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

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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mo fence="false" stretchy="false">{</mml:mo> <mml:mrow> <mml:msub> <mml:mi>C</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>γ</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>C</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>γ</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>C</mml:mi> <mml:mn>3</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>γ</mml:mi> <mml:mn>3</mml:mn> </mml:msub> </mml:mrow> <mml:mo fence="false" stretchy="false">}</mml:mo> </mml:math> increase approximately 9% where C m is hardening modulus, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:msub> <mml:mi>γ</mml:mi> <mml:mi>m</mml:mi> </mml:msub> </mml:math> is decrease rate. The model achives an absolute percent relative error (APE) of 0.18%.