A FUNDAMENTAL DISLOCATION SOLUTION FOR AN INFINITE-PLATE WITH APPLICATION TO RELATED CRACK PROBLEMS

A fundamental solution for the three-dimensional stress field induced in an infinite plate by an infinitesimal dislocation loop in the inter ior of the plate is presented here. The solution is derived from the a ssociated Green's function for the same geometry, which is, in turn, f ound by employing an image method and Muki's formulation [Muki, R. (19 60) Asymmetric problems of the theory of elasticity for a semi-infinit e solid and a thick plate. In Progress in Solid Mechanics, Vol. 1, (ed s I. N. Sneddon and R. Hill) Interscience Publishers, New York, pp. 39 9-439] for an axisymmetric elastic body. The solution obtained falls n aturally into three parts: the first part is singular, and corresponds to the solution for a full space; the second part is regular, and rep resents the image of the first part to account for the presence of the upper surface of the plate; the third part is also regular, and gives the correction term to maintain the lower surface of the plate free o f tractions. The first two terms are expressed in closed form, whilst the third term is expressed in Hankel integral form. Convergence of th e integrals is ensured by an asymptotic analysis. The fundamental disl ocation solution found is then employed to analyze the growth of-plana r cracks in a plate, where the cracks are modelled by a continuous dis tribution of infinitesimal dislocation loops over the crack Faces, i.e ., the eigenstrain procedure. (C) 1997 Elsevier Science Ltd.