Evaluation of mode I fracture characteristics, such as critical opening displacement and process-zone length, is fundamental for the analysis and prediction of crack growth. To identify deformation ...with micron-scale resolution, experiments were performed using digital image correlation, where displacement is determined through a comparison of a pair of digital images by matching a small area from the image before deformation to the image after deformation. The matching process uses a cross-correlation algorithm, and within this study, the correlation is based on a Fast Fourier Transform method. Mode I fracture tests were performed on Berea sandstone using three-point bending. Twelve specimens, of three types, were fabricated: six center notch (0.5mm radius), three smooth boundary, and three reduced-section (6 or 12mm radius notch). The characteristics of tensile fracture, namely opening displacement and crack length, were extracted from detailed displacement measurements. At the onset of unstable propagation (peak load) for the center notch specimens, the critical opening displacement ωc=30μm at the notch tip, and as the crack propagated, the known position of ωc allowed the identification of the process zone throughout the post-peak response. Incremental displacement contours established the tip of the effective crack, and the length of the process zone lp=5–7mm, about 10 times the maximum grain size. In addition, it was observed that the process zone maintained a constant length with constant critical opening for all tests.
► Digital image correlation is used to characterize fracture processes in Berea sandstone. ► Three types of specimens, including center notch (0.5mm radius), smooth boundary, and reduced-section (6 or 12mm radius notch) are tested in the experiments. ► The detailed information involves critical opening displacement ωc=30μm and the length of the process zone lp=5–7mm, about 10 times the grain size.
Elastic and inelastic deformation of fluid-saturated rock Makhnenko, Roman Y.; Labuz, Joseph F.
Philosophical transactions - Royal Society. Mathematical, Physical and engineering sciences/Philosophical transactions - Royal Society. Mathematical, physical and engineering sciences,
10/2016, Volume:
374, Issue:
2078
Journal Article
Peer reviewed
Open access
In situ rock is often saturated with fluid, the presence of which affects both elastic parameters and inelastic deformation processes. Techniques were developed for testing fluid-saturated porous ...rock under the limiting conditions of drained (long-term), undrained (short-term) and unjacketed (solid matrix) response in hydrostatic, axisymmetric and plane-strain compression. Drained and undrained poroelastic parameters, including bulk modulus, Biot and Skempton coefficients, of Berea sandstone were found to be stress dependent up to 35 MPa mean stress, and approximately constant at higher levels of loading. The unjacketed bulk modulus was measured to be constant for pressure up to 60 MPa, and it appears to be larger than the unjacketed pore bulk modulus. An elasto-plastic constitutive model calibrated with parameters from drained tests provided a first-order approximation of undrained inelastic deformation: dilatant hardening was observed due to pore pressure decrease during inelastic deformation of rock specimens with constant fluid content.
This article is part of the themed issue ‘Energy and the subsurface’.
•Fracture initiation in a quasi-brittle material is studied using the three-point bending test.•Specimens were notched at various lengths and positions of the beam edge to produce the desired ...mixed-mode loading condition.•An implicit micropolar peridynamic model is used to simulate the fracture initiation and propagation process.•The conceived peridynamic formulation is extended to fracture problems.•Numerical results were compared with experimental data obtained from electronic speckle pattern interferometry (ESPI) tests.
Mode I opening and mixed-mode I-II fracture experiments were performed with a homogeneous, fine grained sandstone using the three-point bending test. Specimens were notched at various lengths and positions of the beam edge to produce the desired loading condition. A micropolar peridynamic model was used to simulate the fracture initiation and propagation process. The analytical implicit formulation was derived by defining a specific macroelastic energy density function for micropolar non-local lattices, which depends on three deformation parameters: bond stretch, bond shear deformation accounting for the rotational degrees of freedom, and the particle’s relative rotation. The micropolar non-local lattice model is capable of handling a variable Poisson’s ratio, and is suitable for modelling the mechanical behavior of Cauchy isotropic solids subjected to non-homogeneous deformation fields and fracture. A preliminary analysis on a smooth boundary specimen was performed in order to validate the results obtained with the conceived peridynamic model adopting irregular discretizations. The failure process in notched sandstone specimens was simulated numerically in quasi-static conditions. Numerical results were compared with experimental data obtained from electronic speckle pattern interferometry (ESPI) tests, which were used to quantify and detect the fracture phenomena. Due to the intrinsic features of peridynamic theory, realistic crack patterns and crack initiation angles were obtained from the numerical simulations.
•AE and DIC were used to study the nature of microcracking in a brittle rock.•The AE source was modeled as a crack-only mechanism using the moment tensor.•Microcracks were locally mixed-mode dominant ...due to oblique microcrack planes.•Source mechanisms decomposed in the global coordinate system indicated opening.•The AE energy was a small percent of the fracture energy.
