A Comprehensive Mathematical Analysis on Achieving Stress-Strain Behavior at Large Strains in Bulge Test

In this study, a comprehensive mathematical analysis of the bulge test is presented. The geometry of the bulge test and the stress state that prevails in this test are very similar to the expanding thin wall sphere. These similarities may lead many users to confuse the interpretation of incremental change in the radius of the sphere as radial strain and consequently invalid analysis of the instability conditions. Therefore, in this study, emphasis is placed on how to properly use the equations to obtain the strain stress curve by this method precisely. Assuming work hardening behavior to obey power law, based on stress state on the dome, the relationship between fluid pressure and the height of the dome is presented. The instability condition is then determined and compared with Hill's analysis. To confirm the mathematical analysis, the hydraulic machine equipped with a computer system for recording pressure data versus the height of the bulge was used. The bulge test is conducted on two typical sheet metals, copper and commercially pure aluminum. The measured fluid pressure during the deformation and the thickness distribution of the sample well confirmed the results of the analytical analysis.

Automated summary

This study presents a comprehensive mathematical analysis of the bulge test, focusing on addressing potential misinterpretations of the test results by users. The consistency between experimental data and mathematical models confirms the accuracy of this method.