Showing papers on "Fracture (geology) published in 2006"

A mathematical model of stress generation and fracture in lithium manganese oxide

Abstract: Fracture of Li y Mn 2 O 4 is predicted with a numerical model that calculates the stress generated in spherical particles due to lithium intercalation along the 4-V plateau and phase change along the 3-V plateau. In the former case, fracture is probable at the rates typical of high-power applications, while in the latter case, the probability of fracture is linked not to the discharge rate or particle size, but to the LiMn 2 O 4 /Li 2 Mn 2 O 4 phase ratio. The two-phase material should fracture immediately upon lithium extraction. The effects of variation in thermodynamic factor, diffusion coefficient, and lattice parameter are examined in detail.

A scale-independent approach to fracture intensity and average spacing measurement

Abstract: Fracture intensity, the number of fractures per unit length along a sample line, is an important attribute of fracture systems that can be problematic to establish in the subsurface. Lack of adequate constraints on fracture intensity may limit the economic exploitation of fractured reservoirs because intensity describes the abundance of fractures potentially available for fluid flow and the probability of encountering fractures in a borehole. Traditional methods of fracture-intensity measurement are inadequate because they ignore the wide spectrum of fracture sizes found in many fracture systems and the consequent scale dependence of fracture intensity. An alternative approach makes use of fracture-size distributions, which allow more meaningful comparisons between different locations and allow microfractures in subsurface samples to be used for fracture-intensity measurement. Comparisons are more meaningful because sampling artifacts can be recognized and avoided, and because common thresholds of fracture size can be enforced for counting in different locations. Additionally, quantification of the fracture-size distribution provides a mechanism for evaluation of uncertainties. Estimates of fracture intensity using this approach for two carbonate beds in the Sierra Madre Oriental, Mexico, illustrate how size-cognizant measurements cast new light on widely accepted interpretation of geologic controls of fracture intensity.

Bedrock fracture by ice segregation in cold regions

Abstract: The volumetric expansion of freezing pore water is widely assumed to be a major cause of rock fracture in cold humid regions. Data from experiments simulating natural freezing regimes indicate that bedrock fracture results instead from ice segregation. Fracture depth and timing are also numerically simulated by coupling heat and mass transfer with a fracture model. The depth and geometry of fractures match those in Arctic permafrost and ice-age weathering profiles. This agreement supports a conceptual model in which ice segregation in near-surface permafrost leads progressively to rock fracture and heave, whereas permafrost degradation leads episodically to melt of segregated ice and rock settlement.

Prediction of instability in distal radial fractures.

Abstract: BackgroundEffective methods of treating an unstable distal radial fracture are described in the literature, but there is no reliable method of identifying an unstable fracture in time to initiate appropriate treatment. The purposes of this study were to identify the predictors of fracture instabilit

Experimental Rock Mechanics

Abstract: Fracture and flow of rocks under stress and their geophysical and seismological implications raise fundamental questions in rock mechanics, particularly in the areas of tectonophysics and seismology. This text exclusively addresses the deformation and fracture of rock specimens under general triaxial compression, in which all three principal stress

Dynamical fracture instabilities due to local hyperelasticity at crack tips

Abstract: As the speed of a crack propagating through a brittle material increases, a dynamical instability leads to an increased roughening of the fracture surface. Cracks moving at low speeds create atomically flat mirror-like surfaces; at higher speeds, rougher, less reflective ('mist') and finally very rough, irregularly faceted ('hackle') surfaces are formed. The behaviour is observed in many different brittle materials, but the underlying physical principles, though extensively debated, remain unresolved. Most existing theories of fracture assume a linear elastic stress-strain law. However, the relation between stress and strain in real solids is strongly nonlinear due to large deformations near a moving crack tip, a phenomenon referred to as hyperelasticity. Here we use massively parallel large-scale atomistic simulations--employing a simple atomistic material model that allows a systematic transition from linear elastic to strongly nonlinear behaviour--to show that hyperelasticity plays a governing role in the onset of the instability. We report a generalized model that describes the onset of instability as a competition between different mechanisms controlled by the local stress field and local energy flow near the crack tip. Our results indicate that such instabilities are intrinsic to dynamical fracture and they help to explain a range of controversial experimental and computational results.

