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On Mechanistic Approach to Modelling R-Curve Behaviour

As a follow up to my first blog , I would like to know if the experimental data of applied loads and crack sizes or lengths, are sufficient to model the R-curve behaviour via the Fracture Mechanics approach.

In this approach i need to determine the traction stress field and the deflection of ligaments in the bridging zone. Tests were perfomed in 4-Pt-Bending. What are the differences, if any, between the load/load point separation relation/curve of the system on the one hand, and the Traction stress/deflection relation/curve in the bridging zone. Is there any useful theoretical link between them?

[Special comments to Prof. Suo: Thank you for your comment on my earlier blog on the same subject. I have been experiencing difficulties sending comments the usual way. Your comments and references were most helpful and have given me a better understanding of the subject matter]


Zhigang Suo's picture

Dear Samuel:  Thank you for your comments.  Other users have also reported difficulties with posting comments on iMechanica.  The difficulties seem to be restricted to users with Internet Explorer as their browser.  This problem with posting comments can be fixed.  I have also put this link on the right side of iMechanica, under Quick Guide.

Now let me turn to your question about the mechanics of bridged cracks.  Force-displacement curve is what you measure when you apply a mechanical force to your specimen.  The two faces of the crack separate, but part of the crack may be bridged.  Many models assume a relation between the separation of the crack and the traction in the bridge.

In a typical model, the separation-traction relation is given as an input, and one can calculate the force-displacement curve.  In an experiment, of course, you measure the force-displacement curve, and try to infer the separation-traction relation.

These basic ideas are reviewed by G. Bao and Z. Suo, Remarks on crack-bridging concepts," Applied Mechanics Review45, 355-366 (1992).  Many other people have worked on the subject, too.  Let's hope someone can direct you to papers more specific to your experiment.

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