An analytical study on peeling of an adhesively bonded joint based on a viscoelastic Bernoulli–Euler beam model

Abstract

Peeling of a thin film adhesively bonded to a rigid substrate is analytically studied using a Bernoulli–Euler beam theory for viscoelastic materials. The film (adherend) is modeled as a viscoelastic Bernoulli–Euler beam, and the normal and shear stresses on the film-adhesive interface are assumed to satisfy constant traction laws. Closed-form solutions are derived for the following two cases: (i) only the interfacial normal stress is present (mode I loading) and (ii) the interfacial shear stress is acting alone (mode II loading). The Boltzmann superposition integral is used to obtain the constitutive relations for the viscoelastic beam, and the methods of separation of variables and Laplace transforms are employed in the formulation. To illustrate the newly derived analytical solutions, sample cases are quantitatively studied. The three-parameter Kohlrausch–Williams–Watts model is adopted to compute the compliance. The numerical results show that both the vertical displacement under mode I loading and the horizontal displacement under mode II loading increase with time and/or temperature.