Crack tip asymptotic field and K-dominant region for anisotropic semi-circular bend specimen

Abstract

This study reports the coefficients of the crack tip asymptotic field for the semi-circular bend (SCB) specimen made of anisotropic rocks when subjected to pure mode I loading. The finite element over-deterministic method is employed to determine the singular and higher order terms of the crack tip asymptotic field for a wide range of geometry and anisotropy parameters associated with the Mode SCB test. These parameters are helpful when analysing the fracture path and failure mechanism of anisotropic rocks in cases where the process zone is large compared to the crack length. We also apply an energy-based criterion on the crack tip fields to evaluate the size of the K-dominant region as a function of geometry configuration and anisotropy. It is concluded that the ISRMsuggested size requirement for the SCB samples of rock can yield underestimated values of fracture toughness due to the constraints applied to the FPZ development.

Introduction of a Scaling Factor for Fracture Toughness Measurement of Rocks Using the Semi-circular Bend Test

“…A large FPZ may partially stay out of the K-dominant zone in small samples, whereby inducing size-dependent fracture toughness values (Wei et al 2016b(Wei et al , 2017a(Wei et al , 2018aDutler et al 2018). A clear illustration of this process is given in Nejati et al (2020b). As our experiments suggest, even by enlarging the specimen radius to R = 200 − 300 mm, the fracture toughness values may not still experience a plateau, and a further increase is yet anticipated.…”

“…Given that our tested rocks have isotropic elasticity response, the roller supports were placed symmetrically to apply pure mode I loading, with the span length ratio adjusted to S∕R = 0.6 Sedighi et al 2020). It is noteworthy that asymmetrical support spans are required to impose mode I loading for SCB specimens made of anisotropic rocks (Nejati et al 2019(Nejati et al , 2020b.…”

“…2b), the fracture toughness is calculated from K Ic = K * I P c √ a∕(2Rt) , where R and t represent the radius and thickness of the SCB specimen, and a is the length of the notch. Moreover, the geometry factor K * I is a numerically calculated dimensionless parameter, that depends on the specimen geometry and loading configuration, and is adopted from the results by Nejati et al (2019Nejati et al ( , 2020b for the isotropic case. Figure 5a presents the measured values of K Ic against the SCB radius, R. It is observed that, within the entire size range, marble is the strongest material with the largest fracture toughness values, while limestone acquires the least values overall and seems to be rather weaker.…”

“…The FPZ region embodies a zone of highly localised deformation that occurs due to extensive micro-cracking processes. Since K Ic is a measure valid only inside the K-dominant zone, the specimen dimensions (and subsequently K-zone) should be enlarged enough so that the FPZ fits inside the K-dominant region (Nejati et al 2020b). A large FPZ may partially stay out of the K-dominant zone in small samples, whereby inducing size-dependent fracture toughness values (Wei et al 2016b(Wei et al , 2017a(Wei et al , 2018aDutler et al 2018).…”

“…An important subject when dealing with rock materials is the size effect phenomenon, where tests performed on smallsized rock specimens often yield underestimated values of fracture toughness compared to the scale-independent fracture toughness of the rock mass. Many research studies to date have investigated this size effect behaviour in the mode I fracture toughness of rock and concrete, using the single edge notch bend (SENB) test (Bažant 1984;Bažant and Pfeiffer 1987;Karihaloo 1999;Cusatis and Schauffert 2009;Ayatollahi and Akbardoost 2012;Fakhimi and Tarokh 2013;Tarokh et al 2017;Bhowmik and Ray 2019;Carloni et al 2019) or the SCB test (Chong et al 1987;Nath Singh and Sun 1990;Lim et al 1994;Akbardoost et al 2014;Wei et al 2016aWei et al , 2017bZhang et al 2019;Nejati et al 2020b). It is worth noting that this literature consists of experimental, numerical and theoretical approaches, among which the initial studies by Bažant and his co-workers truly stand out and lay the foundation for most of the later research activities in this field.…”