The role of friction in the 3ENF and 4ENF delamination tests: an analytical solution

Abstract

In composite structures, the presence and growth of delamination mechanisms in static or fatigue loading conditions is of paramount interest and the American Society for Testing and Materials (ASTM) has adopted the three-points bend end-notched flexure test (3ENF) as the standard for measurement of mode II toughness. The drawback of the 3ENF test is the unstable crack growth and a modified version of the test, namely the four points bend end-notched flexure test (4ENF), has been proposed. The main advantage of the 4ENF over the 3ENF is that crack growth is stable under displacement control, but it can be strong influenced by the interlaminar frictional effects. The effect of frictional contact between the delamination surfaces has been initially analysed for the 3ENF test, whereas the evaluation of frictional effects on the 4ENF test has been proposed. Recently, the analytical solution of the mode II delamination toughness in the 4ENF test, with interlaminar friction, has been proposed. In the present paper, the analytical solution of the mode II delamination toughness, in presence of friction on the delamination surface, is proposed also for the 3ENF delamination tests. This solution is rigorously developed in the framework of Classical Beam Theory (CBT), under Bernoulli bending condition, and in the framework of linear elastic fracture mechanics. The frictional phenomenon is modelled as rigid perfectly-plastic with Mohr-Coulomb activation condition and non-associative flow rule. The mode II fracture energy is defined by the Griffith approach, by evaluating the energy release rate and the frictional dissipation. The results of the 3ENF and 4ENF mode II delamination toughness are compared for some values of the frictional coefficient.