Multiscale cohesive zone model for propagation of segmented crack fronts in mode I+III fracture

Journal Article · Tue Feb 17 00:00:00 EST 2015 · International Journal of Fracture

DOI:https://doi.org/10.1007/s10704-015-0001-x· OSTI ID:1906117

Leblond, Jean-Baptiste ^[1]; Lazarus, Véronique ^[2]; Karma, Alain ^[3]

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1. Sorbonne Univ., Paris (France)
2. Univ Paris-Sud, Orsay (France)
3. Northeastern Univ., Boston, MA (United States)

Quasistatic crack propagation in mixed-mode I+III fracture is widely observed to be unstable, the instability being characterized by the segmentation of the parent crack into a periodic array of daughter cracks shaped as flat facets rotated towards the principal stress axis. While there has been recent progress to characterize this instability, no global theory is presently available to describe all aspects of the propagation of the segmented front, including both “local” features like the angle of rotation of the facets and the ratio of their width to their spacing, and “global” ones like the effective energy-release-rate of the segmented crack front and the tendency of the facets to coarsen. This paper embarks on the development of such a theory, based on the assumption that the spacing of the facets is much smaller than their length, and asymptotic matching of outer and inner solutions for the mechanical fields on scales comparable to the facet length and spacing, respectively. Here, the inner problem is shown to reduce to a 2D linear elastic fracture mechanics problem in the plane perpendicular to the crack propagation axis. The solution of this problem is used to develop an effective cohesive zone description of the crack front on a scale much larger than the facet spacing. Such a description leads to a system of 1D integral equations for the outer mechanical fields on the cohesive zone, which may be solved numerically. Numerical examples are given that notably illustrate the prediction of the effective energy-release-rate of the segmented crack front in terms of the various geometrical parameters; this energy-release-rate is predicted to be smaller for a segmented front than for the parent planar front, with the conclusion that segmentation acts as a toughening mechanism. Implications upon the phenomenon of facet coarsening are also briefly discussed.

• Research Organization: Northeastern Univ., Boston, MA (United States)
• Sponsoring Organization: USDOE
• Grant/Contract Number: FG02-07ER46400
• OSTI ID: 1906117
• Journal Information: International Journal of Fracture, Vol. 191, Issue 1-2; ISSN 0376-9429
• Publisher: Springer
• Country of Publication: United States
• Language: English