Analytical solution of the 4ENF test with interlaminar frictional effects and evaluation of Mode II delamination toughness

The present paper proposes an analytical solution of the four points bend end-notched flexure test (4ENF) with frictional contact between the delamination surfaces. The analytical solution was developed in the framework of the classic Euler-Bernoulli bending beam theory with orthotropic linear elastic constitutive behavior. The frictional contact was modeled as rigid-perfectly plastic with the Mohr-Coulomb activation function and the nonassociative flow rule. The elastic solution of the partially cracked beam subjected to the four points bending test with frictional contact was developed, and the Mode II delamination toughness was analytically determined by means of the Griffith approach, as a function of the delamination load, geometry specimen, and frictional coefficient. The 4ENF delamination test was also numerically solved by two-dimensional (2D) finite-element analysis with a cohesive-frictional interface, and the results were compared with the analytical beam solutions. The comparison showed a very good accuracy of the analytical solution, even though it was based on the simple beam theory.