The stress fields near a crack front in a ductile solid are essentially three-dimensional (3D) in nature. The objective of this paper is to investigate the structure of these fields and to establish the validity of two-dimensional (2D) plane stress and plane strain approximations near the crack front under mixed mode (combined modes I and II) loading. To this end, detailed 3D and 2D small strain, elastic-plastic finite element simulations are carried out using a boundary layer (small scale yielding) formulation. The plastic zones and radial, angular and thickness variations of the stresses are studied corresponding to different levels of remote elastic mode mixity and applied load, as measured by the plastic zone size with respect to the plate thickness. The 3D results are compared with those obtained from 2D simulations and asymptotic solutions. It is found that, in general, plane stress conditions prevail at a distance from the crack front exceeding half the plate thickness, although it could be slightly smaller for mode II predominant loading. The implications of the 3D stress distribution on micro-void growth near the crack front are briefly discussed.

In this paper, a finite element study of 3D crack tip fields in pressure sensitive plastic solids (such as polymers or metallic glasses) under mode I, small scale yielding conditions is performed. The material is assumed to obey a small strain, Extended Drucker-Prager yield condition. The roles of pressure sensitive yielding, plastic dilatancy and yield locus shape on the 3D plastic zone development and near-crack front fields are systematically studied. It is found that while pressure sensitivity leads to a significant drop in the hydrostatic stress all along the 3D crack front, it enhances the plastic strain and crack opening displacements. The implications of these contrasting trends on ductile fracture processes are discussed in the light of some recent micro-mechanical simulations.

SUMMARYA clearer understanding of the problems associated with reduced integration and optimum integration schemes for the development of Mindlin plate elements is presented. It is shown that an optimal selective integration rule can be found for the 4-node quadrilateral plate bending element which requires 2 x 2 Gaussian integration for bending energy and 1 x 2 and 2 x 1 rules for the shear energy terms from (0, -w ,~) and (0, -w ,~) , respectively. This will give an element of correct rank, without any zero energy mechanisms and without shear locking in the thin plate limit, and better performance in moderately thick situations than the currently available 4-node quadrilaterals using one-point shear integration or modified one-point shear integration due to Hughes et al. The effects of arbitrary orientation of the grid and the non-rectangular form of element are discussed.

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A simple and accurate method is needed for calculating strain energy release rates (G) or the stress intensity factors (K) from the results of finite element analysis of plates with through cracks subjected to bending loads. The purpose of this report is to develop a method to calculate G or K using only nodal forces and displacements from a standard finite element analysis code. It is an extension of the well known Modified Crack Closure Integral (MCCI) approach [1-5] to the bending of plates with through cracks. The significant advantages of this method over other methods commonly used to calculate G or K are:1) It avoids dealing with the details of singular stress fields around crack tips, where there are added complexities of anisotropic material behaviour and mode interaction.2) It permits separation of G into its components, G i (i=I, II and III) in a mixed mode fracture problem.3) It ensures higher accuracy even with a coarse mesh of conventional elements. Both lower-and higher-order elements can be used.4. The finite element modeling does not require the use of singular elements at the crack front. However, if singular elements are also used there is a significant improvement in convergence, accuracy, and computational efficiency.5. The strain energy release rates are calculated directly using crack surface opening displacements and nodal forces at and ahead of crack tips. Therefore computation of element stresses is unnecessary.6) The method requires only one analysis per crack length. It is not restricted to self-similar crack growth.7) It can be applied to homogeneous isotropic as well as laminated anisotropic materials. 8) General purpose finite element analysis codes can be used without any modification.However, application of the MCCI technique to the bending of plates with through cracks has not been reported in the literature.An examination of bending of plates with through cracks based on shear deformation theories [6-10] revealed that the bending stress intenstity factor (K) depends strongly on the ratio of plate thickness (h) and half crack length (a). Hence, there is a need to examine the effect of (h/a) on the accuracy of G and K obtained by the MCCI approach.Int Journ of Fracture 41 (1989)