Machine learning-enabled identification of micromechanical stress and strain hotspots predicted via dislocation density-based crystal plasticity simulations

Highlights

• • A crystal plasticity with first principles-informed dislocation density hardening is adopted to identify the key microstructural features in formation of strain and stress localizations.

  • Ensemble machine learning analysis of micromechanical data reveals the hotspots in the vicinity of the grain boundaries, crystals with higher Taylor/Schmid factors, and high intergranular misorientations.

    • Intergranular misorientations are more responsible in formation of stress hotspots while Schmid factors take the precedence under high accumulated plastic strains.

    • Grain size becomes important only under combined tension/shear loading and high accumulated plastic strains.

Abstract

The present work uses a full-field crystal plasticity model with a first principles-informed dislocation density (DD) hardening law to identify the key microstructural features correlated with micromechanical fields localization, or hotspots, in polycrystalline Ni. An ensemble learning approach to machine learning interpreted with Shapley additive explanation was implemented to predict nonlinear correlations between microstructural features and micromechanical stress and strain hotspots. Results reveal that regions within the microstructure in the vicinity of grain boundaries, higher Schmid factors, low slip transmissions and high intergranular misorientations, are more prone to being micromechanical hotspots. Additionally, under combined loading and large plastic deformations, slip transmissions take precedence over intergranular misorientations in formation of both strain and stress hotspots. The present work demonstrates a successful integration of physics-based crystal plasticity with DD-based hardening into machine learning models to reveal the microscale features responsible for the formation of local stress and strain hotspots within the grains and near the grain boundaries, as function of applied deformation states, grain morphology/size distribution, and microstructural texture, providing insights into micromechanical damage initiation zones in polycrystalline metals.

Introduction

The formation of micromechanical hotspots during loading triggers damage initiation and accumulation, e.g., void nucleation, grain boundary sliding, shear band formation (Eghtesad and Knezevic, 2021; Qin and Beese, 2021). Therefore, to aid in the understanding of microstructural origins of failure, as well as to enable microstructural design for superior properties, it is critical to understand the microstructural characteristics that contribute to the formation of micromechanical hotspots, and if and how these change with microstructure and applied loading state. A quantitative description of plastic deformation and subsequent damage incubation in crystalline materials requires knowledge of how crystallographic texture, grain morphology, and grain boundary (GB) character of polycrystalline microstructures alter the localization of micromechanical fields inside the grains and near the GBs.

Crystal plasticity (CP) models facilitate the modeling of microstructure-sensitive elasto-plastic deformation based on the mechanical response of crystalline grains. Among CP models that capture explicit grain-grain interactions and spatial gradients, the crystal plasticity fast Fourier transform (CPFFT) (Lebensohn and Rollett, 2020; Lucarini et al., 2021; Roters et al., 2019; Shanthraj et al., 2019) and the crystal plasticity finite element method (CPFEM) (Alharbi and Kalidindi, 2015; Cheng et al., 2021; Lakshmanan et al., 2022; Tran et al., 2022; Wang et al., 2020; Yaghoobi et al., 2022; Yaghoobi et al., 2019) are predominant in the literature. Of these two, CPFFT is the more computationally efficient formulation (Eghtesad et al., 2018; Eghtesad et al., 2020), especially with recent developments enabling high-performance computing (HPC) and graphics processing unit (GPU) hardware acceleration.

While HPC has improved the efficiency of CP modeling, simulations of very large datasets are still time-consuming. To address this, recent research has enabled the integration of genetic algorithm (GA), machine learning (ML) and deep learning into microstructure-property linkage and crystal plasticity applications (Batra, 2021; Ibragimova, 2022; Kotha et al., 2019; Liu et al., 2015; Pilania, 2021; Saidi et al., 2022; Sundararaghavan and Zabaras, 2005; Tu et al., 2022; Veasna et al., 2023). ML based self-consistent parametrically-upscaled crystal plasticity model for Ni-based superalloys was studied in (Weber et al., 2022). Tu et al. proposed an instant structure-property prediction model for additive manufactured steel using a crystal plasticity trained deep learning surrogate (Tu et al., 2022). A novel method for reconstruction of orientation data via image processing and optimization was presented using genetic algorithm (Kaushik et al., 2022).