Mixed mode brittle fracture in PMMA—An experimental study using SCB specimens

Abstract: A series of mixed mode I/II fracture tests is conducted on polymethylmethacrylate (PMMA) in the full range from pure mode I to pure mode II using a semi-circular bend (SCB) specimen containing an edge crack. The fracture load and the path of crack growth are obtained from experiments for various crack angles. It is shown that the conventional mixed mode I/II fracture criteria such as the maximum tangential stress (MTS) criterion overestimate the fracture strength of PMMA when the SCB specimen is used for fracture tests, particularly for mode II dominant loading conditions. However, improved predictions of fracture load are achieved when a generalized MTS criterion is employed. While the path of crack growth is straight for pure mode I, it deviates significantly from the angle of fracture initiation for pure mode II and mode II dominant loading conditions. It is shown that the path of crack growth predicted by the generalized MTS criterion is also in a good agreement with the observed fracture path in the fractured SCB samples.

A two-scale approach for fluid flow in fractured porous media

Abstract: A two-scale numerical model is developed for fluid flow in fractured, deforming porous media. At the microscale the flow in the cavity of a fracture is modelled as a viscous fluid. From the micromechanics of the flow in the cavity, coupling equations are derived for the momentum and the mass couplings to the equations for a fluid-saturated porous medium, which are assumed to hold on the macroscopic scale. The finite element equations are derived for this two-scale approach and integrated over time. By exploiting the partition-of-unity property of the finite element shape functions, the position and direction of the fractures is independent from the underlying discretization. The resulting discrete equations are non-linear due to the non-linearity of the coupling terms. A consistent linearization is given for use within a Newton–Raphson iterative procedure. Finally, examples are given to show the versatility and the efficiency of the approach, and show that faults in a deforming porous medium can have a significant effect on the local as well as on the overall flow and deformation patterns. Copyright © 2006 John Wiley & Sons, Ltd.

Development of the local approach to fracture over the past 25 years: Theory and applications

Abstract: This review paper is devoted to the local approach to fracture (LAF) for the prediction of the fracture toughness of structural steels. The LAF has been considerably developed over the past two decades, not only to provide a better understanding of the fracture behaviour of materials, in particular the failure micromechanisms, but also to deal with loading conditions which cannot easily be handled with the conventional linear elastic fracture mechanics and elastic-plastic fracture mechanics global approaches. The bases of this relatively newly developed methodology are first presented. Both ductile rupture and brittle cleavage fracture micromechanisms are considered. The ductile-to-brittle transition observed in ferritic steels is also briefly reviewed. Two types of LAF methods are presented: (i) those assuming that the material behaviour is not affected by damage (e.g. cleavage fracture), (ii) those using a coupling effect between damage and constitutive equations (e.g. ductile fracture). The micromechanisms of brittle and ductile fracture investigated in elementary volume elements are briefly presented. The emphasis is laid on cleavage fracture in ferritic steels. The role of second phase particles (carbides or inclusions) and grain boundaries is more thoroughly discussed. The distinction between nucleation and growth controlled fracture is made. Recent developments in the theory of cleavage fracture incorporating both the effect of stress state and that of plastic strain are presented. These theoretical results are applied to the crack tip situation to predict the fracture toughness. It is shown that the ductile-to-brittle transition curve can reasonably be well predicted using the LAF approach. Additional applications of the LAF approach methods are also shown, including: (i) the effect of loading rate and prestressing; (ii) the influence of residual stresses in welds; (iii) the mismatch effects in welds; (iv) the warm-prestressing effect. An attempt is also made to delineate research areas where large improvements should be made for a better understanding of the failure behaviour of structural materials.

Prediction of cutting forces in machining of Metal Matrix Composites

Abstract: This paper presents a mechanics model for predicting the forces of cutting aluminum-based SiC/Al2O3 particle reinforced MMCs. The force generation mechanism was considered to be due to three factors: (a) the chip formation force, (b) the ploughing force, and (c) the particle fracture force. The chip formation force was obtained by using Merchant's analysis but those due to matrix ploughing deformation and particle fracture were formulated, respectively, with the aid of the slip line field theory of plasticity and the Griffith theory of fracture. A comparison of the model predictions with the authors’ experimental results and those published in the literature showed that the theoretical model developed has captured the major material removal/deformation mechanisms in MMCs and describes very well the experimental measurements.

