeneities create local hotspots for stress and strain localization, leading to void nucleation. Crystal orientation influences the active slip systems around voids, affecting lattice rotation and potentially forming discontinuities. At low triaxiality, voids may change shape due to lower stress, rotation, elongation, and coalescence. At high triaxiality, the correlation between crystal orientation and void growth rate becomes stronger, resembling the behavior observed in isolated single crystals. Therefore, understanding the effects of crystal orientation, heterogeneous strain, and defect evolution is crucial for single crystal fracture characterization. Here, in this work, a coupled phase-field damage (PFD) and crystal plasticity (CP) model is implemented within a finite element framework to analyze crystal deformation and failure. The CP method employs a dislocation density-based constitutive model, while intragranular failure is modeled using an anisotropic PFD method. The PFD model considers both the stored energy due to elastic stretching and the energy release due to defect formation and crack formation. A single crystal Al2219 with an intracrystalline spherical void is chosen to analyze fracture. The study finds that fracture propagation is strongly correlated with crystal orientations. This coupled CP-PFD model provides accurate failure prediction in crystalline materials by incorporating the effects of crystal orientations and existing voids. This study demonstrates how the local microstructure and defects influence plastic deformation and failure mechanisms in metal alloys.
Aluminum alloy↗
Fundamental Mechanisms Controlling Dislocation-Obstacle Interactions in Metals and Alloys
This project combined modeling and experimentation across micro-meso-macro length scales to investigate the role of long-range internal stresses associated with obstacles and dislocation populations, in the deformation response of cubic metals. In addition to unique insights into the physical behavior of metals, advances were also made in modeling techniques and tools at the meso and atomistic level, and new characterization methods were developed and disseminated to the scientific community. Twenty eight journal papers, two dissertations and three theses have served as vehicles to share the gained scientific knowledge, and two opensource software packages have been developed, maintained and distributed. Additional publications are in progress.
36 MATERIALS SCIENCE↗
Modeling inter- and intra-granular dislocation transport using crystal plasticity
Here, this work presents the development of a crystal plasticity material model that incorporates both dislocation transport within grains and dislocation transfer across grain boundaries. This model has been implemented in the open-source finite element code MOOSE. In addition, a novel geometry-based criterion is developed to determine the direction of dislocation transfer across grain boundaries. The transfer criterion incorporates the geometric features of the grain boundary, such as the grain boundary plane normal, and its misorientation, which is accounted for through the orientation of the incoming and outgoing slip systems. The model is tested with several cases, including a copper single crystal, bi-crystal, and polycrystal. The development of the transfer criterion, implementation of the model, and its application to these test cases are discussed in detail.
36 MATERIALS SCIENCE↗
Resolved shear stress intensity coefficient and fatigue crack growth in large crystals
Fatigue crack growth in large grain Al alloy was studied. Fatigue crack growth is caused primarily by shear decohesion due to dislocation motion in the crack tip region. The crack paths in the large crystals are very irregular and zigzag. The crack planes are often inclined to the loading axis both in the inplane direction and the thickness direction. The stress intensity factors of such inclined cracks are approximated from the two dimensional finite element calculations. The plastic deformation in a large crystal is highly anisotropic, and dislocation motion in such crystals are driven by the resolved shear stress. The resolved shear stress intensity coefficient in a crack solid, RSSIC, is defined, and the coefficients for the slip systems at a crack tip are evaluated from the calculated stress intensity factors. The orientations of the crack planes are closely related to the slip planes with the high RSSIC values. If a single slip system has a much higher RSSIC than all the others, the crack will follow the slip plane, and the slip plane becomes the crack plane. If two or more slip systems have a high RSSIC, the crack plane is the result of the decohesion processes on these active slip planes.
Chen, QI↗
A mesoscale crystal plasticity model to predict room-temperature deformation and martensitic transformation of high-strength Quenching and Partitioning (Q&P) Steels and validation with synchrotron X-ray diffraction
Renowned for the superior mechanical properties and adeptness at cold-forming, Quenching and Partitioning (QP) steels have gained prominence as a promising candidate material in fabricating safety-critical components in various industries. The pertinent research on QP steels focus on the martensitic transformation of the Retained Austenite (RA) phase during cold-forming, a crucial mechanism that substantially influences the overall strength and ductility of QP steels. The austenite stability and transformation rate heavily rely on the local strain path and the initial microstructure, which is challenging for analytical prediction. In this paper, a mesoscale model is developed to capture the deformation and transformation kinetics of QP steels inside the microstructure. The model integrates the detailed explicit microstructure, acquired from characterization experiments, into a high-resolution finite element (FE) mesh. It distinctly model the deformation and interaction between the various phases and the effect on the transformation of RA. The model is validated with high energy X-ray diffraction (HEXRD) data, and shows excellent capability in predicting the asymmetric stress-strain behavior under uniaxial tension and compression, as well as the martensitic transformation rate. The model is used to investigate the strain and load partitioning effect of surrounding matrix to the transformation of RA, offering insights into the complex behavior of QP980 and facilitates further material development.
36 MATERIALS SCIENCE↗
Benchmarking Microscale Ductility Measurements (Final Report of the Project DE-NE0008799)
Conventional macroscale experimentation is generally considered to be straightforward with few limitations. Conversely, micro/nanoscale experimentation presents numerous challenges in loading device design, sample preparation and handling, as well as accurate understanding of grain size and local texture effects on recorded measurements. Despite these challenges, nanopillar compression, MEMs based micro-tension, and nanoindentation approaches have been able to provide fundamental contributions to the understanding of material behavior at small lengthscales. However, the overarching shortcoming of these micro/nanoscale experimentation approaches, is the inability to directly translate measurements evaluated at the nm and µm length scales (e.g., hardness) to macroscale tensile material behavior (i.e., elastic modulus, yield strength, and ductility). The objectives of the proposed study are, 1) to establish best practices for obtaining tensile microscale ductility measurements, and 2) to validate methodologies to for comparing microscale ductility measurements to macroscale ductility measurements. In order to achieve these objectives, a multi-lengthscale, multi-temperature testing protocol and simulation framework are executed first on copper as a model material to validate the following approach, and second on reactor grade Zircaloy-2. Experiments are conducted on specimens extracted from the same test piece to ensure nominally identical grain size and texture from specimens to specimen. Motivated by the need to isolate the contribution of size-effects on obtained mechanical property measurements, specimens are manufactured with thicknesses at the micro- (1-10 µm), meso- (10-100's µm), and macroscales (sub-sized ASTM E8). In-situ full-field deformation techniques (scanning electron microscopy (SEM) grid methods and optical DIC) are incorporated into testing at each specimen length-scale to capture plasticity localization and evolution. Experimental testing for all specimens is conducted at both room temperature and elevated temperatures to probe the role of thermal activation on plastic deformation accommodation processes. Simulation efforts focus on examining the mechanical behavior of microscale specimens using a finite element approach with explicitly resolved grain morphologies, and an embedded crystal plasticity model. The cost-efficient implementation method allows for the modeling of a statistically significant number of both real (i.e., digital twin) and generated microstructures to obtain an understanding of the interrelationships between specimen microstructure and geometric variables (grain size, texture, specimen geometry, etc.) on microscale mechanical behavior.
36 MATERIALS SCIENCE↗