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Numerical and data-driven modeling of spall failure in polycrystalline ductile materials

Indrashish Saha, Lori Graham-Brady

TL;DR

This work develops a physics-based, crystal-plasticity–cohesive-zone numerical model to simulate spall failure in polycrystalline copper under plate impact and generates a large dataset of velocity fields. It compares three data-driven surrogates—3D U-Net, FNO-3D, and U-FNO—for predicting the spatiotemporal velocity response from microstructure inputs, finding that U-FNO and 3D U-Net deliver superior accuracy while FNO-3D underperforms, particularly near grain boundaries. The surrogates generalize reasonably to morphologies near the training distribution, with performance degrading for highly different grain counts and orientations; training cost favors 3D U-Net, while U-FNO offers similar accuracy at higher computational expense. A small-scale Bayesian optimization example demonstrates that DL surrogates can accelerate microstructure design by about two orders of magnitude, enabling rapid exploration of spall-strength targets while acknowledging some uncertainty in out-of-distribution predictions.

Abstract

Developing materials with tailored mechanical performance requires iteration over a large number of proposed designs. When considering dynamic fracture, experiments at every iteration are usually infeasible. While high-fidelity, physics-based simulations can potentially reduce experimental efforts, they remain computationally expensive. As a faster alternative, key dynamic properties can be predicted directly from microstructural images using deep-learning surrogate models. In this work, the spallation of ductile polycrystals under plate-impact loading at strain rates of O(10^6 s^-1) is considered. A physics-based numerical model that couples crystal plasticity and a cohesive zone model is used to generate data for the surrogate models. Three architectures - 3D U-Net, 3D Fourier Neural Operator (FNO-3D), and U-FNO were trained on the particle-velocity field data from the numerical model. The generalization of the models was evaluated using microstructures with varying grain sizes and aspect ratios. U-FNO and 3D U-Net performed significantly better than FNO-3D across all datasets. Furthermore, U-FNO and 3D U-Net exhibited comparable accuracy for every metric considered in this study. However, training the U-FNO requires almost twice the computational effort compared to the 3D U-Net, making it a desirable option for a surrogate model.

Numerical and data-driven modeling of spall failure in polycrystalline ductile materials

TL;DR

This work develops a physics-based, crystal-plasticity–cohesive-zone numerical model to simulate spall failure in polycrystalline copper under plate impact and generates a large dataset of velocity fields. It compares three data-driven surrogates—3D U-Net, FNO-3D, and U-FNO—for predicting the spatiotemporal velocity response from microstructure inputs, finding that U-FNO and 3D U-Net deliver superior accuracy while FNO-3D underperforms, particularly near grain boundaries. The surrogates generalize reasonably to morphologies near the training distribution, with performance degrading for highly different grain counts and orientations; training cost favors 3D U-Net, while U-FNO offers similar accuracy at higher computational expense. A small-scale Bayesian optimization example demonstrates that DL surrogates can accelerate microstructure design by about two orders of magnitude, enabling rapid exploration of spall-strength targets while acknowledging some uncertainty in out-of-distribution predictions.

Abstract

Developing materials with tailored mechanical performance requires iteration over a large number of proposed designs. When considering dynamic fracture, experiments at every iteration are usually infeasible. While high-fidelity, physics-based simulations can potentially reduce experimental efforts, they remain computationally expensive. As a faster alternative, key dynamic properties can be predicted directly from microstructural images using deep-learning surrogate models. In this work, the spallation of ductile polycrystals under plate-impact loading at strain rates of O(10^6 s^-1) is considered. A physics-based numerical model that couples crystal plasticity and a cohesive zone model is used to generate data for the surrogate models. Three architectures - 3D U-Net, 3D Fourier Neural Operator (FNO-3D), and U-FNO were trained on the particle-velocity field data from the numerical model. The generalization of the models was evaluated using microstructures with varying grain sizes and aspect ratios. U-FNO and 3D U-Net performed significantly better than FNO-3D across all datasets. Furthermore, U-FNO and 3D U-Net exhibited comparable accuracy for every metric considered in this study. However, training the U-FNO requires almost twice the computational effort compared to the 3D U-Net, making it a desirable option for a surrogate model.

Paper Structure

This paper contains 25 sections, 19 equations, 22 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Numerical model for the plate impact experiment
  4. Plate impact experiments
  5. Crystal plasticity model
  6. Cohesive zone modeling
  7. FE model implementation
  8. Deep learning models for predicting material response
  9. Data configuration
  10. 3D U-Net model
  11. Fourier neural operator
  12. U-FNO
  13. Model training details
  14. Results and discussion
  15. Plate impact simulation
  16. ...and 10 more sections

Figures (22)

  • Figure 1: (a)Experimental setup depicting a flyer plate driven into a target plate made of a polycrystalline ductile material (b) A typical free surface velocity trace obtained from the back face of the target plate using PDV (c) Interaction of waves in the material and around the spall plane using a $x-t$ diagram (d) Damage growth inside the material from the nucleation of voids around grain boundaries to their coalescence and finally fracture at the grain boundaries
  • Figure 2: (a) 2D synthetic microstructure of size $200 \mu m \times 200\mu m$ and 30 grains generated using Neper QUEY20111729 (b) Meshed microstructure consisting of $16996$ CPE3 elements and $784$ COH2D4 elements (c) Meshed microstructure with the applied boundary conditions (d) Pulse function used to simulate impact loading. The actual function is defined in Eq. \ref{['eq:pulse_function']}.
  • Figure 3: Decomposition of the deformation gradient following Eq. \ref{['eq:decomposition']} in finite strain elasto-plasticity theory.
  • Figure 4: (a) Grain boundary cohesive energy as a function of misorientation angle between two grains. The values are normalized by $\Gamma_{max}$ (b)Traction separation law normalized on $\delta_f$ and dependent on the misorientation of grain boundaries. The pink region shows the spread due to the misorientation. The curve also shows the traction separation curve for $\Delta \theta = 0^\circ$ which is significantly higher than the grain boundaries.
  • Figure 5: (a) Magnified region in a polycrystal domain showing the mesh with element sizes $1 \mu m$, $2.5 \mu m$, $4 \mu m$ and $8.0 \mu m$ (b) Free surface velocity traces for different mesh sizes (c) Spall strength variation with the change in mesh size.
  • ...and 17 more figures