645 A NOTE ON THE PROBLEM OF EDGE CRACK IN A SEMI-CIRCULAR PLATE Kailash Nath Srivastava, Mahendra Kumar, and Avinash Chandra Jha Department of Mathematics, Maulana Azad College of Technology Bhopal-7, India tel: 62291, ext 67 The problem of an edge crack in an elastic half-plane has been studied by Koiter [i], Wigglesworth [2], Doran and Buchwald [3], Stallybrass [4], and Sneddon and Das [5]. More recently, we have [6] studied the problem of an edge crack in a semicircular plate under plane strain. However, numerical results were not presented due to lack of computational facilities. The purpose of this note is to present num- erical results and conclusions. We briefly review the problem state- ment: In plane polar coordinates, the edge crack occupies the region 0 < r < I, O = 0. The crack is opened by internal normal pressure. In view o~ symmetry, we need only consider the quarter plate problem. The boundary conditions may be formulated as ~r@(r,0) = 0, 0 < r < c (i) ~@(r,O) = - p(r), 0 < r < 1 (2) UO(r,0) = 0, 1 < r < c (3) On the line @ = ~/2, we have ~o(r,~/2) = ~r0(r,~/2) = 0. (4) In addition to these conditions, we have on r = c > 1 a choice of boundary conditions and select two problems for study. Problem I: Or(C,0) = Sr@(C,@) = 0, 0 < O < ~/2 (5) Problem If: Ur(C,O ) = u@(c,O) = 0, 0 < @ < 7/2 (6) The analysis appears in [6] and need not be repeated here. We note only that the problem is formulated in terms of complex potentials in the usual manner. Following ~5], reduction is made to a pair of simultan- eous Fredholm integral equations which are then further reduced to linear algebraic equations. Gauss integration is used, and the ten point formula gives the desired degree of accuracy. Using p(r) = Po and K = ~ /(r-l)~@(r,O) r+l we compute the stress intensity for various c > I. The variation of stress, intensity factors with c is shown in Fig. i. We observe that the stress concentration is more for small values of radius c and it approaches the value derived by Sneddon and Das [5] when c approaches 4.0. We also observe that the stress concentration is less dominant in the case of rigidly clamped surface. Int Journ of Fracture 12 (1976)