Plane Elastostatic Solution in an Infinite Functionally Graded Layer Weakened by a Crack Lying in the Middle of the Layer

This paper is concerned with an internal crack problem in an infinite functionally graded elastic layer. The crack is opened by an internal uniform pressure along its surface. The layer surfaces are supposed to be acted on by symmetrically applied concentrated forces of magnitude with respect to the centre of the crack. The applied concentrated force may be compressive or tensile in nature. Elastic parameters λ and μ are assumed to vary along the normal to the plane of crack. The problem is solved by using integral transform technique. The solution of the problem has been reduced to the solution of a Cauchy-type singular integral equation, which requires numerical treatment. The stress-intensity factors and the crack opening displacements are determined and the effects of graded parameters on them are shown graphically. 1. Introduction The study relating the behaviour of elastic material under applied load needs special attention and care when the elastic body develops a crack in it. It is obvious that the presence of a crack in a structure not only affects the stress distribution but also drastically reduces the life span of the structure. Propagation of elastic disturbance in a solid is also disturbed by the presence of a crack. But cracks are present essentially in all structural materials, either as natural defects or as a result of fabrication processes. Stress distribution in a body which develops a crack in it is entirely different from that in a body without a crack. In literature, considerable effort has been devoted to the study of cracks in solids, due to their applications in industry in general and in fabrication of electronic components in particular. Presence of a crack in a solid significantly affects its response to the applied load. Stress distributions in the solid with a crack are studied in two regions: the region in the neighbourhood of crack, called the near field region, and the region far away from the crack, called the far field region. Study of stress distribution in the near field region is very important. Stress-intensity factor, crack energy, and so forth are some of the quantities responsible for spreading of a crack. For a solid with a crack in it loaded mechanically or thermally, determination of stress-intensity factor (SIF) becomes a very important topic in fracture mechanics. The SIF is a parameter that gives a measure of stress concentration around cracks and defects in a solid. SIF needs to be understood if we are to design fracture tolerant materials used in bridges, buildings, aircraft, or even bells. A crack