Abstract Directional anisotropic hardening under non-proportional loading is modeled. A recently proposed coupled quadratic-nonquadratic (CQN) yield function (Lee et al., 2017b) successfully captured the directional hardening behavior under the proportional loadings. This paper shows a constitutive equation to capture both directional hardening response and Bauschinger effect through an extended model of the CQN yield function with the homogeneous anisotropic hardening (HAH) model (Barlat et al., 2011). In the present study, the role of the CQN yield model is to capture the directional hardening behavior, and the HAH model is to follow non-proportional loading including the Bauschinger effect. The validation, with some material data, shows that the present model can follow the directional hardening under non-proportional loading in the stress-strain data. It is also shown that the present model can describe the yield surface distortion with Bauschinger and anisotropic hardening response. Finally, it is compared with other pre-existing models in order to analyze the utility of the proposed model.

中文翻译：

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结合各向异性和畸变硬化来描述具有包辛格效应的方向响应

摘要 模拟了非比例加载下的定向各向异性硬化。最近提出的耦合二次-非二次 (CQN) 屈服函数（Lee 等人，2017b）成功地捕获了比例载荷下的定向硬化行为。本文展示了一个本构方程，通过具有均匀各向异性硬化 (HAH) 模型的 CQN 屈服函数的扩展模型来捕获定向硬化响应和包辛格效应（Barlat 等人，2011 年）。在本研究中，CQN 屈服模型的作用是捕捉定向硬化行为，而 HAH 模型的作用是遵循包括包辛格效应在内的非比例载荷。验证，与一些材料数据，表明本模型可以在应力应变数据中遵循非比例加载下的定向硬化。还表明，本模型可以用包辛格和各向异性硬化响应来描述屈服面畸变。最后，将其与其他预先存在的模型进行比较，以分析所提出模型的效用。