Interfacial Stresses in a Lap Shear Joint (LSJ): The "Transverse Groove Effect" (TGE)
Journal of Solid Mechanics and Materials Engineering
A simple and physically meaningful analytical model is developed for the evaluation of the interfacial stresses in a simple lap shear joint (LSJ). The emphasis is on the "peeling" stress, i.e., the stress acting in the through-thickness direction of the joint. The model is a modification and an extension of the model developed earlier for the shearing stress. Based on the developed model, we were able to explain a paradoxical situation due to the "transverse groove effect" (TGE). This effect
... GE). This effect has been detected by one of the authors of this paper (Reinikainen) from the finite-element-analysis (FEA) computations: deep enough transverse grooves deliberately introduced in the LSJ adherends ("pins") resulted in an appreciable reduction in the magnitude, and in a significant improvement in the uniformity, of the distribution of the interfacial shearing stress. It was determined that the stress relief due to the grooves was caused by the favorable effect of the increased interfacial compliance, while the adverse effect of the increased axial compliance of the pins (also due the grooves) was relatively small in a particular LSJ design and was suppressed by the favorable impact of the TGE. We show that the peeling stress in the LSJ is considerably lower than the interfacial shearing stress and that the TGE is even stronger for the peeling stress than for the shearing stress. This is because the grooves affect the peeling stress not only directly, through the increased interfacial compliance, but also indirectly, through the lower gradient of the interfacial shearing stress in the longitudinal direction. We show that this gradient can be reduced considerably if the interfacial compliance is increased, especially in a small size joint. We would like to point out that, although reasonably satisfactory agreement between the analytical and the finite-element analysis (FEA) predictions was obtained, the objective of our analysis was not so much to develop a more or less accurate analytical or a FEA model, but rather to demonstrate that the peeling stress, whatever technique is employed to evaluate it, can be reduced considerably by introducing the transverse grooves. The results of this article can be used in the analyses and design of LSJs, both in electronic packaging and beyond. developed earlier 1 for the evaluation of the interfacial shearing stress. The earlier model explains the paradoxical situation initially detected on the basis of the finite element analysis (FEA): deep enough transverse grooves deliberately introduced in the adherends (pins) (Fig.1) can indeed reduce the magnitude and improve the uniformity of the distribution of the interfacial shearing stress in small size joints (Fig.2) . Such a favorable "transverse groove effect" (TGE) takes place when the positive effect, in terms of the stress relief, due to the increase in the interfacial compliance in a particular LSJ "grooved" design suppresses the negative effect of the increase in the axial compliance of the pins. The objective of the analysis that follows is to find out to what extent the TGE could influence the peeling stress in a LSJ. We would like to point out that the objective of this analysis was not so much to develop a more or less accurate analytical or a FEA model, but rather to demonstrate that the peeling stress, whatever technique is used to evaluate it, can be reduced considerably by introducing the transverse grooves.