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Understanding the inconsistent rock fracture toughness (KIc) measurement results from different test specimen geometries helps provide suitable fracture parameters for engineering applications, predict rock fracture load, and assess the safety of flawed rock engineering structures. In this study, fracture experiments using full- or half-disc specimens with chevron notches or straight-through notches were conducted. Experimental results show that the notch types and loading methods (Brazilian-type diametric compression and three-point bending) significantly affect the KIc measurements. It is indicated that only considering the T-stress or fracture process zone (FPZ) alone cannot explain the test results well, while a good agreement is found between the experimental results and the interpretation based on the combined effects of T-stress and FPZ. Moreover, Brazilian-type compression and three-point bending under a short support span can make the full- or half-disc specimens have higher negative T-stress and larger FPZ, thus producing lower KIc values than three-point bending under a relatively long support span. Compared with KIc measurements using the straight-through notch specimens, those utilizing the chevron-notched ones are less affected by FPZ and yield higher KIc results, providing that the loading method is the same. The notch types have little impact on the T-stresses of the specimens. This study sheds light on the combined influence of T-stress and FPZ on rock fracturing.

The International Society for Rock Mechanics has so far developed two standard methods for the determination of static fracture toughness of rock. They used three different core-based specimens and tests were to be performed on a typical laboratory compression or tension load frame. Another method to determine the mode I fracture toughness of rock using semi-circular bend specimen is herein presented. The specimen is semi-circular in shape and made from typical cores taken from the rock with any relative material directions noted. The specimens are tested in three-point bending using a laboratory compression test instrument. The failure load along with its dimensions is used to determine the fracture toughness. Most sedimentary rocks which are layered in structure may exhibit fracture properties that depend on the orientation and therefore measurements in more than one material direction may be necessary. The fracture toughness measurements are expected to yield a size-independent material property if certain minimum specimen size requirements are satisfied.

Rock naturally contains numerous defects, and both loading rate and defect geometry affect the loading capacity of rock structures when subjected to dynamic impact loads. Understanding the rate-dependent mechanical response and characterizing geometry-related fracture parameter of defected rocks are crucial to safety assessment of rock engineering. In this paper, the effects of loading rate and notch parameter on dynamic brittle fracture behavior of Fangshan granite weakened by a blunt V-notch are experimentally studied. First, the dynamic fracture experiments on blunt V-notched semi-circular bend (BVNSCB) specimen of Fangshan granite with different notch geometries are performed using the split Hopkinson pressure bar (SHPB) system. Second, the dynamic fracture processes of blunt V-notched rocks are recorded using an ultrahigh-speed camera, and the mechanical responses to different impact loading conditions are obtained via digital image correlation (DIC) method. Third, the effects of loading rate and notch parameter on the dynamic fracture parameters including notch fracture toughness, crack propagation toughness, and crack velocity are discussed to reveal the fracture mechanism of blunt V-notched rocks subjected to impact loads. It is found that dynamic notch fracture toughness obtained from DIC method is usually larger than that measured directly from conventional maximum impact load method. The maximum tangential stress (MTS) criterion eliminating the effect of the fracture process zone (FPZ) at blunt V-notch tip is used to correct the apparent notch fracture toughness value measured from the maximum load method. The results show that corrected notch fracture toughness values are in good agreements with those obtained from the DIC method. This study is significant for dynamic fracture analyses and strength assessments of rock masses containing notches or other defects with complex geometry.HighlightsEffects of loading rate and notch geometry on dynamic fracture behavior of blunt V-notched rocks are studied.Dynamic notch fracture toughness and crack propagation toughness are simultaneously determined.DIC method is used to track the development of FPZ at blunt V-notch tip and quantify the FPZ length.

This article discusses the scale dependence of the mode I fracture toughness of rocks measured via the semi-circular bend (SCB) test. An extensive set of experiments is conducted to scrutinise the fracture toughness variations with size for three distinct rock types with radii ranging from 25 to 300 mm. The lengths of the fracture process zone (FPZ) for different sample sizes are measured using the digital image correlation (DIC) technique. A theoretical model is also established that relates the value of fracture toughness to the sample size. This theorem is based on the strip-yield model to estimate the length of FPZ, and the energy release rate concept to relate the FPZ length to the fracture toughness. This theoretical model does not rely on any experimental-based curve-fitting parameter, but only on the tensile strength of the rock type as well as the fracture toughness at a specific sample size. The size effects predicted by the theoretical model is in a good agreement with the experimental data on both fracture toughness and the FPZ length. Finally, theoretical correction factors are introduced for various geometrical configurations of the SCB specimen, using which a scale-independent mode I fracture toughness of the rock material can be estimated from the results of experiments performed on small samples.

Purpose The purpose of this paper is to investigate the effect of layer orientation on the tensile, flexural and fracture behavior of additively manufactured (AM) polycarbonate (PC) produced using fused deposition modeling (FDM). Design/methodology/approach An experimental approach is undertaken and a total number of 48 tests are conducted. Two types of tensile specimens are used and their mechanical behavior and fracture surfaces are studied. Also, circular parts with different layer orientations are printed and two semi-circular bending (SCB) samples are extracted from each part. Finally, the results of samples with different build directions are compared to one another to better understand the mechanical behavior of additively manufactured PC. Findings The results demonstrate anisotropy in the tensile, flexural and fracture behavior of the additively manufactured PC parts with the latter being less anisotropic compared to the first two. It is also demonstrated that the anisotropy of the elastic modulus is small and can be neglected. Tensile strength ranges from 40 MPa to 53 MPa. At the end, mode I fracture toughness prediction curves are provided for different directions of the FDM samples. Fracture toughness ranges from 1.93 to 2.37 MPa.mm1/2. Originality/value The SCB specimen, a very suitable geometry for characterizing anisotropic materials, was used to characterize FDM parts for the first time. Also, the fracture properties of the AM PC have not been studied by the researchers in the past. Therefore, fracture toughness prediction curves are presented for this anisotropic material. These curves can be very suitable for designing parts that are going to be produced by 3D printing. Moreover, the effect of the area to perimeter ratio on the tensile properties of the printed parts is investigated.

