Some remarks concerning the method of determining interlaminar toughness of bi-material interface
Piotr Czarnocki Politechnika Warszawska, Instytut Techniki Lotniczej i Mechaniki Stosowanej, ul. Nowowiejska 24, 00-665 Warszawa
Annals 4 No. 10, 2004 pages 200-204
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abstract Results of number of experimental investigations indicate that the toughness of laminate is a function of the mode mixed ratio, often expressed by phase angle (1). In a case of interface delamination separating layers of the same materials the procedure of determining the phase angle is simple. If delamination separates layers of different materials, the procedure is more complicated since the phase angle is a function of the material elastic constants and distance from the delamination tip (2). The possibility of neglecting this dependence has been discussed for years and rational arguments have been put forward both supporting and contradicting the idea. Perhaps some helpful conclusion could be drown from comparing the changes in results caused by these two approaches against the discrepancy of experimental results due to stochastic variation in strength of tested interfaces. For this purpose two methods of determining the phase angle were applied. The first was based on the virtual crack closure method proposed by Rybicki and Kanninen which allows for direct determination of GI and GII from the nodal forces and displacement obtained by FE analysis. The second was the modification of that of Rybicki’s. It was recently proposed by Bjerken and Persson. This method is based on Malyshev and. Salganik’s expression relating the modulus of the complex stress intensity factor to strain energy release rate (3). The sought phase angle is determined form (9) equating the arguments of complex strain energy release rate and complex stress intensity factor in (5). The expression was modified such that it was possible to take advantage of the results coming from the FEM as in the case of Rybicki’s method. The experimental results were obtained from testing 0/90 layer interface of the carbon fibre/epoxy laminate (Figs. 1, 2). The tests were carried out with the help of the method proposed by Reeder, based on Williams’s global mode separation procedure. The results are presented in Fig. 4. It is clearly visible that the differences resulting in κ from accounting for real value of β and making simplifying assumption that β = 0 become practically meaningless comparing to stochastic differences in toughness of the interface. Key words: delamination fracture mode separation, stress intensity factor, energy release rate, bimaterial interface, phase angle, mode mixity