Multiscale analysis and lifetime prediction of adhesive lap joints in contact with aggressive environments

We formulate a multiscale model of adhesive layers undergoing impurity-dependent cohesive fracture. The model contemplates three scales: i) at the atomic scale, fracture is controlled by interatomic separation and the thermodynamics of separation depends on temperature and impurity concentration; ii) the mesoscale is characterized by the collective response of a large number of interatomic planes across the adhesive layer, resulting in a thickness-dependence strength; in addition, impurities are uptaken from the environment and diffuse through the adhesive layer; and iii) at the macroscale, we focus on lap joints under the action of static loads and aggressive environments. Within this scenario, we obtain closed form analytical solutions for: the dependence of the adhesive layer strength on thickness; the length of the edge cracks, if any, as a function of time; the lifetime of the joint; and the dependence of the strength of the joint on time of preexposure to the environment. Overall, the theory is found to capture well the experimentally observed trends. Finally, we discuss how the model can be characterized on the basis of atomistic calculations, which opens the way for the systematic exploration of new material specifications.