High-strength concrete (HSC) and polypropylene fiber-reinforced concrete (PPFRC) as quasi-brittle materials generally experience fracture failure either in mode I (tensile mode) or in mixed mode I and II (tensile and shear), which are the most common forms of damage in structural engineering. This study investigates the fracture behavior of HSC and PPFRC under Mode I and mixed-mode loading conditions. Both numerical simulation and experimental investigation were conducted to analyze the fracture toughness and crack paths of Semi-Circular Bend (SCB) specimens. The Extended Finite Element Method (X-FEM) was employed in the numerical simulations to model crack propagation under different modes of mixtures. The experimental results showed that the crack followed a curvilinear trajectory under mixed mode loading while propagating parallel to the applied load under pure Mode I loading. The numerical simulations using X-FEM demonstrated good agreement with the experimental results.

This study presents a novel phase-field model for ductile fracture by the introduction of both the plastic driving force and the degrading fracture toughness into crack phase-field computations based on the phenomenological justification for ductile fracture in elastoplastic materials. Assuming that the constitutive work density consists of elastic, pseudo-plastic and crack components, we derive the governing equations from local and global optimization problems within the continuum thermodynamics framework. In addition to the elastic strain energy, the plastic strain energy also works as a driving force to sustain damage evolution. Additionally, we introduce a degrading fracture toughness to reflect the evolution of micro-defects and their coalescences into each other that are caused by accumulated plastic deformation. Equipped with these ingredients, the proposed model realizes the reduction of both stiffness and fracture toughness to simulate the failure phenomena of elastoplastic materials. Several numerical examples are presented to demonstrate the capability of the proposed model in reproducing some typical ductile fracture behaviors. The findings and perspectives are subsequently summarized.

This paper outlines the development of a fracture height growth prediction model that uses the modified rock mechanical properties obtained from a combination of fluid flow and rock material property behavior and applies them during the calibration process to match actual treatment data resulting fracture height growth evolution and profile. The traditional fracture growth models are closely linked with the fracture toughness parameter which is not only difficult to estimate but is also considered dynamic in nature as it may assume various geometry-dependent values rather than a fixed input value. To account for this limitation, this study uses the fluid tip velocity to estimate apparent fracture toughness during the initial model setup process and continuously scales the model during the fracture growth prediction phase. The influence of controllable parameters such as injection rate and fluid viscosity on vertical growth of fractures was studied and applied to field examples. Analysis from the modeling work on two of the case histories presented, indicated a rapid fracture growth in the first few minutes of the treatment that was proportional to the rate of net pressure gain. The influence of the fracture tip on the fracture pressures in the tip region is visible only in the early part of the treatment and are relatively short-lived especially once the contribution from viscous flow pressures dominates the pressure behavior. The findings are presented in detail and are helpful from a treatment planning and execution viewpoint as they provide a detailed insight into fracture propagation. Relevant theory, equations and workflow adopted during the study are presented for ready adaptation in the field.

Thermally conductive polymer nanocomposites integrated with lightweight, excellent flexural strength, and high fracture toughness ( K Ic ) would be of great use in many fields. However, achieving all of these properties simultaneously remains a great challenge. Inspired by natural nacre, here we demonstrate a lightweight, strong, tough, and thermally conductive boron nitride nanosheet/epoxy layered (BNNEL) nanocomposite. Because of the layered structure and enhancing the interfacial interactions through hydrogen bonding and Si–O–B covalent bonding, the resulting nacre-inspired BNNEL nanocomposites show high fracture toughness of ∼ 4.22 MPa·m 1/2 , which is 7 folds as high as pure epoxy. Moreover, the BNNEL nanocomposites demonstrate sufficient flexural strength (∼ 168.90 MPa, comparable to epoxy resin), while also being lightweight (∼ 1.23 g/cm 3 ). Additionally, the BNNEL nanocomposites display a thermal conductivity ( κ ) of ∼ 0.47 W/(m·K) at low boron nitride nanosheet loading of 2.08 vol.%, which is 2.7 times higher than that of pure epoxy resin. The developed nacre-inspired strategy of layered structure design and interfacial enhancement provides an avenue for fabricating high mechanical properties and thermally conductive polymer nanocomposites.

In this contribution, a novel framework for simulating mixed-mode failure in rock is presented. Based on a hybrid phase-field model for mixed-mode fracture, separate phase-field variables are introduced for tensile (mode I) and shear (mode II) fracture. The resulting three-field problem features separate length scale parameters for mode I and mode II cracks. In contrast to the classic two-field mixed-mode approaches, it can thus account for different tensile and shear strength of rock. The two phase-field equations are implicitly coupled through the degradation of the material in the elastic equation, and the three fields are solved using a staggered iteration scheme. For its validation, the three-field model is calibrated for two types of rock, Solnhofen Limestone and Pfraundorfer Dolostone. To this end, double-edge notched Brazilian disk (DNBD) tests are performed to determine the mode II fracture toughness. The numerical results demonstrate that the proposed phase-field model is able to reproduce the different crack patterns observed in the DNBD tests. A final example of a uniaxial compression test on a rare drill core demonstrates that the proposed model is able to capture complex, 3D mixed-mode crack patterns when calibrated with the correct mode I and mode II fracture toughness.