The line crack models, including linear elastic fracture mechanics (LEFM), cohesive crack model (CCM), and extended finite element method (XFEM), rest on the century-old hypothesis of constancy of materials’ fracture energy. However, the type of fracture test presented here, named the gap test, reveals that, in concrete and probably all quasibrittle materials, including coarse-grained ceramics, rocks, stiff foams, fiber composites, wood, and sea ice, the effective mode I fracture energy depends strongly on the crack-parallel normal stress, in-plane or out-of-plane. This stress can double the fracture energy or reduce it to zero. Why hasn’t this been detected earlier? Because the crack-parallel stress in all standard fracture specimens is negligible, and is, anyway, unaccountable by line crack models. To simulate this phenomenon by finite elements (FE), the fracture process zone must have a finite width, and must be characterized by a realistic tensorial softening damage model whose vectorial constitutive law captures oriented mesoscale frictional slip, microcrack opening, and splitting with microbuckling. This is best accomplished by the FE crack band model which, when coupled with microplane model M7, fits the test results satisfactorily. The lattice discrete particle model also works. However, the scalar stress–displacement softening law of CCM and tensorial models with a single-parameter damage law are inadequate. The experiment is proposed as a standard. It represents a simple modification of the three-point-bend test in which both the bending and crack-parallel compression are statically determinate. Finally, a perspective of various far-reaching consequences and limitations of CCM, LEFM, and XFEM is discussed.
- Award ID(s):
- 1644326
- NSF-PAR ID:
- 10289895
- Date Published:
- Journal Name:
- 54th US Rock Mechanics/Geomechanics Symposium
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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null (Ed.)Fracturing in brittle rocks exhibits a significant nonlinear region surrounding the crack tip called the fracture process zone (FPZ). In this study, the evolution of the FPZ under pure mode II loading using notched deep beam under three-point loading was investigated. The experimental setup included the simultaneous monitoring of surface deformation using the two-dimensional digital image correlation technique to characterize various crack characteristics such as its type and FPZ evolution in Barre granite specimens. Both displacement and strain approaches of the two-dimensional digital image correlation were used to identify the mode of fracture under pure mode II loading. Both approaches showed that the crack initiation occur under mode I despite the pure mode II loading at the notch tip. The displacement approach was used for characterizing the evolution of the FPZ which analyzed the crack tip opening displacement and crack tip sliding displacement to identify the transition between the three stages of FPZ evolution, namely, (a) elastic stage, (b) formation of the FPZ, and (c) the macro-crack initiation. The results showed that the evolution of the FPZ of mode I fracture under pure mode II loading is similar to cases of pure mode I loading of the same rock.more » « less
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null (Ed.)Abstract In the standard fracture test specimens, the crack-parallel normal stress is negligible. However, its effect can be strong, as revealed by a new type of experiment, briefly named the gap test. It consists of a simple modification of the standard three-point-bend test whose main idea is to use plastic pads with a near-perfect yield plateau to generate a constant crack-parallel compression and install the end supports with a gap that closes only when the pads yield. This way, the test beam transits from one statically determinate loading configuration to another, making evaluation unambiguous. For concrete, the gap test showed that moderate crack-parallel compressive stress can increase up to 1.8 times the Mode I (opening) fracture energy of concrete, and reduce it to almost zero on approach to the compressive stress limit. To model it, the fracture process zone must be characterized tensorially. We use computer simulations with crack-band microplane model, considering both in-plane and out-of-plane crack-parallel stresses for plain and fiber-reinforced concretes, and anisotropic shale. The results have broad implications for all quasibrittle materials, including shale, fiber composites, coarse ceramics, sea ice, foams, and fone. Except for negligible crack-parallel stress, the line crack models are shown to be inapplicable. Nevertheless, as an approximation ignoring stress tensor history, the crack-parallel stress effect may be introduced parametrically, by a formula. Finally we show that the standard tensorial strength models such as Drucker–Prager cannot reproduce these effects realistically.more » « less
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ABSTRACT: Due to rock mass being commonly subjected to compressive or shear loading, the mode II fracture toughness is an important material parameter for rocks. Fracturing in rocks is governed by the behavior of a nonlinear region surrounding the crack tip called the fracture process zone (FPZ). However, the characteristics of mode II fracture are still determined based on the linear elastic fracture mechanics (LEFM), which assumes that a pure mode II loading results in a pure mode II fracture. In this study, the FPZ development in Barre granite specimens under mode II loading was investigated using the short beam compression (SBC) test. Additionally, the influence of lateral confinement on various characteristics of mode II fracture was studied. The experimental setup included the simultaneous monitoring of surface deformation using the two-dimensional digital image correlation technique (2D-DIC) to identify fracture mode and characterize the FPZ evolution in Barre granite specimens. The 2D-DIC analysis showed a dominant mixed-mode I/II fracture in the ligament between two notches, irrespective of confinement level on the SBC specimens. The influence of confinement on the SBC specimens was assessed by analyzing the evolution of crack displacement and changes in value of mode II fracture toughness. Larger levels of damage in confined specimens were observed prior to the failure than the unconfined specimens, indicating an increase in the fracture resistance and therefore mode II fracture toughness with the confining stress.
1. INTRODUCTION The fracturing in laboratory-scale rock specimens is often characterized by the deformation of the inelastic region surrounding the crack tips, also known as the fracture process zone (FPZ) (Backers et al., 2005; Ghamgosar and Erarslan, 2016). While the influence of the FPZ on mode I fracture in rocks has been extensively investigated, there are limited studies on FPZ development in rocks under pure mode II loading (Ji et al., 2016; Lin et al., 2020; Garg et al., 2021; Li et al., 2021).
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null (Ed.)Recent theoretical and computational progress has led to unprecedented understanding of symmetry-breaking instabilities in 2D dynamic fracture. At the heart of this progress resides the identification of two intrinsic, near crack tip length scales — a nonlinear elastic length scale ℓ and a dissipation length scale ξ — that do not exist in Linear Elastic Fracture Mechanics (LEFM), the classical theory of cracks. In particular, it has been shown that at a propagation velocity v of about 90% of the shear wave-speed, cracks in 2D brittle materials undergo an oscillatory instability whose wavelength varies linearly with ℓ, and at larger loading levels (corresponding to yet higher propagation velocities), a tip-splitting instability emerges, both in agreements with experiments. In this paper, using phase-field models of brittle fracture, we demonstrate the following properties of the oscillatory instability: (i) It exists also in the absence of near-tip elastic nonlinearity, i.e. in the limit ℓ→0, with a wavelength determined by the dissipation length scale ξ. This result shows that the instability crucially depends on the existence of an intrinsic length scale associated with the breakdown of linear elasticity near crack tips, independently of whether the latter is related to nonlinear elasticity or to dissipation. (ii) It is a supercritical Hopf bifurcation, featuring a vanishing oscillations amplitude at onset. (iii) It is largely independent of the phenomenological forms of the degradation functions assumed in the phase-field framework to describe the cohesive zone, and of the velocity-dependence of the fracture energy Γ(v) that is controlled by the dissipation time scale in the Ginzburg-Landau-type evolution equation for the phase-field. These results substantiate the universal nature of the oscillatory instability in 2D. In addition, we provide evidence indicating that the tip-splitting instability is controlled by the limiting rate of elastic energy transport inside the crack tip region. The latter is sensitive to the wave-speed inside the dissipation zone, which can be systematically varied within the phase-field approach. Finally, we describe in detail the numerical implementation scheme of the employed phase-field fracture approach, allowing its application in a broad range of materials failure problems.more » « less
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