The flow functions for plastic deformation have been developed to describe the plastic behavior of sheet metals. In order to explain the plastic behavior of material in metal forming processes via finite element analyses, two basic input functions should be applied. One is the yield function that determines the yielding behavior. The other is flow function to describe the hardening property of sheet metal. To describe the hardening properties of sheet materials under quasi-static tension condition in a wide range of plastic straining, various different equations are known such as classical Swift, Voce, Holloman, combined Swift-Voce, and recently proposed Kim-Tuan equations, etc. Those hardening equations are based on metallurgical or phenomenological investigations, and however the application of each equation has some limitation. In this study, the random growth of the binary tree method is introduced to develop the reliable hardening equations of various sheet metals (i.e. DP980, Pure Ti, AA5052-O, STS304, Ti-Gr2, and Mg-AZ31B) with no knowledge of existing hardening equation types. To evaluate the proposed method, the proposed equations developed by new approach are compared with the Voce, Swift, and Kim-Tuan hardening equations for stress-strain curve and the plastic instability point. Consequently, the proposed approach was proven to be very efficient to find the reliable and accurate hardening equation for any kind of materials.
Prediction of Plastic Instability in Sheet Metals During Forming Processes Using the Loss of Ellipticity Approach
