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Discussion of fracture paper #37 - A Novel Approach Improving Mode I+III Cohesive Zone Modelling

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The advantage of simplicity is that mechanics and physics can be understood and predicted just by using pen and paper. In the end, numerics may have to be used but then you should already have a pretty good idea of what happens. The other way around, starting with numerics and a limited toolbox of models will seldom lead to anything new. 

The paper, "Experimental determination of coupled cohesive laws with an unsymmetrical stiffness matrix for structural adhesive joints loaded in mixed-mode I+III, by Stephan Marzi in Engineering Fracture Mechanics, 283 (2023)", adopts a very interesting view of the cohesive zone models that are based on the energy release rate and the crack tip opening displacement. Instead of using a classical interpolation between single-mode test results that often fails because of changes in the adhesive's physical behaviour, a new model is suggested. The new model is based on direct measurements of various mode I and III mixes, which inevitably ensure that the adhesive behaviour alteration is captured. The method comes with a few requirements that lead to possible limitations that are cleverly discussed.

The paper is well-written and offers very interesting reading. To me, the paper also calls for a reflection. An adhesive is usually stuck between two materials that do not fail easily. This is different from isotropic materials for which the mode I and III mix leads to larger freedom of choice of crack propagation and crack plane morphology. 

Plates of glass or any other brittle material that are exposed to a mixed mode or for that matter pure mode III results in a decrease of the tougher in favour of the less tough mode by tilting the crack plane. A well-known situation is when a window glass is exposed to a remote tearing, appearing as mode III similar results in a propagating mode I crack that is tilted towards the glass surfaces even if it initially was perpendicular.

The selected tilt angle ought to be the one that minimises the required energy release rate. While the crack depth initially may be the plate thickness, i.e., straight through the plate, the tilt to obtain more of the least tough fracture mode may be hampered by an increasing the crack depth. The total dissipated energy in creating a new crack surface is what counts.

Having written this I realise that the tilting crack plane model may be oversimplified. The crack surfaces surely must have a waviness that correlates with the variation of the stress-strain conditions as we move from the front side surface to the back side of the plate. 

I guess that a brittle and thicker adhesive layer could go the same way, but a thinner layer might, in lack of space, develop a favourable zigzag pattern. Ductile adhesives may also shift modus operandi depending on which is the preferred failure mechanism. However, this is on a micro-scale with details that are not required to make use of Marzi's ingenious method for obtaining cohesive properties.

It would be interesting to hear from the author or anyone else who would like to discuss or provide a comment or a thought, regarding the paper, the method, or anything related. If you belong to do not have an iMechanica account and fail to register, please email me at and I will post your comment in your name. 

Per Ståhle

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