توسعه مدل آسيب نرم اصلاح‌شده لمتر به‌منظور پيش‌بيني رشد آسيب در شكل‌دهي ورق‌هاي فلزي با شكل‌پذيري مناسب

Damage is known as an undesirable and progressive phenomenon that leads to the final failure of the material. Therefore, acquiring a comprehensive understanding of this phenomenon can greatly contribute to the production of high-quality components. The utilization of the Lemaitre ductile damage model has become widespread in recent years for eva‎luating the behavior of ductile metals. This is primarily attributed to its acceptable accuracy and the requirement of calculating only two material parameters. However, the Lemaitre’s damage model is unable to accurately predict the damage growth behavior in samples exposed to loads significantly different from the model's calibration point (stress triaxiality of 0.33). Therefore, the current study focuses on the development of the original Lemaitre model to accurately predict the damage behavior in sheet metals subjected to various loading conditions. To achieve this goal, the theoretical foundations of the Lemaitre’s damage model have been introduced initially. Subsequently, the constitutive equations for metal sheets were generalized by considering appropriate assumptions (plane stress condition). The model generalization was presented considering small deformations, isotropic hardening behavior, and damage growth. To determine the material parameters of the model (r), numerical and experimental approaches have been introduced and eva‎luated through investigations on various metals. To address the limitations of the original model, two general approach have been suggested for the development of the model. The first approach involves assuming the damage parameter of the original model to be a function of stress triaxiality. To eva‎luate the impact of the number and placement of calibration points on the accuracy of the developed model, the desired function was calibrated using three, five, and seven calibration points. Additionally, the second approach considers the influence of the Lode parameter in the constitutive equations of the original model. An appropriate subroutine was developed in the Abaqus software environment to predict the damage growth behavior in all examined models using the presented numerical solution algorithms. To eva‎luate the improvement of the proposed developed models, eleven specimens have been introduced under various loading conditions. The simulation of the damage behavior using the introduced models has been performed, and the results have been compared with experimental data. The comparison of the results demonstrates the improved accuracy and effectiveness of all proposed developed models in comparison to the original Lemaitre’s model. To eva‎luate the accuracy and reliability of the developed models in predicting damage behavior during sheet metal forming, compared to the original model, ten different strips were subjected to the Erichsen forming test. Additionally, the fracture loci, fracture surface, and forming limit diagram (FLD) of the proposed developed models were determined and compared with those of the original Lemaitre's model and empirical results. As a result, among the proposed models, the first approach, which involves selecting seven calibration points, followed by the second approach, demonstrates the most significant improvement in the accuracy of predicting damage behavior. The results indicate the effectiveness of the proposed approaches in addressing the limitations of the original model.

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محمد مشايخي