Analytical Study on Adhesively Bonded Joints Using Peeling Test and Symmetric Composite Models Based on Bernoulli-Euler and Timoshenko Beam Theories for Elastic and Viscoelastic Materials

Abstract

Adhesively bonded joints have been investigated for several decades. In most analytical studies, the Bernoulli-Euler beam theory is employed to describe the behaviour of adherends. In the current work, three analytical models are developed for adhesively bonded joints using the Timoshenko beam theory for elastic material and a Bernoulli-Euler beam model for viscoelastic materials. One model is for the peeling test of an adhesively bonded joint, which is described using a Timoshenko beam on an elastic foundation. The adherend is considered as a Timoshenko beam, while the adhesive is taken to be a linearly elastic foundation. Three cases are considered: (1) only the normal stress is acting (mode I); (2) only the transverse shear stress is present (mode II); and (3) the normal and shear stresses co-exist (mode III) in the adhesive. The governing equations are derived in terms of the displacement and rotational angle of the adherend in each case. Analytical solutions are obtained for the displacements, rotational angle, and stresses. Numerical results are presented to show the trends of the displacements and rotational angle changing with geometrical and loading conditions. In the second model, the peeling test of an adhesively bonded joint is represented using a viscoelastic Bernoulli-Euler beam on an elastic foundation. The adherend is considered as a viscoelastic Bernoulli-Euler beam, while the adhesive is taken to be a linearly elastic foundation. Two cases under different stress history are considered: (1) only the normal stress is acting (mode I); and (2) only the transverse shear stress is present (mode II). The governing equations are derived in terms of the displacements. Analytical solutions are obtained for the displacements. The numerical results show that the deflection increases as time and temperature increase. The third model is developed using a symmetric composite adhesively bonded joint. The constitutive and kinematic relations of the adherends are derived based on the Timoshenko beam theory, and the governing equations are obtained for the normal and shear stresses in the adhesive layer. The numerical results are presented to reveal the normal and shear stresses in the adhesive.