Chapter 7 - Mixed-Mode Fracture

Abstract

This chapter discusses the issue of mixed-mode fracture. In establishing the fictitious crack model (FCM) for analyzing the mode-I type of cracks in concrete, Hillerborg et al. (1976) had also indicated the possibility of applying the concept to model other types of fracture, such as the shear fracture of the mode-II or mode-III type. Much effort has since been made to extend the fictitious crack model to mixed-mode fracture because most practical fracture problems in concrete are mixed-mode, involving modes I and II. In modeling the shear transfer mechanism in the fracture process zone (FPZ), numerical studies in this category often rely on interface elements: The stiffnesses of interface connections in the normal and tangential directions are assumed to be functions of the crack surface deformation. However, this approach to introducing shear to the crack surface is inexplicit and approximate. An accurate specification of tangential tractions based on a given shear transfer law can hardly be achieved through regulating the stiffness of tangential connections that lack clear physical meaning. Since the shear transfer law defines the mode-II fracture energy, the lack of accuracy in implementing the law in numerical analysis could lead to erroneous results and misleading conclusions on the role and influence of the mode-II fracture parameters. Hence, a straightforward extension of the FCM is needed. To apply the mixed-mode FCM and EFCM to engineering problems, the fracture tests on scale models of a gravity dam are remodeled as mixed-mode fracture, focusing on the influence of shear on the crack path in dams.