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Verification Testing For Solid-Element Material Models 11-19 in DYNA3D/ParaDyn

This technical report documents the creation and implementation of verification tests for solid-element material models 11 through 19 available in DYNA3D/ParaDyn. The verification tests covered all aspects of each material model, except for the Weibull distribution functionality in material models 15 and 19. General test cases were created to verify the elastic and plastic behavior of the material models. Other additional tests were developed to examine the intricacies of each material model. Each test involved the use a kinematic load case and specification of material parameters necessary to activate corresponding features of the material model. The load cases prescribed the full time history of the kinematic motion for the solid elements, and these loads are independent of the material model or element formulation. When possible, closed form solutions were then derived for each verification test in a continuum setting. The DYNA3D simulations for each test were carried out over a unit time interval, t ϵ [0, 1], and the as implemented DYNA3D response was compared to the closed form solutions evaluated at discrete points in time. A relative error measure was determined for each test to justify the proper implementation of the material model. The relative errors comparing the DYNA3D solution to the analytical solution were, in general, on the order of machine precision except where noted. This signifies the proper implementation of solid-element material models 11-19. In the development of these verification tests, six bugs were found and fixed in the source code. Additionally, this work generated eighteen DYNA3D input decks and answer extraction scripts in the DYNA3D/ParaDyn Software Quality Assurance test suite, which are comprised of a total of 285 solid-element tests. Testing for each material model utilizes two input decks and answer extraction scripts, where one focuses on the linear elastic response and the other examines the inelastic and remaining functionalities of the material model. In total, this work added 285 individual verification test problems in the DYNA3D/ParaDyn test suite.

42 ENGINEERING↗

Model-to-model interface for multiscale materials modeling

A low-level model-to-model interface is presented that will enable independent models to be linked into an integrated system of models. The interface is based on a standard set of functions that contain appropriate export and import schemas that enable models to be linked with no changes to the models themselves. These ideas are presented in the context of a specific multiscale material problem that couples atomistic-based molecular dynamics calculations to continuum calculations of fluid ow. These simulations will be used to examine the influence of interactions of the fluid with an adjacent solid on the fluid ow. The interface will also be examined by adding it to an already existing modeling code, Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) and comparing it with our own molecular dynamics code.

74 ATOMIC AND MOLECULAR PHYSICS↗

Parameter covariance and non-uniqueness in material model calibration using the Virtual Fields Method

Traditionally, material identification is performed using global load and displacement data from simple boundary-value problems such as uni-axial tensile and simple shear tests. More recently, however, inverse techniques such as the Virtual Fields Method (VFM) that capitalize on heterogeneous, full-field deformation data have gained popularity. In this work, we have written a VFM code in a finite-deformation framework for calibration of a viscoplastic (i.e. strain-rate dependent) material model for 304L stainless steel. Using simulated experimental data generated via finite-element analysis (FEA), we verified our VFM code and compared the identified parameters with the reference parameters input into the FEA. The identified material model parameters had surprisingly large error compared to the reference parameters, which was traced to parameter covariance and the existence of many essentially equivalent parameter sets. This parameter non-uniqueness and its implications for FEA predictions is discussed in detail. Lastly, we present two strategies to reduce parameter covariance – reduced parametrization of the material model and increased richness of the calibration data – which allow for the recovery of a unique solution.

304L stainless steel↗

NEML2 - THE NEW ENGINEERING MATERIAL MODEL LIBRARY, VERSION 2

SF-22-157 NEML2 is an extension of an earlier open source code developed at ANL (SF-xxxx) called NEML. These libraries provide tools for constructing and using models of engineering materials, with a focus on high temperature materials for nuclear reactor applications. The software include tools for setting up material models, calibrating models, storing models for later use in other simulations, and running simple "material point" simulations of the material behavior. The main difference between NEML and NEML2 is the new software has been complete restructured to run on GPUs and other accelerators in order to improve the performance of methods used to train constitutive models against data and to improve the performance of the final models in production environments, like finite element software. While over time we expect NEML2 to become more-or-less feature complete with NEML we are filing a new software disclosure because (1) the library has been complete restructured and (2) we want to host NEML2 in a separate repository.

