Material Model Calibration Using Machine Learning: A Comparative Study

Authors

  • Mariana Seabra University of Porto Faculty of Engineering, Porto, Portugal https://orcid.org/0000-0002-0903-507X
  • Ana Costa University of Porto Faculty of Engineering, Porto, Portugal

DOI:

https://doi.org/10.13052/ejcm2642-2085.3115

Keywords:

neural network, material properties, Duplex Stainless Steel, multiscale modeling

Abstract

A methodology based on Machine Learning, namely Fully Connected Neural Networks, is proposed to replace traditional parameter calibration strategies. In particular, the relation between hardness, yield strength and tensile strength is explored. The proposed methodology is used to predict the yield strength and the tensile strength of a Super Duplex Stainless Steel that was not included in the neural network training data base. Moreover, it is also used to determine such material parameters for individual microstructural phases, which feed a multiscale Finite Element simulation. The methodology is experimentally validated.

Downloads

Download data is not yet available.

Author Biographies

Mariana Seabra, University of Porto Faculty of Engineering, Porto, Portugal

Mariana Seabra is an Invited Auxiliary Professor at the Faculty of Engineering, University of Porto. Her research career has been devoted to numerical methods, in particular the Finite Element Method applied to ductile damage, fracture and fatigue problems. More recently it has been focused on machine learning methods and its application to structural mechanics and material science. She is also a member of the LAETA research group.

Ana Costa, University of Porto Faculty of Engineering, Porto, Portugal

Ana Costa is a PhD student at the Faculty of Engineering, University of Porto, working on material science, machine learning methods and its application to structural mechanics. Her research career started as a volunteer work at a physics laboratory and, later, in a mechanical construction materials laboratory. During her degree period, she also worked as an intern at FCA Fiat Chrysler Automóveis. Finally, she enrolled the project of Multi-Scale Methodologies with Order Reduction Models for Advanced Materials and Processes as a research fellow at INEGI during her master’s degree.

References

The high-throughput highway to computational materials design.

I Arrayago, E Real, and Leroy Gardner. Description of stress–strain curves for stainless steel alloys. Materials & Design, 87:540–552, 2015.

T Belytschko and R. de Borst. Multiscale methods in computational mechanics. Int. J. Numer. Meth. Eng, pages 939–1271, 2010.

Giorgos Borboudakis, Taxiarchis Stergiannakos, Maria Frysali, Emmanuel Klontzas, Ioannis Tsamardinos, and George E Froudakis. Chemically intuited, large-scale screening of mofs by machine learning techniques. npj Computational Materials, 3(1):1–7, 2017.

JR Cahoon. An improved equation relating hardness to ultimate strength. Metallurgical and Materials Transactions B, 3(11):3040–3040, 1972.

JR Cahoon, WH Broughton, and AR Kutzak. The determination of yield strength from hardness measurements. Metallurgical transactions, 2(7):1979–1983, 1971.

BD Conduit, Nick G Jones, Howard J Stone, and Gareth John Conduit. Design of a nickel-base superalloy using a neural network. Materials & Design, 131:358–365, 2017.

APO Costa, RO Sousa, LMM Ribeiro, AD Santos, and JMA César de Sá. Multiscale modeling for residual stresses analysis of a cast super duplex stainless steel. Materials Design and Applications III, pages 47–63, 2021.

Daniel Jácome da Cruz. Ensaios mecânicos de tração-compressão em provetes metálicos miniaturizados desenvolvimento de um equipamento especializado. 2019.

Eduardo A de Souza Neto, Djordje Peric, and David RJ Owen. Computational methods for plasticity: theory and applications. John Wiley & Sons, 2011.

Jacob Fish. Practical multiscaling. John Wiley & Sons, 2013.

Ross Girshick. Fast r-cnn. In Proceedings of the IEEE international conference on computer vision, pages 1440–1448, 2015.

A. L. Gurson. Continuum theory of ductile rupture by void nucleation and growth: Part I-Yield criteria and flow rules for porous ductile media. J. Engng.Mat. Tech,, 99:2–15, 1977.

Sergey Ioffe and Christian Szegedy. Batch normalization: Accelerating deep network training by reducing internal covariate shift. In International conference on machine learning, pages 448–456. PMLR, 2015.

Bhavya Kailkhura, Brian Gallagher, Sookyung Kim, Anna Hiszpanski, and T Han. Reliable and explainable machine-learning methods for accelerated material discovery. npj Computational Materials, 5(1):1–9, 2019.

Aarti M Karande and DR Kalbande. Weight assignment algorithms for designing fully connected neural network. International Journal of Intelligent Systems and Applications, 10(6):68, 2018.

Yoon-Jun Kim. Phase transformations in cast duplex stainless steels. Technical report, Ames Lab., Ames, IA (United States), 2004.

John F Kolen and Stefan C Kremer. A field guide to dynamical recurrent networks. John Wiley & Sons, 2001.

