New robust self-consistent homogenization schemes of elasto-viscoplastic polycrystals
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36 MATERIALS SCIENCE↗
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An anisotropic viscoplasticity model for shale based on layered microstructure homogenization
Viscoplastic deformation of shale is frequently observed in many subsurface applications. Many studies have suggested that this viscoplastic behavior is anisotropic—specifically, transversely isotropic—and closely linked to the layered composite structure at the microscale. In this work, we develop a two-scale constitutive model for shale in which anisotropic viscoplastic behavior naturally emerges from semianalytical homogenization of a bilayer microstructure. The microstructure is modeled as a composite of soft layers, representing a ductile matrix formed by clay and organics, and hard layers, corresponding to a brittle matrix composed of stiff minerals. This layered microstructure renders the macroscopic behavior anisotropic, even when the individual layers are modeled with isotropic constitutive laws. Using a common correlation between clay and organic content and magnitude of creep, we apply a viscoplastic modified Cam-Clay plasticity model to the soft layers, while treating the hard layers as a linear elastic material to minimize the number of calibration parameters. We then describe the implementation of the proposed model in a standard material update subroutine. The model is validated with laboratory creep data on samples from three gas shale formations. We also demonstrate the computational behavior of the proposed model through simulation of time-dependent borehole closure in a shale formation with different bedding plane directions.
58 GEOSCIENCES↗
Strain localization criteria for viscoplastic geomaterials
This report presents a viscoplastic localization criterion to detect quasi-instantaneous (i.e., load-induced) and delayed (creep-induced) strain localization in rate-dependent solids. The study is based on the theory of controllability and a viscoplastic description of the mechanical response. Analytical precursors of unstable states are defined through systems of ordinary differential equations (OEDs). The use of the proposed criteria is illustrated at the material point level through a set of strain localization analyses simulating active strain localization of a porous rock. In addition, full-field finite element simulations of compression tests conducted under various pressures are reported to demonstrate the role of local unstable viscoplasticity in the spontaneous propagation of deformation bands under stationary boundary conditions. The study shows that the viscoplastic localization criterion maintains a negative sign as long as the behavior is unstable, that is, the rate of deformation is accelerating. The sign switch coincides with the transition to decelerating deformation. The analyses revealed that pulses of overstress always emerge in correspondence with the growth of unstable behavior, and the peak matches the transition to stable behavior. The local responses recovered from full-field analyses were consistent with those observed in analyses at material point level and the predictions of the presented theory.
36 MATERIALS SCIENCE↗
A comparison of surrogate constitutive models for viscoplastic creep simulation of HT-9 steel
Mechanistic microstructure-informed constitutive models for the mechanical response of polycrystals are a cornerstone of computational materials science. However, as these models become increasingly more complex – often involving coupled differential equations describing the effect of specific deformation modes – their associated computational costs can become prohibitive, particularly in optimization or uncertainty quantification tasks that require numerous model evaluations. To address this challenge, surrogate constitutive models that balance accuracy and computational efficiency are highly desirable. Data-driven surrogate models, that learn the constitutive relation directly from data, have emerged as a promising solution. In this work, we develop two local surrogate models for the viscoplastic response of a steel: a piecewise response surface method and a mixture of experts model. These surrogates are designed to adapt to complex material behavior, which may vary with material parameters or operating conditions. The surrogate constitutive models are applied to creep simulations of HT-9 steel, an alloy of considerable interest to the nuclear energy sector due to its high tolerance to radiation damage, using training data generated from viscoplastic self-consistent (VPSC) simulations. In conclusion, we define a set of test metrics to numerically assess the accuracy of our surrogate models for predicting viscoplastic material behavior, and show that the mixture of experts model outperforms the piecewise response surface method in terms of accuracy.
36 MATERIALS SCIENCE↗
Advanced Newton methods for geodynamical models of Stokes flow with viscoplastic rheologies
Strain localization and resulting plasticity and failure play an important role in the evolution of the lithosphere. These phenomena are commonly modeled by Stokes flows with viscoplastic rheologies. The nonlinearities of these rheologies make the numerical solution of the resulting systems challenging, and iterative methods often converge slowly or not at all. Yet accurate solutions are critical for representing the physics. Moreover, for some rheology laws, aspects of solvability are still unknown. We study a basic but representative viscoplastic rheology law. The law involves a yield stress that is independent of the dynamic pressure, referred to as von Mises yield criterion. Two commonly used variants, perfect/ideal and composite viscoplasticity, are compared. We derive both variants from energy minimization principles, and we use this perspective to argue when solutions are unique. We propose a new stress-velocity Newton solution algorithm that treats the stress as an independent variable during the Newton linearization but requires solution only of Stokes systems that are of the usual velocity-pressure form. To study different solution algorithms, we implement 2-D and 3-D finite element discretizations, and we generate Stokes problems with up to 7 orders of magnitude viscosity contrasts, in which compression or tension results in significant nonlinear localization effects. Comparing the performance of the proposed Newton method with the standard Newton method and the Picard fixed-point method, we observe a significant reduction in the number of iterations and improved stability with respect to problem nonlinearity, mesh refinement, and the polynomial order of the discretization.
