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**Published:** Jan 1988

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**Source: **STP945-EB

An efficient finite-element methodology for evaluating the stress-intensity factors (*K*^{I}, *K*^{II}) and the weight functions (*h*^{I}, *h*^{II}) of a self-similar propagating mixed-mode crack has been established with a single colinear virtual crack extension. This is accomplished through the use of a symmetric mesh in the crack-tip neighborhood that provides the decoupling characteristics for the field parameters of stresses, strains, displacements, tractions, and strain energy release rates into Mode I and Mode II components within the symmetric mesh zone. The application of this newly established technique to the three-point bend specimen has been studied with the mixed fracture mode introduced by deviations from normal test conditions of either loading or support eccentricity. These eccentricity effects on *K*^{I} and *K*^{II} values for three-point bend specimens are detailed in this paper.

The angular dependence of the strain energy release rate, *G*(θ), as a function of eccentricity, is also provided herein to account for the testing irregularities associated with three-point bend tests, which have span-to-width ratio *s/W* = 4 and different crack lengths 0.1 ≤ *a/W* ≤ 0.8. By assuming the crack propagation taking place at the angle (θ^{cr}), with maximum strain energy release rate (*G*^{max}), the predictions are also provided for expressing θ^{cr} angles as a function of both loading and support eccentricities. It is found that the load eccentricity has a more severe effect than that of the support eccentricity as indicated in our numerical results for three-point bend specimen with *s/W* = 4.

Also presented explicitly are the characteristics of the Mode I and Mode II weight functions for three-point bend specimens (equivalent to edge crack geometry) with *s/W* = 4 and 0.1 ≤ *a/W* ≤ 0.8 at the crack faces and other key traction application surfaces. The explicit weight function information at these key traction application boundaries is very useful to the fracture mechanics practitioner and designer for guiding traction application locations and directions that produce the least stress-intensity factor.

For a given crack geometry, the explicit weight functions depend on the constraint conditions. The method of obtaining the required stress-intensity factors of an asymmetric crack geometry under the constraint conditions, which are different from the available weight function for the same asymmetric crack geometry, is also made available here. This is accomplished by combining the predetermined explicit weight functions with self-equilibrium forces, which include both the applied surface tractions and the reaction forces induced by constraints.

**Keywords:**

mixed fracture mode, stress intensity factors, strain energy release rates, explicit weight functions, self-similar crack propagation, crack propagation criterion, eccentric loading effect, ASTM three-point bend specimen

**Author Information:**

Sha, GT *Staff research scientist/engineer, General Motors Corporation, Indianapolis, IN*

Yang, C-T *Research engineer, Center for the Advancement of Computational Mechanics, School of Civil Engineering, Georgia Institute of Technology, Atlanta, GA*

**Committee/Subcommittee:** E08.03

**DOI:** 10.1520/STP23250S