EDGE-CRACKED CIRCULAR DISK UNDER SYMMETRIC PIN-LOADING

A circular disc of radius a, made of homogeneous, isotropic, linearly elastic material, contains a radial edge crack of length b(0 < b < 2a). The disc is in equilibrium in a state of generalized plane stress under various loadings, which are motivated by the fact that this geometry is to become a standard test specimen configuration in the fracture testing of materials. The first cases considered are those in which the disc is loaded by either (i) opposing point forces P normal to the crack, or (ii) opposing point couples M, in each case acting at the crack mouth. The problem of determining the resulting stress field throughout the disc is solved analytically in closed form in each case, and the respective stress intensity factors KP, KM. are given exactly by [Formated text] where K+(0), K+(i) are constants whose values are[Formated text] correct to 6 decimal places. For the case in which the cracked disc is subject to general symmetric ‘pin-loading’ by opposing point forces P, it is proved that the stress intensity factor [Formated text] is given by the asymptotic formula [Formated text] as [R(2a — b)]/R'b -> 0, where c is the distance of the load line from the crack mouth, β is a constant whose value is β = 2.739 593… correct to 6 decimal places, and R, R' are shown in Fig. 4. Corresponding asymptotic formulae are also proved for the opening of the crack at the load-line, and at the crack mouth. These asymptotic formulae (with the appropriate error terms neglected) are compared with numerical results obtained by boundary collocation and excellent agreement is found. © 1979, Cambridge Philosophical Society. All rights reserved.