Adhesive joints have been widely used in a variety of engineering applications, in particular for the sectors where bonding is critical to the safety of structures, e.g., automotive and aerospace industries [
1]. It offers some advantages such as more uniform stress distribution, reduction of stress concentration, less weight and easy to be fabricated in comparison with welding, bolting and fastening [
2]. Single lap joint, double lap joints and scarf joints are the most common bonded joints [
3]. Among them, the single lap joint is the most generally studied owing to its simple geometry and easy to prepare, although it exhibits the worst specific strength in these three different joints configurations [
4]. The poor performance can be attributed to the eccentricity of the applied loads resulting in a bending moment on the joint, which induces the high stress concentrations at the ends of the bonding region [
5]. The performance of the double lap joint is improved by reducing the stress concentration of both peel and shear stresses. The reduction of peel stress is due to the elimination of the eccentricities of applied loads, while shear stress is reduced by removing the differential straining effect [
6]. The scarf joint is considered as the best in terms of strength for the same bonding region, by further reducing the stress concentration because of the elimination of the geometry discontinuity, which appears in the lap joints [
7]. Although, adhesively bonded joints have been used more often than that of mechanical joints in connecting the structural components owing to their advantages such as more uniform interfacial stress distributions, capability of joining different materials and high resistance to fatigue failure [
8,
9]. However, in the adhesively bonded joints, high stress concentration occurs at both ends of the bonding region, which severely affects the strength of the joint. In order to employ the adhesive bonding technique appropriately and to improve the load carrying capacity of the joint, interfacial stresses distributions in the adhesive should be determined accurately [
10].
A variety of techniques have been proposed for adhesively bonded joints, either analytical, numerical or experimental. There are several analytical models available for adhesively bonded joints. Volkersen [
11] reported a simple model for the single lap joint, which assumed shear stress only in the adhesive, while adherends were subjected to longitudinal normal stress. Volkersen’s model is considered as one of the most important and pioneer contributions to the adhesively bonded joints. Goland and Reissner [
12] revised Volkersen’s model by introducing peel stresses and large deflection to the adherends. Later, Hart-Smith [
13] proposed a model, which modified the Goland and Reissner model with plastic deformation in the adhesive. Klarbring and Movchan [
14] proposed an asymptotic modeling for adhesive joints in a thin compound beam with a layered structure. Raous et al. [
15] presented a model coupling adhesion, Coulomb friction and unilateral contact. In their model, adhesion was characterized by an internal valuable to represent the intensity of adhesion. Yousefsani and Tahani [
16] used full layerwise theory to predict the shear stress, peeling stress and von Mises stress in the adhesive layer for adhesively bonded joints subjected to uniaxial tension and bending moment. Wu and Zhao [
17] proposed stress functions of the interfacial shear and peeling stresses for the adhesively bonded joint, then employed the variational method to determine the interfacial stresses using the theory of minimum complimentary strain energy. Fernlund [
18] incorporated the theory of fracture mechanics with energy balance to derive analytical solutions for the maximum shear and peeling stresses at the ends of the overlap region for straight and curved lap joints. Oplinger [
19] presented an alternative model, which included bending deflections of both the adherend and adhesive in the overlap region of the single lap joint. Tsai et al. [
20] derived an analytical solution based on the assumption of linear shear stress distribution across the adherend thickness. Her [
21] reported theoretical solutions for the shear stress in the adhesive and longitudinal normal stress in the adherends using the elasticity theory. Recently, a rapid increase of computational capability has significantly attracted a lot of attention in numerical simulation as an accurate and effective technique, in particular for the finite element method. Extensive review of finite element-based techniques is provided by He [
22]. Mokhtari et al. [
23] used a 3-D finite element commercial code ABAQUS to investigate the influences of material properties including ply thickness, Young’s modulus and orientations on the stress distributions in the composite double lap joint. Stuparu et al. [
24] employed the eXtended finite element method (XFEM) using cohesive zone modelling (CZM) to evaluate the failure of a single-lap joint that adhesively bonded two different materials. Moya-Sanz et al. [
25] developed a 2-D numerical model in the Abaqus/Standard to investigate the effects of geometry such as recessing and chamfering of the adherends and adhesive on the failure load of a single-lap joint under uniaxial tensile force, using the cohesive zone model. Hou et al. [
26] proposed a novel concept to reduce the stress concentration at both ends of the bonding region in a double lap joint by making a slot in the inner adherend using finite element numerical simulation. Santos et al. [
3] employed a numerical method based on XFEM to predict the stress distribution, strength and damage propagation in the adhesively bonded joints. Campilho and Fernandes [
2] used the finite element method and cohesive zone model to investigate the performance of single lap joints with different adhesives. Panigrahi and Pradhan [
27] conducted the 3-D nonlinear finite element analysis to study the initiation and growth of the delamination in the adhesive of a composite double lap joint. Several researchers have conducted experimental tests to determine the strength and failure load of adhesively bonded joints. Khan et al. [
28] performed experimental tests to investigate the influence of the adherend layup, adhesive material property and thickness on the strength of double-lap joint according to ASTM D3528-96 specifications. Ozel et al. [
29] experimentally studied the failure load of a single-lap joint with different adherends. Tsai and Morton [
30] employed the full-field moiré interferometry to examine in-plane deformations of the adhesive in a double-lap joint. Neto et al. [
31] conducted experimental tests on the adhesively bonded composite joints with brittle and ductile adhesives using a cohesive zone model to determine the joint strength. Akhavan-Safar et al. [
32] experimentally investigated the effect of adhesive thickness on the strength of adhesively bonded single lap joints. Gultekin et al. [
33] studied the effect of the adherend width on the strength of an adhesively bonded single lap joint experimentally.
It is essential to understand the stresses acting on an adhesively bonded lap joint to determine whether the structure is safe or failure under the normal operation. Although, in these days, stresses in the adhesively bonded joints can be completely calculated using the finite element method, the need for analytical solutions still exists. Closed-form solutions can provide a better understanding of a phenomenon than that of numerical results. Furthermore, formulae can be of a simple and quick tool to engineers for a preliminary design of joints. Present work studies the double lap joint, and focus on the interfacial stresses including the shear and peel stresses in the adhesive layer. The goal is to provide analytical solutions to predict the shear and peel stresses based on the theory of elasticity. The analytical predictions are validated with the finite element results. The effects of the bonding length, adhesive thickness and elastic moduli of the adherend and adhesive on the shear and peel stresses are investigated through a parametric study.