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SUMMARYThe effect of the quarter-point element size on the solution parameters of fracture criteria is investigated in view of its effect on the computed stress intensity factors. An analytical relationship between the error in calculating crack propagation increment and stress intensity for single mode problems is obtained while, for mixed mode problems, the investigation is based on numerical experimentation. The singular element size is found to have a substantial effect on both crack propagation angle and increment for the geometries considered. INTRODIJCTIONFor the past two decades, the finite element method has been used extensively in numerical studies of fracture mechanics in both the elastic and plastic ranges. Since the determination of stress intensity factors at a crack tip is a key point for any fracture analysis, it has to be evaluated as accurately as possible. A number of finite element based procedures,'-' yielding varying accuracy, have been developed and used for this evaluation. In early studies, a highly refined mesh near a crack tip was used to piecewise continuously simulate the stress gradient' 3 2 and demonstrated the ability to achieve results within the acceptable engineering accuracies of 5 per cent in a single mode stress intensity factor.2 Tracey's special crack tip clement3 were shown to producc 5 per cent accuracy with an order of magnitude fewer degrees-of-freedom than was required using a refined mesh of low order polynomial elements. Barsoum4 and Henshell and Shaw ' havc independently shown that the collapsed quarter-point isoparametric element allows a highly accurate computation of mode I stress intensity factor for linear fracture problems.A good estimate of the separate values of K , and K,, was obtaincd by Chang et aL2 by extrapolating the near tip displacement (or stress) field to the crack tip. The sum of the mixed mode stress intensity factors can be obtaincd with the energy release rate6 and the j-integralapproaches. Procedures exist to calculate the separate values of mixed mode stress intensity factors with the last two approaches. However, multiple finite element analyses, with the same mesh and different boundary conditions, are required for this separation.'A displacement correlation technique, proposed by Shih et aL9, was used for calculating mode 'Assi\tant Profe\sor, Civil Fngineering Department tAssociate Dircctor of CICG and A w m a t e Professor, Civil bngincering Department

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