An efficient machine learning approach to establish structure-property linkages

doi:10.1016/j.commatsci.2018.09.034

Computational Materials Science

Volume 156, January 2019, Pages 17-25

https://doi.org/10.1016/j.commatsci.2018.09.034 Get rights and content

Highlights

•
Machine learning approach to efficiently utilize microstructure based simulations.
•
Structure-property linkages were made with few full-field simulations.
•
Optimal structures were found with few full-field simulations.

Abstract

Full-field simulations with synthetic microstructure offer unique opportunities in predicting and understanding the linkage between microstructural variables and properties of a material prior to or in conjunction with experimental efforts. Nevertheless, the computational cost restrains the application of full-field simulations in optimizing materials microstructures or in establishing comprehensive structure-property linkages. To address this issue, we propose the use of machine learning technique, namely Gaussian process regression, with a small number of full-field simulation results to construct structure-property linkages that are accurate over a wide range of microstructures. Furthermore, we demonstrate that with the implementation of expected improvement algorithm, microstructures that exhibit most desirable properties can be identified using even smaller number of full-field simulations.

Graphical abstract

Introduction

While traditional trial and error has served well in designing material microstructures with desired or even enhanced properties and performance, computational means to aid microstructure design are highly desirable for further accelerating materials design. Unfortunately, the linkage between microstructure and properties is a vastly complex one. The sheer complexity in quantifying the geometry of the microstructure coupled with the uncertainty brought about by how different phases mechanically interact given specific structures are only two of many frustrations in computationally aided microstructure design.

There are several approaches available for establishing structure-property linkages. Some of the conventional approaches include analytical approach based on statistical continuum theories [1], [2], [3], mean-field approach based on Eshelby’s inclusion problems [4], [5], [6], numerical approach based on finite element method (FEM). The approach based on statistical continuum theories, when successfully established, is computationally very cheap. Nonetheless, the approach is hindered by difficulties regarding the derivation of analytic expressions for Green’s function kernels and the convergence of the series expansions employed in the approach [7], [8]. Mean-field approach is also known to be computationally cheap. However, the approach is unable to predict stress or strain localization and often cannot take into account complex morphology and spatial distribution of differing phases. The numerical approach involving FEM is often limited by its computational cost. To date, several works that employed a framework that establishes process-structure-property (PSP) linkages using low dimensional representation of microstructures and regression models as surrogate models are available [9], [10], [11], [12], [13], [14]. In the framework, microstructures are first quantified using two-point correlation statistics. Then, principal component analysis (PCA) is applied to the statistics to reduce its dimension. Finally, a surrogate model is constructed using the low dimensional representation of microstructures as input variables. Some of these works employed full-field simulations to capture the PSP linkages [9], [10], [11], [12], [13], [14]. In particular, Latypov et al. [9] captured structure-property (SP) relations using microstructure based simulation results on synthetic microstructures for multivariate regression.

The advantage of full-field simulations with synthetic microstructures is that these simulations can quantitatively evaluate how microstructural variations affect the mechanical properties of materials [9], [15]. This type of modelling approach already demonstrated its effectiveness in describing and predicting mechanical behavior of composites [16], steels [17], [18], [19], [20], and other alloys [21], [22], [23]. Despite their merits, microstructure based modelling techniques suffer from their high computational cost. In the framework introduced above, the issue is mainly addressed by constructing an approximate model. Approximate model, or surrogate model, is any model that can mimic the behavior of full-field models at a fraction of their computational cost. Nevertheless, any surrogate model to replace full-field simulations will still require output from the simulations. Consequently, the time it takes to develop an accurate surrogate will be proportional to the number of the simulations necessary. Therefore, robust surrogate modelling with an efficient sampling scheme is necessary to expedite the process of constructing SP linkages over a wide range of microstructures.

New opportunities for surrogate modelling have opened up with the recent surge of interest in machine learning (ML) techniques. Many ML methods such as artificial neural network models [24], Gaussian process (GP) based methods [25], decision-tree and random forest models [26], and kernel-based methods [27] can serve as accurate surrogate models. Among these methods, GP methods offer a principled approach in dealing with model uncertainty. In particular, Gaussian process regression (GPR) can predict unobserved values as well as their uncertainty. This allows one to selectively conduct full-field simulations where high uncertainty in the ML model is expected. Furthermore, GPR is known to be suitable for optimization of expensive black-box simulations via Efficient Global Optimization (EGO) method based on expected improvement (EI) algorithm [28], making GPR a very attractive approach for microstructure optimization using full-field simulations. In this work, we extended the recently developed data-driven frameworks for SP linkages [9], [10], [11], [12], [13], [14] by combining synthetic microstructure based simulations and GP based ML to construct SP linkages. Furthermore, we implemented the EI algorithm to find optimal microstructures within a large microstructure database. We first demonstrate effectiveness of the approach in constructing an accurate SP linkages over 1100 synthetic two-phase microstructures using only a fraction of the microstructures for full-field simulations. Afterwards, by implementing the EI algorithm, we show that the approach can search for an optimal microstructure that maximizes specific property within the dataset with even fewer full-field simulations.

