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Determination of R-curve from load/crack data

I need help to determine or contruct the crack reistance (R-curve) of a material that show crack bridging. I have the experimental data of applied load and crack lengths due to these applied loads. the SENB specimen was used and loading was 4-pt-bending. The plot of Kapp versus crack size did not give the usual rising curve which plateaus, but rather increases exponentially. How do I get the Kb (i,e K due to bridging) or the normal R-curve. I am not a mechanical engineer but into applied mechanics.



Zhigang Suo's picture

Your observation may have something to do with large scale bridging.  When the size of the bridging zone is comparable to a characteristic length of the sample (e.g., length of the crack, thickness of the beam), the R-curve is no longer a material property, but also depends on the specimen.  Much work has been done on this topic.  Here is one from my own group:

Z. Suo, G. Bao and B. Fan, "
Delamination R-curve phenomena due to damage",
J. Mech. Phys. Solids. 40, 1-16

Bent F. Sørensen's picture

When dealing with large-scale bridging problems is pays off using specimens suitable for the J integral approach (measuring J and the end-opening of the bridging zone) described in the excellent Suo, Bao, Fan paper for determination of the bridging law.

We used DCB specimens loaded with pure bending moments. For this configuration the J integral evaluated around the external boundaries can be obtained in closed analytical form although the bridging law is unknown. The bridging law is then found by differentiation. It works pretty well.

In a study on crack-bridging by cross-over fibres, we found specimens having different thicknesses had similar bridging laws whereas traditional R-curves (fracture resistance as a function of crack extension) were strongly specimen thickness depend. We also found that the shape of the bridging law was similar to that predicted by a micromechanical model developed by Spearing and Evans. See more in the paper:

Sørensen, B. F. and Jacobsen, T. K., 1998, "Large scale bridging in composites: R-curve and bridging laws", Composites part A, 29A, 1443-51.

In another study, we used the cohesive law obtained from the DCB specimen for predicting the strength of an adhesive butt-joint. The prediction, based entirely on the cohesive law determined from the DCB specimens, came out in excellent agreement with experimental measurements of the strength of the butt-joint.

Sørensen, B. F., 2002, "Cohesive law and notch sensitivity of adhesive joints", Acta Mater., 50, 1053-61.

Thus, my advise would be not to use SENB specimens when large-scale bridging is present. You might consider using DCB specimens loaded with pure bending moments. The test set up is perhaps more complicated but the modelling and interpretation is much easier.


Zhigang Suo's picture

For an update on using double-cantilever beams to determine R-curves and bridging laws, see recent comments by Sergej Tarasov and Bent Sørensen.

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