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Discussion of fracture paper #35 - What is Finite Fracture Mechanics?

ESIS's picture

The subject of this blog is a well-written and technically detailed study of thermal crack initiation where an adhesive joint between two dissimilar materials meets a free surface. The method that is used goes under the group designation finite fracture mechanics. The paper is:

"Predicting thermally induced edge-crack initiation using finite fracture mechanics" by S. Dölling, S. Bremm, A. Kohlstetter, J. Felger, and W. Becker. in Engineering Fracture Mechanics 252 (2021) 107808.

Reading it is a good investment for anyone interested in the analysis of real fracture mechanics, when one does not know all the details of the original crack, or if it even existed at the time before the load was applied.

A body with a bi-material adhesive joint that meets a free surface generally experiences high stresses. Under idealised conditions, a stress singularity occurs. Only pathological loads are exceptions. Crack initiation is assumed to be caused by thermally induced stresses. A criterion based on a coupled stress and energy criterion within the framework of the so-called finite fracture mechanics has been chosen. The essential part of the energy is that required for the initiation of the crack which then commences crack growth. The energy required for initiation is the work needed to stretch the adhesive layer thickness to the point, where the adhesive fails.

The principal numerical method is a boundary integral method. The guidance through the basics of boundary integral methods is educational and enjoyable and greatly appreciated. The method in itself is direct and very intuitive compared to finite difference and finite element methods.

The authors also include a simple dimensional analysis with an elegant demonstration of how the completed study can be extended without requiring additional numerical calculations. The simplifications are based on scaling with the respect to the few length parameters present. The method is evaluated using both boundary integral methods and a finite element method. The result of the coupled stress and energy criterion is also compared with a cohesive zone model that introduces a critical stress and a critical displacement.

I really enjoyed reading this interesting paper. A long time ago when I myself studied small cracks using cohesive zone models in the late 70s under the guidance of Profs. K.B. Broberg and G.I. Barenblatt, our result displayed an unexpected instability. Instead of the expected unstable crack growth, the tip of the cohesive zone kick-started in an uncontrolled rapid crack growth while the crack tip remained stationary. 

Possibly the coupled stress and energy criterion could give a different result. Our result is of course affected by our selected cohesion which continuously decreases with increasing separation of the cohesive zone boundaries. After a short reflection, it seems natural that the cohesive zone tip should start first and the rapid growth comes with the rapidly increasing energy release rate of the short crack. A long time has passed since then, and over the years I have heard about similar observations made by others. 

All comments, thoughts or opinions, regarding the finite fracture model, cohesive zones, the paper, or anything related are encouraged to submit a comment. If you belong to the unfortunate that do not have an iMechanica account and fail to get one, please email the text to me at and I will post your comments under your name.

Per Ståhle


ESIS's picture

Dear Prof. Ståhle, Since I cannot get an iMechanica account I have placed a comment/inquiry on Reasearchgate as you suggested. Here is a link to it: LINK  / Sophie B. Lange

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