Showing papers on "Fracture (geology) published in 2005"

Fracture of brittle metallic glasses: brittleness or plasticity.

Abstract: We report a brittle Mg-based bulk metallic glass which approaches the ideal brittle behavior. However, a dimple structure is observed at the fracture surface by high resolution scanning electron microscopy, indicating some type of "ductile" fracture mechanism in this very brittle glass. We also show, from the available data, a clear correlation between the fracture toughness and plastic process zone size for various glasses. The results indicate that the fracture in brittle metallic glassy materials might also proceed through the local softening mechanism but at different length scales.

Cohesive models for damage evolution in laminated composites

Abstract: A trend in the last decade towards models in which nonlinear crack tip processes are represented explicitly, rather than being assigned to a point process at the crack tip (as in linear elastic fracture mechanics), is reviewed by a survey of the literature. A good compromise between computational efficiency and physical reality seems to be the cohesive zone formulation, which collapses the effect of the nonlinear crack process zone onto a surface of displacement discontinuity (generalized crack). Damage mechanisms that can be represented by cohesive models include delamination of plies, large splitting (shear) cracks within plies, multiple matrix cracking within plies, fiber rupture or microbuckling (kink band formation), friction acting between delaminated plies, process zones at crack tips representing crazing or other nonlinearity, and large scale bridging by through-thickness reinforcement or oblique crack-bridging fibers. The power of the technique is illustrated here for delamination and splitting cracks in laminates. A cohesive element is presented for simulating three-dimensional, mode-dependent process zones. An essential feature of the formulation is that the delamination crack shape can follow its natural evolution, according to the evolving mode conditions calculated within the simulation. But in numerical work, care must be taken that element sizes are defined consistently with the characteristic lengths of cohesive zones that are implied by the chosen cohesive laws. Qualitatively successful applications are reported to some practical problems in composite engineering, which cannot be adequately analyzed by conventional tools such as linear elastic fracture mechanics and the virtual crack closure technique. The simulations successfully reproduce experimentally measured crack shapes that have been reported in the literature over a decade ago, but have not been reproduced by prior models.

Disk-shaped Compact Tension Test for Asphalt Concrete Fracture

Abstract: A disk-shaped compact tension (DC(T)) test has been developed as a practical method for obtaining the fracture energy of asphalt concrete. The main purpose of the development of this specimen geometry is the ability to test cylindrical cores obtained from in-place asphalt concrete pavements or gyratory-compacted specimens fabricated during the mixture design process. A suitable specimen geometry was developed using the ASTM E399 standard for compact tension testing of metals as a starting point. After finalizing the specimen geometry, a typical asphalt concrete surface mixture was tested at various temperatures and loading rates to evaluate the proposed DC(T) configuration. The variability of the fracture energy obtained from the DC(T) geometry was found to be comparable with the variability associated with other fracture tests for asphalt concrete. The ability of the test to detect changes in the fracture energy with the various testing conditions (temperature and loading rate) was the benchmark for determining the potential of using the DC(T) geometry. The test has the capability to capture the transition of asphalt concrete from a brittle material at low temperatures to a more ductile material at higher temperatures. Because testing was conducted on ungrooved specimens, special care was taken to quantify deviations of the crack path from the pure mode I crack path. An analysis of variance of test data revealed that the prototype DC(T) can detect statistical differences in fracture energy resulting for tests conducted across a useful range of test temperatures and loading rates. This specific analysis also indicated that fracture energy is not correlated to crack deviation angle. This paper also provides an overview of ongoing work integrating experimental results and observations with numerical analysis by means of a cohesive zone model tailored for asphalt concrete fracture behavior.

Toughness-dominated Hydraulic Fracture with Leak-off

Abstract: This paper considers the problem of a hydraulic fracture in which an incompressible Newtonian fluid is injected at a constant rate to drive a fracture in a permeable, infinite, brittle elastic solid. The two cases of a plane strain and a penny-shaped fracture are considered. The fluid pressure is assumed to be uniform and thus the lag between the fracture front and the fluid is taken to be zero. The validity of these assumptions is shown to depend on a parameter, which has the physical interpretation of a dimensionless fluid viscosity. It is shown that when the dimensionless viscosity is negligibly small, the problem depends only on a single parameter, a dimensionless time. Small and large time asymptotic solutions are derived which correspond to regimes dominated by storage of fluid in the fracture and infiltration of fluid into the rock, respectively. Evolution from the small to the large time asymptotic solution is obtained using a fourth order Runge–Kutta method.

