Showing papers on "Fracture (geology) published in 1975"

Indentation fracture: principles and applications

Abstract: The basic principles and practical applications of indentation fracture are reviewed.

Equilibrium penny-like cracks in indentation fracture

Abstract: A study is made of the mechanics of two basic types of indentation fracture, cone cracks (“blunt” indenters) and median cracks (“sharp” indenters). The common feature which forms the central theme in this work is that both crack types, in their well-developed stages of growth, may be regarded as essentially “penny-like”. On this basis a universal similarity relation is derived for equilibrium crack dimension as a function of indentation load. Experimental measurements confirm the general form of this relation. A more detailed fracture mechanics analysis is then given, to account for additional, contact variables evident in the data. Notwithstanding certain analytical limitations, the study serves as a useful basis for investigating a wide range of contact-related problems, both fundamental and applied, in brittle solids.

Theory of heat extraction from fractured hot dry rock

Abstract: A theory of heat extraction from fractured hot dry rock is presented, based on an infinite series of parallel vertical fractures of uniform aperture. Fractures are uniformly spaced and drain heat from blocks of homogeneous and isotropic impermeable rock. Cold water enters at the bottom of each fracture, and solutions are given in terms of dimensionless parameters from which the exiting water temperatures at the top of the fractures can be determined. An example of the application of the theory demonstrates how a multiply fractured system provides a more efficient mechanism for heat extraction than a single fracture in hot dry rock.

Deformation of a carbon-epoxy composite under hydrostatic pressure

Abstract: This paper describes the behaviour of a carbon-fibre reinforced epoxy composite when deformed in compression under high hydrostatic confining pressures. The composite consisted of 36% by volume of continuous fibres of Modmur Type II embedded in Epikote 828 epoxy resin. When deformed under pressures of less than 100 MPa the composite failed by longitudinal splitting, but splitting was suppressed at higher pressures (up to 500 MPa) and failure was by kinking. The failure strength of the composite increased rapidly with increasing confining pressure, though the elastic modulus remained constant. This suggests that the pressure effects were introduced by fracture processes. Microscopical examination of the kinked structures showed that the carbon fibres in the kink bands were broken into many fairly uniform short lengths. A model for kinking in the composite is suggested which involves the buckling and fracture of the carbon fibres.

Threshold fracture energies for elastomers

Abstract: Fracture energies have been measured for two types of polybutadiene elastomer, crosslinked to various extents and torn under various conditions. Threshold values, ranging from 40 to 80 jm−2, were observed for samples torn at extremely low rates of tearing, at high temperatures, and in the swollen state. These values were found to be independent of temperature and rate of tearing, and also of the degree of swelling and the nature of the swelling liquid, provided a correction is made for the reduced areal concentration of molecular chains. They decreased somewhat with increased crosslinking, in good agreement with theoretical predictions of Lake and Thomas.6 The results for the two elastomers were substantially the same. These observations are strikingly different from those made at normal temperatures and rates of tearing, when large differences in fracture energy were observed between the elastomers, and between samples crosslinked to different extents, due to energy losses from nonequilibrium deformation processes in addition to the energy required for fracture.

The effect of temperature on the fracture of polycarbonate

Abstract: The fracture toughness of polycarbonate was obtained over the temperature range 20 to − 120° C. There is a strong thickness dependence which is described in terms of plane stress and plane strain values which are insensitive to temperatures above −40° C but the plane stress value increases below this temperature. This change is associated with theβ transition and stable crack growth was observed in this region with accompanying instabilities arising from adiabatic heating at the crack tip.

Formation of fractures around magmatic intrusions and their role in ore localization

