Configurational forces in fracture mechanics: A comprehensive concept of crack initiation and growth

Abstract

AbstractIn engineering structures cracks typically initiate at stress raisers such as holes and notches. In terms of a fracture mechanical assessment, it is important to identify the position xk, the angle ϕc and the length Δac of initiating cracks. Classically a stress based criterion is applied to obtain the position of crack initiation. Recently, the finite fracture mechanics approach [1] was presented, combining a stress and energy based criterion to obtain the positions and initiation lengths of cracks. In this approach, the energy states of the uncracked and the cracked specimens are compared, providing the reduction of the elastic potential ΔΠ due to crack initiation. In general, the global solution ΔΠ(xk, ϕ, Δa) is required for accurately predicting new cracks. In this paper, the material or configurational forces [2] at stress raisers are investigated with respect to the initiation of cracks. The material forces are strongly related to path‐independent integrals, e.g. the J‐integral [3] as crack driving quantity or loading quantity at notches [4]. A new criterion based on configurational forces is suggested, efficiently providing all data of the onset of cracks at stress concentrators.