Size effect on double- K fracture parameters of concrete based on fracture extreme theory
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O R I G I NA L
Longbang Qing · Yimeng Su · Mowen Dong · Yuehua Cheng · Yang Li
Size effect on double-K fracture parameters of concrete based on fracture extreme theory
Received: 3 March 2020 / Accepted: 9 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Based on fracture extreme theory (FET), the size effect on initial fracture toughness K Iini and unstable fracture toughness K Iun of concrete for three-point bending beam was investigated. Nine groups of geometrically similar specimen were simulated to obtain peak load and critical crack mouth opening displacement, of which specimen depth was from 200 to 1000 mm and initial crack length-to-depth ratios were from 0.1 to 0.6. The K Iini and K Iun were calculated by FET and double-K method, in which FET adopted the linear, bilinear, and trilinear cohesive stress distribution assumptions and double-K method only used the linear cohesive stress distribution assumption. With linear cohesive stress distribution assumption, K Iini and K Iun determined by FET and doubleK method were compared. Then, the influence of specimen depth on K Iini and K Iun was discussed. In addition, K Iini /K Iun calculated via FET using different cohesive stress distribution assumptions were analyzed. Keywords Concrete · Size effect · Fracture extreme theory · Cohesive stress distribution assumption · Double-K fracture parameters
1 Introduction The fracture process zone (FPZ) exists at the crack tip in the crack propagation of concrete, which leads to the size effect of fracture parameters [1]. The linear elastic fracture mechanics (LEFM) is not applicable for quasi-brittle materials if the FPZ is not sufficiently small compared with the specimen size. Hence, various nonlinear fracture models considering the FPZ were proposed in determining fracture parameters of quasibrittle materials [2–8]. The fictitious crack model (FCM) [2] regards the FPZ as a fictitious crack which can L. Qing (B) · Y. Su · M. Dong · Y, Cheng · Y. Li School of Civil Engineering and Transportation, Hebei University of Technology, Tianjin 300401, China L. Qing E-mail: [email protected] Y. Su E-mail: [email protected] Y. Li E-mail: [email protected] M. Dong China Academy of Building Research, Beijing 100013, China E-mail: [email protected] Y. Cheng College of Civil Engineering, Tongji University, Shanghai 200092, China E-mail: [email protected]
L. Qing et al.
transfer cohesive stress. The tensile softening curve can describe the relationship between the cohesive stress and crack opening displacement, in which the cohesive stress decreases as the crack opening displacement increases. The fracture process of concrete can be divided into three main stages, i.e., crack initiation, stable crack propagation, and unstable crack propagation, which has been verified by several studies [8,9]. Xu and Reinhardt [8] proposed the double-K fracture model using initial fracture toughness K Iini and unstable fracture toughness K Iun to characterize these three stages. A simplified
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