Analysis of b-value and improved b-value of acoustic emissions accompanying rock fracture

Abstract: Acoustic emissions (AE) produced during the compressive fracture of a brittle rock have been subjected to detailed analysis using an advanced software for the computation of b-value as well as improved b-value. Conventionally, the b-value of AE is calculated using the Gutenberg-Richter relationship, which is widely used in seismology. Determination of improved b-value is a new approach, which is computed from AE amplitude distribution data. It involves filtering of high and low amplitude AE hits (or events) in a selective manner. The results obtained by both these methods to evaluate the fracture process in the rock are compared and discussed.

Multicomponent fluid flow by discontinuous Galerkin and mixed methods in unfractured and fractured media

Abstract: [1] A discrete fracture model for the flow of compressible, multicomponent fluids in homogeneous, heterogeneous, and fractured media is presented in single phase In the numerical model we combine the mixed finite element (MFE) and the discontinuous Galerkin (DG) methods We use the cross-flow equilibrium concept to approximate the fractured matrix mass transfer The discrete fracture model is numerically superior to the single-porosity model and overcomes limitations of the dual-porosity models including the use of a shape factor The MFE method provides a direct and accurate approximation for the velocity field, which is crucial for the convective terms in the flow equations The DG method associated with a slope limiter is used to approximate the species balance equations This method can capture the sharp moving fronts The calculation of the fracture-fracture flux across three and higher intersecting fracture branches is a challenge In this work, we provide an accurate approximation of these fluxes by using the MFE formulation Numerical examples in unfractured and fractured media illustrate the efficiency and robustness of the proposed numerical model

Investigation of the Fracture Resistance of Hot-Mix Asphalt Concrete Using a Disk-Shaped Compact Tension Test

Abstract: In recent years the transportation materials research community has focused a great deal of attention on the development of testing and analysis methods to shed light on fracture development in asphalt pavements. Recently it has been shown that crack initiation and propagation in asphalt materials can be realistically modeled with cutting-edge computational fracture mechanics tools. However, much more progress is needed toward the development of practical laboratory fracture tests to support these new modeling approaches. The goal of this paper is twofold: (a) to present a disk-shaped compact tension [DC(T)] test, which appears to be a practical method for determining low-temperature fracture properties of cylindrically shaped asphalt concrete test specimens, and (b) to illustrate how the DC(T) test can be used to obtain fracture properties of asphalt concrete specimens obtained from field cores following dynamic modulus and creep compliance tests performed on the same specimens. Testing four mixtures wit...

Development of a Single-Edge Notched Beam Test for Asphalt Concrete Mixtures

Abstract: This paper describes the development of a fracture test for determining the fracture energy of asphalt concrete. The test will be used in combination with numerical analysis and field studies to obtain a better understanding of the mechanisms of reflective cracking in asphalt concrete overlays. A review of the literature revealed that a single-edge notched beam (SE(B)) test specimen was the most promising fracture test for the objectives of the reflective cracking study. Existing servohydraulic testing equipment was modified to perform the SE(B) test along with new loading fixtures, sensors, data collection, and analysis procedures. Preliminary tests were conducted to develop test procedures, to obtain a better understanding of crack-front characteristics, to investigate test repeatability, to examine variations of fracture energy with temperature, and to investigate mixed-mode fracture. The results from the tests follow expected trends and test variability appears to be within a range typical for asphalt concrete fracture testing.

