Abstract Size effect plays an important role in coining processes of commemorative coins. To deal with the size effect and improve the simulation accuracy, a constitutive model incorporating the conventional mechanism-based strain gradient (CMSG) plasticity theory was established in this study, with the nonlinear coupling between the statistically stored dislocation (SSD) density and the geometrically necessary dislocation (GND) density determined experimentally. Via the least square method, a bilinear equivalent plastic strain field was constructed for the evaluation of equivalent plastic strain gradient. In this way, the proposed constitutive model was implemented within a home-developed explicit finite element code for coining analyses. Uniaxial tensile tests and a nanoindentation test were conducted to obtain the mechanical properties of the Ag999 material, which was selected to verify the performance of the proposed constitutive model. By simulating the nanoindentation test and the coining process of a typical commemorative coin, it was demonstrated that the proposed constitutive model could provide accurate results in applications involving size effect, outperforming the classical plasticity constitutive model. Therefore, the proposed constitutive model based on strain gradient plasticity theory is suitable for coining simulations of commemorative coins.

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应变梯度塑性在纪念币铸造模拟中的应用

摘要 尺寸效应在纪念币的铸造过程中起着重要作用。为了处理尺寸效应并提高模拟精度，本研究建立了一个结合常规基于机制的应变梯度（CMSG）塑性理论的本构模型，具有统计存储位错（SSD）密度和几何尺寸之间的非线性耦合。必要的位错 (GND) 密度通过实验确定。通过最小二乘法，构建了双线性等效塑性应变场，用于等效塑性应变梯度的评价。通过这种方式，所提出的本构模型是在自制的显式有限元代码中实现的，用于压铸分析。进行单轴拉伸试验和纳米压痕试验以获得 Ag999 材料的机械性能，选择该材料来验证所提出的本构模型的性能。通过模拟典型纪念币的纳米压痕测试和铸造过程，证明所提出的本构模型可以在涉及尺寸效应的应用中提供准确的结果，优于经典的塑性本构模型。因此，所提出的基于应变梯度塑性理论的本构模型适用于纪念币的铸造模拟。结果表明，所提出的本构模型可以在涉及尺寸效应的应用中提供准确的结果，优于经典的塑性本构模型。因此，所提出的基于应变梯度塑性理论的本构模型适用于纪念币的铸造模拟。结果表明，所提出的本构模型可以在涉及尺寸效应的应用中提供准确的结果，优于经典的塑性本构模型。因此，所提出的基于应变梯度塑性理论的本构模型适用于纪念币的铸造模拟。