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Research Papers

Structure of Near-Tip Stress Field and Variation of Stress Intensity Factor for a Crack in a Transversely Graded Material

[+] Author and Article Information

Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur, 208 016, India

Venkitanarayanan Parameswaran1

Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur, 208 016, Indiavenkit@iitk.ac.in

1

Corresponding author.

J. Appl. Mech 76(1), 011014 (Nov 06, 2008) (9 pages) doi:10.1115/1.2966177 History: Received December 05, 2007; Revised June 05, 2008; Published November 06, 2008

Abstract

The existing studies on the behavior of cracks in continuously graded materials assume the elastic properties to vary in the plane of the crack. In the case of a plate graded along the thickness and having a crack in its plane, the elastic properties will vary along the crack front. The present study aims at investigating the effect of elastic gradients along the crack front on the structure of the near-tip stress fields in such transversely graded materials. The first four terms in the expansion of the stress field are obtained by the eigenfunction expansion approach (Hartranft and Sih, 1969, “The Use of Eigen Function Expansion in the General Solution of Three Dimensional Crack Problems  ,” J. Math. Mech., 19(2), pp. 123–138) assuming an exponential variation of the elastic modulus. The results of this part of the study indicated that for an opening mode crack, the angular structure of the first three terms in the stress field expansion corresponding to $r(−1∕2)$, $r0$, and $r1∕2$ are identical to that given by Williams’s solution for homogeneous material (Williams, 1957, “On the Stress Distribution at the Base of a Stationary Crack  ,” ASME J. Appl. Mech., 24, pp. 109–114). Transversely graded plates having exponential gradation of elastic modulus were prepared, and the stress intensity factor (SIF) on the compliant and stiffer face of the material was determined using strain gauges for an edge crack subjected to pure bending. The experimental results indicated that the SIF can vary as much as two times across the thickness for the gradation and loading considered in this study.

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Figures

Figure 6

SIF on the epoxy side (E) and on the glass bead side (G) for an edge crack subjected to pure bending. The SIF for a homogeneous material (H) is also shown for comparison.

Figure 5

Strain on the epoxy side (E) and glass bead side (G) for edge crack subjected to pure bending

Figure 4

Single edge notched plate subjected to four-point bending

Figure 3

Elastic modulus profile of the transversely graded plate

Figure 2

Variation of glass bead volume fraction along the thickness

Figure 1

Transversely graded plate with an edge crack

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