Strength and sharp contact fracture of silicon

Abstract: The fracture strength of Si is considered in the context of yield and reliability of microelectronic and microelectromechanical (MEMS) devices. An overview of Si fracture, including the strength of Si wafers, dice and MEMS elements, highlights the importance of understanding sharp contact flaws, with their attendant residual stress fields, lateral cracks and strength-limiting half-penny cracks in advanced Si device manufacturing. Techniques using controlled indentation flaws, including measurements of hardness, crack lengths, crack propagation under applied stress, and inert and reactive strengths, are applied in an extensive new experimental study of intrinsic, n- and p-type {100} and {110} Si single crystals and polycrystalline Si, addressing many of the issues discussed in the overview. The new results are directly applicable in interpreting the strengths of ground or diced Si wafer surfaces and provide a foundation for studying the strengths of MEMS elements, for which the strength-controlling flaws are less well-defined. Although the indentation fracture behavior of Si is shown to be quite anisotropic, the extensive lateral cracking greatly affects crack lengths and strengths, obscuring the underlying single crystal fracture anisotropy. No effects of doping on fracture are observed. Strength decreases in water and air suggest that Si is susceptible to reactive attack by moisture, although the effect is mild and extremely rapid. Strength increases of indented components after buffered HF etching are shown to be due to reactive attack of the contact impression, leading to residual stress relief.

Nonlinear finite element model predicts vertebral bone strength and fracture site.

Abstract: Study design A study on computed tomography (CT)-based finite element (FE) method that predicts vertebral strength and fracture site using human cadaveric specimens. Objective To evaluate the accuracy of the nonlinear FE method by comparing the predicted data with those of mechanical testing. Summary of background data FE methods may predict vertebral strength and fracture site but the prediction has been difficult because of a complex geometry, elastoplasticity, and thin cortical shell of the vertebra. Methods FE models of the 12 thoracolumbar vertebral specimens were constructed. Nonlinear FE analyses were performed, and the yield load, the fracture load, the sites where elements failed, and the distribution of minimum principal strain were evaluated. A quasi-static uniaxial compression test for the same specimens was conducted to verify these analyses. Results The yield loads, fracture loads, minimum principal strains, and fracture sites of the FE prediction significantly correlated with those measured. Conclusions Nonlinear FE model predicted vertebral strength and fracture site accurately.

Tensile and fracture behavior of polymer foams

Abstract: Tensile and mode-I fracture behavior of cross-linked polyvinyl chloride (PVC) and rigid polyurethane (PUR) foams are examined. Tension tests are performed using prismatic bar specimens and mode-I fracture tests are performed using single edge notched bend (SENB) specimens under three-point bending. Test specimens are prepared from PVC foams with three densities and two different levels of cross-linking, and PUR foam with one density. Tension and quasi-static fracture tests are performed using a Zwick/Rowell test machine. Dynamic fracture tests are performed using a DYNATUP model 8210 instrumented drop-tower test set up at three different impact energy levels. Various parameters such as specimen size, loading rate, foam density, cross-linking, crack length, cell orientation (flow and rise-direction) and solid polymer material are studied. It is found that foam density and solid polymer material have a significant effect on tensile strength, modulus, and fracture toughness of polymer foams. Level of polymer cross-linking is also found to have a significant effect on fracture toughness. The presence of cracks in the rise- and flow direction as well as loading rate has minimal effect. Dynamic fracture behavior is found to be different as compared to quasi-static fracture behavior. Dynamic fracture toughness (Kd) increases with impact energy. Examination of fracture surfaces reveals that the fracture occurs in fairly brittle manner for all foam materials.

Spatial Orientation And Distribution Of Reservoir Fractures From Scattered Seismic Energy

Abstract: Wepresentthedetailsofanewmethodfordeterminingthereflection and scattering characteristics of seismic energy from subsurface fractured formations. The method is based upon observations we have made from 3D finite-difference modeling of the reflected and scattered seismic energy over discrete systems of vertical fractures. Regularly spaced, discrete vertical fracture corridors impart a coda signature, which is a ringing tail of scatteredenergy,toanyseismicwaveswhicharetransmittedthrough or reflected off of them. This signature varies in amplitude and coherence as a function of several parameters including: 1 the difference in angle between the orientation of the fractures and the acquisition direction, 2 the fracture spacing, 3 the wavelength of the illuminating seismic energy, and 4 the compliance, or stiffness, of the fractures. This coda energy is most coherent when the acquisition direction is parallel to the strike of thefractures.Ithasthelargestamplitudewhentheseismicwavelengths are tuned to the fracture spacing, and when the fractures have low stiffness. Our method uses surface seismic reflection tracestoderiveatransferfunctionthatquantifiesthechangeinan apparent source wavelet before and after propagating through a fracturedinterval.Thetransferfunctionforanintervalwithnoor low amounts of scattering will be more spikelike and temporally compact. The transfer function for an interval with high scattering will ring and be less temporally compact. When a 3D survey is acquired with a full range of azimuths, the variation in the derived transfer functions allows us to identify subsurface areas with high fracturing and to determine the strike of those fractures.Wecalibratedthemethodwithmodeldataandthenapplied ittotheEmiliofieldwithafracturedreservoir.Themethodyielded results which agree with known field measurements and previously published fracture orientations derived from PS anisotropy.

