POSED PROBLEM: Apply a remote general loading (mixed mode I+II+III) to a large fracture specimen. Find the achieved fracture surface corresponding to the applied loading. We consider large cracks that correspond to the propagation of fracture over large distance. No reference is made to a starter planar crack.
This problem is tackled in our featured publication "An analysis of non-planar crack under general loading using continuously distributed sinusoidal edge and screw dislocations".
QUESTION: I wonder whether a similar problem has been treated previously?
How do u apply the mixed loading? I have a question. Does the fracture occurs by dislocations in brittle fracture?
Consider a rectangular specimen with edges parallel to Ox, Oy and Oz with Oxy horizontal and Oz vertical. Apply externally, a tension along Oz and shears (// to Oxy) in the Ox and Oy directions. Then, the applied loading is general (mixed mode I+II+III). When a crack responds to the load quasi statically, a framework has been provided (see B.A. Bilby and J.D. Eshelby, in: Fracture, Vol. 1, Ed. H. Liebowitz, Academic Press, New York, 1968 (p. 99)), it is equivalent to a continuous distribution of dislocations with infinitesimal Burgers vectors. This means that the stress field produced by the crack is the same as that of the dislocation distribution in the surrounding medium.
Thanks, I have taken a quick look at the sites. May be I must be more precise and say that I am interested in an explicit expression by which the three-dimensional fracture surface followed by a crack that responds quasistatically to a remote general loading can be found; an expression that could be checked experimentally. We propose a tentative solution.
No much feedback from this "Q&A"! We would like to encourage the reader by saying that the solution we propose may well evolve from "tentative" to "definitive" if it agrees with experiment. Also, we believe our crack analysis to be correct and the various calculations performed exact.
Dear Patrick,
look at our article....
http://www.sciencedirect.com/science/article/pii/S0955221910003821
we also predicted the failure angle of the crack and compared with the experimental crack propagation orientattion. If you can calculate the stress field at critical point, you can use different failure criteria, and predict the angle of crack propagation..
I hope this can help you...
Regards
Serkan
I would really like to read your paper but I have not access to ScienceDirect.
Thanks, I have your paper. I shall read it and let you know my comments.
You suggest predicting "angle of crack propagation". We have performed a similar test: In homogeneous materials, fracture under mixed mode I+III loading generally occurs on a non planar wavy surface. Under such conditions, we have provided an explicit expression of the crack extension force G per unit length of the crack front. A spatial average Gav of G has been obtained for two special cracks having a sinusoidal and segmented front and conditions under which Gav is maximum are established. These conditions conform to experimental measurements of crack-front twist angle versus applied stress. Please refer to our contributions:
1. An analysis of a non-planar crack under mixed mode I+III loading using infinitesimal dislocations with edge and screw average characters .
2. A study of the mixed mode I+III loading of a non planar crack using infinitesimal dislocations .
Other agreements with experiments can be achieved via agreement of our result with Cotterell, B. and Rice, J.R. (1980). Slightly curved or kinked cracks. International Journal of Fracture 16, 155-169. (Please refer to our contribution " An analysis of a non-planar crack under general loading using continuously distributed sinusoidal edge and screw dislocations" for a comparison with Cotterell and Rice)
In the framework of our modelling, the shape of the crack is much more arbitrary. We attach a special non-planar broken surface captured by the modelling.
I think that DCZM is the best method to modeling mixed-mode fracture.
In the present Q&A we restrict ourselves to a linear elastic homogeneous (perfectly brittle) material under general loading. This contrasts with cohesive zone models where localized plastic zones are present at the crack-tip.
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