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27 records · Page 2

Multi-objective surrogate-assisted calibration of CPFEM models using macroscopic response and in situ EBSD measurements of grain reorientation trajectories

Crystal plasticity finite element method (CPFEM) models are widely used to simulate the deformation behaviour of polycrystalline materials, but their calibration is often limited by their high computational cost and the non-convexity of the optimisation landscape. Here, this study develops a multi-objective surrogate-assisted calibration workflow that couples a multi-objective genetic algorithm (MOGA) with an adaptively trained deep neural network (DNN) surrogate model to efficiently identify CPFEM parameters from experimental data. The workflow is demonstrated on three crystal plasticity (CP) formulations of increasing complexity — Voce hardening (VH), two-coefficient latent hardening (LH2), and six-coefficient latent hardening (LH6) — using in situ electron backscatter diffraction (EBSD) measurements of Alloy 617 under uniaxial tensile loading. The CPFEM models are calibrated against the experimentally observed stress–strain response and reorientation trajectories of eight grains, then validated against eight additional trajectories and overall texture evolution. Across the CP formulations, the macroscopic response was reproduced reliably, while differences emerged in the robustness and accuracy of the grain-scale predictions. Including grain reorientation trajectories in the multi-objective calibration improved texture evolution predictions and filtered out physically inconsistent parameter sets that can arise from calibrating against only the stress–strain data. The workflow also demonstrates good transferability of calibrated parameters from a low- to a high-fidelity microstructural model. These results provide practical guidance for integrating in situ microstructural data into CPFEM through efficient, repeatable, and physically meaningful multi-objective calibration.

Crystal plasticity finite element method↗

Crystal plasticity finite element simulation of lattice rotation and x-ray diffraction during laser shock compression of tantalum

Here we present a crystal plasticity model tailored for high-pressure, high-strain-rate conditions that uses a multiscale treatment of dislocation-based slip kinetics. We use this model to analyze the pronounced plasticity-induced lattice rotations observed in shock-compressed polycrystalline tantalum via in situ x-ray diffraction. By making direct comparisons between experimentally measured and simulated texture evolution, we can explain how the details of the underlying slip kinetics control the degree of lattice rotation that ensues. Specifically, we show that only the highly nonlinear kinetics caused by dislocation nucleation can explain the magnitude of the rotation observed under shock compression. We demonstrate a good fit between our crystal plasticity model and x-ray diffraction data and exploit the data to quantify the dislocation nucleation rates that are otherwise poorly constrained by experiment in the dynamic compression regime.

36 MATERIALS SCIENCE↗

Incorporating dynamic recrystallization into a crystal plasticity model for high-temperature deformation of Ti-6Al-4V

During hot deformation of (α + β) titanium alloys, the simultaneous action of strain and temperature in the (α + β) regime facilitates dynamic recovery, dynamic recrystallization (DRX), and phase transformations via non-equilibrium paths. DRX is manifested in the form of fine recrystallized α or β grains. Here, in the present study, a two-phase crystal plasticity finite element framework (CP-DRX) has been developed which incorporates DRX kinetics into the crystal plasticity (CP) model to predict the flow characteristics of Ti-6Al-4V alloys during thermo-mechanical processing. The CP slip system parameters, as well as elastic properties from both α and β phases of Ti, are calibrated for different strain rate conditions. An EBSD-informed two-phase microstructure representation has been utilized in the CP-DRX framework to explore the time-dependent evolution of DRX microstructure and crystal orientation for different strain rate conditions. The proposed CP-DRX can capture the evolution of crystal orientation and plastic flow stress–strain response of polycrystalline Ti-6Al-4V during the deformation process. Furthermore, the proposed model is able to capture the softening behavior, observed in average stress–strain response from experiments performed using a Gleeble thermomechanical simulator and predict the recrystallization texture.

