Abstract The second part of the study presents development of the Dirac delta functions framework to modelling of cyclic hardening and softening of material during cyclic loading conditions for the investigated in Part I low carbon S355J2 steel. A new criterion of plastic strain range change is formulated. This provides more certainty in the cyclic plasticity modelling framework compared to classical plastic strain memorization modelling. Two hardening parameters from the developed kinematic hardening rule are written as functions of both plastic strain range and previously accumulated plastic strain. This representation of hardening parameters is able to accurately match experimental results with different types of loading programs including random loading conditions and considering initial monotonic behaviour with yield plateau deformation. Ratcheting behaviour is simulated by the developed cyclic plasticity framework by considering an approximated form of the Dirac delta function for modelling the deviation effect and introducing an additional supersurface for better prediction of ratcheting rate. The proposed cyclic plasticity model requires up to 21 material constants, depending on application. A clear and straightforward calibration procedure, where sets of material constants are determined for each plasticity phenomenon considered, is presented. Application of the model to different materials under various tension-compression and non-proportional axial-torsion cycles shows very close agreement with test results.

中文翻译：

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非线性运动硬化模型的新公式，第二部分：循环硬化/软化和棘轮

摘要 本研究的第二部分介绍了 Dirac delta 函数框架的发展，用于模拟第一部分低碳 S355J2 钢在循环加载条件下的循环硬化和软化。制定了塑性应变范围变化的新准则。与经典的塑性应变记忆建模相比，这在循环塑性建模框架中提供了更多的确定性。来自开发的运动硬化规则的两个硬化参数被写入为塑性应变范围和先前累积塑性应变的函数。硬化参数的这种表示能够将实验结果与不同类型的加载程序（包括随机加载条件）准确匹配，并考虑初始单调行为和屈服平台变形。通过考虑 Dirac delta 函数的近似形式对偏差效应进行建模并引入额外的超表面以更好地预测棘轮速率，通过开发的循环塑性框架模拟棘轮行为。建议的循环塑性模型需要多达 21 个材料常数，具体取决于应用。提供了一个清晰而直接的校准程序，其中为所考虑的每个塑性现象确定了材料常数组。该模型在各种拉压和非比例轴扭循环下对不同材料的应用与测试结果非常吻合。