A NEW UNCONDITIONAL CONVERGENCE ALGORITHM FOR CALCULATING FLC BASED ON M-K MODEL

It has important theoretical significance and research value to meet the requirements of unconditional convergence and rapid solution of the M-K instability model for obtaining the forming limit curve (FLC) in sheet metal forming. And the above requirements are also considered as the difficulties of the theoretical calculation of FLC. However, when calculating the FLC based on advanced yield criteria within the framework of the M-K instability model, convergence results cannot be guaranteed by employing the traditional Newton iterative algorithm. Besides, the fixed increment rule takes too long to calculate, seriously restricting the application scenarios of the M-K instability model. Therefore, in this study, an adaptive incremental algorithm is proposed and zirconium alloys are consumed as the experiment material. This algorithm adaptively adjusts the iteration step size through iterative error information and oscillation conditions, which not only ensures calculation accuracy and meets unconditional convergence requirements, but also significantly improves calculation speed. Moreover, the calculation accuracy of the FLC of zirconium alloys by using the adaptive incremental method has been verified in this study while the impacts of the algorithm's iteration error as well as the initial strain increment on the FLC prediction results are also analyzed. The results show that the adaptive incremental method has the advantages of unconditionally ensuring convergence and fast calculation speed, and the calculation results are not affected by the initial iteration step size. While its calculation time is only 0.43% of that of the fixed incremental method. In addition, this investigation suggests that an iteration error of less than 10−6 and an initial strain increment of less than 0.001 in the initial parameters are prerequisites for obtaining stable FLC results. According to the prediction results of the FLC, it can be concluded that the plastic behavior of zirconium alloys can be well described by employing the adaptive incremental method based on the Yld2000-2d yield criterion theory within the M-K model framework. Due to the advantages of simplicity, user friendly as well as the high computational efficiency, the adaptive incremental iteration method should be considered as a promising algorithm in the development of subroutines in finite element software, accelerating its calculation speed and improving the accuracy of numerical simulation of zirconium alloys. © 2024 Chinese Society of Theoretical and Applied Mechanics. All rights reserved.