Acoustic emission (AE) and digital image correlation were used to monitor mode I fracture in center notch and smooth boundary specimens. The AE source was characterized as a microcrack and represented by the moment tensor, which was obtained by minimizing the error between displacements calculated from an elastodynamic solution and those measured, subjected to the constraint of a microcrack source. Results showed that microcracking was locally mixed-mode dominant because of oblique microcrack planes within a tortuous fracture. However, the microcrack mechanisms decomposed in the global coordinate system indicated mainly mode I opening with modes II and III ten times smaller.
Silicon carbide (SiC) fiber‐reinforced SiC matrix (SiC/SiC) composites have emerged as a new material candidate for fuel claddings in light water reactors. Recent studies showed that the load ...capacity of SiC/SiC materials exhibits a considerable statistical variation. Therefore, reliability analysis plays a critical role in design of SiC/SiC composite claddings. This paper presents a probabilistic model for the lifetime distribution of SiC/SiC composites. The model is anchored by a multiaxial stress‐based failure criterion and subcritical damage accumulation mechanism. Based on the kinetics of subcritical damage growth, the lifetime distribution of a laboratory test specimen for any given loading history can be calculated. A finite weakest‐link model is used to extrapolate the lifetime distribution of test specimens to full‐length claddings. It is shown that the damage accumulation mechanism has a strong influence on the lifetime distribution of the cladding. This finding highlights the importance of understanding the static fatigue behavior of SiC/SiC composites. The present analysis also demonstrates an intricate length effect on the failure probability of the cladding, which is expected to play a crucial role in design extrapolation.
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•Opening and mixed mode fracture processes were characterized by digital imaging.•The cohesive zone was dominated by opening displacement under mixed mode loading.•Opening ...displacement at peak was 45μm for mixed mode, 30μm for mode I fracture.•Cohesive zone length was 10–12mm for mixed mode, 5–7mm for mode I fracture.
Fracture tests were performed on sandstone specimens under three-point bending with a variety of notch positions to achieve KII/KI=0–12%. At peak load, the maximum crack opening displacement measured by digital image correlation was 45μm under mixed mode loading and 30μm under mode I, and these values were used to determine the length of the cohesive zone: 10–12mm for mixed mode and 5–7mm for mode I. For mixed mode fracture, the displacement in the cohesive zone was identified to be opening only, while sliding and opening were detected along the remaining length.
•Acoustic emission (AE) and digital image correlation (DIC) were used for observations.•Complementary information by AE and DIC characterizes the fracture process zone (FPZ).•Energy evaluation by AE ...and DIC is consistent with a linear softening law for the FPZ.•The FPZ length of sandstone is about 10 times longer than the maximum grain size.•Fracture energy of sandstone is estimated seven times greater than that based on LEFM.
Acoustic emission (AE) and digital image correlation (DIC) were used to characterize the fracture process zone (FPZ) in Berea sandstone, a quasi-brittle material with a maximum grain size of 1 mm. The complementary techniques of AE and DIC provide information on (i) damage throughout the volume, including AE locations and relative energy, and (ii) detailed DIC measurements of opening displacements associated with the FPZ. Three types of specimens were tested by three-point bending: center notch, smooth boundary, and large radius center notch. Experimental results indicate the following: (1) The length of FPZ is about 10 times longer than the maximum grain size. (2) The evaluation of energy based on the two different measurements, AE and DIC, is consistent with a linear softening law for the FPZ. (3) The fracture energy is estimated to be 120–140 J/m2, about seven times greater than the fracture energy based on linear fracture mechanics.
Rock fracture and the induced displacement field are investigated through physical and numerical experiments. A Berea sandstone specimen with a central notch was tested in three-point bending. ...Digital image correlation (DIC) was used to obtain the displacement patterns as the fracture initiated and propagated. The DIC results clearly show the development of a damage zone and displacement discontinuity along the center line of the beam at peak load. It is suggested that a traction-free or cohesionless crack may exist before the unstable growth, a condition normally ruled out in the literature based on numerical modeling within the frame work of a cohesive zone finite element analysis. In this note, the displacement profiles determined from DIC are compared with those from numerical simulations using (i) nonlinear finite element and (ii) bonded particle models. It is shown that the bonded particle model is capable of reproducing the physical displacement field with better accuracy compared to that from the finite element model with softening. Furthermore, as supported by experiments and bonded particle simulations, it appears that a cohesionless crack can develop at peak load, an observation that is not confirmed by the nonlinear finite element analysis.
•Fracture of rock and resulting crack displacements are studied.•Nonlinear fracture mechanics and bonded particle models are used for simulation.•The measured crack displacements using digital image correlation are reproduced by bonded particle model.•The bonded particle model suggests the existence of a cohesionless crack at peak load.
Highlights
Laboratory experiments were designed to measure Skempton coefficient
B
for Dunnville sandstone using small and large specimens.
The pore volume
V
p
of the small specimen was on the same ...order as the system volume
V
l
, while
V
p
of the large specimen was 100 times
V
l
.
The large specimen provided a direct measurement of
B
.
For Dunnville sandstone, Skempton coefficient
B
calculated with the appropriate poroelastic model and material parameters agrees with the measured
B
.
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