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All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Experimental verification of a crystal plasticity-based simulation framework for predicting microstructure and geometric shape changes: Application to bending and Taylor impact testing of Zr

This paper is concerned with experimental verification of a recently developed multi-scale simulation framework for plastic deformation of metallic materials from quasi-static to impact deformation conditions. The framework is a visco-plastic self-consistent (VPSC) polycrystalline model embedded in an implicit finite element method (FE-VPSC) to provide a microstructure-sensitive constitutive response at each material point. Each material point of the FEM model is a polycrystalline aggregate with crystallographic deformation mechanisms operating at the single crystal scale with their evolving activity based on a dislocation density-based hardening law and texture. Four beams and three cylinders machined in different orientations from a textured plate of high-purity zirconium are tested quasi-statically in 4-point bending and at speeds of 100 m/s, 170 m/s and 243 m/s during Taylor impact tests, respectively. The variation in dimensional changes resulting from different sample orientations in the plate with respect to loading directions is measured for each sample. Moreover, texture and twinning characterization is performed using electron backscattered diffraction (EBSD). The deformation processes and underlying evolution of microstructure are successfully simulated using the FE-VPSC framework. In doing so, the model parameters are optimized and validated across a broad range of strain rates and temperatures. Simulation results in terms of geometrical changes and microstructural evolution are compared with the experimental measurements. The model predicts anisotropic material flow resulting from the hard-to-deform crystallographic directions, the development of gradients in texture and twinning through the geometries, tension–compression asymmetry, as well as the extent of plasticity under impact.

42 ENGINEERING↗
DOE OSTI2020

Mechanical behavior and texture evolution of WE43 magnesium-rare earth alloy in Split-Hopkinson Pressure Bar and Taylor Impact Cylinder Testing

Mechanical behavior and texture evolution of Mg rare-earth alloy WE43 is investigated for strain-rates 10 -3 /s to upwards of 10 5 /s for the two material conditions - as-cast (AC) and T6 age hardened, rolled plate (RT6). The high strain-rate behavior is tested using both Taylor cylinder impact tests (TC) and split Hopkinson pressure bar tests (SHB) and bulk textures are obtained using neutron diffraction. Unlike the quasi-static strained material, AC and RT6 SHB retained high hardening rates throughout the test, even up to 30% true strain. Moreover, the high strain-rate data revealed that the RT6 material has a much higher strength than the AC material, but similar hardening rates despite significantly different initial texture. The flow stress near yield increased up to I 0% for RT6 and up to 30% for AC as the strain-rate increased six orders of magnitude from quasi-static rates 10 -3 /s to 10 3 /s. Neither material exhibited significant plastic anisotropy over the broad range of strain rates, despite the fact that the RT6 material had a moderately strong initial texture. In the TC tests, the geometric cross-sectional changes and texture along the cylinder from the cylindrical sample foot to head are measured and from the neutron diffraction texture analysis, upper-bound estimates of twin volume fraction are obtained as well as dislocation density from analyzing diffraction peak broadening. Recorded geometrical changes along several loading directions show that the material has deformed remarkably homogeneously under impact. Analysis of deformed textures indicates that {101¯2} extension deformation twinning occurred in the RT6 condition over the range of strain rates, with an upper bound estimate of 40% twin volume fraction for approximately 0.10-0.25 true strain. The peak texture components after the impact have their c-axes closely aligned with the impact direction. As a result, these observations are presented and rationalized in the paper.

42 ENGINEERING↗
DOE OSTI2021

Bayesian calibration of strength model parameters from Taylor impact data

Materials strength plays a key role in determining the mechanical response of engineered structures. As such, accurate strength models are crucial in simulations involving complex loading conditions, particularly when deformation in the plastic regime is deemed important. In this work, a Gaussian process based surrogate for a finite element simulation of a Taylor impact test is developed and used for Bayesian calibration of the Preston–Tonks–Wallace strength model. Here, the surrogate model is shown to closely approximate the salient features of the Taylor cylinder deformation and is validated against simulation output before being used in the strength model calibration routine. The results show that Taylor impact test data can be used in the calibration of constitutive equations through the use of a combination of data science techniques, namely Gaussian processes and Bayesian inference.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Simulation of dynamic crystal plasticity with a Lagrangian discontinuous Galerkin hydrodynamic method

