FRP adhesive lap-joints: a micro-scale mechanical approach

As it is well-known, when dealing with thin films the size effect (i.e. the thinner, the stiffer) is often observed [1-2]. Such an effect also occurs in the case of adhesive interfaces between FRP profiles, where the glue layer can be few μm thick. Due to the lack of internal material length scale parameters, classical models cannot be able to capture the microstructure dependent size effect and, therefore, need to be extended by using high order non-local continuum theories. Both the classical couple stress elasticity theory elaborated by Koiter [3] and some other higher-order elasticity theories available in literature [4-8] include four material constants: two classical and two additional. In particular, the two additional parameters, related to the symmetric and antisymmetric part of the curvature tensor, cannot be determined from single experiments as the twisting of a thin cylinder or the pure bending test of a thin film. Combinations of both types of test are required. In order to overcome the difficulties related to the evaluation of two microstructure length scale parameters [9-10], a modified couple stress theory has been recently developed by means of restricting the couple stress tensor to be symmetric [11]. As a consequence, the strain energy does not depend on the antisymmetric part of the curvature tensor and, therefore, only one additional material length scale parameter is required. Based on this modified couple stress theory, some one-dimensional models have been very recently proposed for studying both the Bernulli-Euler [12-13] and Timoshenko [14] beam problems. The aim of this paper is to apply the modified couple stress theory [11] for investigating the behavior of FRP adhesive lap-joints under generic external loads. Two-dimensional elasticity fields are utilized for simulating both the response of the adherents (plane stress) and that one of the adhesive films (plane strain); in the last case, the mechanical model takes into consideration the internal material length scale parameter too. The mechanical model proposed by the authors also accounts for the most common interfacial cohesive laws [15-18]: elastic moduli of the thin adhesive layers, in fact, are step-by-step modified in such a way so that the value of the strain energy density is equal to that one corresponding to the cohesive mixed-mode fracture law considered. The goal is to extend the numerical investigation already developed by the authors -without considering the scale effect- for predicting the ultimate behavior of FRP adhesive lap-joints [19-20]