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

Xiang‐Fa Wu ,Youhao Zhao,Оксана Жолобко

doi:10.3390/jcs5080197

Xiang‐Fa Wu , Youhao Zhao + Show 1 more

Open Access

https://doi.org/10.3390/jcs5080197

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Abstract

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.

Highlights

A generalized stress-function variational method was successfully formulated for stress analysis of adhesively bonded joints (ABJs) subjected to mechanical and thermomechanical loads
Was to introduce two unknown shear and normal stress functions at each interface of the ABJ, and all the stress components in the adherends and the adhesive layer of the ABJ could be expressed in terms of these unknown interfacial stress functions within the framework of the classic Euler-Bernoulli beam theory and linear elasticity
It can be concluded that the set of governing ordinary differential equations (ODEs) formulated by the authors in this and previous studies is universal for all the three-layered ABJs as shown in Figure 1, except for matrix D given in

Summary

Introduction

To effectively approach the stress conditions in ABJs, in particular the traction-free conditions at the free-edges of ABJs, Chang [97,98,99,100] expressed the interfacial peeling and shear stresses on the bonding lines in terms of the sums of an infinite series of sine or cosine functions, respectively, with their coefficients determined via minimization of the strain energy of the entire ABJs. During the process, the axial stress in each elastic adherend and adhesive layer was assumed to linearly vary across the thickness of the corresponding layer as that of classic Euler-Bernoulli beams, and the related transverse normal stresses and shear stresses were determined by evoking the 2D stress equilibrium equations. Discussions and conclusions of the present study are made in consequence

Static Equilibrium Equations of General ABJs

Planar Stresses in the Adherends and Adhesive Layer of an ABSLJ

Scaling Analysis of Interfacial Shear and Normal Stresses of ABSLJs Due to

Stress Resultants in the Upper and Lower Adherends and Adhesive Layer of the

Planar Stress Components in the Adherends and Adhesive Layer of the ASSJ

Conclusions