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Research Papers

Evaluation of Mixed-Mode Stress Intensity Factors for a Sharp Notch-tip With Curved and Stressed Edges

[+] Author and Article Information
J. H. Chang, J. F. Fan

Department of Civil Engineering, National Central University, Chungli, 320001 Taiwan

J. Appl. Mech 76(3), 031004 (Mar 05, 2009) (9 pages) doi:10.1115/1.3002333 History: Received October 11, 2006; Revised August 31, 2007; Published March 05, 2009

Abstract

For a sharp notch with curved edges and subjected to surface tractions along the edges, the fracture parameters (in particular, the stress intensity factors and the size of a singular-dominant zone) are significantly affected by the near-tip geometric and loading conditions. In this paper, a pair of contour integrals termed $JkR$ is presented for calculating the mixed-mode stress intensity factors at such a sharp notch-tip. Furthermore, by proper use of the integrals, the extent of the singular-dominant zone can be effectively characterized. Since no a priori auxiliary (or, complementary) solutions are required in its formulation, the approach appears to be feasible for problems of arbitrary notch angles and curved shapes. Also, no special treatments are required for the modeling of the near-tip singular behavior so that the integration can be performed by direct use of numerical schemes such as finite element method.

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Figures

Figure 1

An elastic body in a 2D field, containing a notch of asymptotically tangential angle β at tip O

Figure 2

The values of λ1 and λ2, as functions of the notch angle β

Figure 3

The variations of a, b, and c with respect to β

Figure 4

An elastic body containing a wedge-shaped defect

Figure 5

The variations of JkR/JkRo with respect to R/2l for (σ,τ)=(30,−20) kPa (loading case (i), mixed-mode, Problem 1)

Figure 6

The variation of J1R/J1Ro with respect to R/2l for (σ,τ)=(30,0) kPa (loading case (ii), Mode I, Problem 1)

Figure 7

The variations in local mode mixity η with respect to r/2l for (σ,τ)=(30,−20) kPa (loading case (i), mixed-mode, Problem 1)

Figure 8

A homogeneous elastic body containing a curved wedge-shaped and pressurized defect

Figure 9

(a) The finite element model (of β=π/2) for the specimen in Fig. 8 and (b) the local finite element mesh in the near-tip area

Figure 10

Three integration paths for the JkR-integrals for the instance of β=π/2

Figure 11

The variations of JkR/JkRo with respect to R/2l for (σ,τ,p)=(30,−20,10) kPa (loading case (iii), mixed-mode, Problem 2.1)

Figure 12

The variation of J1R/J1Ro with respect to R/2l for (σ,τ,p)=(30,0,10) kPa

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