Micromechanical Model of Composite Materials Subjected to Ball Indentation

Abstract

Recent results on continuous ball indentation tests of unidirectional com posite materials have demonstrated that this technique is sensitive to fiber/matrix interfa cial quality. In order to quantitatively determine the micro-parameters of interest such as interfacial shear strength, by a meso-test such as this one a micromechanical formulation is necessary. In this article, we present an approximate micromechanical model to predict local stress states and local strength parameters from experimentally determined data. This macro/micro analysis utilizes an existing elasticity solution to develop the global stress state for the ball indentation problem of an infinite transversely isotropic half space. These stresses are then used to pose the traction boundary conditions on a fiber-matrix element. With the use of trigonometric approximations, which yield a more tractable solu tion, and the equilibrium equations, which provide stress relations, the stress variations in the fiber and matrix are predicted. The analytical model suggests that certain regions of the composite are subjected to high stresses as a result of the indentation process. These regions are a zone of large compressive stress directly under the ball near the surface and a high shear stress region near the outer edge of the ball deep inside the material. The micromechanics model is utilized in conjunction with ball indentation test results to gener ate quantitative values for the fiber/matrix interfacial shear strength. Computed interfacial shear stress (ISS) values for AU-4/Epon 828 MPDa are compared to other test meth odologies presently being employed by the scientific community to measure this value.