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A short paper on T-stress of an interfacial crack in a bi-material strip

The attached file is on T-stress of an interfacial crack in a bi-material strip. The geometry of the problem is the same with that of Suo and Hutchinson (1990, IJF). Using a conservation integral technique, a formula for T-stress is derived with two numerical factors.

Any comments are welcomed.

PDF icon T-stress-LettersFRAC_revised_ff.pdf221.98 KB


L. Roy Xu's picture

Dear Jae-Hyun,

Very nice paper.  Your simplified results will be valuable to our fracture experiments such as DCB tests. Indeed, T-stress research is still an open area.  Our paper on the T-stress changes across crack kinking will be published by ASME J of Applied Mechanics soon. Since an interfacial crack in a bi-material strip tends to kink into the weak part, the role of  the T-stress is critical (as discussed by He and Hutchinson in 1989).  We still have many topics on the T-stress to explore.  


Dear Luoyu,


Thanks for your nice comments. I'm happy to hear that you have been interested in T-stress. Vlassak group in Harvard Univ. has conducted several fracture tests (DCB and 4 point bending) on a thin film layer sandwiched between two thick silicon substrates. The thin film is a low-k dielectric layer made of Organosilica Glass(it's very brittle). Oscillatory cracks (or wavy crack) have been observed in some specimens during 4 point bending tests. Our paper on T-stress was motivated by this observation. I have a discussion point:

- T-stress is a non-singular term in the eigen function expansion of a crack tip stress field. For an infinite homogeneous solid or bimaterial solid, it should be a good parameter for the crack stability. For a sandwiched thin layer(500nm thick), T-stress seems weak to govern the crack stability because it is the non-signular term. The crack in the sandwiched layer experiences a dramatic change in the stress state depending on its location in the layer(Fleck et al., 1991). I suspect the role of T-stress in this case. Would you comment this?

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