PSI - Issue 13

Christopher Schmandt et al. / Procedia Structural Integrity 13 (2018) 799–805 C. Schmandt, S. Marzi / Structural Integrity Procedia 230 (2018) ECF22

805

7

dependencies of relevant model parameters as fracture energy and cohesive strength on crack opening velocity. Analytical functions considering those dependencies are proposed. It can be stated that the predictions delivered from these analytical functions can only be considered as reliable within the experimentally tested range of crack opening velocities prior to crack propagation. Characterizing the mode I cohesive law, subsequent statements summarize the achieved observations:  The fracture energy significantly increases at increasing crack opening velocity.  The cohesive strength slightly increases with increasing crack opening velocity.  A dependency of cohesive stiffness on crack opening velocity is not observed. In a second step, tests are driven by controlling the testing machine on various constant cross head velocities to investigate processes of crack growth. Unaffected by loading rate, subcritical crack growth starts while J is still increasing and turns to overcritical dynamic propagation when J reaches its maximum. Afterwards, overcritical crack growing arrests and changes to subcritical crack growth anew. This alternating in crack propagation rate can occur many times, giving the curve a saw tooth shape. The amplitude of those self-sustained oscillations seems to have a maximum in the range of cross head velocities in between 0.01 to 1 mm/s. Even higher or even lower cross head velocities yield lower amplitudes, which implies that jerky crack propagation abates outside the investigated range of loading rates and tends to a stable manner in case of quasi-static loading or impact, respectively. The results shall be used in future works to postulate a cohesive zone model that is appropriate to consider the observed effects e.g. in numerical simulations. Further tests on mode II, III and mixed mode are still required as well as mode I tests at impact loading and creep conditions for a comprehensive model definition. 5. Acknowledgements The work has been partially funded by Federal State Hessen, Germany, within the internal program “Strategischer Forschungsfonds” of TH Mittelhessen. The financial support is gratefully acknowledged. Furthermore, the authors would like to thank Sabine Wenig (SIKA Automotive AG, Romanshorn, Switzerland) for supplying the adhesive and Ihssane Kididane (TH Mittelhessen) for supporting the experimental work. References Anthony, J. and Paris, P. C. (1988) ‘Instantaneous evaluation of J and C’, International Journal of Fracture , vol. 38, no. 1, R19-R21. Barenblatt, G. I. (1962) ‘The Mathematical Theory of Equilibrium Cracks in Brittle Fracture’, in Advances in Applied Mechanics Volume 7, Elsevier, pp. 55–129. Biel, A., Stigh, U. and Walander, T. (2012) ‘A Critical Study of an Alternative Method to Measure Cohesive Properties of Adhesive Layers’, ECF19 . Dillard, D. A., ed. (2010) Advances in structural adhesive bonding [Online], Boca Raton, Fla, Oxford, Woodhead Pub. Ltd. Available at http:// site.ebrary.com/lib/alltitles/docDetail.action?docID=10654043. Dugdale, D. S. (1960) ‘Yielding of steel sheets containing slits’, Journal of the Mechanics and Physics of Solids , vol. 8, no. 2, pp. 100–104. Kinloch, A. J. and Yuen, M. L. (1989) ‘The Mechanical Behaviour of Polyimide/Copper Laminates Part 2: Peel Energy Measurements’, The Journal of Adhesion , vol. 30, 1-4, pp. 151–170. Loh, L. and Marzi, S. (2018) ‘Mixed-mode I+III tests on hyperelastic adhesive joints at prescribed mode-mixity’, International Journal of Adhesion and Adhesives , vol. 85, pp. 113–122. Loureiro, A. L., da Silva, Lucas F. M., Sato, C. and Figueiredo, M. A. V. (2010) ‘Comparison of the Mechanical Behaviour Between Stiff and Flexible Adhesive Joints for the Automotive Industry’, The Journal of Adhesion , vol. 86, no. 7, pp. 765–787. Maugis, D. and Barquins, M. (1988) ‘Stick-Slip and Peeling of Adhesive Tapes’, in Allen, K. W. (ed) Adhesion 12, Dordrecht, Springer Netherlands, pp. 205–222. May, M., Hesebeck, O., Marzi, S., Böhme, W., Lienhard, J., Kilchert, S., Brede, M. and Hiermaier, S. (2015) ‘ Rate dependent behavior of crash optimized adhesives ‐ Experimental characterization, model development, and simulation ’ , Engineering Fracture Mechanics , vol. 133, pp. 112–137. Rice, J. R. (1968) ‘A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks’, Journal of Applied Mechanics , vol. 35, no. 2, p. 379. Schmandt, C. and Marzi, S. (2018) ‘Effect of crack opening velocity and adhesive layer thickness on the fracture behaviour of hyperelastic adhesive joints subjected to mode I loading’, International Journal of Adhesion and Adhesives , vol. 83, pp. 9–14. Webb, T. W. and Alfantis, E. C. (1995) ‘Oscillatory fracture in polymeric materials’, International Journal of Solids and Structures , vol. 32, 17-18, pp. 2725–2743. Yamini, S. and Young, R. J. (1977) ‘Stability of crack propagation in epoxy resins’, Polymer , vol. 18, no. 10, pp. 1075–1080.