(α+ β)-Titanium (Ti) Alloys↗

Crystal mechanics-based thermo-elastic constitutive modeling of orthorhombic uranium using generalized spherical harmonics and first-order bounding theories

In earlier works, a mathematical procedure for invertible microstructure-property linkages was developed using computationally efficient spectral methods for polycrystalline cubic and hexagonal metals. This paper formulates such invertible microstructure–property linkages for orthorhombic polycrystalline metals relying on the generalized spherical harmonics (GSH) spectral basis. The procedure is used to compute property closures of orthorhombic polycrystals. The closures represent the complete set of theoretically possible combinations of effective properties for a selected material. The procedure relies on the first-order bounding theories and considers orientation distribution functions (ODFs) as the main microstructural descriptor influencing homogenized properties. Numerous examples of these closures involving second-rank thermal expansion and fourth-rank elastic stiffness tensorial properties over a broad range of temperatures are presented for α-uranium (α-U). In doing so, certain key properties of these closures are exploited to facilitate their computation with drastically reduced computational effort. Along with the recently developed GSH-based interpolation procedure for ODFs from coarsely spaced experimental measurement grids to finely spaced finite element mesh resolution grids presented in Barrett et al., the developed computationally efficient ODF-effective property linkages are used to establish a crystal mechanics-based simulation framework coupled with the finite element method (FEM). The ODF dependent thermal expansion and elastic stiffness tensors are efficiently calculated at every integration point and used by the FEM to predict the overall distortion of a hemispherical part made of α-U during heating. In conclusion, it is shown that the developed framework can be used to simulate microstructurally heterogeneous components under thermo-mechanical loadings in a computationally efficient manner.

36 MATERIALS SCIENCE↗

Crystallographic orientation and spatially resolved damage in a dispersion-hardened Al alloy

The in-situ neutron diffraction technique, in combination with both the full-field crystal elasto-viscoplastic finite element model and microstructural characterization, was used to study the deformation-induced damage anisotropy in a commercial Al alloy, subjected to uniaxial tensile and cyclic loading. The simulations capture well the crystallographic-orientation-dependent lattice strain behavior. The hard grains, e.g. those orientated with the <111> and <422> orientations parallel with the uniaxial loading direction (LD), feature large Taylor factors and seem more prone to form damage-related band structures. Their effective elastic moduli decrease with the accumulation of damage, which are different from the soft grains orientated with the <200> orientation along the LD. Correlation between the distribution of voids and that of the residual lattice strain developed after failure may exist. The maximum tensile type residual lattice strain observed after failure may be resulted from the band structure formed in the hardest <111> grains. It was revealed that the band structure triggered by the hard particles could be one of sources of damage. In addition, while the specimen was obviously damaged, a fast stress relief was evidenced after unloading from the tension, especially at the beginning of unloading. Our present investigations provide a novel method for exploring the damage mechanisms of polycrystalline materials during plastic deformation.

36 MATERIALS SCIENCE↗

Volumetric analysis and mesh generation of real and artificial microstructural geometries

Producing a viable finite element mesh of realistic microstructural structural geometry is a critical step in analyzing the thermo-mechanical behavior of complex multi-material composites. Advancements in imaging technology such as micro computed tomography have allowed modelers to access high resolution mesoscale geometries for direct numerical simulation. However, converting from voxel based 3D images to usable finite element meshes has been challenging. A robust method including algorithms and software scripts for generating finite element meshes from 3D imaged microstructures is presented in this paper. It includes a routine for inserting cohesive elements around material interfaces to enable modeling of interface properties including delamination and damage. The algorithms and procedures presented in this method leverage currently available software packages for processing surface based geometry into volume based meshes. In addition to converting real geometry from physical imaging systems, algorithms for producing numerically generated and statistically equivalent microstructural geometry are also included. These artificial microstructures can be a valuable resource for modelers when physical specimens do not exist or are limited in quantity: Method establishes a workflow from voxel data to viable finite element mesh including interface information, and Includes a method for synthetic geometry generation based on metrics from real microstructures.

36 MATERIALS SCIENCE↗

Modeling Microstructural Effects on Heterogeneous Temperature Fields within Polycrystalline Explosives

The paper addresses the role of crystal anisotropy on the evolution of heterogeneous temperature fields in plastic-bonded explosives (PBXs) under conditions of weak shock. The modeling approach is based on simplified idealizations of PBX microstructure including RDX grains and estane binder regions subjected to velocity boundary conditions representative of impact conditions in situ. The constitutive description of the microstructure constituents includes a dislocation-based, anisotropic, single crystal plasticity model for the explosive grains and a linear viscoelastic model to represent the estane binder. Large suites of simulations were used to systematically study the correlation in heating of the grains with local wave dynamics, crystal orientation, and the microstructural neighborhood. These correlations were identified through the selection of characteristics of crystal anisotropy including oriented wave speeds and Taylor factor. A key observation is that the wave dispersion within a certain distance from the impact interface plays a dominant role in the temperature field. Beyond this distance, individual crystal orientations play a more dominant role, but cannot entirely account for the observed heterogeneity without consideration of the local microstructure neighborhood.

