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Stress intensity factors for a slanted crack under compression
Here is the problem I have: I'm modeling the geometry of a simple straight edge crack in a 2D elastic medium using Abaqus. I assume plain stress conditions. The crack makes an angle with the horizontal, is small enough to be considered as embedded in an infinite domain (ratio crack length/size of domain < 1/10) and I apply a vertical compressive load on top of my domain. I fixed one point in displacement at the bottom of it and the whole bottom edge is constrained not to move vertically.
Abaqus allows the computation of the J-integral and the stress intensity factors KI, KII by use of the Contour integral keyword. Results in tension are pretty accurate, however I seem to get problems when it comes to compressive loads. According to many authors ([Maji91], [Lauterbach98], [Rao03], [Zhu05], [Albrecht06], etc.), this problem gives non-zero shear mode SIF (KII=σ∞√(πa).cosα.sinα), which is understandable, but zero mode I SIF, which I explain as the closed character of the crack under such conditions. Abaqus gives rather good values for KII and their path-independence is correct, but also gives very negative values for KI, of the same order as the values of KII. The J-integral is calculated with Abaqus according to the following formulation (as defined by Rice, for instance):
This integral is then transformed into a surface integral (using the well-known ramp function q), and an interaction integral method can be used to separate modes I and II stress intensity factors, using the fact that in the framework of linear elastic mechanics in an homogeneous medium, we have:
Of course the compressive character of the fields is not taken into account in the definition of the J-integral presented above, which is valid in case the crack is opened. I have been trying to reconstruct the analytical field around the crack tip in the conditions of my problem (that is a slanted crack subjected to a remote compressive vertical load in an infinite domain), but did not quite manage to do so using simple terms. My questions are:
- Do you think there would be any way to "extract" the compressive part of the stress field and substract it from the whole field to get the singular field around the crack tip -- then use this field to compute the SIF?
- Does the negative character of mode I stress intensity factor physically mean anything? I personally would not think it does, since plugging those negative values of KI into the singular displacement field fomulation around a crack tip (in √r) would impose an interpenetration of the crack lips.
- Is there any closed-form formulation for the displacement/stress fields for such a problem?
Thank you in advance for any remarks/suggestions you may have regarding my issue.
Ph.D student at the University of Illinois at Chicago