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Crack length in fracture mechanics


Could please any one knows give me an idea about solving a problem which I face for the ages.

I have modelled a beam with a sharp edge at the corner of a rectangular hole with ABAQUS. I have introduced different crack length and using LEFM, I have made some predictions for the failure load of the beam. Now the predicted load is dependent on the crack length. How can I chooose the right crack length?

Thank you

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You need to furnish more details about your problem. What type of loading are you subjecting your beam to? If you want to choose the right crack length, you need some relationship between a/W (crack length/Width of beam) vs. the applied load. Usually, you can get a formula for the fracture toughness of the beam (depending on type of loading, try making it depend on a single mode). Then, if you know your material fracture toughness, you can solve for your critical a/W value.


Hope this helps,



Thank you for your comment. I have a beam with a rectangular hole loaded at the mid-span under concentrated load.

in this case, mixed mode fracture criterion happens in the beam. Would you please give a an example of how to solve this problem.

If you need more details please let me know.

Thank you,


Hi Manoochehr,

You can try this paper by Prof. Suresh from MIT. 

"Mixed mode fracture toughness of ceramic materials" Journal of American Ceramic Society. 73(5), 1990, 1257-67. 

They use a different specimen, but the method might be applicable for your case. 


Hi Manoochehr,

If I understand you correctly, you have beam with stress concetrator (but
without crack) and need to calculate critical load, when the crack start to
grow? In this case you cannot solve your problem with LEFM alone. There are several approaches how to
handle similar problems, sometimes called "critical distances theory". There is
also book by D.Taylor "The Theory of Critical Distances". Or you can look at the papers about crack initiation from notches.


Thank you for your reply. I think that  "The Theory of Critical Distances" can indicate another method for detecting the crack length.Meanwhile, I would like to ask you another question if the crack length is fixed for a beam with a hole. I mean if the hole is changing its loaction and diameter in the beam can we still use of a fixed crack length or not?

Thank you

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