基于应变梯度塑性理论的纪念币压印成形数值模拟

中国机械工程

基于应变梯度塑性理论的纪念币压印成形数值模拟

易国锋1;李巧敏2;钟文2;柳玉起2

1.湖北工业大学机械工程学院，武汉，430068
2.华中科技大学材料成形与模具技术国家重点实验室，武汉，430074

出版日期:2018-06-10 发布日期:2018-06-08
基金资助:
国家自然科学基金资助项目（51275184）
National Natural Science Foundation of China （No. 51275184）

Coining Simulation of Commemorative Coins Based on Strain Gradient Plasticity Theory

YI Guofeng1;LI Qiaomin2;ZHONG Wen2;LIU Yuqi2

1.School of Mechanical Engineering， Hubei University of Technology， Wuhan， 430068
2.State Key Laboratory of Materials Processing and Die & Mould Technology， Huazhong University of Science and Technology， Wuhan， 430074

Online:2018-06-10 Published:2018-06-08
Supported by:
National Natural Science Foundation of China （No. 51275184）

摘要/Abstract

摘要： 为了准确体现纪念币压印成形工艺中由于精细浮雕导致的尺寸效应，从Taylor位错模型出发，基于应变梯度塑性理论，建立了压印成形的本构方程。采用纳米压痕试验，获得了Ag999的材料内禀尺寸以及统计存储位错密度和几何必须位错密度的非线性耦合关系。将建立的本构方程用于计算某钥匙纪念币压印成形过程中的压印力变化曲线，并与试验结果进行对比，结果表明，建立的本构方程能够体现压印成形工艺中的尺寸效应，可有效改善压印力的预测精度。

关键词: 纪念币, 压印成形, Taylor位错模型, 应变梯度塑性, 尺寸效应

Abstract: To exactly describe the size effects caused by the fine patterns in coining simulation of commemorative coins， a constitutive equation was developed based on the Taylor dislocation model and the strain gradient plasticity theory.A nanoindentation test was conducted to obtain the mechanical properties of the Ag999 material， including the intrinsic material length and the nonlinear coupling relation between the statistically stored dislocation density and the geometrically necessary dislocation density.The proposed constitutive equation was applied to calculate the coining processes of a key-shaped coin， with the obtained coining force curves compared with the experimental ones.It is demonstrated that the proposed constitutive equation is capable of reflecting the size effects in coining and improves the accuracy in predicting coining forces.

Key words: commemorative coin, coining, Taylor dislocation model, strain gradient plasticity, size effect

中图分类号:

TP391.9

易国锋1;李巧敏2;钟文2;柳玉起2. 基于应变梯度塑性理论的纪念币压印成形数值模拟[J]. 中国机械工程.

YI Guofeng1;LI Qiaomin2;ZHONG Wen2;LIU Yuqi2. Coining Simulation of Commemorative Coins Based on Strain Gradient Plasticity Theory[J]. China Mechanical Engineering.

