Anisotropic power diagrams for polycrystal modelling: Efficient generation of curved grains via optimal transport
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Buze, M. (ORCID:000000018617974X)↗
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Data-Driven Constitutive Model for the Inelastic Response of Metals: Application to 316H Steel
Here, predictions of the mechanical response of structural elements are conditioned by the accuracy of constitutive models used at the engineering length-scale. In this regard, a prospect of mechanistic crystal-plasticity-based constitutive models is that they could be used for extrapolation beyond regimes in which they are calibrated. However, their use for assessing the performance of a component is computationally onerous. To address this limitation, a new approach is proposed whereby a surrogate constitutive model (SM) of the inelastic response of 316H steel is derived from a mechanistic crystal plasticity-based polycrystal model tracking the evolution of dislocation densities on all slip systems. The latter is used to generate a database of the expected plastic response and dislocation content evolution associated with several instances of creep loading. From the database, a SM is developed. It relies on the use of orthogonal polynomial regression to describe the evolution of the dislocation content. The SM is then validated against predictions of the dead load creep response given by the polycrystal model across a range of temperatures and stresses. When the SM is used to predict the response of 316H during complex non monotonic loading, extrapolating to new loading conditions, it is found that predictions compare particularly well against those from the physics-based polycrystal model.
36 MATERIALS SCIENCE↗
Sensitivity Study of Multiscale and Phenomenological Elasto-Viscoplastic Grade 91 Material Models for Component-Scale Response
Many advanced nuclear reactor concepts currently being developed are targeting higher operating temperatures relative to the current fleet of light water nuclear reactors, for efficiency gains and other operational considerations. The design of high temperature structural components with reliable long-term operational performance will depend on material models that accurately capture the inelastic deformation mechanisms active in these environments. In this work, we perform a detailed parameter sensitivity analysis of two unified elasto-viscoplastic Grade 91 material models capable of capturing long term high temperature creep deformation. The first model is a phenomelogical material model from the Nuclear Engineering Material Library (NEML) developed at Argonne National Lab. The NEML model parameters and their uncertainty were fit to a range of Grade 91 experimental data using Bayesian Markov Chain Monte Carlo analysis. The second model is a LAROMance data-driven surrogate material model developed at Los Alamos National Lab. The LAROMance model is fit to a large database of responses produced by a mechanistic crystal plasticity based polycrystal model. Parameters for the LAROMance surrogate material model reflect the pedigree of the Grade 91 microstructure. Both material models have been integrated into the Grizzly code, based on the open-source MOOSE multiphysics simulation framework, to simulate both the progression of aging mechanisms and the effects of that aging on nuclear power plant structures. Grizzly is used analyze a three-dimensional Grade 91 piping system to compare the long-term inelastic response predicted by these two fundamentally different models and assess the sensitivity of the material model input parameters on this quantity of interest.
42 ENGINEERING↗
Size effect in stainless steel thin wires under tension
Miniaturization of modern devices drives the exploration into how materials behave in small dimensions. However, the mechanical behaviors of micro-scale specimens under varied loading conditions are still challenging to characterize and predict. In this work, specimen size-dependent weakening effect was experimentally revealed in 316L stainless steel thin wires under tension with wire diameter decreasing from 200 μm down to 61 μm. The underlying mechanisms were primarily associated with surface grain softening and strain localization, which were largely dependent on the number of grains across wire diameter. Through an analog composite model with surface and interior grains that follows the Hall-Petch relation, the extent of surface grain softening was found to coincide with the flow stress reduction due to lack of boundary strengthening. Further using elasto-plastic self-consistent polycrystal modeling, the stress-strain behaviors of interior and surface grains were well described in analogy to those of bulk materials with similar-size grains and extremely large grains, respectively. Subsequently, the analog composite model well simulated the specimen size-dependent weakening effect under tension. This article provided more insights into the size effect exploration and proposed a practical model for describing size-dependent mechanical behaviors of small-scale materials to be applied to miniaturized devices.
