Determining the double-K fracture parameters for three-point bending notched concrete beams using weight function

Abstract

Parameters of universal form of weight functions having four terms and five terms are derived for edge cracks in finite width of plate. The standard Tada Green's function is taken as the basis for the derivation. The shape of universal form of weight functions considered enables closed form expressions for cohesive toughness of three-point bending test geometry of notched concrete beams due to linear cohesive stress distribution in the fictitious fracture zone. This solution provides a viable method to determine the double-K fracture parameters: the initiation toughness, inline image and the unstable toughness inline image for mode I fracture of concrete beam. A comparison with existing analytical method shows that the weight function method for determination of the double-K fracture parameters yields results without any appreciable error. The use of weight function will not only simplify the calculation to obtain the double-K fracture parameters, inline image and inline image but also it will avoid the need of skilled numerical integration technique due to singularity problem at the integral boundary.