Analysis of Plastic Deformation of Pipes Due to Deflagration to Detonation Transition Using Static Equivalent Pressure

Explosions of premixed gases with deflagration to detonation transition (DDT) are a risk in the process industry with potentially catastrophic consequences. Robust and simple design methods are required for industrial use. Such a simplified design method based on finite element analysis is proposed to model the dynamic behavior of pipes loaded by gas explosions of premixed gases including DDT. The focus is on so-called long pipes, where the DDT is not affected by reflections at blind flanges. First, it is reviewed how the pressure load of the gas explosion and the resulting material behavior has been modeled in previous publications. The analytical equations are then extended for describing the pressure load as a function of time and location by considering the leading compression wave as it affects the pressure load of the overdriven detonation. The extended analytical equations are parameterized using Chapman-Jouguet conditions and experimental results from publications for both static equivalent pressure and the location of the DDT. To describe the plastic material behavior at high strain rates, the well-known Johnson-Cook plasticity model is used. The material parameters of the model are derived from simple experiments, which are available in an industrial environment. The comparison of a finite element simulation with experimental data shows that the concept of equivalent static pressure can be extended to an finite element analysis, which in the future will allow the sizing of complete pipe systems including tees, bends, and flanges while considering plastic deformation.