MESSNER, MARK↗

Shell Element Material Model Verification Problems for DYNA3D: Part II

A suite of supplementary shell element material model verification tests were developed for the explicit finite element program DYNA3D, in continuation of the work performed in LLNL-TR-792469 (Shell Element Material Model Verification Problems for DYNA3D). The testing procedure developed in the preceding report is extended, and used to verify all remaining untested shell model features and inputs. A collection of 78 feature-specific verification tests are proposed, some of which are applicable to multiple material models, though many are specialized to a particular model. The collective suite of tests cover all 27 currently available material models in DYNA3D. In the course of developing the proposed test suite, 24 separate shell model-related issues were identified and have subsequently been resolved.

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↗

Material Models and Credibility for System Level Abnormal Mechanical ModSim Applications

The purpose of this document is to provide evidence for assessing the adequacy of parameterized material models for a collection of materials used in a finite element analyses setting. “Adequacy” is relative to the intended use of the material in particular analyses. The intended application of the material models covered within this document is for system level abnormal mechanical solid mechanics analyses. Generally, material model parameterizations should be valid from temperatures of approximately -50 to 70° C, across a range of strain rates, and (depending on details of the parts involved) large deformations. Each material covered in this document is presented in its own chapter with a common format across materials. Model assumptions, limitations, existing validation results, readiness for use with uncertainty quantification, general usage guidance, and failure considerations are all provided along with specific parameterization inputs suitable for the finite element analysis code Sierra/Solid Mechanics.

36 MATERIALS SCIENCE↗

Analysis of Element Size and Element Type on SS304L Material Model Performance

Finite element solutions are only valid if the information inputted into the models is a valid assumption. This is why it is important to determine if the model behaves as expected especially in the material response. Material models that consider deformation in the elastic and plastic regions are desirable. As a material deforms plastically, hardening will occur until the ultimate strength is reached due to the reduction of the cross sectional area in a uniaxial tensile test environment. A phenomenological approximation of this behavior which is known as power law hardening (plh) can be expressed as σ = σ y + K $ϵ^{n}_{p}$ where K and n are empirically determined constants, and σ y is the proportional limit of the material. The first objective of this study is to verify the behavior for a calibrated plh material model for selective deviatoric hexahedral elements when applied to a different material stock. The Sierra SM input for this calibrated model can be found in the appendix. The second objective of this study is to determine the differences in failure characteristics for considerably large shell elements versus that of fine hexahedral elements.

36 MATERIALS SCIENCE↗

Identification Uncertainty in Inverse Material Model Parameter Determination: A Sensitivity‐Based Decision Process for Load Path Selection

This research proposes a sensitivity-based framework for selecting the optimal prescribed loading path for a biaxial cruciform specimen. Optimality here is determined by the direction and magnitude of the prescribed displacement that minimizes the influence of random noise on the material model parameter identification. Using simulated experimental data based on finite element simulation, in this work, we identify the material model parameters of a Ludwik hardening model and plane stress implementation of the Hill-48 yield criterion using finite element model updating (FEMU). Our analysis reveals that the identification (or estimator) uncertainty of model parameters depends on the displacement boundary conditions (i.e., loading sequence) and the ground-truth value of the individual parameters. Optimal experimental design (OED) criteria based on the Fisher information matrix were investigated to mitigate indecision in the choice of optimal load path when the identification uncertainty of different material model parameters optimized at different load paths. The determinant of the Fisher information matrix was chosen here as the more useful metric due to its ability to capture uncertainty of the most influential material model parameters. The proposed framework demonstrates potential for real-time automated load step selection using scalar criteria derived prior to mechanical loading. The framework can be generalized to other geometries, boundary conditions and material models, allowing this procedure to be utilized for different experimental configurations and materials.