Section snippets

Summary of the method

The overall schematic for the proposed approach is presented in Fig. 1. Firstly, a database consisting of large amount of synthetic microstructures are generated (Section 2.2). The microstructures are then quantified using two-point correlation statistics, which has been successfully used in microstructure quantifications for surrogate models [9], [10], [11], [12], [13], [14]. Following the works that establish PSP linkages [9], [10], [11], [12], [13], [14], the two-point correlation statistics

Microstructure based simulation results

Microstructure based simulations were conducted over 1100 different synthetic microstructures to calculate the uniform elongation (U.El), ultimate tensile strength (UTS), and strain localization index ( $X_{1}$ ) defined in soft phase of each microstructure. With $ε_{i}$ representing the equivalent plastic strain of phase i, the strain localization index of the soft phase is defined as $X_{1} = \frac{ε_{1}}{ε_{bulk}} .$

For uniaxial tension, U.El and UTS can be found using Considère criterion defined as $\frac{\partial σ_{bulk}}{\partial ε_{bulk}} = σ_{bulk},$ where $σ_{}$

Conclusions

The proposed framework provides a very efficient means of computationally aided materials design by training GPR models with low dimensional representation of microstructures as inputs and full-field simulations as outputs. Using the GPR with uncertainty driven sampling scheme, we established accurate SP linkages over a microstructure database composed of over 1100 synthetic microstructures by evaluating only a small fraction of the entire microstructure database. Moreover, using the GPR with

Data availability

The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.

Acknowledgment

This study was supported by POSCO (2017Y054) and Brain Korea 21 PLUS project for Center for Creative Industrial Materials (F16SN25D1706).

Author contribution

Jaimyun Jung and Hyung Keun Park contributed to the implementation of the computer code and supporting algorithms. Jaimyun Jung and Hyoung Seop Kim have contributed to development of the methodology and preparation of the manuscript. Jaimyun Jung, Jae Ik Yoon, Jin You Kim, and Hyoung Seop Kim have contributed to conceptualization.

References (46)

A. Mikdam et al.
Effective conductivity in isotropic heterogeneous media using a strong-contrast statistical continuum theory
J. Mech. Phys. Solids
(2009)
E. Kröner
Bounds for effective elastic moduli of disordered materials
J. Mech. Phys. Solid.
(1977)
B. Raju et al.
A review of micromechanics based models for effective elastic properties of reinforced polymer matrix composites
Compos. Struct.
(2018)
L.F.A. Bernardo et al.
Modeling and simulation techniques for polymer nanoparticle composites – a review
Comput. Mater. Sci.
(2016)
A. Abdul-Latif et al.
Modeling the mechanical behavior of heterogeneous ultrafine grained polycrystalline and nanocrystalline FCC metals
Mech. Mater.
(2018)
D.T. Fullwood et al.
A strong contrast homogenization formulation for multi-phase anisotropic materials
J. Mech. Phys. Solid
(2008)
S. Torquato
Effective stiffness tensor of composite media – I. Exact series expansions
J. Mech. Phys. Solids
(1997)
M.I. Latypov et al.
Data-driven reduced order models for effective yield strength and partitioning of strain in multiphase steels
J. Comput. Phys.
(2017)
Y.C. Yabansu et al.
Extraction of reduced-order process-structure linkages from phase-field simulations
Acta Mater.
(2017)
N.H. Paulson et al.
Reduced-order structure-property linkages for polycrystalline microstructures based on 2-point statistics
Acta Mater.
(2017)

V. Picheny et al.

Noisy kriging-based optimization methods: a unified implementation within the DiceOptim package

Comput. Stat. Data Anal.