Abstract: An exact solution of three-dimensional theory of elasticity in an infinite elastic rock medium around magma reservoirs of various aspect ratios and the criteria of rock fracturing provide an important tool for the interpretation of the origin and nature of distribution of many ore-bearing fracture systems around magmatic bodies in the world. Theoretical analyses suggest the conditions and regions of formation of (1) dominant radial fractures, (2) dominant concentric fractures or combination of radial and concentric fractures, and (3) central subsidence (or graben) in domal uplift related to intrusions of magma bodies of various shapes and sizes. The relations of these fracture systems to the deposition of ore-bearing fluids are discussed in the light of excess magma and hydrothermal fluid pressures. Caldera subsidence and dominant concentric fractures, such as in the San Juan Mountains mining district in Colorado, are, according to our analyses and interpretations, related to intrusion(s) of vertically elongated magma cupolas and high magma and hydrothermal fluid pressures. This differs from Anderson's original contention (1936) that caldera subsidence and outward-dipping ring fractures are due to lower relative magma pressure than lithostatic pressure. Wedging action of magma immediately above a vertically elongated prolate magma body is suggested as a cause of central graben bounded by funnel-shaped normal faults over wide domal uplift. Displacement along normal faults causes underground subsidence above magma cupolas. Extension of such faults close to the surface and displacement along them can produce surface caldera subsidence. Vein-type deposits commonly associated with funnel-shaped felsic (rhyolitic) bodies may be related to near-surface caldera subsidence. The origin of arcuate zones of breccia pipes such as in Silverton cauldron, Colorado, appears to be related to axial symmetric stress condition (s) due to vertically elongated magma body at depth. Estimation of stress distribution around spheroidal and prolate magma bodies suggests development of possible zonal distribution of fractures from the periphery of the magma outward in the order of (1) continuous tension fracture zone, (2) brittle fault zone, (3) ductile fault zone followed by no fault zone. Brittle fault and continuous tension fracture zones provide excellent sites for ore mineral localization. The zonal distribution of fractures also suggests, in a general way, mode of origin and possible extent of distribution of various fracture types, hydrothermal zoning, and their alterations.

Crack propagation and fracture in silicon carbide

Abstract: Fracture mechanics and strength studies performed on two silicon carbides — a hot-pressed material (with alumina) and a sintered material (with boron) — have shown that both materials exhibit slow crack growth at room temperature in water, but only the hotpressed material exhibits significant high temperature slow crack growth (1000 to 1400‡ C). A good correlation of the observed fracture behaviour with the crack growth predicted from the fracture mechanics parameters shows that effective failure predictions for this material can be achieved using macro-fracture mechanics data.

The fracture stress and its dependence on slow crack growth

Abstract: An analysis is presented which enables the fracture strength, (under constant stress-rate conditions) to be predicted from fracture mechanics data obtained during slow crack growth — by identifying and evaluating several key parameters. The predicted strength characteristics are illustrated using fracture mechanics data obtained for a soda lime silicate glass. Finally, the predicted strengths are compared with strengths measured in flexure on abraded soda lime silicate glass specimens. A good correlation is obtained, indicating an equivalence between micro- and macro-crack propagation conditions for this material.

Strength Degradation of Brittle Surfaces: Blunt Indenters

Abstract: Indentation fracture mechanics is used to develop a theoretical basis for predetermining the strength properties of brittle surfaces in prospective contact situations. Indenters are classified as blunt or sharp; only the first is considered in the present work. The classical Hertzian cone crack conveniently models the fracture damage incurred by the surface in this class of indentation event. Significant degradation is predicted at a critical contact load; when the load is increased beyond this critical level, further degradation occurs at a relatively slight rate. Bend tests on abraded glass slabs confirm the essential features of the theoretical predictions. The controlling variables in the degradation process, notably starting flaw size and in-denter radius, are investigated systematically. An indication is also given as to optimization of material parameters.

Effect of Fracturing Fluids on Fracture Conductivity

Abstract: Measurements and predictions of the effect of fracturing fluids on fracture conductivity were made. The residue from guar polymer was found to greatly reduce fracture conductivity under some conditions, and these conditions could be predicted based on residue volume measurements. Some other polymers were found to decrease fracture conductivity because insufficient breaker was present in the simulated fracture. Fluid loss additives at normal concentrations had negligible effect on fracture conductivity. The technique developed to simulate reservoir fracture conditions can be used to test any fracturing fluid for its effect on fracture conductivity.

Fracture toughness and mechanical behaviour of an epoxy resin

Abstract: The variation of fracture and mechanical properties of epoxy resin Epikote 828, cured with diaminodiphenyl-methane by variation of the resin/amine ratio has been determined. Observations of the crack tip have shown that fracture toughness variations can be attributed to the different blunting characteristics of the various resin/amine compositions. A systematic variation in the thermal transitions of the resins also occurs as a function of composition. Investigations by chemical etching and small angle X-ray scattering have failed to reveal a structural entity which can be invoked to explain the trends in fracture and mechanical properties. It has been found that care must be taken when choosing the method of evaluation of fracture parameters in order that meaningful comparisons can be made between different resin compositions.