参考文献

[1]俞晓萍.北京奥运会纪念币——从中国走向世界[J].中国金币，2008（9）：13-14.
YU Xiaoping.Commemorative Coins for Beijing Olympic Games—From China to the world[J].China Gold Coin，2008（9）：13-14.
[2]XU J， LIU Y，LI S，et al.Fast Analysis System for Embossing Process Simulation of Commemorative Coin-COINFORM[J].Computer Modeling in Engineering & Sciences，2008，38（3）：201-216.
[3]钟文，柳玉起，许江平，等.金银纪念币压印成形中的缺陷预测[J].中国机械工程，2012，23（1）：109-112.
ZHONG Wen，LIU Yuqi，XU Jiangping，et al.Defect Prediction in Coining Process for Au-Ag Commemorative Coins[J].China Mechanical Engineering，2012，23（1）：109-112.
[4]ZHENG W，WANG G，LIN X，et al.The Experimental Investigation of Size Effect on Micro-cylinder Deformation in Coining Process[J].Materials and Manufacturing Processes，2014，29（6）：687-690.
[5]FLECK N A，HUTCHINSON J W.A Phenomenological Theory for Strain Gradient Effects in Plasticity[J].Journal of the Mechanics and Physics of Solids，1993，41（12）：1825-1857.
[6]FLECK N A，HUTCHINSON J W.Strain Gradient Plasticity[J].Advances in Applied Mechanics，1997， 33：296-361.
[7]NIX W D，GAO H.Indentation Size Effects in Crystalline Materials：a Law for Strain Gradient Plasticity[J].Journal of the Mechanics and Physics of Solids，1998，46（3）：411-425.
[8]GAO H，HUANG Y，NIX W D，et al.Mechanism-based Strain Gradient Plasticity—I.Theory[J].Journal of the Mechanics and Physics of Solids，1999，47（6）：1239-1263.
[9]HUANG Y，GAO H，NIX W D，et al.Mechanism-based Strain Gradient Plasticity—II.Analysis[J].Journal of the Mechanics and Physics of Solids，2000， 48（1）：99-128.
[10]HUANG Y，QU S，HWANG K C，et al.A Conventional Theory of Mechanism-based Strain Gradient Plasticity[J].International Journal of Plasticity，2004， 20（4/5）：753-782.
[11]ZHANG F，HUANG Y，HWANG K C，et al.A Three-dimensional Strain Gradient Plasticity Analysis of Particle Size Effect in Composite Materials[J].Materials and Manufacturing Processes，2007，22（2）： 140-148.
[12]TAYLOR G I.The Mechanism of Plastic Deformation of Crystals.Part I.Theoretical[J].Proceedings of the Royal Society of London Series A，1934，145（855）： 362-387.
[13]WIEDERSICH H.Hardening Mechanisms and the Theory of Deformation[J].Journal of Metals，1964，16 （5）：425-430.
[14]VOYIADJIS G Z，Al-RUB R A.Determination of the Material Intrinsic Length Scale of Gradient Plasticity Theory[J].International Journal for Multiscale Computational Engineering，2004，2（3）：377-400.
[15]张帆.CMSG低阶应变梯度塑性理论及其应用[D].北京：清华大学，2005.
ZHANG Fan.Conventional Theory of Mechanism- based Strain Gradient Plasticity（CMSG） and Its Applications[D].Beijing：Tsinghua University，2005.
[16]ZHANG F，SAHA R，HUANG Y，et al.Indentation of a Hard Film on a Soft Substrate： Strain Gradient Hardening Effects[J].International Journal of Plasticity，2007，23（1）：25-43.
[17]LI Q，ZHONG W，LIU Y，et al.A New Locking-free Hexahedral Element with Adaptive Subdivision for Explicit Coining Simulation[J].International Journal of Mechanical Sciences，2017，128/129：105-115.
[18]SWADENER J G，GEORGE E P，PHARR G M.The Correlation of the Indentation Size Effect Measured with Indenters of Various Shapes[J].Journal of the Mechanics and Physics of Solids，2002，50（4）：681-694.
[19]MCELHANEY K W，VLASSAK J J，NIX W D.Determination of Indenter Tip Geometry and Indentation Contact Area for Depth-sensing Indentation Experiments[J].Journal of Materials Research，1998，13（5）：1300-1306.
[20]LEE W B，CHEN Y P.Simulation of Microindentation Hardness of FCC Single Crystals by Mechanism- based Strain Gradient Crystal Plasticity [J].International Journal of Plasticity，2010，26（10）： 1527-1540.
[21]易国锋，李巧敏，钟文，等.六面体单元在压印成形模拟中的应用[J].中国机械工程，2017，28（15）：1879-1883.
YI Guofeng，LI Qiaomin，ZHONG Wen，et al.A Hexahedral Element Applied to Coining Simulations [J].China Mechanical Engineering，2017，28（15）： 1879-1883.