Modelling feasibility constraints for materials design: Application to inverse crystallographic texture problem

Abstract The cornerstone of materials design is solving materials-related optimization problems to obtain microstructural or processing variables that lead to the most desirable material properties. Because the objective of materials design is to maximize their performance, the related optimization problems often require a global solution. This type of unconstrained optimization overlooks the feasibility of the solution, which is a key engineering issue. For any practical application, feasibility should be reflected in the constraints included in the optimization problems. Nevertheless, the constraints related to feasibility are considerably complex due to the high dimensionality of the design space and non-physical aspects of the constraints, such as machine specifications, material dimensions, and available initial microstructure. In this work, we propose the use of a simple support vector machine (SVM) trained with information in an existing database to model complex feasibility constraints for material optimization. We present a problem involving optimization of the initial texture of a body-centered cubic (BCC) polycrystalline material to obtain specific target textures after cold-rolling. Both unconstrained and constrained optimizations are conducted for comparison, and the results demonstrate that constrained optimizations yield viable solutions while unconstrained optimizations do not.

[1]  Yue Liu,et al.  Materials discovery and design using machine learning , 2017 .

[2]  David T. Fullwood,et al.  Microstructure Sensitive Design for Performance Optimization , 2012 .

[3]  Antonio Harrison Sánchez,et al.  Limit state function identification using Support Vector Machines for discontinuous responses and disjoint failure domains , 2008 .

[4]  Chih-Jen Lin,et al.  LIBSVM: A library for support vector machines , 2011, TIST.

[5]  Hamid Garmestani,et al.  Processing path optimization to achieve desired texture in polycrystalline materials , 2007 .

[6]  David B. Brough,et al.  Microstructure-based knowledge systems for capturing process-structure evolution linkages. , 2017, Acta materialia.

[7]  Claude Esling,et al.  Texture development by plastic deformation , 1984 .

[8]  A. Çeçen,et al.  Development of high throughput assays for establishing process-structure-property linkages in multiphase polycrystalline metals: Application to dual-phase steels , 2017 .

[9]  Noah H. Paulson,et al.  Reduced-order structure-property linkages for polycrystalline microstructures based on 2-point statistics , 2017 .

[10]  Surya R. Kalidindi,et al.  Building texture evolution networks for deformation processing of polycrystalline fcc metals using spectral approaches: Applications to process design for targeted performance , 2010 .

[11]  I. M. Robertson,et al.  Initial texture effects on the thermal stability and grain growth behavior of nanocrystalline Ni thin films , 2016 .

[12]  O. Engler,et al.  Effect of r-value and texture on plastic deformation and necking behavior in interstitial-free steel sheets , 2017, Metals and Materials International.

[13]  J. Inoue,et al.  Effect of initial texture and microstructure of Mg on mechanical properties of Mg – Stainless steel laminated metal composites , 2017 .

[14]  Hyoung-Seop Kim,et al.  Effect of the interfacial condition on the microtexture near the interface of Al/Cu composites during multi-pass caliber rolling , 2015 .

[15]  Olvi L. Mangasarian,et al.  Smoothing methods for convex inequalities and linear complementarity problems , 1995, Math. Program..

[16]  Yuksel C. Yabansu,et al.  Extraction of reduced-order process-structure linkages from phase-field simulations , 2017 .

[17]  Siqi Shi,et al.  The onset temperature (Tg) of AsxSe1−x glasses transition prediction: A comparison of topological and regression analysis methods , 2017 .

[18]  Moo Young Huh,et al.  Effect of intermediate annealing on texture, formability and ridging of 17%Cr ferritic stainless steel sheet , 2001 .

[19]  H. Schaeben,et al.  Texture Analysis with MTEX – Free and Open Source Software Toolbox , 2010 .

[20]  Implementation of VPSC polycrystal model into rigid plastic finite element method and its application to Erichsen test of Mg alloy , 2017, Metals and Materials International.

[21]  R. Arróyave,et al.  A data-driven machine learning approach to predicting stacking faulting energy in austenitic steels , 2017, Journal of Materials Science.

[22]  Jaimyun Jung,et al.  An efficient machine learning approach to establish structure-property linkages , 2019, Computational Materials Science.

[23]  Vu C. Dinh,et al.  Support Vector Machine Informed Explicit Nonlinear Model Predictive Control Using Low-Discrepancy Sequences , 2017, IEEE Transactions on Automatic Control.

[24]  Michael Selzer,et al.  Data science approaches for microstructure quantification and feature identification in porous membranes , 2017 .

[25]  Brian L. DeCost,et al.  Exploring the microstructure manifold: Image texture representations applied to ultrahigh carbon steel microstructures , 2017, 1702.01117.

[26]  Alok Choudhary,et al.  A predictive machine learning approach for microstructure optimization and materials design , 2015, Scientific Reports.

[27]  A generalized spherical harmonic deconvolution to obtain texture of cubic materials from ultrasonic wave speed , 2015 .

[28]  P. Houtte,et al.  γ-Fibre recrystallization texture in IF-steel: an investigation on the recrystallization mechanisms , 1997 .

[29]  Wei Chen,et al.  Toward the development of a quantitative tool for predicting dispersion of nanocomposites under non-equilibrium processing conditions , 2016, Journal of Materials Science.

[30]  X. Li,et al.  Effect of initial texture on texture and microstructure evolution of ME20 Mg alloy subjected to hot rolling , 2013 .

[31]  Surya R. Kalidindi,et al.  Data-driven reduced order models for effective yield strength and partitioning of strain in multiphase materials , 2017, J. Comput. Phys..

[32]  Jun Li,et al.  Texture, microstructure and mechanical properties of aluminum modified ultra-pure 429 ferritic stainless steels , 2016 .

[33]  M. Seefeldt,et al.  Modeling grain fragmentation and deformation textures for titanium using a combined approach of the viscoplastic self-consistent model and a shear fluctuation model , 2017, Journal of Materials Science.

[34]  Robert P. W. Duin,et al.  Support Vector Data Description , 2004, Machine Learning.

[35]  Jingyuan Li,et al.  Influence of differential speed rolling ratio on the ridging behavior of ultra purified 17%Cr ferritic stainless steel , 2018 .

[36]  Yuksel C. Yabansu,et al.  Material structure-property linkages using three-dimensional convolutional neural networks , 2018 .

[37]  A. Basudhar,et al.  Adaptive explicit decision functions for probabilistic design and optimization using support vector machines , 2008 .

[38]  Nicholas Lubbers,et al.  Inferring low-dimensional microstructure representations using convolutional neural networks , 2016, Physical review. E.

[39]  Siqi Shi,et al.  Multi-scale computation methods: Their applications in lithium-ion battery research and development , 2016 .

[40]  Dong-Hoon Choi,et al.  Feasibility classification of new design points using support vector machine trained by reduced dataset , 2012, International Journal of Precision Engineering and Manufacturing.