Analysis of Die less Explosive Forming of Bimetallic Circular Plates using “Energy Conservation law”

Die less explosive forming of circular plates is one of the most useful methods in the industries especially chemical applications. Manufacturing of large vessel's head, multilayer rings and some parts of heat exchangers are the example of applying this method. Many theoretical and experimental researches about examining the explosive forming of simple and single layer plate have been done. The purpose of most studies was prediction of transversal displacement of plate and its profile of deformation with respect to the amount of impulsive load due to the explosion. On the other hand, no study has been done for analysis of behavior of bimetallic plate in the explosive forming process. However it can be easily shown that with some small change in plasto-dynamic equations of a simple plate, the behavior of a bimetallic plate in explosive forming process would be analyzed. The used methods in analysis of plasto-dynamic behavior of plates can be divided up to two categories. Some of them have used the equations of motion and wrote these equations for two or three phases of time. This routine is really complex especially in large deformation problems. In other hand, some researchers have applied energy methods for their analytical purposes. The major advantages of this routine is its simplicity. Because there is not necessary to consider the effect of plastic hinge motion for calculating desired parameters. In this paper, die less explosive forming of bimetallic circular plate is analyzed with “energy conservation law” very simply and comprehensively. It will be shown that with calculating full plastic moment and force of a bimetallic plate, the dynamic-plastic’s equations for the simple plates can be used and the displacement of plate's center and its deformed profile can be predicted. Also the presented model has some special capabilities. For example it considers the effects of bending moments and membrane forces simultaneously. Also it is possible to calculate the influence of rotatory inertia and high strain rate effect on the displacement of plate. Further with this analytical model the effect of various supporting condition and the different shape of profile of pressure can be studied. The accuracy and reliability of presented model will be verified with comparison of experimental results and analytical data. Also die less explosive forming process of bimetallic plate have been simulated with Ansys-Lsdyna software. Comparison of different results approves the capabilities of presented model in this article.