Fayad, Samuel S. [University of Illinois at Urbana↗

Preface for focus issue on uncertainty quantification in materials modeling

This focus issue is motivated by the growing demand for rigorous uncertainty quantification (UQ) in materials modeling, which is driven by the need to use these tools, in conjunction with experiments, to support decision making in materials design, development, and deployment. Traditionally, predictive materials modeling has focused on gaining qualitative insight into the range of mechanisms that control material behavior and how those mechanisms interact to govern material properties and processes. In that context, quantitative evaluation of modeling uncertainty was not a priority. As materials modeling advances, there is increased impetus to employ it in the context of materials design and qualification. This trend is manifested in the establishment of integrated computational materials engineering (ICME) as a growing sub-discipline, as well as by initiatives such as the materials genome in the USA and similar efforts around the globe. Current practice and future needs are described in several recent reports including NASA's Vision 2040: A Roadmap for Integrated, Multiscale Modeling and Simulation of Materials and Systems. Invariably, these studies point out the need for the field to embrace the challenge of UQ.

36 MATERIALS SCIENCE↗

Modeling physical vapor deposition of energetic materials

Morphology and microstructure of organic explosive films formed using physical vapor deposition (PVD) processes strongly depends on local surface temperature during deposition. Currently, there is no accurate means of quantifying the local surface temperature during PVD processes in the deposition chambers. This study focuses on using a multiphysics computational fluid dynamics tool, STARCCM+, to simulate pentaerythritol tetranitrate (PETN) deposition. The PETN vapor and solid phase were simulated using the volume of fluid method and its deposition in the vacuum chamber on spinning silicon wafers was modeled. The model also included the spinning copper cooling block where the wafers are placed along with the chiller operating with forced convection refrigerant. Implicit time-dependent simulations in two- and three-dimensional were performed to derive insights in the governing physics for PETN thin film formation. PETN is deposited at the rate of 14 nm/s at 142.9 °C on a wafer with an initial temperature of 22 °C. The deposition of PETN on the wafers was calculated at an assumed heat transfer coefficient (HTC) of 400 W/m 2 K. This HTC proved to be the most sensitive parameter in determining the local surface temperature during deposition. Previous experimental work found noticeable microstructural changes with 0.5 mm fused silica wafers in place of silicon during the PETN deposition. This work showed that fused silica slows initial wafer cool down and results in ~10 °C difference for the surface temperature at 500 μm PETN film thickness. It was also found that the deposition surface temperature is insensitive to the cooling power of the copper block due to the copper block's very large heat capacity and thermal conductivity relative to the heat input from the PVD process. Future work should incorporate the addition of local stress during PETN deposition. Lastly, based on simulation results, it is also recommended to investigate the impact of wafer surface energy on the PETN microstructure and morphology formation.

36 MATERIALS SCIENCE↗

Shell Element Material Model Verification Problems for DYNA3D

A suite of shell element material model verification tests were developed for the explicit finite element program DYNA3D. Each test consists of a single quadrilateral shell element, whose nodal displacements and rotations have been prescribed such that the deformation of the material is fully controlled throughout the analysis. At one of the element’s integration points, the numerically computed stress, through-thickness strain, and equivalent plastic strain are compared against closed-form reference solutions that are derived to be consistent with the theory of finite deformation elasto-plasticity. A collection of 31 feature-specific verification tests are proposed, each of which may be used to verify all models which share in common the tested feature of interest. For each material model, a subset of these tests are selected and used to verify the correct behavior of all features of the model. The collective suite of tests cover 26 of the 27 currently available material models in DYNA3D. In the course of developing the proposed test suite, 18 implementation bugs were identified and have subsequently been resolved.