Rudi, Johann↗
Athermal glass work at the nanoscale: Engineered electron-beam-induced viscoplasticity for mechanical shaping of brittle amorphous silica
Amorphous silica deforms viscoplastically at elevated temperatures, which is common for brittle glasses. The key mechanism of viscoplastic deformation involves interatomic bond switching, which is thermally activated. Here, for this study, we precisely control the mechanical shaping of brittle amorphous silica at the nanoscale via engineered electron–matter interactions without heating. We observe a ductile plastic deformation of amorphous silica under a focused scanning electron beam with low acceleration voltages (few to tens of kilovolts) during in-situ compression studies, with unique dependence on the acceleration voltage and beam current. By simulating the electron–matter interaction, we show that the deformation of amorphous silica depends strongly on the volume where inelastic scattering occurs. The electron–matter interaction via e-beam irradiation alters the Si–O interatomic bonds, enabling the high-temperature deformation behavior of amorphous silica to occur athermally. Finally, by systematically controlling the electron–matter interaction volume, it is possible to mechanically shape the brittle amorphous silica on a small scale at room temperature to a level comparable to glass shaping at high temperatures. The findings can be extended to develop new fabrication processes for nano- and microscale brittle glasses.
36 MATERIALS SCIENCE↗
A note on the instability and pattern formation of shrinkage cracks in viscoplastic soils
In this work we present a theoretical study on the conditions for the onset of cracks, as well as the corresponding pattern formation, in saturated viscoplastic soils under isotropic loading (extension). The type of stress applied is left unspecified, to cover a variety of loadings including shrinkage due to desiccation, isotropic thermal expansion, mechanical loading and so forth. By treating the saturated soil as rigid viscoplastic, we obtain a 2D extension of the Cnoidal Waves equations (Veveakis and Regenauer-Lieb, 2015). By numerically solving the corresponding boundary value problem, we retrieve conditions for the onset of cracking instability in 2D loading, and identify the characteristic spacing between cracks to be a length scale combining all the hydro-mechanical parameters of the problem. Finally, we show that in a rectangular slab of clay under isotropic extension, patterns of triangular, rectangular and hexagonal cracks can tessellate the domain, with the hexagonal pattern being the energetically favored, as it minimizes the free energy of the system.
58 GEOSCIENCES↗
Experimental Determination of Constitutive Response of Alloy 800H in Support of Viscoplastic Constitutive Model Development for ASME Section III, Division 5, Class A Applications
In FY 2022, a development effort was initiated at the US Department of Energy’s Argonne National Laboratory (Argonne) and Oak Ridge National Laboratory (ORNL) to develop the Alloy 800H viscoplastic constitutive model so that inelastic analysis methods can support high-temperature gas-cooled reactor (HTGR) designs. The viscoplastic constitutive equations will be developed at Argonne. The ORNL effort focuses on generating test data from various high-temperature experiments with specially designed loading histories to probe Alloy 800H’s constitutive response.
36 MATERIALS SCIENCE↗
Data-Driven Surrogate Modeling with Microstructure-Sensitivity of Viscoplastic Creep in Grade 91 Steel
Abstract To support the development of advanced steel alloys tailored to withstand extreme conditions, it is imperative to account for the mechanical performance of components, while considering the influence of local microstructure on the macroscopic response. To this end, this study focuses on the development of microstructure-sensitive constitutive models for the mechanical response of Grade 91 steel exposed to extreme thermo-mechanical environments. Polynomial chaos expansion (PCE) surrogates are used to emulate high-fidelity polycrystal simulations of the viscoplastic response of Grade 91 steel as a function of the microstructure fingerprint (e.g., dislocations and precipitates). To cover a wide temperature–stress domain, two separate PCE surrogates—one that captures softening and the other that captures hardening behavior—are combined using another (sparse) Gaussian process regression model. The resulting constitutive creep surrogate model is integrated within the MOOSE finite element framework to simulate the intricate effects of microstructure, in particular MX-phase precipitates, on a component with a graded microstructure. Surrogate sensitivity analysis is applied to quantify the relevant impact of spatially varying microstructure on the creep response in a test-case involving a Grade 91 alloy with a prototypical weld.