A model for P-wave attenuation and dispersion in a porous medium permeated by aligned fractures

Abstract: SUMMARY Fractures in a porous rock can be modelled as very thin and highly porous layers in a porous background. First, a dispersion equation for a P wave propagating in periodically layered poroelastic medium is obtained using propagator matrix approach applied to Biot equations of poroelasticity with periodic coefficients. Then in the limit of low stiffness and thickness this dispersion equation yields an expression for the effective P-wave modulus of the fractured porous material. When both pores and fractures are dry, this material is equivalent to a transversely isotropic elastic porous material with linear–slip interfaces. When saturated with a liquid this material exhibits significant attenuation and velocity dispersion due to wave-induced fluid flow between pores and fractures. In the low-frequency limit the material properties are equal to those obtained by anisotropic Gassmann (or Brown–Korringa) theory applied to a porous material with linear-slip interfaces. At low frequencies inverse quality factor scales with the first power of frequency ω. At high frequencies the effective elastic properties are equal to those for isolated fluid-filled fractures in a solid (non-porous) background, and inverse quality factor scales with ω−1/2. The magnitude of both attenuation and dispersion strongly depends on both the degree of fracturing and background porosity of the medium. The characteristic frequency of the attenuation and dispersion depends on the background permeability, fluid viscosity, as well as fracture density and spacing.

Constraint effects in adhesive joint fracture

Abstract: Constraint effects in adhesive joint fracture are investigated by modelling the adherents as well as a finite thickness adhesive layer in which a single row of cohesive zone elements representing the fracture process is embedded. Both the adhesive and the adherents are elastic-plastic with strain hardening. The bond toughness Gamma(work per unit area) is equal to Gamma(0) + Gamma(p), where Gamma(0) is the intrinsic work of fracture associated with the embedded cohesive zone response and FP is the extra contribution to the bond toughness arising from plastic dissipation and stored elastic energy within the adhesive layer. The parameters of the model are identified from experiments on two different adhesives exhibiting very different fracture properties. Most of the tests were performed using the wedge-peel test method for a variety of adhesives, adherents and wedge thicknesses. The model captures the constraint effects resulting from the change in Gamma(p): (i) the plastic dissipation increases with increasing bond line thickness in the fully plastic regime and then decreases to reach a constant value for very thick adhesive layers; (ii) the plastic dissipation in the fully plastic regime increases drastically as the thickness of the adherent decreases. Finally, this model is used to assess a simpler approach which consists of simulating the full adhesive layer as a single row of cohesive elements. (c) 2005 Elsevier Ltd. All rights reserved.

Plane-Strain Propagation of a Fluid-Driven Fracture: Small Toughness Solution

Abstract: The paper considers the problem of a plane-strain fluid-driven fracture propagating in an impermeable elastic solid, under condition of small (relative) solid toughness or high (relative) fracturing fluid viscosity. This condition typically applies in hydraulic fracturing treatments used to stimulate hydrocarbons-bearing rock layers, and in the transport of magma in the lithosphere. We show that for small values of a dimensionless toughness K, the solution outside of the immediate vicinity of the fracture tips is given to O1 by the zero-toughness solution, which, if extended to the tips, is characterized by an opening varying as the 2/3 power of the distance from the tip. This near tip behavior of the zero-toughness solution is incompatible with the Linear Elastic Fracture Mechanics (LEFM) tip asymptote characterized by an opening varying as the 1/2 power of the distance from the tip, for any nonzero toughness. This gives rise to a LEFM boundary layer at the fracture tips where the influence of material toughness is localized. We establish the boundary layer solution and the condition of matching of the latter with the outer zero-toughness solution over a lengthscale intermediate to the boundary layer thickness and the fracture length. This matching condition, expressed as a smallness condition on K, and the corresponding structure of the overall solution ensures that the fracture propagates in the viscosity-dominated regime, i.e., that the solution away from the tip is approximately independent of toughness. The solution involving the next order correction in K to the outer zero-toughness solution yields the range of problem parameters corresponding to the viscosity-dominated regime. DOI: 10.1115/1.2047596

Designing Against Size Effect on Shear Strength of Reinforced Concrete Beams Without Stirrups: I. Formulation

Abstract: The shear failure of reinforced concrete beams is a very complex fracture phenomenon for which a purely mathematical approach is not possible at present. However, detailed modeling of the fracture mechanism is not necessary for establishing the general form of the size effect. The first part of this paper shows that the general approximate mathematical form of the size effect law to be calibrated by experimental data can be deduced from two facts: (1) the failure is caused by cohesive (or quasibrittle) fracture propagation; and (2) the maximum load is attained only after large fracture growth (rather than at fracture initiation). Simple dimensional analysis yields the asymptotic properties of size effect, which are characterized by: (1) a constant beam shear strength vc (i.e., absence of size effect) for sufficiently small beam depths; and (2) the linear elastic fracture mechanics size effect vc ∼ d−1∕2 for very large beam depths d . Together with the recently established small- and large-size second-orde...

