Stress Calculations for Bonded Joints

Richard worked with many industrial partners to encourage the bonding process in design circumstances where the increased performace available with adhesives provided improved, economic and durable structures. This was exemplified when he was selected as the adhesive consultant for the Thrust SSC project, where the world land speed record was raised by 130 mph to match the speed of sound. 

The art of creating structures is limited by the selected technique of fastening components together. We all have a concept of robust and dependable assemblies 

Handbook of Adhesives and Sealants Volume 2 P. Cognard (Editor) 

Keywords Adhesive modulus Adhesys expert system Co-axial joints Compression Concealed joints Creep Elastic limit Epoxy Epoxy composite Einite element analysis Glue line thickness Goland and Reissner Hart-Smith Heat exchanger Hooke s Law Joint designs Joint thickness Lap shear strength Peel Plastic behaviour Polyurethane Pipe bonding Shear stresses Shear modulus Stress distribution Thick adherend shear test Tubular joints Volkersen equation Young s modulus 

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Water uptake by polymers is accommodated largely by swelling. For uptakes of only a few mass per cent, volumetric swelling would be of a similar or lower order(98, 99), and barely measurable. Moire fringe interferometry has been used to quantify the swelling stresses developed in a layer of adhesive upon exposure to water(lOO), and Comyn(90) describes some other work related to calculations of the stresses induced in bonded joints by water sorption. 

A paper of Myshko and Garf [175] was the first to attempt to create a method of calculating the distribution of the shrinkage internal stresses along an adhesive-bonded joint cross-section for a cantilevered specimen made of two plates of different flexural rigidity with an adhesive layer between them—i.e., to generalize the equations from [160] for adhesive-bonded joints. 

By measuring water uptake, the diffusion coefficient and equilibrium concentration of water for the bulk adhesive were obtained at different temperatures. A value of 37 kJ/mol was also calculated for the activation energy of diffusion. A value for the plane-strain stress intensity factor, Kic, for the bulk adhesive was obtained using compact tension specimens. Tensile butt joints were prepared from mild steel blocks bonded with the epoxy adhesive and the fracture stress determined as a function of time of exposure to water at the different temperatures. An activation energy of 32 kJ/mol was calculated for joint failure, in close agreement with that obtained for the diffusion of water. This supports the view that the processes responsible for loss of joint strength are controlled by water diffusion. It was found that joints exposed to 20°C/55% RH showed no reduction in strength, even... 

Another compressive shear test used for wood joints is ASTM D905-49. Test joints are prepared by bonding two blocks of wood, free from defects, with the grain of each block parallel to the length direction. Test specimens are cut from this bonded joint and tested in a special shearing apparatus (Figure 13). Loads are applied using a crosshead movement of 0.015 inch/min. The shear stress is calculated with the failure load and bonded shear area. 

MI/SI techniques have been utilized in measuring the in-plane surface deformation of the overlap region for FRP adhesively bonded joint specimens, but have not been systematically implemented for FRP adhesive/adherend stress calculations. 

Consider a lap joint with an overlap of 25 mm and a length for the purposes of stress calculation of only 25 mm. For the initial assessment two pieces of mild steel of thickness 1.5 mm are bonded together using an adhesive of modulus 0.4 GPa, an elastic limit of 19 MPa and a glue line thickness of 0.05 mm. When a high load of 3000 N is applied, the distribution of stress is calculated to be as follows (Fig. 11). 

Analytical approaches for adhesively bonded structures are presented in this chapter. Stress analysis for adhesively bonded joints is conducted using the classical adhesive-beam model and the other adhesive-beam models. Closed-form solutions of symmetric joints are presented and analytical procedures of asymmetric and unbalanced joints are discussed. Load update for single lap joints is investigated in detail. Numerical results calculated using the classical and other formulations are illustrated and compared. It is shown that the nonlinear adhesive-beam model based on the Timoshenko beam theory provides enhanced results compared to the linear adhesive-beam model based on the Euler beam theory for adhesively bonded composite structures. Analytical solutions of energy release rates for cohesive failure and delamination are presented, and several failure criteria are reviewed and discussed. 

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