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ANALITICAL AND NUMERICAL STUDY OF IMPACT LOADED CYLINDRICAL SAMPLE

Levan Japaridze

Abstract

The fundamentals challenges of shock loading impact are known as complex nonlinear problems with variable contact conditions. Even the simplified solution of these problems often bring in essential mathematical complexity related with: shock or elastic waves parameters, distribution of contact stresses, elasto-plastic deformation of the bodies in collision, balance and dissipation of energy, and others. Therefore, and in practice we often use simplified analytical approaches to resolve engineering challenges even in not so sophisticated conditions. It is demonstrated that the static and dynamic contact forces in the interaction of solid bodies are reciprocally proportional and therefore it is possible to calculate the structure under impact loads using static methods and then the external forces, internal stresses and deformations, determined in such a way, are multiplied by the appropriate dynamic impact factor (DIF) for adequate model calculations. This is important for the design and applications in Defense, where the parameters of assessment of the impact resistance of solid materials and structural elements are understood as the ratio of the maximum dynamic to average static load. However, the DIF is taken by some authors also as ratio of the dynamic to static strength of the material and are often reported as a function of the strain rate. The tensile as well as shear strength are key material parameters in the analysis of structures under these conditions. They are generally determined using either a direct tensile test or an indirect splitting tensile test setup. Both tests are simple in concept, but have proven quite complicated to run in such a way that reliable results, independent of specimen and platens size, shapes, and boundary conditions, are often difficult to obtain. The indirect tensile testing method, known as the Brazilian Test, developed by Carneiro and Barcellos, has found widespread application because of its practical convenience for determining the static and dynamic tensile strength of rocks, concretes, glasses, and many other brittle and not quite brittle materials such as nuclear wastes, asphalt concretes and others. The Brazilian test has been reviewed and investigated by numerous scientists. However ever since the development of this method scientists have been interested in answering questions such as: why and when samples are not split along the loading diameter, as to the basic idea of the Brazilian test, but at some distance away from it; and how and why does the Brazilian test overestimate the tensile strength of these materials? In this paper we suggest formulas for the dynamic impact factor for Cylindrical Specimen applying the Standard Test Method for Splitting Strength of samples on the drop hammer facility and using the Split Hopkinson Pressure bar. The main solutions take into account several factors such as the nonlinear interaction between the loading bearing platens and specimen, the curvatures of the jaw surfaces, and elastic parameters of the materials. The DIF here is understood as the ratio of maximum dynamic load, internal stress and displacement from falling body related to the static load, stress and deformation, caused by the action of the weight of this body. The fundamental static challenges are solved by appling elasticity theory methods, and the analytical solutions are compared to the results of numerical modeling, conducted by "Rocksciense" under the Fase 2 program. These results show adequate agreement.

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