Crack Paths 2012

The integral expressions of ¢1(a;z) and o2 (a; z) are found to diverge in this limit, but

not those of ¢l(a;z)—¢'(a;0) and ¢2(a;z)—¢2(a;0) which suffice to characterize the

deviations of the front from straightness and are given by

¢1(o;Z)-¢‘(o;0)=%[(1+u)1u(]1+u|)+(1-u)h1(]1-u])]

d

[(l+u)ln(l+u)+(l—u)ln(l—u)] if]u|§1, , = 3(22)

¢2(a;Z) —¢2(a;0) =

[at —SgI1(u)) 1h[”—+]] + 2111 2] if ]t| 21 ,,_

_ Z

Figure 2 shows the results obtained for various values of 8. The perturbation

so‘ (a; z) + 82¢2(a;z) has been divided here by e to evidence the non-proportionality of

the two quantities, and the curves have been madeto coincide on the boundaries of the

obstacle (z : i d) rather than at its center (2 : 0) to facilitate their comparison.

[(¢1+e<§>2)(z)-(¢1+E¢Z)(d)l d1'

Figure 2: The shape of a crack front deformedby the presence of an obstacle.

R E F E R E N C E S

1. Rice, IR. (1985). A S M E J .Appl. Mech. 52, 571-579.

2. Gao, H., Rice, J R(1989). A S M E J .Appl. Mech. 56, 828-836.

3. Chopin, J. (2010). P h DThesis, Université Pierre et Marie Curie (Paris VI), France (in

French).

4. Rice, J.R. (1989). In: Fracture Mechanics: Perspectives and Directions (Twentieth

Symposium), pp. 29-57, Wei and Gangloff (Eds), American Society for Testing and

Materials STP 1020, Philadelphia.

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