Hydraulic fracturing method for creating horizontal fractures

Abstract: This specification discloses a method of creating a horizontally disposed fracture in a subterranean formation that is penetrated by a wellbore. Two packers are set in the wellbore against the formation to be fractured to define with the wellbore and intermediate the packers a fracture treatment zone. Hydraulic pressure is applied to the fracture treatment zone in an amount slightly less than that required to create a vertical fracture in the formation. Acoustical energy is applied in the fracture treatment zone to form a resonant condition therein and to provide rigid coupling of acoustic stress pulses between the packer and the formation and form a horizontal fracture in the formation. The horizontal fracture is propagated into the formation by the continued application of the hydraulic pressure to the fracture treatment zone.

Ultrasonic study of normal and fractured bone.

Abstract: Ultrasonic velocity measurement in bone can be used as a clinical tool that will accurately and objectively monitor the progress of fracture healing. This technique may provide a rational basis for evaluating the effectiveness of various modalities in clinical treatment. The eventual goal of this technique is to determine the status of healing fractures, prescribe appropriate treatment, give the rationale for the timing and form of a rehabilitative program that would accelerate the patient's return to productivity. An instrument has been developed to measure ultrasonic velocity in the long bones of the extremities. Serial measurements of tibial fractures and the measurement of a large group of normals shows no statistically significant differences in ultrasonic measurements have been found on the basis of race, sex, or pregnancy among normals. But a numerically small but statistically significant variation with age was found. While the number of fracture cases observed was small, the evidence is clear that ultrasonic measurement in fractured tibia may give a more reliable indication of the general pattern of healing response than the clinical and roentgenographic examination.

The validity of various fracture mechanics methods at creep temperatures

Abstract: The application of stress intensity factors derived from linear elastic fracture mechanics (LEFM) to fracture at creep temperatures has been considered. From tensile creep rupture tests on single edge notched and notched centre hole specimens of solution treated A.I.S.I. type 316 stainless steel, it is shown that a LEFM approach is inapplicable to predicting creep crack growth rates, whilst the net section stress is found to correlate well with the crack growth rates. These observations have been explained by considering the creep relaxation that takes place at the notch root, smoothing out the local stresses and thus making the LEFM stress distribution inapplicable. The resulting stress distribution supports the observation that the net section stress is a successful criterion on which to predict creep rupture in stainless steel.

The micromechanics of polymer fracture

Abstract: Formation of incipient submicroscopic cracks in polymers under load have been studied by small-angle X-ray scattering. The main regularities of crack formation under different loading conditions have been analyzed. The connection between the submicrocrack concentration and the deformation of a stressed polymer has been shown. The main parameters of crack formation defining the strength properties of a polymer, i.e., the size of initial submicrocracks transverse to the axis of loading, which is determined by the structural heterogeneity of a material, and the concentration of submicrocracks before rupture, have been established. The analysis of the quantitative correlation between these parameters allows one to formulate the main statements regarding the micromechanics of polymer fracture. From comparing the volume and surface parameters of crack formation of a stressed polymer, the dominating role of the surface in the process of fracture has been demonstrated.

Method for selectively orienting induced fractures in subterranean earth formations

Abstract: The orientation of hydraulically-induced fractures in relatively deep subterranean earth formations is normally confined to vertical projections along a plane parallel to the maximum naturally occurring (tectonic) compressive stress field. It was found that this plane of maximum compressive stress may be negated and, in effect, re-oriented in a plane projecting generally orthogonal to the original tectonic stress plane by injecting liquid at a sufficiently high pressure into a wellbore fracture oriented in a plane parallel to the plane of tectonic stress for the purpose of stressing the surrounding earth formation in a plane generally orthogonal to the plane of tectonic stress. With the plane of maximum compressive stress re-oriented due to the presence of the induced compressive stress, liquid under pressure is injected into a second wellbore disposed within the zone influenced by the induced compressive stress but at a location in the earth formation laterally spaced from the fracture in the first wellbore for effecting a fracture in the second wellbore along a plane generally orthogonal to the fracture in the first wellbore.