42 ENGINEERING↗

Validation of material models for puncture of 7075-T651 aluminum plate

Plate puncture simulations are challenging computational tasks that require advanced material models including high strain rate and thermal-mechanical effects on both deformation and failure, plus finite element techniques capable of representing large deformations and material failure. The focus of this work is on the material issues, which require large sets of experiments, flexible material models and challenging calibration procedures. In this study, we consider the puncture of 12.7 mm thick, 7075-T651 aluminum alloy plates by a cylindrical punch with a hemispherical nose and diameter of 12.7 mm. The plasticity and ductile failure models were isotropic with calibration data obtained from uniaxial tension tests at different temperatures and strain rates plus quasi-static notched tension tests and shear-dominated tests described here. Sixteen puncture experiments were conducted to identify the threshold penetration energy, mode of puncture and punch acceleration during impact, The punch was mounted on a 139 kg mass and dropped on the plates with different impact speeds. Since the mass was the same in all tests, the quantity of interest was the impact speed. The axis and velocity of the punch were perpendicular to the plate surface. The mean threshold punch speed was 3.05 m/s, and the mode of failure was plugging by thermal-mechanical shear banding accompanied by scabbing fragments. Application of the material models in simulations of the tests yielded accurate estimates of the threshold puncture speed and of the mode of failure. Time histories of the punch acceleration compared well between simulation and test. Remarkably, the success of the simulations occurred in spite of even the smallest element used being larger than the width of the shear bands.

36 MATERIALS SCIENCE↗

Theory and Computation for Mesoscopic Materials Modeling

Accurate and efficient computational modeling of material behavior is essential to the DOE's mission of advancing the development of devices and components needed for power generation and storage. One of the outstanding challenges in atomistic simulation of condensed systems, such as solids, liquids, and glasses, is access to experimentally meaningful length and time scales. The project developed and improved several solution methods to overcome these challenges: diffusive molecular dynamics, adaptive kinetic Monte Carlo, coarse-graining of transition state theory, finite temperature coarse-graining methods for crystalline defects, and optimization-based atomistic-to-continuum coupling methods.

97 MATHEMATICS AND COMPUTING↗

An Overview of Material Models in the BISON Fuel Performance Code

BISON is a modern finite element-based nuclear fuel performance code that has been under development at Idaho National Laboratory (INL) since 2009. The code is applicable to both steady and transient fuel behavior and supports the use of one-, two-, and three-dimensional meshes. BISON is designed to be a multi-fuels code. Although primarily applied to Light Water Reactor (LWR) fuel to date, the code has been used to analyze TRISO-coated particle fuel and metal fuel in rod and plate form, design and interpret fuel irradiation experiments and investigate novel fuel concepts. Nuclear fuel operates in an extreme environment that induces complex multiphysics phenomena occurring over distances ranging from inter-atomic spacing to meters, and times scales ranging from microseconds to years. To simulate this behavior requires a wide variety of material models which are often complex and nonlinear. Nearly all of the material models currently available in BISON are empirical, using correlations from existing fuel performance codes or material property libraries. Although these models perform adequately under many conditions, they have well-understood limitations. One obvious weakness is that the models are only valid in the domain of the associated experimental data, and extrapolating beyond this domain can result in substantial errors. A further weakness is that these models are often correlated in terms of imprecise quantities, such as burnup. Materials can, for example, reach a given burnup under very different circumstances, leading to very different material behavior. To overcome these weaknesses, efforts are underway with BISON to develop models based on a multi-scale approach, where material behavior is described with a series of interdependent microstructure based models. This paper provides an overview of the material models available in BISON. To keep the scope manageable, only LWR fuel will be considered. The first section focuses on UO{sub 2} fuel, identifying the models generally required and briefly describing those that have been implemented in the code. The second section repeats this approach for Zircaloy cladding. A final section provides examples of areas where multi-scale material modeling has been applied to BISON. BISON is a modern 2D and 3D nuclear fuel performance code that is applicable to multiple fuel forms. A wide variety of complex and nonlinear material models are required to simulate fuel behavior. Focusing on UO{sub 2} fuel and Zircaloy cladding (LWR fuel), the set of empirical models currently implemented in BISON have been reviewed. To overcome some of the deficiencies associated with empirical models, multi-scale material models are being developed. Two multi-scale models that have been used in BISON were reviewed. (authors)

