Unified simulation of hardening and softening effects for metals up to failure

doi:10.1007/s10483-021-2793-6

Applied Mathematics and Mechanics (English Edition) ›› 2021, Vol. 42 ›› Issue (12): 1685-1702.doi: https://doi.org/10.1007/s10483-021-2793-6

• 论文 • 下一篇

Unified simulation of hardening and softening effects for metals up to failure

Siyu WANG¹, Lin ZHAN¹, Huifeng XI¹, O. T. BRUHNS², Heng XIAO¹

1. School of Mechanics and Construction Engineering, MOE Key Lab of Disaster Forecast and Control in Engineering, Jinan University, Guangzhou 510632, China;
2. Institute of Mechanics, Ruhr-University Bochum, Bochum D-44780, Germany

收稿日期:2021-08-08 修回日期:2021-09-20 出版日期:2021-12-01 发布日期:2021-11-23
通讯作者: O.T.BRUHNS ,E-mail:otto.bruhns@rub.de;Heng XIAO ,E-mail:xiaoheng@shu.edu.cn
基金资助:
the National Natural Science Foundation of China (Nos. 12172149 and 12172151) and the Start-up Fund from Jinan University of China

Unified simulation of hardening and softening effects for metals up to failure

Siyu WANG¹, Lin ZHAN¹, Huifeng XI¹, O. T. BRUHNS², Heng XIAO¹

1. School of Mechanics and Construction Engineering, MOE Key Lab of Disaster Forecast and Control in Engineering, Jinan University, Guangzhou 510632, China;
2. Institute of Mechanics, Ruhr-University Bochum, Bochum D-44780, Germany

Received:2021-08-08 Revised:2021-09-20 Online:2021-12-01 Published:2021-11-23
Contact: O.T.BRUHNS ,E-mail:otto.bruhns@rub.de;Heng XIAO ,E-mail:xiaoheng@shu.edu.cn
Supported by:
the National Natural Science Foundation of China (Nos. 12172149 and 12172151) and the Start-up Fund from Jinan University of China

摘要/Abstract

摘要： Toward accurately simulating both hardening and softening effects for metals up to failure, a new finite strain elastoplastic J₂-flow model is proposed with the yield strength therein as a function of the plastic work in the explicit form. With no need to identify any adjustable parameters, the uniaxial stress-strain response predicted from this new model is shown to automatically and accurately match any given data from monotonic uniaxial extension tests of bars. As such, the objectives in three respects are achieved for the first time, i.e., (i) both the hardening and softening effects up to failure can be simulated in the sense of matching test data with no errors, (ii) the usual tedious implicit procedures toward identifying numerous unknown parameters need not be involved and can be totally bypassed, and (iii) the model applicability can be ensured in a broad sense for various metallic materials with markedly different transition effects from hardening to softening. With the new model, the complete response features of stretched bars and twisted tubes up to failure are studied, including the failure effects of bars under monotonic extension and tubes under monotonic torsion and, furthermore, the fatigue failure effects of bars under cyclic loading. The results show accurate agreement with the uniaxial data, and the results for both the shear stress and the normal stress at the finite torsion display realistic hardening-to-softening transition effects for the first time.

关键词: metal, hardening, softening, failure, necking, yield strength, accurate approach

Abstract: Toward accurately simulating both hardening and softening effects for metals up to failure, a new finite strain elastoplastic J₂-flow model is proposed with the yield strength therein as a function of the plastic work in the explicit form. With no need to identify any adjustable parameters, the uniaxial stress-strain response predicted from this new model is shown to automatically and accurately match any given data from monotonic uniaxial extension tests of bars. As such, the objectives in three respects are achieved for the first time, i.e., (i) both the hardening and softening effects up to failure can be simulated in the sense of matching test data with no errors, (ii) the usual tedious implicit procedures toward identifying numerous unknown parameters need not be involved and can be totally bypassed, and (iii) the model applicability can be ensured in a broad sense for various metallic materials with markedly different transition effects from hardening to softening. With the new model, the complete response features of stretched bars and twisted tubes up to failure are studied, including the failure effects of bars under monotonic extension and tubes under monotonic torsion and, furthermore, the fatigue failure effects of bars under cyclic loading. The results show accurate agreement with the uniaxial data, and the results for both the shear stress and the normal stress at the finite torsion display realistic hardening-to-softening transition effects for the first time.

Key words: metal, hardening, softening, failure, necking, yield strength, accurate approach

中图分类号:

74A99

Siyu WANG, Lin ZHAN, Huifeng XI, O. T. BRUHNS, Heng XIAO. Unified simulation of hardening and softening effects for metals up to failure[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(12): 1685-1702.

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Unified simulation of hardening and softening effects for metals up to failure

Unified simulation of hardening and softening effects for metals up to failure

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