Indentation of a Functionally Graded Plate by a Rigid Spherical Indenter in the Presence of a Semi-Elliptic Surface Crack

Graded materials, also known as functionally graded materials (FGMs), are multiphase composites mainly composed of a ceramic and a metal; thus, they exploit the heat, oxidation and corrosion resistance typical of ceramics, and the strength, ductility and toughness typical of metals. These materials are mainly used as heat barriers. In addition, many of the present and potential applications of FGMs involve contact problems. On the other hand, the production process of FGMs is somewhat complex and leaves some defects in the produced structure. One of the most important defects in such structures is surface cracks. Here, the combination of the contact and crack problems is investigated in a functionally graded rectangular plate containing a semi–elliptic surface crack indented by a frictionless rigid spherical indenter. The plate is simply supported and the crack is located in the middle of the plate surface in the tension part. The crack surface is parallel to one of the plate edges. The gradient of mechanical properties variation is considered through the thickness of the plate and the volume fraction distribution of the constituting phases is modeled by a polynomial function and the Poisson’s ratio is kept constant. The analyzing of the problem is divided into two steps. At the first step, for an uncracked plate the equations of equilibrium are derived in terms of the displacement field and are solved numerically to find the contact rule. As the second step in studying the problem, the contact problem of a cracked plate is modeled by using ABAQUS finite element package. The aim of this step is to find the effect of the presence of the crack on the contact rule. The optimum mesh for the ABAQUS model is found by using the results of the first step. In order to do so, an ABAQUS model is created for the uncracked plate. The analytical results and the obtained results from ABAQUS for specified plate and indenter dimensions and material properties are compared. After finding the optimum mesh, a crack is added to the ABAQUS model of the plate under contact loading. The effects of gradient changes and indenter dimensions on the contact rule and stress distribution at the crack tip are then investigated by using the obtained ABAQUS model. The acquired results show that the influence of the material nonhomogeneity on the stress distribution around the crack tip and in the plate (uncracked and cracked) and contact rule can be quite significant. In general, increasing the overall volume fraction of the metal phase increases the load carrying capacity in an uncracked plate. In a cracked plate, the changes in material distribution as well as the changes of the indenter diameter does not affect the results that much.