Localization of mining-induced horizontal fractures along rock layer interfaces in overburden: field measurements and prediction

Abstract: The locations of mining-induced horizontal fractures along rock interfaces in the overburden of Donetsk Coal Basin were identified using an original experimental device. The device traps methane from horizontal fracture zone (100–fold coal seam thickness) over an active longwall mining excavation. Presence or absence of horizontal fractures along rock layer interfaces is correlated with physical characteristics of the overburden, such as thickness, uniaxial compressive strength of overburden rock layers, location of rock layer interfaces and thickness of extracted coal seams. As a result, a combined criterion based on these physical characteristics is proposed to predict the presence of overburden horizontal fracturing in coal mine operations.

Relationship between internal porosity and fracture strength of die-cast magnesium AM60B alloy

Abstract: A die-cast magnesium alloy was examined with the use of X-ray tomography. Five tensile samples cut from different locations of a thin-walled, high-pressure magnesium die-casting were analyzed. The size and locations of pores in each sample were obtained from the X-ray tomography data. A critical local strain model was used to predict the fracture properties of the tensile samples. The validity of the model was exhibited by comparison of the predicted results with results from tensile tests. The location of the plane of fracture, the fracture strain, and the fracture stress were predicted to within 8%, 22%, and 11% accuracy, respectively. It was concluded that the local areal fraction of porosity is the primary factor in determining the tensile properties of the magnesium alloy specimens.

Fracture toughness determination and micromechanics of rock under mode I and mode II loading

