A novel combined hardening rule for the brass cartridge case using crimping simulation and optimization

Abstract

A cartridge shell case, a critical component in the defence industry, undergoes a crimping process to form one end for the insertion of a bullet. The shell case is primarily composed of brass. The crimping process is simulated using a novel plasticity model that combines a hardening rule with the Hill48 yield criterion and the associated flow rule. This study focuses primarily on the hardening rule, where a bilinear isotropic hardening (BISO) and Chaboche's nonlinear kinematic hardening (CHAB) rules are combined to develop a novel hardening model. The raw parameters of the models are calculated by regression performed on the data from monotonic tensile test and low-cycle fatigue (LCF) test. A multi-objective genetic algorithm is used to calibrate the raw parameters by the inverse analysis. The performance of the models is evaluated on the diameter of the shell considering the work-hardening. The novelty of this study lies in the acquisition of calibrated hardening rule parameters for the crimping process, which involves a multi-axial deformation pattern, using only data from uniaxial tensile and LCF tests, which are simpler to conduct. The force-moment requirements, springback, and material flow path are also calculated. The results provide a valuable insight into the combined hardening model, its parameters, and their sensitivity for the crimping process. The calibration process results in significant improvements in material properties, particularly yield strength (YS) and tangent modulus (TM). For the crimping, YS is observed to increase by 37.82% and TM is observed to decrease by 13.84% while parameters $\{C_1,{\gamma }_1,C_2,{\gamma }_2,C_3,{\gamma }_3\}$ increase approximately 9% where C_m is hardening modulus, and ${\gamma }_m$ is decrease rate. The model achives an absolute percent relative error (APE) of 0.18%.

Graphical abstract

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