Elastic-plastic Shock Processes Similarity

Abstract

In the process of working out the design of the object, preliminary studies are carried out, including modeling (mathematical, physical or a combination of them) and comprehensive tests. In physical modeling, based on the methods of the theory of similarity and dimensions, the preparatory stages are implemented on the basis of an adequate mathematical model of the object or an in-depth description of its physical features. During stand testing the most complex problem is the problem of simulating an excitation in the form of intense single shock pulse. In stand shock testing in the contact is usually set an elastic-plastic, impact deformed element (crusher). The semi-empirical theory of impact is based on the assumption that only local elastic-plastic deformations could be taken into account. The study of the impact process is first illustrated using the method of physical modeling. In this two independent criteria of similarity of the shock processes are substantiated. Then, based on the analysis and numerical solution of the differential equation of impact, it is shown that the dimensionless complex arising from the theory of similarity and dimensions can be used to separately determine the main parameters of the shock process for given shock conditions – the duration of the load front and the maximum values of the contact force (overload) and local deformation. The experimental data obtained by means of a vertical pneumatic shock stand, having a small spread relative to the calculated results, are presented. The features of the process in the case of elastic-plastic impact of an elongated, rod type body are briefly considered. The criterion allowing to estimate quantitatively the relative role of wave processes in this variant of impact is offered which enables to validate conditions of considering the impacting body as a solid one.