The use of digital-image correlation to investigate the cohesive zone in a double-cantilever beam, with comparisons to numerical and analytical models

Abstract

Abstract Digital-image correlation (DIC) is used to analyze an adhesively-bonded double-cantilever beam (DCB), and to determine the traction-separation law for a cohesive-zone model. The issues involved with how to extract useful information from the digital data of DIC are addressed. In addition, DIC is used to explore how the cohesive zone evolves, and to determine how the elastic arms deform in response to the loading and to the adhesive. The results of these observations are compared to numerical and analytical models for the DCB geometry. In particular, the well-known concept of root rotation is demonstrated. It is shown that, by combining the effects of shear into an effective root rotation, it is possible to use a simple Euler-beam approximation to describe the compliance of the DCB. The experiments and analysis also illustrate the lesser-known concept that significant compression can occur beyond the tensile region in the cohesive zone ahead of a DCB crack tip. Therefore, for accurate numerical predictions, a cohesive-zone model must incorporate compressive deformation. The DIC results are further used to illustrate the concept of a cohesive-length scale. This is defined in terms of the work done against crack-tip tractions, the opening displacement, the stiffness of the arms, and a characteristic geometrical length. The cohesive-length scale is measured experimentally in this paper, and its magnitude is shown to indicate when linear elasticity can be used to describe the deformation of a DCB geometry. The cohesive-length scale is shown to correlate with both the root rotation and the length of a cohesive zone in a fashion that is very similar to what is predicted analytically by elastic-foundation models. Finally, it is demonstrated that, when used in a cohesive-zone model of the geometry, the experimentally determined traction-separation law gives excellent predictions for the evolution of the cohesive zone and for the deformation of the elastic beams. A very minor discrepancy is associated with in-plane tensile stresses that must develop within an adhesive layer in response to the deformation of the beams.