What are elastic instability and inelastic instability?

Baidu states that when instability occurs, the compressive stress in the thin film on the wall of the vessel is less than the material’s proportional limit; when stress is proportional to strain according to Hooke’s law, it is referred to as elastic instability. At this point, the critical pressure for instability is independent of the material’s yield limit, and depends only on the elastic modulus E and Poisson’s ratio μ. Since the differences in E and μ among various steels are not significant, replacing low-strength steel with high-strength steel has little effect on improving the elastic stability of the container. If the compressive stress in the wall of the vessel at the time of instability exceeds the proportional limit of the material, and the relationship between stress and strain becomes nonlinear, it is referred to as inelastic instability. The critical pressure at inelastic instability is related to the material’s yield limit. Replacing low-strength steel with high-strength steel at this point can improve the stability of the container.

During the elastic instability stage, the allowable external pressure is related to the elastic modulus of the material, and the elastic moduli of metal materials differ little; therefore, replacing low-strength steel with high-strength steel has little effect on improving the ability to withstand external pressures. In the stage of inelastic instability, increasing the strength grade of the material enhances the container’s ability to resist external pressure.