In order to solve the nonlinear integral difficulty of the Mises yield criterion, a linear yield criterion, called the collaborative approximation (CA) yield criterion, is proposed by the collaborative control method. According to the approximation method, the mathematical expression of the CA yield criterion is derived as a linear function of the three principal stresses. The theoretical results based on the yield criterion in the form of the Lode parameter are verified with the classical test data, and a good agreement is found. Meanwhile, for the purpose of proving the effectiveness of the yield criterion, its specific plastic power is derived and applied to establish the rolling force model of an extra-thick plate. In the modeling, the internal power of plastic deformation is obtained by using the derived specific plastic power, while the shear power dissipation and the frictional power dissipation are obtained by using the methods of strain vector inner product and average velocity integration. Then, the analytical solution of the rolling force is obtained and then extended to the one accounting for the temperature rise. The maximum errors of the predicted rolling torque and rolling force without considering the temperature rise are 12.72% and 11.78%, respectively, while those considering the temperature rise decrease to 3.54% and 5.23%, respectively. Moreover, the influence of relative reduction, friction factor, surface temperature, and the temperature rise of the workpiece on the theoretical results is discussed.

中文翻译：

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CA准则的超厚板滚动力分析。

为了解决米塞斯（Mises）收益准则的非线性积分难度，通过协作控制方法提出了一种线性收益准则，称为协作近似（CA）收益准则。根据近似方法，CA屈服准则的数学表达式被推导为三个主应力的线性函数。通过经典测试数据验证了基于Lode参数形式的屈服准则的理论结果，并找到了很好的一致性。同时，为了证明屈服准则的有效性，推导了其屈服强度，并将其用于建立超厚板的轧制力模型。在建模中，通过使用导出的比塑性功率来获得塑性变形的内部功率，利用应变矢量内积和平均速度积分的方法获得了剪切功率耗散和摩擦功率耗散。然后，获得轧制力的解析解，然后扩展到考虑温度上升的解析解。不考虑温度上升的情况下的预测轧制转矩和轧制力的最大误差分别为12.72％和11.78％，而考虑温度上升的预测误差分别降至3.54％和5.23％。此外，还讨论了相对减小量，摩擦系数，表面温度和工件的温升对理论结果的影响。然后，获得轧制力的解析解，然后扩展到考虑温度上升的解析解。不考虑温度上升的预测滚动转矩和滚动力的最大误差分别为12.72％和11.78％，而考虑温度上升的预测误差分别降至3.54％和5.23％。此外，还讨论了相对减小量，摩擦系数，表面温度和工件的温升对理论结果的影响。然后，获得轧制力的解析解，然后扩展到考虑温度上升的解析解。不考虑温度上升的情况下的预测轧制转矩和轧制力的最大误差分别为12.72％和11.78％，而考虑温度上升的预测误差分别降至3.54％和5.23％。此外，还讨论了相对减小量，摩擦系数，表面温度和工件的温升对理论结果的影响。而考虑温升的人分别下降到3.54％和5.23％。此外，还讨论了相对减小量，摩擦系数，表面温度和工件的温升对理论结果的影响。而考虑温升的人分别下降到3.54％和5.23％。此外，还讨论了相对减小量，摩擦系数，表面温度和工件的温升对理论结果的影响。