Experimental and theoretical study on the failure of sandwich specimens with tabs under four-point bending

The problem of testing sandwich specimens with composite facing layers and a transversally soft core for four-point bending was formulated. The localized external load from the loading rollers to the facing layer of the specimen was assumed to be transmitted through composite tabs, which reduced the stress concentration in the compressed facing layer. The external facing layers and tabs were analyzed for deformation mechanics using S.P. Timoshenko’s kinematic model. The model considered compression in the facing layers but not in the tabs. The core was classified as transversally soft with zero tangential stresses. The tabs were connected to the facing layers through adhesive interlayers, and the displacement vectors of the front surfaces of the tabs were coupled kinematically with the displacement vectors of the front surfaces of the facing layers. The relationships between the transverse shear stresses and strain in the facing layers were assumed to be physically nonlinear, with the shear modulus being a function of the shear strain.
Using the generalized variational principle of virtual displacements, a system of nonlinear differential equilibrium equations for the facing layers and tabs was derived. The system was closed by three more equations, which were the conditions for the kinematic coupling of the facing layers with the core based on tangential displacements. To numerically solve the formulated problem, the finite sum method, also known as the method of integrating matrices, was employed. This method involved reducing the original boundary value problem to integro-algebraic equations with Volterra-type operators of the second kind and additional relations for determining the unknown integration constants. The algorithm of the developed method was implemented as an application software, which facilitated a series of computational experiments. The results obtained were compared with the experimental data on the four-point bending of sandwich specimens with the facing layers made of a unidirectional fiber-reinforced composite characterized by specific geometric and physico-mechanical properties, as well as with tabs under the loading rollers. It was shown that the use of tabs significantly increases the ultimate compressive failure stresses in the facing layers.