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Mixed Mode and Interface Fracture Rui Huang The University of Texas at Austin Spring 2008. Mixed mode fracture. The stress field near a crack tip may be a mixture of modes I, II, and III crack-tip field.
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The University of Texas at Austin
By symmetry, the crack on the mid-plane is in pure mode I and would grow straight ahead.
However, the crack path is unstable. Any slight perturbation to the crack path will cause the crack to deflect further away from the mid-plane.
Different crack trajectories observed in adhesively bonded double cantilever beam specimens (Chen and Dillard, Int. J. Adhesion Adhesives 21, 357-368, 2001 )
Spiral crack in a drying thin layer of precipitate. Neda et al., PRL 88, 095502 (2002).
Oscillating cracks in quenched glass plates. Yuse and Sano, Nature 362, 329-331, 1993.
For an interface between two elastic materials, the crack behavior depends on the elastic mismatch.
No mismatch: = = 0;
Stiff film on compliant substrate: > 0;
Compliant film on stiff substrate: < 0;
If f = s = 0.5, = 0;
If f = s = 1/3, = /4;
Both and change signs when the materials are switched.
Under the remote loading, at the right crack tip:
Independent of .
Reduce to Griffith’s solution when = 0.
Take l = 2a, then:
Following the energy approach by Griffith and Irwin.
Work of adhesion:
Other contributions to the interface fracture toughness include plastic dissipation, interface friction:
Interface fracture condition:
Interface crack often grows under mixed mode, and the interface toughness strongly depends on the mode mix.
Rule of transformation:
Using a specimen length renders the toughness dependent on the specimen size, while using an intrinsic material length would avoid such artificial size effect.
Volinsky et al., Acta Mat. 50, 441-466, 2002.
Sandwich bending methods (Double cantilever, Four-point bending, etc.)
Bulge and blister test
Bagchi et al., J. Mater. Res. 9, 1734-1741, (1994).
PDouble cantilever test
Dauskardt et al., Engineering Fracture Mechanics 61, 141-162 (1998).
Lane et al., J. Mater. Res. 15, 2758-2769 (2000).
Lane, Annual Rev. Mat. Res. 33, 29-54 (2003).
Freund and Suresh: Chapter 4;
Suo, Reliability of Interconnect Structures. In Comprehensive Structural Integrity (Milne, Ritchie, Karihaloo, Editors-in-Chief), Volume 8: Interfacial and Nanoscale Failure (Gerberich and Yang, Editors), Elsevier, 2003.
Hutchinson and Suo, Advances in Applied Mechanics 29, 63-191 (1992);
Rice, J. Appl. Mech. 55, 98-103 (1988).