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Temperature dependence of cohesive laws for an epoxy adhesive in Mode I and Mode II loading

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Abstract

The influence of the temperature on the cohesive laws for an epoxy adhesive is studied in the glassy region, i.e. below the glass transition temperature. Cohesive laws are derived in both Mode I and Mode II under quasi-static loading conditions in the temperature range \(-30\le T \le 80^{\,\circ }\)C. Three parameters of the cohesive laws are studied in detail: the elastic stiffness, the peak stress and the fracture energy. Methods for determining the elastic stiffness in Mode I and Mode II are derived and evaluated. Simplified bi-linear cohesive laws to be used at any temperature within the studied temperature range are derived for each loading mode. All parameters of the cohesive laws are measured experimentally using only two types of specimens. The adhesive has a nominal layer thickness of 0.3 mm and the crack tip opening displacement is measured over the adhesive thickness. The derived cohesive laws thus represent the entire adhesive layer as having the present layer thickness. It is shown that all parameters, except the Mode I fracture energy, decrease with an increasing temperature in both loading modes. The Mode I fracture energy is shown to be independent of the temperature within the evaluated temperature span. At \(80^{\,\circ }\)C the Mode II fracture energy is decreased to about 2/3 of the fracture energy at \(-30^{\,\circ }\)C. The experimental results are verified by finite element analyses.

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Notes

  1. The superscripted \(^{\sim }\) is used to distinguish between a variable to be integrated and an integration constant. The variables \(w\) and \(v\) are the peel and shear deformations of the adhesive layer at the start of the adhesive layer. The notation should understood to say that \(f(x,y)\) indicates that for each \(x,y\) there exists one, and only one \(f\).

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Acknowledgments

The authors would like to thank Mr. Stefan Zomborcsevics at the University of Skövde for helping with manufacturing the specimens, Mr Gunnar Åkerström at Volvo Material Technology in Gothenburg for help with performing the ENF-experiments and SAAB Automobile in Trollhättan for letting us use their climate chambers. Dr Svante Alfredsson and Dr Stephan Marzi are gratefully acknowledged for their help and fruitful discussions. The authors also thank the Knowledge Foundation for funding this work through the project MASLIM.

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  1. University of Skövde, 541 28 , Skövde, Sweden

    Tomas Walander, Anders Biel & Ulf Stigh

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  1. Tomas Walander
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  2. Anders Biel
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  3. Ulf Stigh
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Correspondence to Tomas Walander.

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Walander, T., Biel, A. & Stigh, U. Temperature dependence of cohesive laws for an epoxy adhesive in Mode I and Mode II loading. Int J Fract 183, 203–221 (2013). https://doi.org/10.1007/s10704-013-9887-3

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  • DOI: https://doi.org/10.1007/s10704-013-9887-3

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