316L stainless steel↗
The effects of free surfaces on deformation twinning in HCP metals
Deformation twinning is a predominant mode of plastic deformation for hexagonal close packed metals, like Mg and Ti. The heterogenous microstructure and the local stresses associated with twinning play a key role in their mechanical response and fracture. Surface analyses, like electron microscopy, are frequently employed to spatially map microstructure and micromechanical fields in order to study twinning behavior. However, these measurements are inherently influenced by the vicinity of the free surface. In this work, an elasto-visco-plastic fast-Fourier-transform (EVP-FFT) polycrystal modeling approach is employed to investigate the effects of free surfaces on twin development before and after loading. We compare calculated micromechanical fields on free surfaces with those calculated inside the bulk and, in some cases, experimental surface measurements. The results indicate that the creation of free surfaces can promote twin propagation and growth and can influence twin morphology by causing a twin lamella to become larger, more blunted and irregular. The structure along the twin boundaries are also affected, due to the higher driving stresses that extend prismatic-basal and basal-prismatic facets. Furthermore, free surfaces invoke different slip activities in the twin and the surrounding parent crystal by enhancing basal, prismatic and pyramidal slip in some localized regions, while reducing slip in others. We demonstrate that the simulated free-surface effects lead to better qualitative and quantitative agreement with experimental measurements from scanning electron microscopy and digital image correlation.
36 MATERIALS SCIENCE↗
Complete development of LAROMance-type surrogate models for Zircaloy, as well as initial integration and testing in MOOSE, which addresses industry needs for licensing advanced LWR fuels
This milestone report details the progress in the constitutive surrogate modeling framework for Zircaloy’s mechanical behavior under extreme conditions, within the NEAMS program throughout the U.S. fiscal year 2024 (FY24). The presented work expands on the spectral based mechanical solver and the mechanistic material model for Zircaloy, which were introduced in the NEAMS program during FY22 and detailed in the previous fiscal year (FY23). As part of the NEAMS program, the current effort described in this report focused on the development of a novel viscplastic (creep) surrogate for the mechanistic, polycrystal-based model. To this end, the work was subdivided into two interdependent components related to the necessary improvements to the LApx constitutive model and algorithm and, to the development and use of a surrogate model.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Mechanistic Modeling of Creep and Aging for Time Extrapolation in LPBF 316 SS - LANL
A polycrystal constitutive model was extended to quantify the effects heterogeneity in the microstructure, porosity, and internal stresses on the mechanical response (creep, tensile) of 316H steel processed by additive manufacturing. The starting point is a recently developed and fully calibrated advanced microstructuresensitive mechanistic constitutive model fit to literature data pertaining to conventionally processed steels. The model is embedded within the full field fast Fourier transform framework (LApx) and several hundred simulations were performed. Synthetic microstructures with different grain aspect ratios were generated using the Neper package to study the role of grain morphology on the mechanical responses. The effect of initial cell interior dislocation density, cell-wall density, precipitate content, porosity, and internal stresses on creep rates are quantified for different polycrystalline microstructures. The study allowed to prospectively quantify the role of distinct features of the microstructure on the mechanical response under tension and creep loading scenarios. Critically it is found that minor anisotropies in the tensile response of samples, emanating from the aspect ratio of grains correlated into significant differences in creep rate as a function of loading directions. The study also allows to identify initial microstructure porosities below which the materials response only moderately degraded by the initial microstructure.
36 MATERIALS SCIENCE↗
Using machine-learning to understand complex microstructural effects on the mechanical behavior of Ti-6Al-4V alloys
Structural materials properties are highly dependent on their microstructure. Their microstructure is in turn affected by multiple fabrication and thermo-mechanical treatment parameters, all of which conform a highly-dimensional parametric space with often hidden correlations that are difficult to extract by experimentation alone. This is particularly true for alloys of the dual-phase Ti-6Al-4V family, with their greatly complex and rich microstructures, which combine several intrinsic length scales associated with multiple grain and subgrain structures, grains with different crystal lattices (α and β phases), and complex chemistry. In this paper we use a comprehensive set of machine learning techniques to develop predictive tools relating the yield strength and hardening rate of these alloys to a set of input parameters covering extensive ranges. The data generator is a finite-element crystal plasticity model for polycrystal deformation that takes into account slip anisotropy and employs standard dislocation evolution models for the α and β phases of Ti-based alloys. Our dataset includes over two thousand independent simulations and is used to train the machine learning models, which are then used to establish correlations between microstructural parameters and the alloys’ mechanical response. Our results point to the most influential parameters affecting yield strength and hardening rate, information that can then be used to guide experimental synthesis and characterization efforts to save time and resources.