36 MATERIALS SCIENCE↗

Material Model Parameters Optimization in Liquid Mercury Target Dynamics Simulation With Machine Learning Surrogates

A pulsed spallation target is subjected to very short (∼0.7μs) but intense loads (23.3 kJ) from repeated proton pulses, which knock away neutrons from the mercury atoms’ nuclei for a wide range application in physics, engineering, medicine, petroleum exploration, biology, chemistry, etc. The effect of this pulsed loading on the stainless-steel target module which contains the flowing mercury target material is difficult to predict not only due to its short but intense explosive-like physical reaction, but also the nonlinear material behavior of the liquid mercury in the structure. Injecting small helium bubbles in the mercury has been an efficient method of mitigating the pressure wave at high power level stage. However, prediction of the resultant loading on the target is more difficult when helium gas is intentionally injected into the mercury. A 2-phase material model that incorporates the Rayleigh-Plesset (R-P) model is expected to address this complex multi-physics dynamics problem by including the bubble dynamics in the liquid mercury. A parameter sensitivity study was firstly employed to understand their impact on the simulation strains. The investigated parameters included E, μ, γ, σ, n, VFgas, and gas cumulative volume curve control parameters a and b. Verification and validation results from sparse polynomial expansions (SPE) method and directional Gaussian smoothing (DGS) optimization show that the surrogate model had training error of ∼7% and validation error of ∼15%, indicating that machine learning methods and surrogate models can help optimize the uncertain parameters in the complex 2-phase material model. This approach is expected to fill the knowledge gap between unknown liquid-gas mixture material model and measured vessel strain responses.

Lin, Lianshan↗

A non-orthogonal material model of woven composites in the preforming process

Woven composites are considered as a promising material choice for lightweight applications. An improved non-orthogonal material model that can decouple the strong tension and weak shear behaviour of the woven composite under large shear deformation is proposed for simulating the preforming of woven composites. The tension, shear and compression moduli in the model are calibrated using the tension, bias-extension and bending experiments, respectively. The interaction between the composite layers is characterized by a sliding test. The newly developed material model is implemented in the commercial finite element software LS-DYNA® and validated by a double dome study.

36 MATERIALS SCIENCE↗

Finite Element Simulation of Compression Molding of Woven Fabric Carbon Fiber/Epoxy Composites: Part I Material Model Development

Woven fabric carbon fiber/epoxy composites made through compression molding are one of the promising choices of material for the vehicle light-weighting strategy. Previous studies have shown that the processing conditions can have substantial influence on the performance of this type of the material. Therefore the optimization of the compression molding process is of great importance to the manufacturing practice. An efficient way to achieve the optimized design of this process would be through conducting finite element (FE) simulations of compression molding for woven fabric carbon fiber/epoxy composites. However, performing such simulation remains a challenging task for FE as multiple types of physics are involved during the compression molding process, including the epoxy resin curing and the complex mechanical behavior of woven fabric structure. In the present study, the FE simulation of the compression molding process of resin based woven fabric composites at continuum level is conducted, which is enabled by the implementation of an integrated material modeling methodology in LS-Dyna. Specifically, the chemo-thermo-mechanical problem of compression molding is solved through the coupling of three material models, i.e., one thermal model for temperature history in the resin, one mechanical model to update the curing-dependent properties of the resin and another mechanical model to simulate the behavior of the woven fabric composites. Preliminary simulations of the carbon fiber/epoxy woven fabric composites in LS-Dyna are presented as a demonstration, while validations and models with real part geometry are planned in the future work.

36 MATERIALS SCIENCE↗