Evaluation of prediction error resulting from using average state variables in the calibration of ductile fracture criterion

Abstract

In order to evaluate the prediction error resulting from using average state variables in the calibration procedure of the ductile fracture criterion, a series of experiments and corresponding simulations were performed to extract the evolution of fracture-related state variables such as stress triaxiality (η), Lode parameter, and equivalent strain to fracture at the fracture initiation points. The average stress triaxiality, average Lode parameter, and equivalent strain to fracture were used to calibrate the Lou-Huh (L-H) ductile fracture criterion. The average induced prediction error was evaluated by comparing the accumulated damage value, which was computed with the calibrated L-H ductile fracture criterion at the fracture initiation point, with the critical threshold value. Comparisons based on a series of experiments covering a wide range of values for stress triaxiality indicated the existence of an average induced prediction error for the compression tests, and demonstrated that different values of embedded-constants C₁ and C₂ of L-H ductile fracture criterion resulted in entirely different average induced prediction errors. Thus, a parameter study was performed to investigate the influences of C₁, C₂, the relationship of η and equivalent plastic strain ( $\overline{\varepsilon }$ ), and the internal function of the integral formula on the average induced relative error. The influence of the relationship of $\eta \propto \overline{\varepsilon }$ could be represented by the influence of the exponent a, the intercept for the stress triaxiality, and the allocation of equivalent strain for the segmented function. Among these influence factors, the value of C₂, the value of the exponent a, and the value of the negative intercept for stress triaxiality contributed significantly to an increase in relative error.