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Effect of Residual stresses on the Interfacial Fracture Toughness of polymer/Metal Interface

shirangi's picture

When a bi-material sample for the characterization of interfacial fracture toughness is manufactured, the sample is not usually stress-free at room temperature. If an interface between a metallic substrate and a polymeric adhesive is considered, there are essentially two sources of residual stresses for a dry sample at room temperature:

1-    The mismatch between the Coefficient of Thermal Expansion (CTE) of adhesive and substrate induces a concave or convex warpage, depending on the CTE values of the two materials.

2-    An important effect which is usually neglected is the cure shrinkage of the polymeric adhesives during their cross-linking. When a polymeric adhesive adheres to a substrate at a high temperature, it experiences a gel to solid phase transition which causes normally a volumetric decrease in polymer only. This is the source of the so called “Cure Shrinkage”.

There are many methods in literature for the calculation of the Strain Energy Release Rate (SERR) of standard beam structures (such as 4PB, ENF, DCB, and …). However, most of these analytical solutions do not consider the residual stresses. That is why FEA-based methods like VCCT should be applied in order to consider the effect of these residual stresses.

In the attached figure, you can see the influence on thermal and cure stresses on the apparent interfacial fracture toughness of copper/Epoxy interface for an End-Notched Flexure (ENF) test.  Significant influence of the thermal stresses (arising from the CTE-mismatch between epoxy and leadframe which induces a warpage because of higher leadframe shrinkage bycooling from mold temperature to room temperature) and chemical cure stresses (due to shrinkage of epoxy during the crosslinking of the epoxy) was observed, which suggests that using the analytical solutions or only consideration of the thermal stresses for the calculation of SERR can cause errors. Compressive stresses in general impede the crack propagation while tensile stresses facilitate it. Hence, any determination of critical energy release rate without considering these stresses should be avoided.  


Shirangi M.H., Gollhardt A., Fischer A., Müller W.H., Michel B., „Investigation of fracture toughness and displacement fields of copper/polymer interface by image correlation technique“ , Proc. 41st International Symposium on Microelectronics (IMAPS), 2008, Providence, RI, USA, pp. 1072-1089.

contact: hossein.shirangi @

Image icon ENF2.JPG33.31 KB



This is a interesting topic for the effect of cure shrinkage. Can you attach the full paper? I can't find the paper online. Thanks!



shirangi's picture

dear Guojun, thanx, please contact me per email.

Very interesting. I wrote a paper recently about shrinkage influence: "a simple method to simulate shrinkage-induced cracking..." in the journal of "computational mechanics"

i am a student at university of algeria, now i'm working in the FEM analysis of process thermal residual stresses in multimaterial, so i use Abaqus , but the results are large 

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