A Parametric Study of the Peel Test

The force required to peel a film from a substrate is generally a complex function of geometry, the constitutive properties of the film and substrate, and the interfacial cohesive properties. In most analyses, the effects of the transverse shear force that is an integral aspect of almost any peel test are neglected, although they can be incorporated in an indirect fashion through models that invoke a root-rotation angle. In this study, a complete elastic solution that incorporates all the components contributing to crack-tip deformation, including bending moment, transverse shear force and axial force, is derived in a selfconsistent way. In particular, it is shown that, for a strong interface that requires a reasonably large peel strain, the transverse shear results in a significant deviation of the phase angle from earlier analyses that neglected the shear term. The present analysis also links the transverse shear component to the root-rotation angle. A cohesive-zone analysis is presented for the peeling of an elastic-plastic film. In this analysis the interface is modeled using cohesive elements, and the film is modeled by a full, two-dimensional, finite-element analysis. This analysis allows the full effects of bending, axial loading, and transverse shear to evolve, with no a-priori assumptions being made about their relative magnitudes. The numerical results show how the peel force depends on the film thickness. When the film is relatively thin, the peel force increases with an increase in thickness as the extent of plasticity increases. This increase in plasticity is associated with (i) an increase in the contribution of bending to the deformation at the crack tip, relative to the contribution of transverse shear, and (ii) an increase in the physical limits imposed by the dimensions of the film on the volume of any crack-tip plastic zone. When the film is relatively thick, elasticity dominates the deformation of the film, and small-scale yielding effects become important. The peel force is dictated by the toughness of the interface and by crack-tip plasticity (if any) induced by the cohesive stresses. Therefore, peel forces tend to minimum values for both thick and thin films. A maximum peel force is exhibited for films with an intermediate thickness.