(2014)

Cited by (79)

Data-driven texture design for reducing elastic and plastic anisotropy in titanium alloys
2024, Acta Materialia
Polycrystalline titanium alloys exhibit anisotropic elastic and plastic properties, which hinder their extensive application as structural components. Overcoming this anisotropy via texture control is challenging due to the anisotropy intrinsic to the titanium single crystal. We propose a theoretical framework to derive textures that minimize anisotropy while maximizing Young’s modulus or flow stress. The workflow integrates data-driven methods, convex optimization theory, and computational crystal plasticity, using measured elastic constants and the alloy’s three slip modes. Optimization constraints are applied to predict textures that satisfy an anisotropy-reducing texture-property relationship. Examples include minimizing both elastic and plastic anisotropy while maximizing stiffness or flow stress, maximizing both stiffness and flow stress, and minimizing the number of distinct orientations. Deformation crystal plasticity simulations of 3D polycrystal microstructure realizations of the example textures demonstrate the achievement of target properties. We show that uniformly distributed (or no) textures or textures designed to purely reduce elastic anisotropy are accompanied by reduced moduli. Counterintuitively, the analysis reveals that appropriate fractions of a relatively small number of select orientations can reduce elastic or plastic anisotropy. Moreover, we derive anisotropy-reducing textures constrained to achieve similarity to those from common metal forming processes like rolling. Finally, we show that anisotropy-reducing textures from this framework can be effectively used for minimizing anisotropy in other Ti alloys, without the need to repeat the data-collection and optimization processes. This study offers new insights into the link between microstructure texture and structural properties, providing a novel approach to designing materials of anisotropic hexagonal close-packed crystals.
Tailoring the mechanical properties of 3D microstructures: A deep learning and genetic algorithm inverse optimization framework
2023, Materials Today
Materials-by-design has been historically challenging due to complex process-microstructure-property relations. Conventional analytical or simulation-based approaches suffer from low accuracy or long computational time and poor transferability, limiting their applications in solving the inverse material design problem. Here, we establish a deep learning and genetic algorithm framework that integrates forward prediction and inverse exploration. This framework provides an end-to-end solution to achieve application-specific mechanical properties by microstructure optimization. In this study, we select the widely used Ti-6Al-4V alloy to demonstrate the effectiveness and efficiency of this framework. We realize this by tailoring its 3D microstructures to achieve various yield strengths and elastic moduli across a large design space, while minimizing stress concentration factors. Compared with conventional methods, our framework is efficient, versatile, and readily transferrable to a wide range of materials and properties. Paired with emerging additive manufacturing techniques in controlling local microstructural features, our method offers far-reaching potentials for the accelerated development of application-specific, high-performing materials.
Machine learning-based identification of interpretable process-structure linkages in metal additive manufacturing
2023, Additive Manufacturing
The use of data-driven methods for metal additive manufacturing (AM) is currently gaining importance as indicated by the increasing number of scientific literature in this field. Incorporation of data-driven methods has the potential to eliminate current bottlenecks in microstructure design given the diverse and complex nature of microstructures in additively manufactured metals. So far, coupling of existing simulation methods, e.g. physics-based process and microstructure models, to simulate AM microstructures with desired morphological characteristics requires extensive computational resources, high computation times and therefore, allows no scalable output. The extension of experimental- and simulation-based approaches by machine learning (ML) algorithms enables fast and computationally efficient predictions. However, the underlying architecture of ML algorithms often does not allow domain experts to interpret how predictions of the model were made and which features are responsible to what extent. This is why ML models are often referred to as black- box models. In this study, we present a data-driven framework based on physics-based simulation data to reveal explainable process-(micro)structure (P-S) linkages for metal AM. We provide an open-source dataset of 960 unique 3D microstructures created by simulation of powder bed fusion in metal AM. We employed the stochastic parallel particle kinetic simulator (SPPARKS) that is based on the kinetic Monte Carlo (kMC) method as an exemplary AM microstructure generator. Selected ML regression algorithms aim to predict 3D chord length distributions (CLDs), as a morphology descriptor, depending on the associated process parameter combinations. Various dimension reduction algorithms are applied for computationally efficient use of the data space. The proposed methodology allows (i) microstructure predictions under given processing conditions and (ii) to navigate experts in the process parameter space to achieve target microstructures. In this context, SHAP (SHapley Additive exPlanations) values are used to decipher the contribution of individual process parameters to the microstructure evolution. In particular, SHAP values calculated in this study unfold the width of the melt pool and the heat-affected zone as dominant features on the model output. We provide open-access to the used dataset and methods for the scientific community to gain experience with the proposed approach.