Ben Kröse, Ben Krose, Patrick Van der Smagt, and Patrick Smagt. An introduction to neural networks. 1993.

Steve Lawrence, C Lee Giles, and Ah Chung Tsoi. Lessons in neural network training: Overfitting may be harder than expected. In AAAI/IAAI, pages 540–545. Citeseer, 1997.

Pierre Lison. An introduction to machine learning. Language Technology Group (LTG), 1(35):1–35, 2015.

MATLAB. version 7.10.0 (R2010a). The MathWorks Inc., Natick, Massachusetts, 2010.

C Meena and V Uthaisangsuk. Micromechanics based modeling of effect of sigma phase on mechanical and failure behavior of duplex stainless steel. Metallurgical and Materials Transactions A, 52(4):1293–1313, 2021.

J-O Nilsson. Super duplex stainless steels. Materials science and technology, 8(8):685–700, 1992.

J-O Nilsson, P Kangas, A Wilson, and T Karlsson. Mechanical properties, microstructural stability and kinetics of σ-phase formation in 29cr-6ni-2mo-0.38 n superduplex stainless steel. Metallurgical and materials Transactions A, 31(1):35–45, 2000.

EJ Pavlina and CJ Van Tyne. Correlation of yield strength and tensile strength with hardness for steels. Journal of materials engineering and performance, 17(6):888–893, 2008.

Ning Qian. On the momentum term in gradient descent learning algorithms. Neural networks, 12(1):145–151, 1999.

R Rodrıguez and I Gutierrez. Correlation between nanoindentation and tensile properties: influence of the indentation size effect. Materials Science and Engineering: A, 361(1-2):377–384, 2003.

Jonathan Schmidt, Mário RG Marques, Silvana Botti, and Miguel AL Marques. Recent advances and applications of machine learning in solid-state materials science. npj Computational Materials, 5(1):1–36, 2019.

S&G. Steel grades, 2021 [Online].

Andrew JR Simpson. Over-sampling in a deep neural network. arXiv preprint arXiv:1502.03648, 2015.

Michael Smith. ABAQUS/Standard User’s Manual, Version 6.9. Dassault Systèmes Simulia Corp, United States, 2009.

Ricardo Sousa. Phase Transformations and Modelling of Thermal Stresses in a Cast Super Duplex Stainless Steel. PhD thesis, University of Porto, Faculty of Engineering, 2021.

RO Sousa, P Lacerda, PJ Ferreira, and LMM Ribeiro. On the precipitation of sigma and chi phases in a cast super duplex stainless steel. Metallurgical and Materials Transactions A, 50(10):4758–4778, 2019.

Nitish Srivastava. Improving neural networks with dropout. University of Toronto, 182(566):7, 2013.

David Tabor. A simple theory of static and dynamic hardness. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 192(1029):247–274, 1948.

Ping Tao, Jian-ming Gong, Yan-fei Wang, Yong Jiang, Yang Li, and Wei-wei Cen. Characterization on stress-strain behavior of ferrite and austenite in a 2205 duplex stainless steel based on nanoindentation and finite element method. Results in Physics, 11:377–384, 2018.

Sherif Abdulkader Tawfik, Olexandr Isayev, Michelle JS Spencer, and David A Winkler. Predicting thermal properties of crystals using machine learning. Advanced Theory and Simulations, 3(2):1900208, 2020.

V. Tvergaard and A. Needleman. Analysis of the cup-cone fracture in a round tensile bar. Acta Metallurgica, 32(1):157–169, 1984.

Guido Van Rossum and Fred L Drake Jr. Python reference manual. Centrum voor Wiskunde en Informatica Amsterdam, 1995.

Alfredo Vellido, José David Martín-Guerrero, and Paulo JG Lisboa. Making machine learning models interpretable. In ESANN, volume 12, pages 163–172. Citeseer, 2012.

João Pedro Portella Guedes Visconti. A simple image segmentation approach to overcome microstructure analysis and homogenization problems. to decide, 2021.

Jie Xiong, TongYi Zhang, and SanQiang Shi. Machine learning of mechanical properties of steels. Science China Technological Sciences, 63(7):1247–1255, 2020.

Qionghua Zhou, Shuaihua Lu, Yilei Wu, and Jinlan Wang. Property-oriented material design based on a data-driven machine learning technique. The journal of physical chemistry letters, 11(10):3920–3927, 2020.

Olek C Zienkiewicz, Robert L Taylor, and Jian Z Zhu. The finite element method: its basis and fundamentals. Elsevier, 2005.

Published

2022-05-07

How to Cite

Seabra, M. ., & Costa, A. . (2022). Material Model Calibration Using Machine Learning: A Comparative Study. European Journal of Computational Mechanics, 31(01), 127–154. https://doi.org/10.13052/ejcm2642-2085.3115

Issue

Section

Original Article