A New Approach to Comprehensive Modeling of Sheet Metal Tensile Test Data Using a Universal Exponential Expression

This work aims to providing an improved fit to continuously describe tensile test behavior over arbitrary quasi-static regression fit techniques. The tensile test, commonly defined by elastic, transient, and exponential regions, is represented here by a continuous curve spanning from the unstrained state to the post uniform regions. Since the model is continuous, proportionality and yield points between regions are not defined. This continuous behavior is described by an exponential expression defined in the logarithmic stress-strain coordinate system, from which the model fit is determined. In this logarithmic scale, we found that the data is bound by segments of concave and/or convex curvatures which end approach asymptotically towards straight lines. The coordinates of the fit in the logarithmic scale are defined at the intersection of the asymptotes, and the material fits are found from the optimum regression fit. The accuracy of the fit was validated at quasi-static speeds for four different sheet materials: cold rolled deep drawing quality, dual phase DP590, and dual phase DP780 steels, and an aluminum alloy AA6916. The fitting accuracies improved with the number of material fits. Accuracies for steel grades at any the point on the full range varied from 0.2%. to 3.8%, with 90% of the curve below 1% accuracy. The maximum dispersions for the aluminum alloy studied, modeled with two material fits, is found to be only 2% higher.