Quantification of similarity and physical awareness of microstructures generated via generative models
2023, Computational Materials Science
Large repositories of microstructure realizations lie at the centre of developing effective structure–property correlations in materials. It is, however important that the microstructure generation procedures not only reconstruct a large number of microstructures in a computationally inexpensive manner but also hold awareness regarding the physical significance of the underlying microstructure. While machine learning techniques are used for computationally efficient microstructure generation, the similarity and physical awareness of the generated microstructures with the ground truth are rarely quantified. In this work, we use a variant of generative adversarial network (GAN) i.e. StyleGAN2, to generate microstructures with varied morphologies from a small dataset of Dual Phase (DP) steels. The similarity between the generated and the original microstructures is quantified using various metrics such as structure similarity index (SSIM), peak signal to noise ratio (PSNR) and signal to noise ratio (SNR). The physical awareness is quantified by comparing the predictions of macroscopic mechanical properties of the GAN generated and original microstructures using a reduced order model. We also qualitatively estimate the learning of the GAN latent space in terms of microstructure morphology. It is observed that there exists a relationship between the microstructure morphological information and the similarity assessment metrics.
Machine learning-based multi-objective optimization for efficient identification of crystal plasticity model parameters
2023, Computer Methods in Applied Mechanics and Engineering
Citation Excerpt :
In particular, polynomial approximation of response surfaces and canonical correlation analyses were used in sensitivity and parameter identification studies [18,31]. Gaussian process (GP) models, also known as Kriging, have been used in constructing structure–property linkages [38], more recently, in fluid dynamics simulation [39], and in linking crystal plasticity results to part scale simulations [33]. Barton et al. used a metric-tree database for course-scale queries, which explores a pre-determined region, and Kriging as an adaptive scheme to search for optimal points under some threshold [33].
A set of constitutive model parameters along with crystallography governs the activation of deformation mechanisms in crystal plasticity. The constitutive parameters are typically established by fitting of mechanical data, while microstructural data is used for verification. This paper develops a Pareto-based multi-objective machine learning methodology for efficient identification of crystal plasticity constitutive parameters. Specifically, the methodology relays on a Gaussian processes-based surrogate model to limit the number of calls to a given crystal plasticity model, and, consequently, to increase the computational efficiency. The constitutive parameters pertaining to an Elasto-Plastic Self-Consistent (EPSC) crystal plasticity model including a dislocation density-based hardening law, a backstress law, and a phase transformations law are identified for two materials, a dual phase (DP) steel, DP780, subjected to load reversals and a stainless steel (SS), 316L, subjected to strain rate and temperature sensitive deformation. The latter material undergoes plasticity-induced martensitic phase transformations. The optimization objectives were the quasi static flow stress data for the DP steel case study, while a set of strain-rate and temperature sensitive flow stress and phase volume fraction data for the SS case study. The procedure and results for the two case studies are presented and discussed illustrating advantages and versatility of the developed methodology. In particular, the efficiency of the developed methodology over an existing genetic algorithm methodology is discussed. Additionally, the parameters identified for the SS case study were utilized to simulate three biaxial tensile loading paths using a finite element implementation of EPSC for further verification.
Machine learning accelerates the materials discovery
2022, Materials Today Communications
As the big data generated by the development of modern experiments and computing technology becomes more and more accessible, the material design method based on machine learning (ML) has opened a new paradigm for materials science research. With its ability to automatically solve complex tasks, machine learning is being used as a new method to help discover the relevance of materials, understand materials' properties, and accelerate the discovery of materials. This paper first introduces the general process of machine learning in materials science. Secondly, the applications of machine learning in material properties prediction, classification and identification, auxiliary micro-scale characterization, phase transformation research and phase diagram construction, process optimization, service behavior evaluation, accelerating the development of computational simulation technology, multi-objective optimization and inverse design of materials are reviewed. Finally, we discuss the main challenges and possible solutions in machine learning, and predict the potential research directions.

View all citing articles on Scopus

View full text

An efficient machine learning approach to establish structure-property linkages

Highlights

Abstract

Graphical abstract

Introduction

Section snippets

Summary of the method

Microstructure based simulation results

Conclusions

Data availability

Acknowledgment

Author contribution

J. Mech. Phys. Solids

J. Mech. Phys. Solid.

Compos. Struct.

Comput. Mater. Sci.

Mech. Mater.

J. Mech. Phys. Solid

J. Mech. Phys. Solids

J. Comput. Phys.

Acta Mater.

Acta Mater.

Acta Mater.

Acta Mater.

Int. J. Plast.

Comput. Mater. Sci.

Acta Mater.

Scr. Mater.

Comput. Mater. Sci.

Acta Mater.

Comput. Mater. Sci.

Comput. Mater. Sci.

Comput. Methods Appl. Mech. Eng.

Comput. Methods Appl. Mech. Eng.

Comput. Stat. Data Anal.