Stress-function variational method for interfacial stress analysis of adhesively bonded joints

The use of adhesively bonded joints in place of traditional joining techniques such as bolted or rivet joints is becoming greatly popular in recent years. Interfacial stress in the adhesive is critical to the strength of adhesively bonded joints. It is necessary to predict the interfacial stresses accurately to ensure the safety of joints. In this work, an analytical model is explicitly presented to evaluate the stresses in a double lap joint. The equilibrium equations in the adhesive overlap region are derived on the basis of elasticity theory. The governing equations are presented in terms of shear and peel stresses in the adhesive. Analytical solutions are derived for the shear and peel stresses, which are considered to be the main reason for the failure of the double lap joint. To verify the analytical solutions, the finite element method is conducted using the commercial package ANSYS. Results from the analytical solution agree well with finite element results and numerical investigations available in the literature. The effect of the adhesive thickness, shear modulus, adherend Young’s modulus and bonding length on the shear and peel stresses in the adhesive of the double lap joint are studied. Numerical results demonstrate that both the maximum shear and peel stress occur at both ends of the bonding region. The maximum values of the shear and peel stresses increase as the adhesive thickness decreases and as the adhesive shear modulus increases provided that the adhesive thickness is sufficiently small. The simplicity and capability to obtain analytical expressions of the shear and peel stresses for double lap adhesive bonded joints makes the proposed analytical model applicable for the stress analysis and preliminary structural design.

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Stress-Function Variational Method for Accurate Free-Edge Interfacial Stress Analysis of Adhesively Bonded Single-Lap Joints and Single-Sided Joints

Journal of Composites Science ◽

10.3390/jcs5080197 ◽

2021 ◽

Vol 5 (8) ◽

pp. 197

Author(s):

Xiang-Fa Wu ◽

Youhao Zhao ◽

Oksana Zholobko

Keyword(s):

Variational Method ◽

Stress Analysis ◽

Stress Function ◽

Free Edge ◽

Lap Joints ◽

Interfacial Stress ◽

Strength Analysis ◽

Adhesively Bonded ◽

Interfacial Stresses ◽

Single Lap Joints

Large free-edge interfacial stresses induced in adhesively bonded joints (ABJs) are responsible for the commonly observed debonding failure in ABJs. Accurate and efficient stress analysis of ABJs is important to the design, structural optimization, and failure analysis of ABJs subjected to external mechanical and thermomechanical loads. This paper generalizes the high-efficiency semi-analytic stress-function variational methods developed by the authors for accurate free-edge interfacial stress analysis of ABJs of various geometrical configurations. Numerical results of the interfacial stresses of two types of common ABJs, i.e., adhesively bonded single-lap joints and adhesively single-sided joints, are demonstrated by using the present method, which are further validated by finite element analysis (FEA). The numerical procedure formulated in this study indicates that the present semi-analytic stress-function variational method can be conveniently implemented for accurate free-edge interfacial stress analysis of various type of ABJs by only slightly modifying the force boundary conditions. This method is applicable for strength analysis and structural design of broad ABJs made of multi-materials such as composite laminates, smart materials, etc.

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