36 MATERIALS SCIENCE↗
Predicting the viscoplastic response of a crystallizing fluoropolymer using transient network theory
We employ a molecular theory of dynamic polymer networks to describe the viscoplastic response of rubbery FK-800, a thermoplastic copolymer of chlorotrifluoroethylene and vinylidene fluoride, over a broad range of thermal histories. The kinetics of crystallization at different annealing temperatures was modeled using a modified Avrami equation, whose parameters were found to evolve through simple relationships over the full temperature range of the rubbery state. By fitting experimental compression data, we discovered predictable trends for the physical parameters in our mechanical model over its full range of crystallinities (up to ≈20%) and provided insights based on molecular-level physics to justify them. Using this, an end-to-end model was developed to predict the yielding and post-yield behavior of rubbery FK-800 for arbitrary thermal histories. The model successfully predicted the highly nonlinear evolution of characteristic mechanical signatures (stiffness, yield point, post-yield drop) throughout the crystallization process. A statistical analysis of variance test was employed to determine that the measured variations in the mechanical behavior of rubbery FK-800 are primarily dictated by its fractional crystallinity, regardless of its exact thermal history.
36 MATERIALS SCIENCE↗
Modeling of the thermo-mechanical response and texture evolution of WE43 Mg alloy in the dynamic recrystallization regime using a viscoplastic self-consistent formulation
This paper presents a microstructure sensitive model for predicting mechanical response and texture evolution of metals in the dynamic recrystallization regime. A recently proposed viscoplastic self-consistent (VPSC) formulation for the prediction of recrystallization driven by strain energy and intragranular misorientation is extended to hexagonal close-packed (hcp) metals. The model is applied to the dynamic recrystallization of magnesium alloy WE43 at different temperatures and strain rates. Model predictions in terms of stress-strain response and texture evolution are compared to the experimental measurements and acceptable agreement is achieved. According to the model predictions, superplastic behavior of nuclei was found to be the dominant softening mechanism at high temperatures and low strain rates. High concentration of precipitates at the grain boundaries and presence of alloying elements are the likely causes of low boundary mobility, resulting in nucleation dominated dynamic recrystallization. Relatively strong basal compression textures indicate dominant activity of basal slip, which can be achieved only through large difference in slip resistance between soft basal and hard prismatic and pyramidal modes.
36 MATERIALS SCIENCE↗
Implementation and experimental validation of nonlocal damage in a large-strain elasto-viscoplastic FFT-based framework for predicting ductile fracture in 3D polycrystalline materials
Ductile materials, such as metal alloys, can undergo substantial deformation before failure. Additionally, these materials are usually of polycrystalline composition and exhibit strongly anisotropic behavior at small length scales. Previously developed fast Fourier transform (FFT)-based models can model ductile fracture of isotropic materials or the elastic–plastic behavior of anisotropic polycrystalline materials; however, there remains a need to couple both capabilities. This work extends a large-strain FFT-based crystal plasticity model to simulate ductile fracture of polycrystalline materials. In this work, a triaxiality-based continuum damage mechanics (CDM) formulation is incorporated into a large-strain elasto-viscoplastic FFT (LS-EVPFFT) framework. The CDM formulation is augmented with an integral-based nonlocal regularization approach that correctly handles gas-phase material necessary to model unconstrained surfaces. To validate the damage-enabled LS-EVPFFT framework, mesoscale copper tensile coupons were machined using microwire electrical discharge machining and experimentally characterized using electron backscatter diffraction. In-situ optical digital image correlation was performed during uniaxial testing to provide a side-by-side comparison of the experimental and computational strain fields and stress–strain responses. The damage-enabled LS-EVPFFT framework can simulate the complete macroscopic stress–strain response of ductile polycrystals to failure. The model reproduces necking behavior that qualitatively agrees with experimental observations. By leveraging the relatively low computational cost of the damage-enabled LS-EVPFFT framework, the framework presented here allows the ductile fracture response of 3D polycrystalline materials to be tractably predicted.
36 MATERIALS SCIENCE↗
Bayesian analysis for estimating statistical parameter distributions of elasto-viscoplastic material models
High temperature design methods rely on constitutive models for inelastic deformation and failure typically calibrated against the mean of experimental data without considering the associated scatter. Variability may arise from the experimental data acquisition process, from heat-to-heat material property variations, or both and need to be accurately captured to predict parameter bounds leading to efficient component design. Applying the Bayesian Markov Chain Monte Carlo (MCMC) method to produce statistical models capturing the underlying uncertainty in the experimental data is an area of ongoing research interest. This work varies aspects of the Bayesian MCMC method and explores their effect on the posterior parameter distributions for a uniaxial elasto-viscoplastic damage model using synthetically generated reference data. From our analysis with the uniaxial inelastic model we determine that an informed prior distribution including different types of test conditions results in more accurate posterior parameter distributions. The parameter posterior distributions, however, do not improve when increasing the number of similar experimental data. Additionally, changing the amount of scatter in the data affects the quality of the posterior distributions, especially for the less sensitive model parameters. Moreover, we perform a sensitivity study of the model parameters against the likelihood function prior to the Bayesian analysis. The results of the sensitivity analysis help to determine the reliability of the posterior distributions and reduce the dimensionality of the problem by fixing the insensitive parameters. The comprehensive study described in this work demonstrates how to efficiently apply the Bayesian MCMC methodology to capture parameter uncertainties in high temperature inelastic material models. Quantifying these uncertainties in inelastic models will improve high temperature engineering design practices and lead to safer, more effective component designs.