36 MATERIALS SCIENCE↗
Analytic model of dislocation density evolution in fcc polycrystals accounting for dislocation generation, storage, and dynamic recovery mechanisms
Here, an analytic model of the evolution of dislocation density in fcc polycrystals is described. The evolution equations approximately account for most known dislocation storage, dynamic recovery, and dislocation generation mechanisms in fcc polycrystals. Specifically, the model incorporates network (forest) and grain boundary storage, mobile-network and mobile–mobile annihilation, screw–screw annihilation via athermal and thermal single cross-slip, generation by double cross-slip (Koehler mechanism, including dipole formation), Frank-Read sources, grain boundary nucleation, and mobile–immobile dislocation nucleation due to shock loading. Single cross-slip is assumed to proceed through the Friedel–Escaig (FE) mechanism; the corresponding activation energy is calculated using a modified FE model. The activation energy for double cross-slip is calculated for the first time by extending the FE model. The exact evolution equations are integro-differential equations, and as such are difficult to implement in a code; hence, the evolution equations are simplified by making several approximations. Preliminary results on copper are presented, including comparisons to experimental data.
36 MATERIALS SCIENCE↗
An FFT-based approach for Bloch wave analysis: application to polycrystals
A method based on the Fast Fourier Transform is proposed to obtain the dispersion relation of acoustic waves in heterogeneous periodic media with arbitrary microstructures. The microstructure is explicitly considered using a voxelized Representative Volume Element (RVE). The dispersion diagram is obtained solving an eigenvalue problem for Bloch waves in Fourier space. To this aim, two linear operators representing stiffness and mass are defined through the use of differential operators in Fourier space. The smallest eigenvalues are obtained using the implicitly restarted Lanczos and the subspace iteration methods, and the required inverse of the stiffness operator is done using the conjugate gradient with a preconditioner. The method is used to study the propagation of acoustic waves in elastic polycrystals, showing the strong effect of crystal anistropy and polycrystaline texture on the propagation. It is shown that the method combines the simplicity of classical Fourier series analysis with the versatility of Finite Elements to account for complex geometries proving an efficient and general approach which allows the use of large RVEs in 3D.
97 MATHEMATICS AND COMPUTING↗
Deformation of Hydrous Phases Egg [AlSiO 3 (OH)], δ [AlO(OH)] and Stishovite [Si 1‐n H 4n O 2 ] Relevant to Anisotropy of the Earth's Mantle
Seismic anisotropy of the Earth's mantle has been mostly attributed to crystallographic preferred orientation (CPO) generated during subduction and convection of an anhydrous mantle. But some hydrous phases are also stable at mantle conditions. Here we present results from diamond-anvil cell deformation experiments at high pressure and temperature on hydrous phases Egg [AlSiO 3 (OH)], δ [AlO(OH)] and hydrous stishovite [Si 1-n H 4n O 2 ], transformed from the clay mineral kaolinite. They develop strong CPO during axial compression, suggesting that they likely contribute to seismic anisotropy and heterogeneity in the mantle. Comparing experimental results with viscoplastic polycrystal plasticity models suggest that phase Egg deforms dominantly by (001) slip, δ by (010) slip and stishovite by {100} slip which could be incorporated in future models of mantle geodynamics.
58 GEOSCIENCES↗
Solidification and grain formation in alloys: a 2D application of the grand-potential-based phase-field approach
Solidification is a significant step in the forming of crystalline structures during various manufacturing and material processing techniques. Solidification characteristics and the microstructures formed during the process dictate the properties and performance of the materials. Hence, understanding how the process conditions relate to various microstructure formations is paramount. In this work, a grand-potential-based multi-phase, multi-component, multi-order-parameter phase-field model is used to demonstrate the solidification of alloys in 2D. This model has several key advantages over other multi-phase models such as it decouples the bulk energy from the interfacial energy, removes the constraints for the phase concentration variable, and prevents spurious third-phase formation at the two phase interfaces. Here, the model is implemented in a finite-element-based phase-field modeling code. The role of various modeling parameters in governing the solidification rate and the shape of the solidified structure is evaluated. It is demonstrated that the process conditions such as temperature gradient, thermal diffusion, cooling rate, etc, influence the solidification characteristics by altering the level of undercooling. Furthermore, the capability of the model to capture directional solidification and polycrystalline structure formation exhibiting various grain shapes is illustrated. In both these cases, the process conditions have been related to the growth rate and associated shape of the dendritic structure. As a result, this work serves as a stepping stone towards resolving the larger problem of understanding the process–structure–property–performance correlation in solidified materials.
36 MATERIALS SCIENCE↗
LANL end of the year report (2023)
This report summarizes the advances made by LANL in the XMAT-H2 program over FY23. In summary LANL was tasked with leading efforts related to (1) the development of models predicting hydrogen (H) redistribution within polycrystals (H redistribution model), (2) the development of models for the mechanical performance of metals/steels under H environments (Model for H effects on plasticity), The development of a framework to quantify the uncertainty in model parameters (Uncertainty in model parameters), (3) small scale characterization of the mechanical response of 347H (Microstructure characterization).
