Failure mechanisms of laminated composite specimens under three-point bending

Abstract

In this article, a three-point bending problem for specimens made of fiber-reinforced plastic is formulated in order to investigate the mechanisms of their failure due to transverse shear stresses reaching critical levels. The specimen deformation process is described by a laminated composite model, in which S. P. Timoshenko's model is used to approximate the displacements of each layer, with allowance for through-thickness compression. The physical nonlinearity of each composite lamina is accounted for by a nonlinear relationship between the transverse shear stresses and transverse shear strains. The physically and geometrically nonlinear problem is solved numerically by the finite sum method in its integrating-matrix version, in which the original problem is reduced to Volterra integral equations of the second kind with additional relations for determining the unknown integration constants. A unique advantage of this method is the numerical stability of its solutions even under extensive mesh refinements, making it easy to obtain solutions with very large gradients in small mesh regions. A numerical study of the behavior of laminated composite beams under three-point bending is performed, with physical and geometric nonlinearity taken into consideration. Characteristic failure mechanisms, such as localized shear buckling in the surface layers and interlaminar delamination, are identified.