Showing papers on "Fracture (geology) published in 2000"

Introduction to Contact Mechanics

Abstract: Mechanical Properties of Materials.- Linear Elastic Fracture Mechanics.- Delayed Fracture in Brittle Solids.- Statistics of Brittle Fracture.- Elastic Indentation Stress Fields.- Elastic Contact.- Hertzian Fracture.- Elastic-Plastic Indentation Stress Fields.- Hardness.- Elastic and Elastic-Plastic Contact.- Depth-Sensing Indentation Testing.- Indentation Test Methods.

The Tip Region of a Fluid-Driven Fracture in an Elastic Medium

Abstract: The focus of this paper is on constructing the solution for a semi-infinite hydraulic crack for arbitrary toughness, which accounts for the presence of a lag of a priori unknown length between the fluid front and the crack tip. First, we formulate the governing equations for a semi-infinite fluid-driven fracture propagating steadily in an impermeable linear elastic medium. Then, since the pressure in the lag zone is known, we suggest a new inversion of the integral equation from elasticity theory to express the opening in terms of the pressure. We then calculate explicitly the contribution to the opening from the loading in the lag zone, and reformulate the problem over the fluid-filled portion of the crack. The asymptotic forms of the solution near and away from the tip are then discussed, It is shown that the solution is not only consistent with the square root singularity of linear elastic fracture mechanics, but that its asymptotic behavior at infinity is actually given by the singular solution of a semi-infinite hydraulic fracture constructed on the assumption that the fluid flows to the tip of the fracture and that the solid has zero toughness. Further, the asymptotic solution for large dimensionless toughness is derived, including the explicit dependence of the solution on the toughness. The intermediate part of the solution (in the region where the solution evolves from the near tip to the far from the tip asymptote) of the problem in the general case is obtained numerically and relevant results are discussed, including the universal relation between the fluid lag and the toughness.

Explanation for fracture spacing in layered materials

Abstract: The spacing of opening-mode fractures in layered materials--such as certain sedimentary rocks and laminated engineering materials--is often proportional to the thickness of the fractured layer. Experimental studies of this phenomenon show that the spacing initially decreases as extensional strain increases in the direction perpendicular to the fractures. But at a certain ratio of spacing to layer thickness, no new fractures form and the additional strain is accommodated by further opening of existing fractures: the spacing then simply scales with layer thickness, which is called fracture saturation. This is in marked contrast to existing theories of fracture, such as the stress-transfer theory, which predict that spacing should decrease with increasing strain ad infinitum. Recently, two of us (T.B. and D.D.P.) have used a combination of numerical simulations and laboratory experiments to show that, with increasing applied stress, the normal stress acting between such fractures undergoes a transition from tensile to compressive, suggesting a cause for fracture saturation. Here we investigate the full stress distribution between such fractures, from which we derive an intuitive physical model of the process of fracture saturation. Such a model should find wide applicability, from geosciences to engineering.

True triaxial strength and deformability of the German Continental Deep Drilling Program (KTB) deep hole amphibolite

Abstract: We designed and fabricated a true triaxial loading system and used it to determine deformational and strength characteristics of the amphibolite penetrated by the superdeep hole drilled in the Bohemian massif of southeastern Germany under the German Continental Deep Drilling Program (KTB). Amphibolite is found between 3200 and 7300 m and thus the dominant rock in this 9100-m boring. Our loading system enables the application of three unequal principal stresses to a rectangular prismatic rock specimen. During a test we maintained the least principal (σ3) and the intermediate (σ2) stresses constant and increased the major principal stress (σ1) until brittle failure occurred, in the form of a fracture steeply dipping in the σ3 direction. Typically, for the same σ3 level the amphibolite compressive strength increased substantially with the magnitude of σ2, demonstrating the inadequacy of Mohr-like failure criteria that ignore the effect of the intermediate principal stress on rock strength. We found that a general criterion for the amphibolite could be expressed in the form of a power function relating the octahedral shear stress at failure to the mean normal stress acting on the plane containing the fracture. With respect to deformation, we established that for the same σ3 the onset of dilatancy increases significantly with the magnitude of σ2. Thus the intermediate principal stress appears to extend the elastic range of the stress-strain behavior for a given σ3 and hence to retard the onset of the failure process. Scanning electron microscopy observations of the failure process reveal that microcracks develop mainly parallel to σ2 direction, as the intermediate stress grows beyond σ3, localizing in close proximity of the eventual main fracture.

