Abstract

Micromechanical modeling of material behavior has become an accepted approach to describe the macroscopic mechanical properties of polycrystalline materials in a micro- structure-sensitive way. The microstructure is modeled by a representative volume ele- ment (RVE), and the anisotropic mechanical behavior of individual grains is described by a crystal plasticity model. Such micromechanical models are subjected to mechanical loads in a finite element (FE) simulation and their macroscopic behavior is obtained from a homogenization procedure. However, such micromechanical simulations with a discrete representation of the material microstructure are computationally very expensive, in par- ticular when conducted for 3D models, such that it is prohibitive to apply them for process simulations of macroscopic components. In this work, we suggest a new approach to de- velop microstructure-sensitive, yet flexible and numerically efficient macroscopic material models by using micromechanical simulations for training Machine Learning (ML) algo- rithms to capture the mechanical response of various microstructures under different loads. In this way, the trained ML algorithms represent a new macroscopic constitutive relation, which is demonstrated here for the case of damage modeling. In a second application of the combination of ML algorithms and micromechanical modeling, a proof of concept is presented for the application of trained ML algorithms for microstructure design with respect to desired mechanical properties. The input data consist of different stress-strain curves obtained from micromechanical simulations of uniaxial testing of a wide range of microstructures. The trained ML algorithm is then used to suggest grain size distributions, grain morphologies and crystallographic textures, which yield the desired mechanical response for a given application. For validation purposes, 1the resulting grain microstructure parameters are used to generate RVEs, accordingly and the macroscopic stress-strain curves for those microstructures are calculated and compared with the target quantities. The two examples presented in this work, demonstrate clearly that ML methods can be trained by micromechanical simulations, which capture material behaviour and its relation to microstructural mechanisms in a physically sound way. Since the quality of the ML algorithms is only as good as that of the micromechanical model, it is essential to validate these models properly. Furthermore, [...]

Highlights

  • Most of the processes that happen in nature are too complex to analyze, have too many independent parameters, and sometimes even the interrelation between parameters is unknown

  • Mangal and Holm investigated the formation of stress hotspots in polycrystalline materials (Mangal and Holm, 2018) under uniaxial tensile deformation by integrating full field crystal plasticity based deformation models and Machine Learning (ML) techniques

  • The same randomly partitioned data set for the training and the testing process is used for both algorithms

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Summary

Introduction

Most of the processes that happen in nature are too complex to analyze, have too many independent parameters, and sometimes even the interrelation between parameters is unknown. Swaddiwudhipong et al used least square support vector machines (LS-SVMs) to relate load displacement curves from indentation directly to the elastic modulus and yield stress of materials obeying power law hardening They used data from a simulation of indentation of different geometries in ABAQUS (Swaddiwudhipong et al, 2005). Mangal and Holm investigated the formation of stress hotspots in polycrystalline materials (Mangal and Holm, 2018) under uniaxial tensile deformation by integrating full field crystal plasticity based deformation models and ML techniques. They used synthetic 3D microstructures and a number of crystallographic and geometric factors are defined to describe the relevant features. They showed that Random Forest models can predict stress hotspots with receiving an operating characteristic curve (ROC-AUC) metric equal to 0.7403 in FCC material

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