Response of two-layer composite beams with interlayer slip and damaging interfaces

Beams and columns made of different materials or reinforced with steel or composite elements are only some examples of two-layer structural systems. The combination of different elements improves the performances of the system but introduces weak elements such as interfaces. A perfect connection that retains relative displacements between the layers would allow a complete transmission of the stresses and ensure optimal performance in terms of global stiffness and strength. However, in practice, this is difficult to obtain, so that relative displacements between the layers can occur and only a partial composite action follows. As a consequence, the mechanical behavior of multi-layer composite beams depends not only on the geometrical and mechanical properties of the single layers but also on the nature of the bond between them. The optimal design of such composite systems needs to account for the response of interfaces and the progressive interface damaging as further global failure mechanism. The problem of the equilibrium of multi-layer beams consisting of elastic layers elastically bonded has been the object of a large number of studies. Only a little attention has been focused on the nonlinear interfacial behavior. On the other hand, under loading conditions that generate interlaminar stresses flaws and defects due to manifacturing errors or impacts may propagate or, alternatively, mechanical shear devices such as nails and steel studs may yield. This leads to a further reduction of the degree of the connection between the layers and, as a consequence, of the global stiffness and strength of the system and even to its premature collapse when the layers are still elastic. 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 structural composite elements, in order to optimize their design and performance in practical applications. In the framework of a multi-scale treatment of the problem, composite beams are modelled as beams having a higher number of degrees of freedom than classical homogeneous beams and governed by additional compatibility and constitutive equations accounting for relative displacements between the layers. The analysis builds on previous works by the authors in which fundamental analytical solutions for two-layer beams with interlayer slip and non-proportional linear interface constitutive laws are obtained. The formulation is restricted to the analysis of bonds realized, for instance, by the use of nails for which the stiffness in the transverse direction can be assumed to be infinite, so that uplifts between the layers are not allowed and only slips between the layers in their longitudinal direction can occur. According to classical elastic beam theory, each layer is modelled as an elastic Euler-Bernoulli beam. The connection in the longitudinal direction is modelled as a continuous distribution of shear tractions related to displacement discontinuities between the layers through a multi-linear law. Such a multi-linear law represents the evolution of the interfacial behavior during a loading process and allows simple analytical solutions for each its linear branch representing a regime the interface can undergo. With reference to beams subjected to simple loading and constraining conditions, 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 parameters characterizing the interface law have the most influence on the global response of the composite system. Future developments deal with the interaction of this failure mechanism with failure mechanisms involving layer materials and the influence of such interaction on the global mechanical response.