42 ENGINEERING↗

Crystal plasticity modeling of strain-induced martensitic transformations to predict strain rate and temperature sensitive behavior of 304 L steels: Applications to tension, compression, torsion, and impact

This paper advances crystallographically-based Olson-Cohen (direct γ → α’) and deformation mechanism (indirect γ→ε→α’) phase transformation models for predicting strain-induced austenite to martensite transformation. Here, the advanced transformation models enable predictions of not only strain-path sensitive, but also of strain-rate and temperature sensitive deformation of polycrystalline stainless steels (SSs). The deformation of constituent grains in SSs is modeled as a combination of anisotropic elasticity, crystallographic slip, and phase transformation, while the hardening is based on the evolution of dislocation density and explicit shifts in phase fractions. Such grain-scale deformation is implemented within the meso-scale elasto-plastic self-consistent (EPSC) homogenization model, which is coupled with the implicit finite element (FE) method to provide a constitutive response at each FE integration point for solving boundary value problems at the macro-scale. Parameters pertaining to the hardening and transformation models within FEEPSC are calibrated and validated on a suite of data including flow curves and phase fractions for monotonic compression, tension, and torsion as a function of strain-rate and temperature for wrought and additively manufactured (AM) SS304L. To illustrate the potential and accuracy of the integrated multi-level FE-EPSC simulation framework, geometry, mechanical response, phase fractions, and texture evolution are simulated during gas-gun impact deformation of a cylinder and quasi-static tension of a notched specimen made of AM SS304L. Details of the simulation framework, comparison between experimental and simulation results, and insights from the results are presented and discussed.

304L steels↗

Unraveling the implications of finite specimen size on the interpretation of dynamic experiments for polycrystalline aluminum through direct numerical simulations

Normal and Pressure-shear plate impact (NPI and PSPI) experiments are popular experimental techniques for studying the mean-field macroscopic behavior of polycrystalline metals under high-rate dynamic loading. However, since both configurations rely upon geometry for subjecting the specimen to high strain rates, these experiments often involve a limited specimen size. Moreover, because of the inherent heterogeneities present within polycrystalline metals, it is difficult to ascertain if the size of the specimen and/or regions where measurements are made are sufficiently large for making representative inferences about the mean-field macroscopic properties from single-point velocity measurements. In the present study, we quantify the expected measurement variability on observable point measurements in NPI and PSPI experiments by carrying out direct numerical simulations (DNS) of statistically representative polycrystalline microstructures subjected to dynamic compression and compression-shear loading. In particular, we consider the role of specific material heterogeneities (e.g. the grain-to-grain difference in size, crystallographic orientation) on dispersion in the normal and transverse particle velocity records and on local fluctuations in key state variables (e.g. velocity, accumulated plastic strain) by incorporating these effects directly into a representative synthetic microstructure geometry and crystalline description of pure polycrystalline aluminum. The form of the present study is a large parametric investigation, consisting of ten ensembles of one hundred simulations. Each of the thousand simulations reflects a randomly realized synthetic microstructure in one of five cases of decreasing average grain size for the two loading configurations. Our analysis of the DNS results demonstrates that for both of these experimental configurations, the grain size directly correlates with the coefficient of variation (CV) in simulated point measurements, showing a convergent decrease in CV to zero (i.e. particle velocity record approaches the mean-field value) with decreasing grain size. Remarkably, the magnitude of variations in the particle velocity record is shown to be largest where the deviatoric stresses are most significant. In the case of NPI, this occurs at the elastic and plastic wavefront, whereas, in the case of PSPI, the magnitude of fluctuations are approximately constant throughout the experimental window time. The reasoning for the scatter in particle velocity due to the heterogeneous microstructure is demonstrated to be dependent on the mechanisms for accommodating deformation and on the interaction of reflection waves generated at sites of heterogeneities occurring at the scale of grains. Lastly, we develop a power-law description for the magnitude of scattering versus characteristic length, which provides a statistical framework for assessing the required number of grains per characteristic specimen dimension for minimizing scatter within these two experimental configurations (NPI, PSPI).

36 MATERIALS SCIENCE↗