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The Quadratic Constitutive Model Based on Partial Derivative and Taylor Series of Ti6242s Alloy and Predictability Analysis
To solve the problem of insufficient predictability in the classical models for the Ti6242s alloy, a new constitutive model was proposed, based on the partial derivatives from experimental data and the Taylor series. Firstly, hot compression experiments on the Ti6242s alloy at different temperatures...
Autores principales: | , , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2023
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10096400/ https://www.ncbi.nlm.nih.gov/pubmed/37049222 http://dx.doi.org/10.3390/ma16072928 |
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author | Zhang, Jiansheng Xiao, Guiqian Deng, Guoyong Zhang, Yancheng Zhou, Jie |
author_facet | Zhang, Jiansheng Xiao, Guiqian Deng, Guoyong Zhang, Yancheng Zhou, Jie |
author_sort | Zhang, Jiansheng |
collection | PubMed |
description | To solve the problem of insufficient predictability in the classical models for the Ti6242s alloy, a new constitutive model was proposed, based on the partial derivatives from experimental data and the Taylor series. Firstly, hot compression experiments on the Ti6242s alloy at different temperatures and different strain rates were carried out, and the Arrhenius model and Hensel–Spittel model were constructed. Secondly, the partial derivatives of logarithmic stress with respect to temperature and logarithmic strain rate at low, medium and high strain levels were analyzed. Thirdly, two new constitutive models with first- and second-order approximation were proposed to meet the requirements of high precision. In this new model, by analyzing the high-order differential data of experimental data and combining the Taylor series theory, the minimum number of terms that can accurately approximate the experimental rheological data was found, thereby achieving an accurate prediction of flow stress with minimal material parameters. In the new model, by analyzing the high-order differential of the experimental data and combining the theory of the Taylor series, the minimum number of terms that can accurately approximate the experimental rheological data was found, thereby achieving an accurate prediction of flow stress with minimal material parameters. Finally, the prediction accuracies for the classical model and the new model were compared, and the predictabilities for the classical models and the new model were proved by mathematical means. The results show that the prediction accuracies of the Arrhenius model and the Hensel–Spittel model are low in the single-phase region and high in the two-phase region. In addition, second-order approximation is required between the logarithmic stress and logarithmic strain rate, and first-order approximation is required between logarithmic stress and temperature to establish a high-precision model. The order of prediction accuracy of the four models from high to low is the quadratic model, Arrhenius model, linear model and HS model. The prediction accuracy of the quadratic model in all temperatures and strain rates had no significant difference, and was higher than the other models. The quadratic model can greatly improve prediction accuracy without significantly increasing the material parameters. |
format | Online Article Text |
id | pubmed-10096400 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2023 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-100964002023-04-13 The Quadratic Constitutive Model Based on Partial Derivative and Taylor Series of Ti6242s Alloy and Predictability Analysis Zhang, Jiansheng Xiao, Guiqian Deng, Guoyong Zhang, Yancheng Zhou, Jie Materials (Basel) Article To solve the problem of insufficient predictability in the classical models for the Ti6242s alloy, a new constitutive model was proposed, based on the partial derivatives from experimental data and the Taylor series. Firstly, hot compression experiments on the Ti6242s alloy at different temperatures and different strain rates were carried out, and the Arrhenius model and Hensel–Spittel model were constructed. Secondly, the partial derivatives of logarithmic stress with respect to temperature and logarithmic strain rate at low, medium and high strain levels were analyzed. Thirdly, two new constitutive models with first- and second-order approximation were proposed to meet the requirements of high precision. In this new model, by analyzing the high-order differential data of experimental data and combining the Taylor series theory, the minimum number of terms that can accurately approximate the experimental rheological data was found, thereby achieving an accurate prediction of flow stress with minimal material parameters. In the new model, by analyzing the high-order differential of the experimental data and combining the theory of the Taylor series, the minimum number of terms that can accurately approximate the experimental rheological data was found, thereby achieving an accurate prediction of flow stress with minimal material parameters. Finally, the prediction accuracies for the classical model and the new model were compared, and the predictabilities for the classical models and the new model were proved by mathematical means. The results show that the prediction accuracies of the Arrhenius model and the Hensel–Spittel model are low in the single-phase region and high in the two-phase region. In addition, second-order approximation is required between the logarithmic stress and logarithmic strain rate, and first-order approximation is required between logarithmic stress and temperature to establish a high-precision model. The order of prediction accuracy of the four models from high to low is the quadratic model, Arrhenius model, linear model and HS model. The prediction accuracy of the quadratic model in all temperatures and strain rates had no significant difference, and was higher than the other models. The quadratic model can greatly improve prediction accuracy without significantly increasing the material parameters. MDPI 2023-04-06 /pmc/articles/PMC10096400/ /pubmed/37049222 http://dx.doi.org/10.3390/ma16072928 Text en © 2023 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Zhang, Jiansheng Xiao, Guiqian Deng, Guoyong Zhang, Yancheng Zhou, Jie The Quadratic Constitutive Model Based on Partial Derivative and Taylor Series of Ti6242s Alloy and Predictability Analysis |
title | The Quadratic Constitutive Model Based on Partial Derivative and Taylor Series of Ti6242s Alloy and Predictability Analysis |
title_full | The Quadratic Constitutive Model Based on Partial Derivative and Taylor Series of Ti6242s Alloy and Predictability Analysis |
title_fullStr | The Quadratic Constitutive Model Based on Partial Derivative and Taylor Series of Ti6242s Alloy and Predictability Analysis |
title_full_unstemmed | The Quadratic Constitutive Model Based on Partial Derivative and Taylor Series of Ti6242s Alloy and Predictability Analysis |
title_short | The Quadratic Constitutive Model Based on Partial Derivative and Taylor Series of Ti6242s Alloy and Predictability Analysis |
title_sort | quadratic constitutive model based on partial derivative and taylor series of ti6242s alloy and predictability analysis |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10096400/ https://www.ncbi.nlm.nih.gov/pubmed/37049222 http://dx.doi.org/10.3390/ma16072928 |
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