Progressive interface failure of 2-layer composite beams with interlayer slip

The mechanical behavior of multi-layer structural elements (wood laminated beams, beams and columns either made of different materials or repaired with steel plates or fiber composite strips connected by adhesive bonding) is strongly influenced by the constituent materials of the layers and by their connection. The nature of the bond, in particular, strongly affects the mechanical behavior of the interfacial region and of the element itself as a consequence. A perfect connection would permit the complete transmission of the normal and shear stresses between the layers but it can hardly be obtained in practice. Thus, only a partial interaction between the layers can be realized and an interlayer slip often develops. A typical damage and failure mechanism is then represented by the initiation and propagation of decohesion zones at the interface between the layers. On increasing size of the damaged area stresses transmitted across the interface decrease and vanish when decohesion zones occur. Such a process may reduce the stiffness and the strength of the system leading to its failure. Single adhesive joints have been largely studied in the literature: many experimental, analytical and numerical studies on both failure modes and strength have been made. A large number of works exists on the mechanical response of structural elements with an elastic connection but only a little attention has been focused on the progressive interface damage and failure of multi-layer systems. This work, trying to fill this gap, develops basic understanding of the essential features of such particular failure mechanism that affects the mechanical response and strength of the structural elements in order to optimize their performance in practical applications. Starting from previous studies by the authors, wherein simple structural models of the adhesion test for the determination of the shear strength of adhesive joints were developed, and following a commonly used "multiscale approach", on the basis of the classical beam theory, a model for a two-layer beam with partial interaction between the layers is developed. Each layer is modelled as an Euler-Bernoulli elastic beam and for the connection a bilinear constitutive law is adopted. The analytical solution for each of the three phases that interface can experience (elastic, softening and detached) is obtained and employed in the solution of the nonlinear equilibrium problem by the finite element method. In order to do that, a two nodes nonlinear element with eight degrees of freedom is developed starting from the analytical solution to obtain the exact stiffness matrix. With reference to three-point bending beams, a complete simulation from damage initiation to ultimate failure of the damage process at the bond is conducted in order to investigate the mechanical response and the collapse of the system and to understand which model parameters have the main influence on them.