42 ENGINEERING↗
Elasto-viscoplastic fast Fourier transform modeling framework for assessing microstructural effects on stress intensity factors characterizing fracture toughness
A large-strain elasto-viscoplastic fast Fourier transform (LS-EVPFFT) model with non-periodic (NP) velocity-based boundary conditions is adapted to simulate the sensitivity of stress intensity factors on microstructure for 304L stainless steel. The material was characterized via electron backscattered diffraction (EBSD) serial-sectioning to obtain a measured 3-D microstructural cell to perform simulations. The NP-LS-EVPFFT model, including the simulation setup and boundary conditions, was verified using a crystal plasticity finite element (CPFE) model. To this end, the generation of meshes of notched specimens was developed, which involved creating Python scripts for mesh “cutting” in Abaqus, and Sculpt scripts in Cubit for meshing of the measured microstructural cell processed with DREAM.3D. The complexity of the mesh preparation highlighted the advantages of the FFT-based model, which circumvents the mesh generation process. Given the efficiency of the FFT-based model, statistical distribution of stress intensity factors in function of crystal orientation at the crack tip, grain structure, and crystallographic texture surrounding the crack tip were predicted. Further, the distributions reveal about 10% variation of stress intensity factors with microstructure with the most significant sensitivity found to be the crystal orientation at the crack tip. The methodology developed in this work is discussed as a practical simulation tool for predicting the sensitivity of stress intensity factors on microstructural variability in metallic materials.
36 MATERIALS SCIENCE↗
A viscoelastic viscoplastic damage model (VPVD)
This report documents the development, implementation, and parameter estimation procedures for aviscoelastic-viscoplastic-viscodamage model. This model is being developed to improve the predictive accuracy of simulations involving plastic bonded explosives (PBX). A representative PBX is PBX9501, which is 95% by weight HMX, 2.5% estane binder and 2.5% nitroplasticizer. Mechanical deformation of this material is primarily accommodated by straining of the polymer binder and rearranging the relatively rigid HMX crystals.
45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
Big Hill Geomechanical Analysis Using M-D Viscoplastic Material Model
The integrity of wellbores at the interbed between the caprock and salt is a serious concern in the Big Hill site. For the remediation and life extension of wellbores, more accurate predictions from the global model are needed. The Big Hill global model is improved using the M-D viscoplastic contact surface model and the mesh containing the interbed layer with contact surfaces between the salt and caprock layers, and fault blocks in overburden and caprock layers. The model calibration has been performed based on the cavern volumetric closures obtained from the Caveman calculations. The results agree well from 1991 to the early 2000s. The difference starts to widen after that, it might be because of frequent fluid movement and raw water injection. Therefore, the predictions from this improved model could be used to examine the structural integrity of caverns in Big Hill salt dome.
42 ENGINEERING↗
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↗
Modeling the viscoplastic behavior of a semicrystalline polymer
In this study, a complex constitutive relation is identified using inverse modeling with the nominal mechanical response as sole experimental input. The methodology is illustrated for a semicrystalline thermoplastic in the presence of strain localization at finite deformations. The experimental database includes cylindrical tensile bars, compression pins and round notched bars loaded at strain rates spanning up to five decades and temperatures below and above T g . The data is organized into a calibration set and a validation set. The response of tensile specimens is determined using finite element analyses and a two-phase constitutive relation for semicrystalline polymers that accounts for temperature- and rate-sensitive plastic flow, pressure-sensitivity, small-strain softening and large-strain orientational hardening of the amorphous phase, along with the evolution of crystallinity. The large number of constitutive parameters is identified using an optimization tool coupled with the finite element solver and the calibration set from experiments. The methodology is shown to be successful in predicting the response of round notched bars and replicating the effects of temperature and strain rate on the severity of necking in tensile bars. The proposed model identification strategy is both simple and effective in comparison with other elaborate methods that attempt to access intrinsic behavior directly from high-fidelity experimental measurements.
36 MATERIALS SCIENCE↗