Here we present a new Lagrangian modal discontinuous Galerkin (DG) hydrodynamic method that supports a dynamic dislocation based crystal plasticity model for simulating the mechanical behavior of crystallographic materials, both single crystal and polycrystalline, under dynamic conditions. A modal DG approach is used to evolve fields relevant to conservation laws. These fields are approximated by Taylor series polynomials of varying degree. These polynomials describe macro-scale hydrodynamic behavior while their evolution is determined by evaluating the dynamic crystal plasticity model at material points within the element. The dynamic crystal plasticity model is sensitive to the time increment size, with too large of time increments leading to instability in the model. To mitigate this, the temporal evolution of the dynamic crystal plasticity model is achieved with the combination of a sub-incrementing scheme with Heun’s third-order time integration scheme, which is also used to temporally evolve the governing equations. The implementation of the dynamic crystal plasticity model within the DG framework is tested using a 2D approximation of the Taylor impact test with a single crystal material, using quadratic elements that have faces that can bend. In addition to the standard continuous material modeling, we propose a new simulation method that would represent the heterogeneous behavior of polycrystalline microstructures within an element by varying the position and material properties of the material points within the element. This method is demonstrated using random orientation distributions on materials points that are arranged in both structured and random configurations.

42 ENGINEERING↗
DOE OSTI2022

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↗
DOE OSTI2020

Assessment of reverse gun taylor cylinder experimental configuration

Experimental efforts for Taylor-anvil impact tests have often been limited to near room temperature. The ‘Reverse Gun’ method proposed by Gust in 1982 allows for the Taylor impact specimen to be uniformly heated without temperature losses before impact. Through the use of finite element analysis, we explore two topics in this work. First, we examine whether the reverse gun experimental configuration is comparable to the traditional Taylor-anvil setup. Second, we assess the accuracy of several commonly employed flow strength models in terms of their ability to predict the reverse gun experimental results which involve dynamic loading conditions and complex thermo-mechanical coupling. The reverse gun simulations are performed for tantalum targets at initial temperatures in the range 295 K to 1295 K and velocities from 135 m/s to 242 m/s. We show that with suitable care in the modeling of the preheated reverse gun experiments one can make valuable assessments of flow strength models. Given the conditions explored, these observations probe the thermal softening, strain hardening, and strain rate sensitivity of the material.

42 ENGINEERING↗
DOE OSTI2022

FY2021 Improvements to the New CTH Code Verification & Validation Test Suite

Over the past few years, the CTH multiphysics hydrocode has overhauled its software quality and testing processes, implementing current best practices in software quality and building a robust V&V test suite comprised of traditional hydrocode verification problems, including ASC Tri-Lab Test Suite and Enhanced Tri-Lab Test Suite problems, as well as validation problems for some of CTH’s most frequently used equations of state, materials models, and other key capabilities. Substantial progress towards building this new test suite was made in FY19 and FY20. In FY21, the test suite has been expanded to include verification and validation tests of the Steinberg-Guinan-Lund (ST) viscoplastic model and the Johnson Cook (JFRAC) fracture model. Additionally, two new verification tests were added, covering hydrodynamics and high explosive (HE) modeling capabilities: the Kidder Gaussian density problem and the Escape of HE Products (EHEP) problem from the Tri-Lab Test Suite. This report discusses each of these test problems in detail. Verification test results are compared to analytic solutions. Validation test results are compared to experimental data. Wherever possible, convergence or mesh refinement studies are included. Additionally, while implementing the Kidder verification problem, a bug was identified that affects the use of tables to initialize pressure or density in 1D or 2D calculations. A brief discussion of the bug and its fix is included. CTH demonstrates good performance overall on the new test suite problems. Simulation results showed good agreement with analytic solutions for the Kidder problem, with convergence rates ranging between 1.8 and sub-linear, and relatively good agreement for the EHEP problem, though convergence rates for pressure and density were nearly 0. The ST and JFRAC strain rate loading verification tests show good agreement with analytic solutions. Likewise, CTH simulation results show good agreement with experimental validation data, including Taylor rod impact testing, for the materials tested. Future V&V work will focus on adding 2D and 3D versions of existing verification tests as well as adding validation tests of other frequently used capabilities such as other fracture models.

