On a paradoxical situation related to lap shear joints: could transverse grooves in the adherends reduce the interfacial stresses?

Abstract

A simple analytical model has been developed to explain a paradoxical situation that has previously been detected on the basis of the finite element analysis (FEA) by one of the authors (Reinikainen): deep enough transverse grooves in the adherends (pins) resulted, for small size joints in an appreciable reduction in, and a more uniform distribution of, the interfacial stresses. In this analysis we address the situation using analytical (mathematical) modelling. The analysis is limited to the evaluation of the shearing stresses. The numerical example indicates that the ‘observed’ phenomenon is due to the increase in the interfacial compliance of the bonding structure: the grooves ‘convert’ the adherend portions located between the inner portions of the grooves and the bonding layer into parts of the bonding structure, thereby increasing the compliance of this structure with respect to the shearing deformations. This positive effect overwhelms, as far as the magnitude and the distribution of the interfacial stresses are concerned, the negative effect of the increased axial compliance of the loaded portions of the adherends because of the grooves. The analytical predictions agree satisfactorily with FEA data, despite the FEA overestimation of the increase in the interfacial stresses in the proximity of the joint edges (as is known, the FEA method, which is based on one of the numerical methods of elasticity theory, usually leads to singular stresses at the edges of assemblies comprising dissimilar materials). The obtained information explains the physics of the phenomenon in question. The developed analytical models can be used in the analysis and physical design of the lap shear joints, as well as test specimens in micro- and opto-electronic packaging. It is also concluded that analytical modelling is able not only to come up with a relationship that clearly indicates ‘what affects what and what is responsible for what’ but, more importantly, can explain the physics of phenomena that neither FEA modelling (simulation) nor even actual experimentation is able to explain.