Physical deterioration of sedimentary rocks subjected to experimental freeze–thaw weathering

Abstract: Ten types of sedimentary rock were subjected to repeated cycles of freezing and thawing. In addition to monitoring sample weight loss throughout testing, a detailed graphic record was made of deterioration mode and its relationship to pre-existing rock flaws. Results suggest that the presence or absence of rock flaws alone does not control deterioration mode, but rather that it is the coupled relationship between these flaws, and rock strength and textural properties which exerts greatest influence. While some pre-existing flaws such as syndepositional deformation structures do not appear to influence breakdown, others such as incipient fractures, cavities and minor lithological boundaries frequently coincide with concentrations of deterioration. A characteristic mode of deterioration which is independent pre-existing flaws tends to develop in sandstones, indicating the influence, in this case, of rock texture. Particularly strong rocks such as crystalline limestone and metasediment tend to fracture preferentially along distinct linear weaknesses such as mineral veins, stylolites and incipient fractures. Particularly weak rocks, such as low-density chalk, break down in a random fashion without regard to pre-existing flaws. In addition to providing some insight into the role of pre-existing flaws in rock deterioration, this work also has practical implications for (i) the study of landform development due to weathering, and (ii) the selection of representative rock samples in durability testing for building stone. Copyright (C) 2000 John Wiley and Sons, Ltd.

Combining Outcrop Data and Three-Dimensional Structural Models to Characterize Fractured Reservoirs: An Example from Wyoming

Abstract: Combining a detailed outcrop characterization of fracture and fault occurrence with attributes from a three-dimensional model of an anticlinally folded clastic reservoir body, we determine which characteristics of the structural form and evolution are most closely related to the development of important reservoir-scale structures. Our example reservoir body studied is the Frontier Formation 1 sandstone in Oil Mountain, an asymmetric anticline on the western flank of Casper arch in central Wyoming. The three-dimensional model of the structure was constructed using an iterative scheme designed to maximize interpretation accuracy and precision. The model was analyzed to determine the spatial variance in morphologic and kinematic attributes. Using a quantitative testing approach, we found that the intensity of tectonically produced fractures is closely related spatially to rate of dip change and total curvature, with the former having the strongest correlation. This folding is a low-strain process compared to tear faulting, which has the strongest spatial correlation to larger strains. The location and magnitude of these higher strain areas can be adequately predicted by three-dimensional restoration and forward modeling of the upper bounding surface of the reservoir body. We use these results to build a predictive model for fault and fracture distribution at Oil Mountain and to discuss how this approach can aid in the exploitation of analogous producing reservoirs.

Fracture toughness of polysilicon MEMS devices

Abstract: Polysilicon fracture mechanics specimens have been fabricated using standard microelectro-mechanical systems (MEMS) processing techniques, with characteristic dimensions comparable to typical MEMS devices. These specimens are fully integrated with simultaneously fabricated electrostatic actuators that are capable of providing sufficient force to ensure catastrophic crack propagation. Thus, the entire fracture experiment takes place on-chip, eliminating the difficulties associated with attaching the specimen to an external loading source. The specimens incorporate atomically sharp cracks created by indentation, and fracture is initiated using monotonic electrostatic loading. The fracture toughness values are determined using finite element analysis (FEA) of the experimental data, and show a median value of 1.1 MPa m 1/2 .

Deformation and fracture of aluminium foams

Abstract: The tensile and compressive properties and the fracture resistance of two aluminium alloy foams have been measured. The yield strength, unloading modulus and toughness increase with relative density in such a manner that the closed cell foams of this study behave as open cell foams. These relationships can be described adequately by power law fits. Experimental results, when compared with theoretical models based on idealised foam structures, reveal unexpected discrepancies. We conclude that they are caused by morphological defects in the microstructures of the foams, the effects of which were not included in the models. Tests on samples with deep sharp notches show that the tensile and compressive strengths are notch-insensitive. Fracture toughness measurements show an R-curve behaviour. This is analysed in terms of the underlying microstructure — the major cause of the R-curve was observed to be the development of crack bridging ligaments behind the crack tip. The compact tension specimens employed were sufficiently small for the uncracked ligaments to suffer plastic yielding during the fracture tests. The crack bridging response was quantified in terms of the normal traction versus plastic displacement curve; the area under this curve for a deep double edge-notched specimen is approximately equal to the measured steady state toughness. The accuracy of an existing micromechanical model for the fracture toughness of brittle open cell foams is assessed, and a new toughness model for ductile foams is derived.

Interfacial Rate Processes in Adhesion and Friction

Abstract: Adhesion between solid materials results from intermolecular interactions The fracture resistance of an adhesive joint is, however, determined jointly by the mechanical deformation in the bulk material and the strength of the interfacial bond The force needed to break an interfacial bond does not have a fixed value; it depends on the thermal state of the system and the rate at which the force is transmitted to the bond The concomitant energy dissipation arising from the extension and the relaxation of the interfacial bonds contributes a significant resistance to fracture, which is clearly evident in elastomeric polymers This issue of interfacial dissipation and its relationship to the length of the interfacial bridges and the rate of crack propagation are addressed with the kinetic theory of bond rupture in the tradition of the models developed by Eyring, Tobolsky, Zhurkov, Bueche, Schallamach, Kausch, and more recently, by Evans and Ritchie Next, the method is extended to address the velocity-depend

Using new pattern fracturing rules for optical proximity correction mask-making to improve critical dimension uniformity

Abstract: This invention describes methods of using pattern fracture rules to form mask pattern segments and the mask for the mask pattern segments. The mask pattern segments have optical proximity correction and are separated into regular pattern elements and optical proximity correction elements. Regular fracture elements and special fracture elements are used. The special fracture elements are parallel to the regular fracture elements, perpendicular to the regular fracture elements, or both parallel to and perpendicular to the regular fracture elements. The special fracture elements are used to define the regular pattern elements and prevent the formation of resist residue in the completed mask. The optical proximity correction elements are formed using the regular fracture elements.

