Strength of a joint under stress concentration

Abstract

formulate strength conditions in the presence of stress concentration. In this work, using the sectioning method, which is well known in engineering mechanics, we examine the strength of a joint in composite bodies with exponential strengthening of materials in the presence of stress concentration. The use of the sectioning method in the linear mechanics of cracks is covered in [3]. Let a composite body be made of two dissimilar materials. The stress and strain intensities are related by the exponential dependence or0 = kr n. For both materials, the values of the parameter m are considered equal and the values of k different. We assume that at the end of the contact surface of the composite body there is a reentrant angular "cut" with stress concentration at the tip. Assume that we know a solution of the corresponding problem ignoring the stress concentration caused by the "cut." This stressed state will be called nominal. Further, using this solution for the neighborhood of the angular point, we should find the strength condition for the end of the joint with the stress concentration state. 1. Twisting. We consider a composite bar of constant cross section made of materials strengthening by an exponential law. The bar has a reentrant angle at the end of the contact surface and is twisted by the moments M applied at the end cross sections. Initial Relations. We assume that the nominal solution, i.e., without an angular cut, is specified in the polar coordinate system p~a (Fig. 1). We denote stresses by Tpi(p, ~a) and T~i(p,~a), and displacements by Wi(p, ~a). Here and below, the subscript i = 1 and 2 denotes the values of the constituent materials. Longitudinal shear strains occur in the vicinity of the angular point r = 0. According to [2], this solution is representable as 7"0i -= kir(A-1)m f~xi , 7"ri --__ Akir(A-1)rn fixi '