Abstract: (TYPE=)This thesis work describes a new experimental method for the determination of Mode II (shear) fracture toughness, KIIC, of rock and compares the outcome to results from Mode I (tensile) fracture toughness, KIC, testing using the International Society of Rock Mechanics (ISRM) Chevron-Bend (CB-) method. The fracture toughness describes the resistance of rock to fracturing. This parameter is therefore important when estimating the failure of rock and rock structures using rock fracture mechanics principles. Critical Mode I fracture growth at ambient conditions was studied by carrying out a series of experiments on a clay bearing sandstone at different loading rates, i.e. clip-gage opening rates of 5·10‑6 m/s to 5·10‑10 m/s. The range of loading rates provides macroscopic fracture velocities that have been shown to cause time-dependent fracture growth in other test set-ups. The mechanical data shows that time- and loading rate dependent crack growth occurs in the test material. Crack density measurements on scanning electron microscopy micrographs show constant size of the symmetric fracture process zone (~ 700-800 µm) independent of loading rate. Fracture surface roughness is constant for all loading rates. Acoustic emission location data demonstrates that the fracture process zone has a constant size of 5 mm in width and ~ 20 mm in length. The number of located acoustic emission events decreases with slower loading rates. The fracture propagating in the CB-samples is therefore not a pure Mode I fracture on the microscale. On the macroscale the fracture propagates co-planar under the Mode I loading. Mode I fracture toughness was determined on six rock types, i.e. Flechtingen sandstone, Rudersdorf limestone, Carrara marble, Aspo diorite, Mizunami granite, and Aue granite. KIC is 1.2 MPa m1/2, 1.1 MPa m1/2, 2.4 MPa m1/2, 3.8 MPa m1/2, 2.4 MPa m1/2, and 1.6 MPa m1/2, respectively. The newly developed set-up for determination of the Mode II fracture toughness is called the Punch-Through Shear (PTS-) test. It uses drill core that is available from most engineering site investigations. Notches were drilled to the end surfaces of 50 mm long samples. These act as friction free initial fractures. An axial load punches down the central cylinder introducing a high localised shear load in the remaining rock bridge. To the mantle of the cores a confining pressure may be applied to simulate a normal stress on the shear zone. The application of confining pressure favours the growth of Mode II fractures as large pressures suppress the growth of tensile (Mode I) cracks. The stress intensity factor at the critical loading condition in the PTS- test is calculated using a Displacement Extrapolation Technique (DET) based on Finite Element Modelling (FEM). Comparison of the results to KIIC values from other estimation methods confirmed the results. Mode II loading experiments were carried out on the same six rock types as used in Mode I testing.Unstable macroscopic shear fracture growth is achieved at peak load in the PTS-test. Cyclic loading in the post peak region provides controlled fracture propagation and shows constant compliance change for the different rock types. Variation of displacement rates from 3.3·10-8 to 1.7·10‑3 m/s do not change the calculated critical stress intensity factor for most rock types. Variation of geometrical parameters, i.e. notch depth, notch diameter, notch width, and sample diameter, leads to an optimisation of the PTS- geometry. Increase of confining pressure, i.e. normal load, on the shear zone increases KIIC bi-linear. High slope is observed at low confining pressures (< 30 MPa); at pressures above 30 MPa low slope increase is evident. The maximum confining pressure, P, applied is 70 MPa. KIIC increases for the Aspo diorite from 5.1 (at P = 0 MPa) to 12.4 MPa m1/2 (at P = 70 MPa), for Aue granite from 4.1 to 13.2 MPa m1/2, for Mizunami granite from 4.9 to 14.2 MPa m1/2, for Carrara marble from 3.1 to 7.9 MPa m1/2, for Flechtingen sandstone from 1.9 to 5.4 MPa m1/2, and for Rudersdorf limestone from 2.3 to 6.7 MPa m1/2. With increase of shear stress from axial loading, primary macroscopic wing fractures develop at about 30 % of the maximum stress. They propagate out of the stressed zone and stop. Further elevation of shear stress results in development of a process zone leading to a secondary ‘shear’ fracture. Consequently the energy requirement for the formation of the two types of fractures is different. Increase of confining pressure to above 30 MPa is shown to suppress the wing fractures. Carrara marble develops an asymmetric process zone with two different regimes of preferred microcrack orientation and a straight main separation. The acoustic emission analysis indicates mixed mode cracking on the microscale. Increase of confining pressure changes the orientation of the main fracture and the cracks within the process zone. These tend to reach constant orientation at P = 30-50 MPa. The Punch-Through Shear (PTS-) test provides controlled testing conditions and reproducible results. Five different evaluation approaches give consistent results for the Mode II fracture toughness. The asymmetry of the evolving fracture process zone in Carrara marble was shown. This result is consistent with the prediction from stress field analysis and it has also been observed in field studies of shear zones. The existence of Mode II fracture in rock is a matter of debate in the literature. Comparison of the results from Mode I and Mode II testing, mainly regarding the resulting fracture pattern, and correlation analysis of KIC and KIIC to physico-mechanical parameters emphasised the differences between the response of rock to Mode I and Mode II loading. On the microscale, neither the fractures resulting from Mode I the Mode II loading are pure mode fractures. On macroscopic scale, Mode I and Mode II do exist.

Method of estimating fracture geometry, compositions and articles used for the same

Abstract: Disclosed herein is a method of determining the fracture geometry of a subterranean fracture comprising introducing into the fracture a target particle and/or proppant; transmitting into the fracture electromagnetic radiation having a frequency of about 300 megahertz to about 100 gigahertz; and analyzing a reflected signal from the target particle to determine fracture geometry. Disclosed herein too is a method of determining the fracture geometry of a subterranean fracture comprising introducing into the fracture a target particle and/or proppant; wherein the target particle and/or proppant comprises a high dielectric constant ceramic having a dielectric constant of greater than or equal to about 2; transmitting into the fracture electromagnetic radiation having a frequency of less than or equal to about 3 gigahertz; and analyzing a reflected signal from the target particle and/or proppant to determine fracture geometry.