42 ENGINEERING↗
DOE OSTI2021

Strength models for stainless steel 304L alloys

This report provides nominal, weak and strong calibrations of Preston- Tonks-Wallace (PTW) plasticity model [1] parameters for stainless steel 304L alloys. The data sets shown indicate that for these alloys, the material’s prove- nance plays an important role in accurate characterization. First we provide a parameter set fit to compression-tested annealed samples, both quasistatic (QS) and split Hopkinson pressure bar (SHPB), from the MST-8 group at LANL within the last year. Then we compare simulations using the FLAG hydrocode [2], with this and other parameter sets, to data from a Taylor cylinder impact test performed within the same group around 2013.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Calibration and validation of the foundation for a multiphase strength model for tin

In this work, the Common Model of Multi-phase Strength and Equation of State (CMMP) model was applied to tin. Specifically, calibrations of the strength-specific elements of the CMMP foundation were developed with a combination of experiments and theory, and then the model was validated experimentally. The first element of the foundation is a 10 multi-phase analytic treatment of the melt temperature and the shear modulus for the solid phases. These models were parameterized for each phase based on ab initio calculations using the software VASP (Vienna Ab initio Simulations Package) based on density functional theory (DFT). The shear modulus model for the ambient β phase was validated with ultrasonic sound speed measurements as a function of pressure and temperature. The second element of the foundation is a viscoplastic strength model for the β phase, upon which strength for inaccessible higher-pressure phases can be scaled as necessary. The stress-strain response of tin was measured at strain rates of 10 -3 to 3 x 10 3 s -1 and temperatures ranging from 87 to 373 K. The Preston-Tonks-Wallace (PTW) strength model was fit to that data using Bayesian model calibration. For validation, six forward and two reverse Taylor impact experiments were performed at different velocities to measure large plastic deformation of tin at strain rates up to 10 5 s -1 . The PTW model accurately predicted the deformed shapes of the cylinders, with modest discrepancies attributed to the inability 20 of PTW to capture the effects of twinning and dynamic recrystallization. Some material in the simulations of higher velocity Taylor cylinders reached the melting temperature, thus testing the multiphase model because of the presence of a second phase, the liquid. In simulations using a traditional modeling approach, the abrupt reduction of strength upon melt resulted in poor predictions of the deformed shape and non-physical temperatures. With CMMP, the most deformed material points evolved gradually to a mixed solid-liquid but never fully liquid state, never fully lost strength, 25 stayed at the melt temperature as the latent heat of fusion was absorbed, and predicted the deformed shape well.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Extending a 10‐node composite tetrahedral finite element for solid mechanics

Abstract We propose to extend the composite tetrahedral finite element first introduced by Thoutireddy et al. (2002) and recently reformulated by Ostien et al. (2016). We generalize the gradient operator and mass matrix to curved domains through analytical expressions weighted by subtetrahedra Jacobians. Optimal integration weights are constructed to increase the accuracy of Gaussian quadrature. We preserve the variational structure of the formulation through a new five‐field functional with additional, independent fields for the Jacobian and the pressure. This approach not only obviates volumetric locking but also yields symmetry. A deleterious soft mode, common to both the quadratic and composite tetrahedral element with constant pressure formulations is effectively stabilized through a novel convex energy penalty function. Numerous numerical examples spanning a patch test to the impact of a Taylor bar demonstrate the accuracy, robustness, and convergence of the extended composite tetrahedral element for application to structural metals.

Foulk III, James W.↗
DOE OSTI2023

Fracture of PC and PMMA cylinders in the Taylor tests

The present paper analyzes failure observed in polymer rods collided with a steel anvil under the Taylor cylinder impact experiments. The experimental and numerical analysis demonstrates that association of the failure patterns with the loading mode depends on the rod material. Two materials are considered in the paper, specifically, polymethylmethacrylate (PMMA) and polycarbonate (PC). Damage in PMMA rods at the Taylor tests is shown to be dominated by the shear load resulting in plastic deformation. In contrast, the major mechanism of damage in PC rods is governed by omni-directional (pressure) mode of load. Analysis of the damage in sections of the rods associated with the glass transition is also addressed in the present theoretical study. Failure in these polymers follows the traditional fracture wave mechanism for brittle glass-type materials due to load in the corresponding mode. Numerical analysis employs a two-phase model with improved inter-phase thermal balance accounting for the inter-phase mass, momentum, and heat exchanges during the glass phase transition, while damage being accumulated in time. In conclusion, the simulation results demonstrate a good correlation with the experimental results.

