This study uses the Marciniak and Kuczynski (M-K) method to present an analytical forming limit diagram (FLD) for sheet metals. The procedure for the analytical FLD prediction is described in detail and step-wise manner, and an algorithm is written using MATLAB. First, an appropriate algorithm is determined to establish the theoretical analyses, and various anisotropic yield functions, such as Hill’s 48, Barlat 89, and Hosford, are considered. The predicted FLDs are compared with experiments involving a typical AA6016-T4 aluminum alloy. Second, the Gurson model that considers damage growth is implemented when Hosford is the yield function, as Hosford criterion predicts the best comparable analytical FLD with experiments among the yield functions. Third, a parametric study is performed to investigate the effects of parameters on the FLD prediction. Results indicate that an extremely low value for the initial void volume fraction in the safe and groove zones has minimal effects on the FLD prediction. Lastly, the values of void volume fractions are calculated assuming no geometrical imperfections and the imperfection is because of higher void volume fraction in groove zone than that in safe zone.

这项研究使用Marciniak和Kuczynski（MK）方法提出了钣金的分析成形极限图（FLD）。逐步详细描述了FLD分析预测的过程，并使用MATLAB编写了算法。首先，确定适当的算法以建立理论分析，并考虑各种各向异性屈服函数，例如Hill's 48，Barlat 89和Hosford。将预测的FLD与涉及典型AA6016-T4铝合金的实验进行比较。其次，当Hosford是收益函数时，会考虑考虑损害增长的Gurson模型，因为Hosford准则预测了在收益函数中具有最佳可比性的分析FLD。第三，进行参数研究以研究参数对FLD预测的影响。结果表明，安全区和沟槽区中初始空隙体积分数的极低值对FLD预测的影响极小。最后，在没有几何缺陷的情况下计算空隙体积分数的值，并且该缺陷是由于凹槽区域中空隙体积分数高于安全区域中的空隙体积分数所致。