Neural networks (NN) and convolutional neural networks (CNN) have been utilized for a wide range of applications in crystal plasticity. Donegan et al. used CNN based on microstructural images to predict stress localization during the thermoelastic response of particulate microstructures (Donegan et al., 2019). CNN in CPFEM model was used to predict the localized deformation in aluminum alloys (Ibragimova et al., 2022). Bonatti et al. formulated a recurrent neural network (RNN) surrogate model of crystal plasticity as a computationally-efficient surrogate for CPFFT and CPFEM models (Bonatti et al., 2022). Fuhg et al. presented an input convex NN (ICNN) framework for predicting texture-dependent smooth and convex macroscopic yield functions from crystal plasticity simulations of textured polycrystals (Fuhg et al., 2022). A new artificial neural networks (ANN) based crystal plasticity model for FCC materials and its application to non-monotonic strain paths was proposed in (Ibragimova et al., 2021).

Fatigue, creep, damage and micro-void crystal plasticity modeling using ML has also gained interest recently. Zhang et al. predicted the key factors affecting the grain boundary damage using XGBoost ML algorithm (Zhang et al., 2022). Cyclic damage in Inconel 718 superalloy was investigated using NN (Ye et al., 2022). Microstructure-dependent fatigue performance of martensitic steel was investigated using ML (Wang et al., 2023). Liu at al. proposed a novel deep learning model to predict the microvoid growth in heterogeneous polycrystals (Liu et al., 2022a). Hiemer et al. identified the time to failure in creep simulations by machine learning (Hiemer et al., 2022). Fatigue-induced void formation was investigated using K-nearest neighbor classification (KNN) by (Indeck et al., 2022).

Several studies have explored the formation of stress hotspots within polycrystalline microstructures. Rollett et al. investigated stress hotspots under uniaxial tension in Cu using the CPFFT model with Voce hardening (Rollett et al., 2010). Chief findings of a study of strain localization under rolling conditions were that strain concentrations occur at triple junctions or quadruple points and then interconnect with further straining to create shear bands that extend across the polycrystalline structure (Ardeljan et al., 2015). Particularly, the triggering strain hotspots occurred at junctions of grains with dissimilar reorientation propensities, while cold spots were formed vice-versa, i.e., at junctions of grains with similar reorientation trends. Fatigue stress hotspots in polycrystalline Cu were explored by a combination of high resolution EBSD (HR-EBSD) and CPFEM by Wan et al (Wan et al., 2016).

Mangal et al. investigated the formation of stress hotspots in Cu and alpha-titanium alloy was investigated by integrating ML techniques and the CPFFT model with a phenomenological Voce hardening law (Mangal and Holm, 2018a, 2019). The methodology was based on grain-wise averaging of the stress fields and intergranular misorientations of neighboring grains. The most relevant microstructural features related to the stress hotspots formed under uniaxial loading were identified using a Least Absolute Shrinkage and Selection Operator (LASSO) linear regression criterion (Ranstam and Cook, 2018). A grain-wise averaging method reduces the complexity of micromechanical variations and local gradients in the vicinity of grain boundaries.

In most practical applications, materials are subjected to complex multiaxial loading conditions, which affect the intragranular fields in ways that are lost during homogenization. Additionally, it has been shown that the local distribution of stresses and strains within a microstructure is heavily dependent on the hardening law (Patil et al., 2021). Phenomenological models such as Voce, in contrast to the physics-based dislocation density hardening law used here, underestimate the heterogeneity of spatial distributions by introducing spurious grain-wise homogenizations. To identify the dominant microstructural features responsible for stress and strain hotspots, the present work adopts a CPFFT model with a physics-based dislocation density (DD) hardening model informed by density functional theory (DFT) (Eghtesad et al., 2022b). A set of microstructures varying in crystallographic texture and grain morphology was generated and plastically deformed under a range of complex deformation states under combined tension and shear. To capture heterogeneities in the vicinity of grain boundaries, micromechanical descriptors as well as hotspots were identified locally in place of grain-wise averaging. Ensemble machine learning interpreted with Shapley additive explanation was then applied to identify the microstructural features most strongly associated with local stress and strain hotspots in pure polycrystalline Ni.