Abstract A fourth order polynomial yield criterion (Poly4) and a non-quadratic yield function are coupled under associated flow rule to describe the evolution of anisotropic yielding behavior analytically. The Poly4 part takes a great role in describing the evolution of these anisotropic behaviors throughout deformation history. The non-quadratic part is isotropic under uniaxial tension loading, which is supposed to control the curvature of yield surface. The parameters in the proposed yield criterion can be determined by analytical expressions using the four hardening curves along 0, 45, 90° and biaxial directions and also r-values, which doesn't need an optimization process and an interpolation method for describing the evolution of yield loci. Beyond the r-values along 0, 45, and 90°, additional two r-values can be used to analytically determine the nine parameters based on the availability of the data. To guarantee the convexity of the proposed yield criterion, an analytical method is developed by using the method of order principal minor determinant. The accuracy and effectiveness of the proposed yield criterion are verified with six different materials and compared with the Yld2000-2d yield criterion. The results show that the proposed yield function maintains great accuracy for anisotropic hardening with increasing equivalent plastic strain (EPS) beyond the initial yield loci. This yield criterion not only can accurately predict the yield stresses along four monotonic loading conditions, but also significantly reduces the error along other monotonic loading conditions. The proposed yield criterion is implemented into the implicit FEM code AutoForm R8 using user yield function in the development version and it accurately predicted the eight ears of AA3104-H19 and AA5042-H2 after a circular cup drawing.

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在相关流动规则下具有分析描述的各向异性硬化的耦合屈服准则：建模和验证

摘要 将四阶多项式屈服准则（Poly4）和非二次屈服函数在关联流动法则下耦合，解析地描述了各向异性屈服行为的演化。Poly4 部分在描述整个变形历史中这些各向异性行为的演变方面发挥了重要作用。非二次部分在单轴拉伸载荷下是各向同性的，应该控制屈服面的曲率。所提出的屈服准则中的参数可以通过使用沿 0、45、90°和双轴方向的 4 条硬化曲线以及 r 值的解析表达式确定，不需要优化过程和用于描述演变的插值方法产量位点。超出 0、45 和 90° 的 r 值，额外的两个 r 值可用于根据数据的可用性分析确定九个参数。为了保证所提出的屈服准则的凸性，利用阶主次要行列式方法开发了一种解析方法。所提出的屈服准则的准确性和有效性用六种不同的材料进行了验证，并与 Yld2000-2d 屈服准则进行了比较。结果表明，当等效塑性应变 (EPS) 超过初始屈服轨迹时，所提出的屈服函数对各向异性硬化保持了很高的准确性。该屈服准则不仅可以准确预测四种单调加载条件下的屈服应力，而且显着降低了其他单调加载条件下的误差。