Analytical Model of the Confined Compression Test Used to Characterize Brittle Materials

Numerical and analytical simulations of projectiles penetrating brittle materials such as ceramics and glasses are a very challenging problem. The difficulty comes from the fact that the yield surface of brittle materials is not well characterized (or even defined), and the failure process may change the material properties. Recently, some works have shown that it is possible to characterize and find the constitutive equation for brittle materials using a confined compression test, i.e., a test where a cylindrical specimen, surrounded by a confining sleeve, is being compressed axially by a mechanical testing machine. This paper focuses on understanding the confined compression test by presenting an analytical model that explicitly solves for the stresses and strains in the sample and the sleeve, assuming the sleeve is elastic and the specimen is elastoplastic with a Drucker–Prager plasticity model. The first part of the paper briefly explains the experimental technique and how the stress-strain curves obtained during the test are interpreted. A simple and straightforward approach to obtain the constitutive model of the material is then presented. Finally, a full analytical model with explicit solution for displacements, strains, and stresses in the specimen and the sleeve is described. The advantage of the analytical model is that it gives a full understanding of the test, as well as information that can be useful when designing the test (e.g., displacements of the outer radius of the specimen).