36 MATERIALS SCIENCE↗
NASA NTRS1991

Parameter estimation for distributed parameter models of complex, flexible structures

Distributed parameter modeling of structural dynamics has been limited to simple spacecraft configurations because of the difficulty of handling several distributed parameter systems linked at their boundaries. Although there is other computer software able to generate such models or complex, flexible spacecraft, unfortunately, neither is suitable for parameter estimation. Because of this limitation the computer software PDEMOD is being developed for the express purposes of modeling, control system analysis, parameter estimation and structure optimization. PDEMOD is capable of modeling complex, flexible spacecraft which consist of a three-dimensional network of flexible beams and rigid bodies. Each beam has bending (Bernoulli-Euler or Timoshenko) in two directions, torsion, and elongation degrees of freedom. The rigid bodies can be attached to the beam ends at any angle or body location. PDEMOD is also capable of performing parameter estimation based on matching experimental modal frequencies and static deflection test data. The underlying formulation and the results of using this approach for test data of the Mini-MAST truss will be discussed. The resulting accuracy of the parameter estimates when using such limited data can impact significantly the instrumentation requirements for on-orbit tests.

Taylor, Lawrence W., Jr.↗
DOE OSTI2020

Fast strength model characterization using Bayesian statistics

A variety of flow stress models exist with new models constantly being developed. These models aim to approximate the strength of materials in a variety of regimes from quasistatic loading through shock scenarios. All models contain an array of parameters which need to be tuned to the material under study. Some models perform well under limited conditions, requiring adjustment of the parameters when venturing outside of those predefined ranges. Other models perform well over a wide range of conditions with a set of parameters, but may be outperformed by other models optimized on a tighter range of conditions. Recent research by Los Alamos demonstrated the ability to optimize the Johnson Cook (JC) model using a set of 3 plate-impact experiments on Aluminum. They utilized Bayesian statistics and emulation to determine optimal parameters for the model with a quantification of parameter uncertainty. We present an extension of this capability to incorporate velocimetry from plate-impact tests, stress-strain data from split Hopkinson pressure bar and quasistatic compression tests, plus profiles from Taylor cylinders in a unified fashion. Statistically robust comparisons of the performance and uncertainty of different realizations of the JC flow stress model were carried out based on calibration to several possible combinations of these three different experiment types.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

A high-order, localized-artificial-diffusivity method for Eulerian simulation of multi-material elastic-plastic deformation with strain hardening

A high-order method for Eulerian simulation of material undergoing large elastic–plastic deformation is developed. Thermodynamically consistent hyperelastic constitutive relations are assumed, facilitating the treatment of solids, liquids, and gases in a unified manner. Here, the method enables the simulation of multi-material interactions using a diffuse interface approach. Numerical capturing of material interfaces, shock waves, contact surfaces, and elastic-plastic strain discontinuities using high-order compact-difference schemes is assisted by Localized Artificial Diffusivity (LAD). In the new setting involving elastic–plastic deformation, the previously established terms for the artificial properties are verified to effectively regularize normal shocks. Additional LAD terms are introduced to the elastic and plastic kinematic equations to regularize shear shocks and other strain discontinuities, improving solution stability. Other important features of the method that improve robustness include the numerical treatment of compatibility terms in the kinematic equations, and the treatment of rotation. Particular emphasis is focused toward new advancements of the methods for plastic-deformation integration and the associated strain hardening of the material, including rate-dependent plasticity. The method is demonstrated on a variety of test problems, including 1-D impacts, a variant of the Shu-Osher problem, a Taylor impact, and a Richtmyer-Meshkov instability between two elastic–plastic solids with strain hardening.

42 ENGINEERING↗
NASA NTRS1998

Tests of the Giant Impact Hypothesis

The giant impact hypothesis has gained popularity as a means of explaining a volatile-depleted Moon that still has a chemical affinity to the Earth. As Taylor's Axiom decrees, the best models of lunar origin are testable, but this is difficult with the giant impact model. The energy associated with the impact would be sufficient to totally melt and partially vaporize the Earth. And this means that there should he no geological vestige of Barber times. Accordingly, it is important to devise tests that may be used to evaluate the giant impact hypothesis. Three such tests are discussed here. None of these is supportive of the giant impact model, but neither do they disprove it.

Jones, J. H.↗