08 HYDROGEN↗
Statistical evaluation of microscale stress conditions leading to void nucleation in the weak shock regime
Here, we investigate the heterogeneity of the stress state driven by anisotropic deformation response at the single crystal level through five statistical volume element (SVE) calculations of polycrystalline BCC tantalum. This work focuses on grain boundaries as a prominent material defect type prone to void nucleation based upon experimental observations of predominantly intergranular void nucleation in this material. The SVEs are constructed to be statistically representative of larger volumes of material and are meshed such that mean and standard deviation of grain size and orientation information is reconstructed. The computational meshes feature hexahedral (brick) elements and smooth conformal grain boundaries where significant stress concentration is known to occur, a tail effect of interest in the extreme events process of dynamic ductile damage. An existing micromechanical crystallographic plasticity model shown to capture the single crystal behavior of BCC tantalum well is used to perform the polycrystal calculations. The model includes representation of the non-Schmid effect of non-planar screw dislocation kinetics in tantalum. A three-dimensional stress state time profile predicted by damage modeling of a flyer plate impact experiment is applied as boundary conditions to each SVE. Resulting grain boundary stress state statistics are strongly non-Gaussian. Significant structural evolution is observed within the compressive hold before unloading into tension in the stress profile. Strong angular dependence of grain boundary traction magnitude with shock direction is observed. Non-Schmid effects continue to suggest their influence on propensity of microstructural defect types to nucleate voids. A general void nucleation criterion is proposed using probability theory. The general framework is specified to polycrystalline BCC tantalum in the weak shock regime to include the SVE calculations and literature molecular dynamics calculations of grain boundary void nucleation strength. Probability density functions (PDFs) are used to describe the interaction between the local stress state heterogeneity and the distributed grain boundary void nucleation strength state. A causation entropy maximization procedure removes the requirement for ad hoc selection of a PDF functional form and provides a rigorous procedure for data-based PDF determination. The resulting physically informed PDF describes the spatial appearance frequency of nucleated voids as a function of applied macroscale pressure. Lower length scale physics are thus packaged in a precise and computationally efficient way to provide computational plasticity insight to macroscale dynamic ductile damage models.
36 MATERIALS SCIENCE↗
Multiscale modeling of twinning and detwinning behavior of HCP polycrystals
A multiscale scheme is presented here to capture the twinning and detwinning mechanisms during cyclic loading of HCP polycrystals. In the current framework, the crystal plasticity finite element (CPFE) method is employed at the microstructural scale. The response of twinned regions at a material point is calculated using a novel homogenization scheme via a Taylor-type model. The homogenized behavior is then used in the CPFE to obtain the response of a polycrystal. An efficient rate-independent crystal plasticity model that has been incorporated into the open source PRISMS-Plasticity software is introduced here to capture the response of the twinned region. Accordingly, the corresponding algorithmic tangent modulus is derived. Finally, this multiscale scheme is validated against data available for the cyclic response of Mg alloy ZK60A. The results show that the multiscale model can capture the key elements of the sample response observed during the experiment.
36 MATERIALS SCIENCE↗
Phase-field framework with constraints and its applications to ductile fracture in polycrystals and fatigue
Abstract Modeling of ductile fracture in polycrystalline structures is challenging, since it requires integrated modeling of cracks, crystal plasticity, and grains. Here we extend the typical phase-field framework to the situations with constraints on the order parameters, and formulate two types of phase-field models on ductile fracture. The Type-I model incorporates three sets of order parameters, which describe the distributions of cracks, plastic strain, and grains, respectively. Crystal plasticity is employed within grain interiors accommodated by J 2 plasticity at grain boundaries. The applications of the Type-I model to single crystals and bicrystals demonstrate the influences of grain orientations and grain boundaries on crack growth. In the Type-II model, J 2 plasticity is assumed for the whole system and grain structures are neglected. Taking advantage of the efficiency of the fast Fourier transform, our Type-II model is employed to study low cycle fatigue. Crack closure and striation-like patterning of plastic strain are observed in the simulations. Crack growth rate is analyzed as a function of the J -integral, and the simulated fatigue life as a function of plastic strain agrees with the Coffin–Manson relation without a priori assumption.
36 MATERIALS SCIENCE↗