Electromagnetic effects at metallic fracture

Abstract: JUST at the instant of tensile fracture of low-carbon iron specimens a transient magnetic field of the order of 1,000 gauss is produced1. This phenomenon is observed even in the absence of any external magnetic field. Only the surface region of the fractured pieces are magnetised, with the fractured ends exhibiting distinct and opposite polarities. The magnetisation of each piece varies along the length, with maximum at the fractured end. Moreover, the induced magnetisation is retained for about 15 d in larger specimens and then decays almost exponentially. Iron specimens fractured under impact forces did not show any magnetisation. I now report observations of the complementary phenomenon of generation of an electric field at the instant of tensile fracture of metallic specimens, ferromagnetic as well as non-ferromagnetic.

Fracture-dislocation of the hip.

Abstract: This report reviews two groups of cases: 194 fracture dislocations of the hip reviewed in 1952, and a follow-up of 222 additional fracture dislocations of the hip seen since then. The report describes the methods of treatment used in terms of the various classifications of fracture dislocations of the hip and analyses the results, the complications and the comparative results in these two groups of patients. Recommendations as to the proper form of management for each type of fracture dislocation are presented.

Piezoelectric properties of bone as functions of moisture content

Abstract: FUKADA and Yasuda1 showed that dry bone is piezoelectric in the classic sense, that is, mechanical stress produces polarisation (direct effect) and application of an electric field produces strain (converse effect)2. The possibility that the mechanism for osteogenesis is electrical3 has aroused interest in an investigation of such effects in the more nearly physiological condition represented by wet bone. Recent developments in electrical stimulation of fracture healing4,5 have further emphasised the importance of characterising the piezoelectric properties of wet bone. As the piezoelectricity of wet collagen6 decreases to zero at a moisture content equal to 45% of the dry weight (which corresponds to almost 100% humidity)7, there is some doubt as to whether wet bone could be piezoelectric. Observations of voltages in wet bone under stress, have been made under conditions giving such ambiguous results that they suggested alternative concepts to that of classic piezoelectricity8–11. In view of the confusion about the nature of the voltage developed when wet bone is stressed, we have used a simple longitudinal stress system with sinusoidally varying drive, to measure both converse and direct piezoelectric coefficients of bone as functions of humidity (and ultimately of moisture content). The results show unambiguously that wet bone behaves as a piezoelectric material.

Fracture processes in polystyrene

Abstract: The model for the craze controlled fracture process in polystyrene has been developed further by taking into consideration the micromorphology of the crazes in which the nucleation and propagation of cracks occurs. The micromorphology of crazes formed in thin films of polystyrene, some of which had fractured, has been characterized by means of transmission electron microscopy. The observed micromorphological detail has been shown to be consistent with the micromorphology of the fracture surfaces of bulk specimens. In particular, the slow and fast regions of crack propagation which result in distinctly different fracture surface morphologies have been shown to be associated with differences in micromorphology which occur along the length of a craze.

The Material Properties of Gelatin Gels

Abstract: : A collection of physical and mechanical properties have been examined for 20% gelatin gels made from Pharmagel A. Among those parameters measured are density, thermal conductivity, specific heat, specific capacitance, ultrasonic wave velocity, and coefficient of rolling friction. The critical field strength above which electrical properties change radically is documented. An equivalent passive circuit model is proposed. Fracture stress and elastic modulii are measured. Shear stress at fracture and shear modulii are measured. Fracture strains are also documented for many strain rates. The gelatin is examined for piezo-electric effects and electro-optic effects which would modify its stress birefringence by application of an electric field. Surface polarization effects are also examined. The nature of the fracture surface as a function of crack propagation rate is characterized. A visco-elastic transition strain rate is also documented. Finally, changes of density with storage time at fixed temperature and humidity and changes of density with variations in composition are examined.

Material Characterization on the Fracture of Filament-Reinforced Composites

Abstract: The mixed mode fracture of unidirectional composites is investigated by application of the strain energy density theory. Two analytical models are used. The first assumes that the composite is an ideal homogeneous anisotropic body, and the second assumes that failure takes place in a layer of matrix material whose edges are bonded to two orthotropic plates. The expressions for the strain energy density factor, S, are derived for both models, and brittle fracture is assumed to occur when the S-factor in an element of material ahead of the crack reaches a critical value, Sc. Results are presented for E-glass fiber reinforced plastics, stainless steel fiber reinforced aluminum and graphite fiber epoxy materials and compared with available experimental data. The latter model is preferred as it accounts for the effect of nonhomogeneity that is inherent in the filament-reinforced composites.