{"title":"直接学习预测亚稳TiAl金属间化合物复杂流动行为的可行性:本构分析、建模和数值实现","authors":"Huashan Fan, Liang Cheng, Lingyan Sun, Zhihao Bai, Jiangtao Wang, Jinshan Li","doi":"10.1007/s12540-025-01947-2","DOIUrl":null,"url":null,"abstract":"<div><p>The deformation behavior of a TiAl alloy with a (β<sub>o</sub> + γ) structure was studied in the temperature range of 1000 ~ 1150 °C and strain rates of 10<sup>0</sup> ~ 10<sup>–3</sup> s<sup>−1</sup>, which was characterized by intricate and irregular flow hardening/softening primarily due to the initial metastable microstructure and the onset of phase transition during deformation. As a consequence, the flow behavior was quite difficult to be modelled by the conventional constitutive relations even utilizing the highly flexible strain-compensated hyperbolic-sine law. Therefore, in this study we tried to develop an accurate constitutive model based on the multilayer feed-forward neural networks (FFNN). To this end, the FFNNs with various widths (nodes-per-layer) and depths (number of hidden layers) were constructed and evaluated. A dual-cycle training strategy was proposed to achieve the best performance for each FFNN, whereby an optimal architecture with four hidden layers and four nodes-per-layer was selected to balance the overfitting and underfitting. After systematic verification, it was demonstrated that the optimized FFNN showed superior predictivities in terms of excellent reproducibility of existing flow data, powerful interpolation and reasonable extrapolation, which notably outperformed those of the classical constitutive models. To further test the applicability of the FFNN-based model in numerical simulations, it was implemented into the finite-element (FE) code together with an efficient automatic differentiation programme. The reasonable prediction of the heterogeneous metal flow during the benchmark compression test manifested the feasibility of the multilayer FFNNs as advanced constitutive models, which were trained directly from the experimental flow data.</p><h3>Graphical Abstract</h3>\n<div><figure><div><div><picture><source><img></source></picture></div></div></figure></div></div>","PeriodicalId":703,"journal":{"name":"Metals and Materials International","volume":"31 11","pages":"3243 - 3259"},"PeriodicalIF":4.0000,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s12540-025-01947-2.pdf","citationCount":"0","resultStr":"{\"title\":\"Feasibility of Direct Learning in Predicting Complex Flow Behavior of Metastable TiAl Intermetallics: Constitutive Analysis, Modelling and Numerical Implementation\",\"authors\":\"Huashan Fan, Liang Cheng, Lingyan Sun, Zhihao Bai, Jiangtao Wang, Jinshan Li\",\"doi\":\"10.1007/s12540-025-01947-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The deformation behavior of a TiAl alloy with a (β<sub>o</sub> + γ) structure was studied in the temperature range of 1000 ~ 1150 °C and strain rates of 10<sup>0</sup> ~ 10<sup>–3</sup> s<sup>−1</sup>, which was characterized by intricate and irregular flow hardening/softening primarily due to the initial metastable microstructure and the onset of phase transition during deformation. As a consequence, the flow behavior was quite difficult to be modelled by the conventional constitutive relations even utilizing the highly flexible strain-compensated hyperbolic-sine law. Therefore, in this study we tried to develop an accurate constitutive model based on the multilayer feed-forward neural networks (FFNN). To this end, the FFNNs with various widths (nodes-per-layer) and depths (number of hidden layers) were constructed and evaluated. A dual-cycle training strategy was proposed to achieve the best performance for each FFNN, whereby an optimal architecture with four hidden layers and four nodes-per-layer was selected to balance the overfitting and underfitting. After systematic verification, it was demonstrated that the optimized FFNN showed superior predictivities in terms of excellent reproducibility of existing flow data, powerful interpolation and reasonable extrapolation, which notably outperformed those of the classical constitutive models. To further test the applicability of the FFNN-based model in numerical simulations, it was implemented into the finite-element (FE) code together with an efficient automatic differentiation programme. The reasonable prediction of the heterogeneous metal flow during the benchmark compression test manifested the feasibility of the multilayer FFNNs as advanced constitutive models, which were trained directly from the experimental flow data.</p><h3>Graphical Abstract</h3>\\n<div><figure><div><div><picture><source><img></source></picture></div></div></figure></div></div>\",\"PeriodicalId\":703,\"journal\":{\"name\":\"Metals and Materials International\",\"volume\":\"31 11\",\"pages\":\"3243 - 3259\"},\"PeriodicalIF\":4.0000,\"publicationDate\":\"2025-05-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s12540-025-01947-2.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Metals and Materials International\",\"FirstCategoryId\":\"88\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s12540-025-01947-2\",\"RegionNum\":3,\"RegionCategory\":\"材料科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Metals and Materials International","FirstCategoryId":"88","ListUrlMain":"https://link.springer.com/article/10.1007/s12540-025-01947-2","RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, MULTIDISCIPLINARY","Score":null,"Total":0}
Feasibility of Direct Learning in Predicting Complex Flow Behavior of Metastable TiAl Intermetallics: Constitutive Analysis, Modelling and Numerical Implementation
The deformation behavior of a TiAl alloy with a (βo + γ) structure was studied in the temperature range of 1000 ~ 1150 °C and strain rates of 100 ~ 10–3 s−1, which was characterized by intricate and irregular flow hardening/softening primarily due to the initial metastable microstructure and the onset of phase transition during deformation. As a consequence, the flow behavior was quite difficult to be modelled by the conventional constitutive relations even utilizing the highly flexible strain-compensated hyperbolic-sine law. Therefore, in this study we tried to develop an accurate constitutive model based on the multilayer feed-forward neural networks (FFNN). To this end, the FFNNs with various widths (nodes-per-layer) and depths (number of hidden layers) were constructed and evaluated. A dual-cycle training strategy was proposed to achieve the best performance for each FFNN, whereby an optimal architecture with four hidden layers and four nodes-per-layer was selected to balance the overfitting and underfitting. After systematic verification, it was demonstrated that the optimized FFNN showed superior predictivities in terms of excellent reproducibility of existing flow data, powerful interpolation and reasonable extrapolation, which notably outperformed those of the classical constitutive models. To further test the applicability of the FFNN-based model in numerical simulations, it was implemented into the finite-element (FE) code together with an efficient automatic differentiation programme. The reasonable prediction of the heterogeneous metal flow during the benchmark compression test manifested the feasibility of the multilayer FFNNs as advanced constitutive models, which were trained directly from the experimental flow data.
期刊介绍:
Metals and Materials International publishes original papers and occasional critical reviews on all aspects of research and technology in materials engineering: physical metallurgy, materials science, and processing of metals and other materials. Emphasis is placed on those aspects of the science of materials that are concerned with the relationships among the processing, structure and properties (mechanical, chemical, electrical, electrochemical, magnetic and optical) of materials. Aspects of processing include the melting, casting, and fabrication with the thermodynamics, kinetics and modeling.