Trapping zones: The effect of fracture roughness on the directional anisotropy of fluid flow and colloid transport in a single fracture

Abstract: [1] In this paper we quantify the influence of geometry and distribution of surface roughness to the directional anisotropy of fluid flow and transport properties of a single fracture. Roughness of fractures appears to have first order control on how they behave mechanically and hydraulically. We directly quantified the surface roughness of a single fracture using high-resolution laser scanning confocal microscopy. This roughness was input into directly coupled numerical models of fluid flow and transport. We simulated the transport of colloids (microspheres) through the fracture. We found tailing in the breakthrough and sensitivity of the breakthrough to flow direction in the fracture. Microspheres were observed to be trapped in low velocity zones on the lee side of fracture walls. This was not observed in smooth or sinusoidal varying fracture wall geometries. These observations have significant implications for quantifying the transport of dissolved and solid phase materials (colloids) through fractured rock.

Two-dimensional scaling properties of experimental fracture surfaces

Abstract: The self-affine properties of postmortem fracture surfaces in silica glass and aluminum alloy were investigated through the 2D height-height correlation function. They are observed to exhibit anisotropy. The roughness, dynamic, and growth exponents are determined and shown to be the same for the two materials, irrespective of the crack velocity. These exponents are conjectured to be universal.

The role of friction and secondary flaws on deflection and re‐initiation of hydraulic fractures at orthogonal pre‐existing fractures

Abstract: SUMMARY In this study, we explore the nature of plane-strain hydraulic fracture growth in the presence of pre-existing fractures such as joints without or with secondary flaws. The 2-D plane-strain fracture studied can be taken as a cross-section through the short dimensions of an elongated 3-D fracture or as an approximate representation of the leading edge of a 3-D fracture where the edge curvature is negligible. The fluid-driven fracture intersects a pre-existing fracture to which it is initially perpendicular and is assumed not to immediately cross, but is rather deflected into the pre-existing fracture. The intersection results in branching of the fracture and associated fluid flow into the pre-existing fracture. Further growth results in opening and frictional sliding along the pre-existing fracture. Fracture propagation in an impermeable homogeneous elastic medium and fluid invasion into a pre-existing fracture are both driven by an incompressible, Newtonian fluid injected at a constant rate. The frictional stress on the surfaces of pre-existing fractures is assumed to obey the Coulomb law. The governing equations for quasi-static fluid-driven fracture growth are given and a scaling is introduced to help identify important parameters. The displacement discontinuity method and the finite difference method are employed to deal with this coupling mechanism of rock fracture and fluid flow. In order to account for fluid lag, a method for separately tracking the crack tip and the fluid front is included in the numerical model. Numerical results are obtained for internal pressure, frictional contact stresses, opening and shear displacements, and fluid lag size, as well as for fracture re-initiation from secondary flaws. After fracture intersection, the hydraulic fracture growth mode changes from tensile to shearing. This contributes to increased injection pressure and to a reduction in fracture width. In the presence of pre-existing fractures, the fluid-driven cracks can be arrested or retarded in growth rate as a result of diversion of fluid flow into and frictional sliding along the pre-existing fractures. Frictional behaviour significantly affects the ability of the fluid to enter or penetrate the pre-existing fracture only for those situations where the fluid front is within a certain distance from the intersecting point. Importantly, fluid penetration requires higher injection pressure for frictionally weak pre-existing fractures. Fracture re-initiation from secondary flaws can reduce the injection pressure, but re-initiation is suppressed by large sliding on pre-existing fractures that are frictionally weak.

Failure criteria for linear elastic materials with U-notches

Abstract: This paper provides a simple, albeit accurate, criterion for prediction of the rupture loads of brittle, or quasi-brittle, U-notched samples, where linear elastic fracture mechanics is not applicable because blunted notches do not exhibit stress singularities. Good agreement is found between numerical predictions and experimental results. The results of fracture tests from 18 different ceramic materials and a polymer (at − 60°C) are summarized and are used as a reference for checking the fracture criterion. Seven fracture criteria are reviewed and it is shown that all can be recast into the proposed criterion.