Calibration Methods And Adaptablity For Parameter Identification Of Ductile Fracture Criterion

It's common to find parts be scraped due to ductile fracture in the process of industry production.Thus,it's of great significance to forecast the crack initiation and propagation by using numerical simulation.The accuracy of numerical simulation depends on the damage model.Due to good portability,a lot of ductile fracture criterions have been inserted in many mainstream commercial finite element software and these could be used by inputting parameters.However,many ductile fracture criterions include more than one parameter.Ductile fracture criterion of different parameters generate different results of numerical simulation.Parameter identification can be identified from a series of test with different states of stress,which are not static in plastic forming process.So the average state variables were used to calibrate parameters of ductile fracture criterions.Besides,the prediction error induced by using the average state variables in the calibration procedure of ductile fracture criterion has not been evaluated.Thus,comparison of different calibration methods and their adaptability are of great significance on the application of numerical simulation.To evaluate the prediction error induced by using the average state variables in the calibration procedure of ductile fracture criterion,a series of experiments and the corresponding simulations were performed to extract the evolution of the fracture related state variables like stress triaxiality,Lode parameter and equivalent strain to fracture at the fracture initiation points.Meanwhile the average stress triaxiality,average Lode parameter and equivalent strain to fracture were used to calibrate the L-H ductile fracture criterion.Thereafter 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.According to the comparisons based on a series of experiments which cover wide range of stress triaxiality,average induced prediction error exists in the cases of compression tests,and with different values of C₁ and C₂ the amount of average induced prediction error is completely different.Thus parameter study was performed to investigate the influence of C₁,C₂,the relationship of????and the internal function of the integral formula on the average induced relative error.The influence of the relationship of????could be represented by the influence of the exponent a,stress triaxiality intercept 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 stress triaxiality intercept show much more significant contributions to the increase of relative error.Besides the commonly used inverse analysis method and surface fitting method based on hybrid experimental and numerical method,a new calibration method based on the integral of fracture threshold value is proposed in this paper.With the help of a series experimental results covering the wide range of stress triaxiality,a newly published L-H ductile fracture criterion was calibrated by using these three calibration methods,and it was inversely used to predict the fracture initiation of these tests.On this basis,the comparison of these three calibration methods were performed.It could be found that in contrast to the normal inverse analysis method,surface fitting method and the new method both have good computing efficiency.Meanwhile the new method could provide better accuracy for the prediction of fracture than the surface fitting method.There are no ductile fracture criterions can be well applied to the wide range of stress triaxiality,and the extension of ductile fracture criterion is limited to the generalization of high range of stress triaxiality to low or negative range of stress triaxiality.Hence,a finite extend L-H ductile fracture criterion considering a changeable cut-off value for stress triaxiality was proposed by considering the damage mechanism in axial symmetry stress state and the damage transformation from high stress triaxiality state to low stress triaxiality state.The simulation results show that the extend L-H ductile fracture criterion has better accuracy.After analyzing the damage surface,it is found that the data point of the low negative stress triaxiality state and the high stress triaxiality and low lode parameter state coincide well with the damage surface.However,some errors in the data point of high stress triaxiality and high lode parameter state and high lode parameter state are still possibly exist.