The optimum size of quarter-point crack tip elements

Ingraffea and Manu¹ and Lynn and Ingraffea² have shown that the size of the quarter-point elements can affect the computed elastic stress intensity factor. The nature of the effect is such that, all other details remaining constant, there is a particular crack tip element size which minimizes the error in the computed stress intensity factor. Here, size of element means the radial edge length. The reasons for this size dependence are discussed below. It will be seen that the discussion is in terms of the need to simultaneously represent the singular and finite stress terms in a given problem. The discussion has relevance to other formulations of crack tip elements.