3-D non-linear stress analysis on the adhesively bonded composite joint under bending moment Salih Akpinar a,n , Murat Demir Aydin b a Department of Mechanical Engineering, Erzurum Technical University, 25050 Erzurum, Turkey b EMYO, Atatürk University, 25240 Erzurum, Turkey article info Article history: Received 13 May 2013 Received in revised form 14 November 2013 Accepted 19 February 2014 Available online 27 February 2014 Keywords: Finite element analysis Adhesive Composite lap joint Ply stacking sequence Three-dimensional effects abstract This paper presents an approach to predict the three-dimensional effects (anti-clastic, free edge and bending–twisting coupling effects) and to assess the effects of the fiber orientation angle of the laminates on the stress distributions and the failure prediction in the Single Lap Composite Joints (SLJs) subjected to a bending moment via a 3-D non-linear finite element method. In the analysis, the composite adherends (AS4/3501-6) with five different fiber orientation angles ([90/ 745/0] 2s , [0/90] 4s , [45/ 45] 4s , [0] 16 and [90] 16 ) were assumed to behave as linearly elastic materials while the adhesive layer (FM 73) was assumed to be nonlinear. Also, the nonlinear geometric deformations of the SLJs were also taken into account. Consequently, it is seen that the state of stress in the vicinity of the free edge of the joint is fully three dimensional which has not been taken into account in any classical theory so far and the normal and shear stress distributions are extremely sensitive to this three-dimensional effects. From this aspect, the three-dimensional finite element analysis is a necessity for understanding explicitly the stress and failure states. Also, for both the adherends and the adhesive layer, the ply stacking sequence has a significant effect on the stress distribution and the failure. & 2014 Elsevier Ltd. All rights reserved. 1. Introduction Composite materials in advanced engineering structures have gained great popularity over the past decades because of their high strength/weight ratios and high damping capacity. Tradi- tional methods of joining, such as riveting and screwing, became the first choice due to their relatively low cost and ease of assembly. However, as widely known, even when such joints are used with traditional materials, high stress concentrations can be developed at the point of joining, and the joint can be brought to failure at far lower stress levels than expected [1]. Therefore, adhesively bonded joints are more preferable to a mechanical joint in the joining of composite materials [2]. On the other hand, the analysis of adhesively bonded joints requires a reliable and efficient tool to obtain stresses and strains distributions. For this purpose, different techniques (analytical modeling and numerical solution) have been used in the past to predict the strength and stress distributions of adhesively bonded composite joints. Several analytical models have been developed for analysis of adhesively bonded joints [2–11]. Historically speaking, one would cite the work of Goland and Reissner [4] as one of the earliest investigations performed on the cylindrical bending plate analysis of a Single Lap Joint (SLJ). Since then several workers performed work on this subject; for instance, Hart-Smith [5] developed a layered beam model to solve the SLJ problem. Oplinger [6] also developed a beam method by considering the overlap bending moments and introducing the individual tensile forces in the upper and lower adherends at the overlap section. In order to ensure that the stress-free boundary conditions would be satisfied at the free ends, some researchers employed two-dimensional elasticity theory in conjunction with the variational method, such as a minimum strain method [7,8] and the principle of comple- mentary energy method [9]. Numerical methods provide a general tool for analysis arbitrary geometries and loading conditions. Among the numerical methods, the finite element method (FEM) has been extensively used with success and countless studies on the various adhesively bonded joints via this technique were performed by many authors [12–24]. On the other hand, unlike the isotropic adherend, laminated composite adherends have relatively low transverse strength and shear stiffness compared to the in-plane material properties. Also laminates suffer from material non-homogeneity, residual stresses and free edge problems. These factors make the problem of adhesively bonded joints with the composite adherends more complex than that with homogeneous isotropic adherends [25,26]. The free-edge effect occurs due to the discontinuity of material properties in the composite laminates. The major phenomenon of Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/ijmecsci International Journal of Mechanical Sciences http://dx.doi.org/10.1016/j.ijmecsci.2014.02.024 0020-7403 & 2014 Elsevier Ltd. All rights reserved. n Corresponding author. Tel.: þ90 532 363 1099. E-mail address: salih.akpinar@erzurum.edu.tr (S. Akpinar). International Journal of Mechanical Sciences 81 (2014) 149–157