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

Abstract

A B S T R A C T 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, K ini IC and the unstable toughness K un IC 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, K ini IC and K un IC but also it will avoid the need of skilled numerical integration technique due to singularity problem at the integral boundary.

Numerical evaluation of simplified extreme peak load method for determining the double – K fracture parameters of concrete

“…From the results presented by authors [37], it can be seen that the error in results of K IC ini and K IC un for many specimens is more than ±20% which needs further attention for the validity of simplified extreme peak load method. It has been established from the extensive experimental and numerical studies [20][21][22][23][24][25][26]30] that the values of double -K fracture parameters (K IC ini and K IC un ) determined using experimental method and conventional analytical methods (GaussChebyshev integral method, weight function method) are in excellent agreement. Hence, in authors' opinion, the conventional analytical methods (Gauss-Chebyshev integral method, weight function method) can be considered as the standard analytical methods for determining the double -K fracture parameters.…”

“…The double-K fracture parameters using weight function method is based on linear asymptotic superposition assumption which uses linear elastic fracture mechanics formulas [26]. Here, WFM with four terms of universal weight function is used for computing the double-K fracture parameters of standard three point bend test (TPBT).…”

“…Further, the traditional extreme peak load method Qing et al [35] requires complicated integration procedure to calculate the critical effective crack length whereas the integration procedure is avoided in the simplified extreme peak load method [37]. Qing et al [37] determined the double-K fracture parameters for the experimental data [38] using simplified extreme peak load method (SEPLM) and compared the results with those obtained using weight function method (WFM) [26]. From the comparison, it has been pointed out that the simplified extreme peak load method yields generally smaller values of K IC ini and K IC un as compared to those obtained using conventional weight function method.…”

Influence of specimen geometry on determination of double-K fracture parameters of concrete: a comparative study

“…38, 39 with the help of three parameters M 1 , M 2 and M 3 of weight function for single edge cracked specimen of finite width plate subjected to a pair of normal forces, with less than 3% error for 0 ≤ a/D ≤ 0.95 in the range of 0 ≤ x/a ≤ 0.98 (Kumar and Barai 2008a).…”

“…Later, a simplified approach (Xu and Reinhardt 2000) was proposed using two empirical formulae to obtain the double-K fracture parameters for TPBT configuration. Recently, a closed form equation for determining the values of double-K fracture parameters based on weight function approach (Kumar and Barai 2008a) was presented.…”