Finite Element Modelling of Composite Materials and Structures

Abstract: Part 1 Review of composite materials: Overview Fundamentals of composites. Part 2 Fundamentals of finite element analysis. Part 3 Finite elements applied to composite materials: Composites and finite element analysis Definition of composite materials in finite element analysis. Part 4 Analytical and numerical modelling: Interlaminar stresses and free edge stresses Fracture and fracture mechanics Delamination Joining Fatigue.

Numerical simulations of the propagation path and the arrest of fluid‐filled fractures in the Earth

Abstract: SUMMARY We use a boundary element method to study the growth and quasi-static propagation of £uid-¢lled fractures in regions with inhomogeneous and deviatoric stresses. The wholesale migration of fractures due to their opening at one end and closing at the other can be simulated when using a ¢nite £uid mass contained in a fracture and considering £uid compression or expansion with changing fracture volume; these fractures are driven by stress gradients and by the density diierences between the £uid and the surrounding rock. Contrary to commonly held beliefs, the fracture growth and the propagation directions are not controlled only by the direction of the principal stresses, but also by tectonic stress gradients, apparent buoyancy forces and the length of the fractures themselves. The models help to explain the formation of sills, the lateral migration of magmas under volcanoes and the absence of volcanoes under the shallow parts of the Nazca plate.

Atomistic Aspects of Brittle Fracture

Abstract: The mechanical properties of materials are ultimately determined by events occurring on the atomic scale. In the case of brittle fracture, this connection is obvious, since the crack in a perfectly brittle material must be atomically sharp at its tip. The crack moves by breaking individual bonds between atoms and can therefore be regarded as a macroscopic probe for the atomic bonding. Nevertheless, traditional analysis of brittle-fracture processes resorts to the treatment of Griffith,1 which implies thermodynamic equilibrium. The Griffith criterion for the mechanical stability of a crack can be formulated as a balance of the crack driving force, the energyrelease rate G, and the surface energy ɣs of the two freshly exposed fracture surfaces: G = 2ɣs. The crack driving force can be obtained from elasticity theory. Within linear elasticity, the crack is characterized by a singularity in the stress field that decays as the inverse square root of the distance R from the crack. The strength of the singularity is characterized by the stressintensity factor K, the square of which directly gives access to the energy-release rate (G = K2/E′, where E′ is an appropriate elastic modulus). While this linear elastic description of the material is not disputed for brittle materials, except for a few atomic bonds around the crack, the assumption that the resistance of the material to crack propagation will only be characterized by the surface energy of the fracture surfaces is certainly worth some further consideration. Such considerations should range from examining atomic details at the tip of a single brittle crack to the relevance of more complex fracture events involving additional irreversible processes and complex crack geometries.

Karst Aquifer evolution in fractured, porous rocks

Abstract: The evolution of flow in a fractured, porous karst aquifer is studied by means of the finite element method on a two-dimensional mesh of irregularly spaced nodal points. Flow within the karst aquifer is driven by surface recharge from the entire region, simulating a precipitation pattern, and is directed toward an entrenched river as a base level. During the early phase of karstification both the permeable rock matrix, modeled as triangular elements, and fractures within the rock matrix, modeled as linear elements, carry the flow. As the fractures are enlarged with time by chemical dissolution within the system calcite–carbon dioxide–water, flow becomes more confined to the fractures. This selective enlargement of fractures increases the fracture conductivity by several orders of magnitude during the early phase of karstification. Thus flow characteristics change from more homogeneous, pore-controlled flow to strongly heterogeneous, fracture-controlled flow. We study several scenarios for pure limestone aquifers, mixed sandstone-limestone aquifers, and various surface recharge conditions as well as the effect of faulting on the aquifer evolution. Our results are sensitive to initial fracture width, faulting of the region, and recharge rate.

Fracture mechanics analysis of a crack in a residual stress field

Abstract: The standard definition of the J integral leads to a path dependent value in the presence of a residual stress field, and this gives rise to numerical difficulties in numerical modelling of fracture problems when residual stresses are significant. In this work, a path independent J definition for a crack in a residual stress field is obtained. A number of crack geometries containing residual stresses have been analysed using the finite element method and the results demonstrate that the modified J shows good path-independence which is maintained under a combination of residual stress and mechanical loading. It is also shown that the modified J is equivalent to the stress intensity factor, K, under small scale yielding conditions and provides the intensity of the near crack tip stresses under elastic-plastic conditions. The paper also discusses two issues linked to the numerical modelling of residual stress crack problems-the introduction of a residual stress field into a finite element model and the introduction of a crack into a residual stress field.