A revised virtual crack closure technique for physically consistent fracture mode partitioning

The virtual crack closure technique (VCCT) is a well-established method for computing the energy release rate when analysing fracture problems via the finite element method. For mixed-mode fracture problems, the VCCT is also commonly used to partition the fracture modes, i.e. to determine the energy release rate contributions related to the three classical fracture modes. A perhaps little known fact, however, is that in some circumstances the standard VCCT predicts physically inconsistent, negative values for the modal contributions to the energy release rate. Focusing on I/II mixed-mode problems, this paper presents a revised VCCT which furnishes a physically consistent partitioning of fracture modes by associating the mode I and II contributions to the amounts of work done in a suitably defined two-step process of closure of the virtually extended crack. Deeper investigation pinpoints the origins of the physically inconsistent predictions of the standard VCCT in the lack of energetic orthogonality between the crack-tip force components used to compute the modal contributions. Further insight into the problem is offered by a geometric construction, which introduces the ‘ellipse of crack-tip flexibility’. In closing, the phenomena of contact, interpenetration, and friction between the crack surfaces are briefly touched upon.