Showing papers on "Fracture (geology) published in 1970"

A statistical theory of material strength with application to composite materials

Abstract: A Statistical theory of material strength is proposed. Materials are considered to be imperfect heterogeneous continua composed of discrete volume elements whose characteristics are related to material structure and imperfections. The strength of the elements is assumed to be a statistic a quantity, and as the material is loaded elements fracture randomly throughout the body causing localized stress concentrations. The accumulation of these breaks results in overall failure. By relating strength to material structure this theory attempts to bridge the gap between the microscopic and continuum approaches to fracture mechanics. The theory is applied to composite materials reinforced with whiskers and continuous fibers. Comparisons with experimental data show good agreement. Results for whisker-reinforced composites appear to provide a good prediction of strength and an explanation of the disparity between the strength of individual whiskers and the strength of the composites made from them.

Fracture of Bone

Abstract: Fracture of bone is investigated by measuring the energy required to propagate a crack and by observing, microscopically, the mechanism of fracture. At low strain rates bone displays very high resistance to crack propagation comparable even to some metallic materials. The type of fracture is similar to fiber‐reinforced composite materials.

Formation evaluation by inspection with the borehole televiewer

Abstract: The televiewer takes an oriented acoustic picture of the inside of the well bore in the form of a continuous well log. The resulting log is a representation of the well bore wall as if it were split vertically along magnetic north and laid out flat. Both induced and natural fractures are defined in remarkable detail. Well bores can be filled with any homogeneous liquid such as lease crude oil, water, or drilling mud. Resolution of the tool is sufficient to locate fractures 1/32 inch wide. Examples of natural fractures in extremely fractured formations, in shales, and also drilling‐induced fractures are discussed. Fracture orientation information useful for local and regional tectonic studies is presented.

Strength Behavior of Polycrystalline Alumina Subjected to Thermal Shock

Abstract: Theoretical predictions of crack propagation behavior in brittle solids under conditions of thermal shock were verified by water quenching of cylindrical polycrystalline alumina rods followed by strength testing. The calculated quenching temperature difference (ΔTO) required to initiate thermal-stress fracture agreed fairly well with experiment. When fracture was initiated, strength decreased catastrophically, in agreement with theory. An expression for the strength remaining after thermal stress fracture was derived in terms of the pertinent physical parameters. Values of surface fracture energy similar to those reported in the literature agreed with experiment. Strength after thermal shock was predicted to be inversely proportional to the 1/4 power of the rod diameter; this prediction was supported by experimental data for two rod sizes. Over a range of quenching temperature differences ΔTΔT0 strength remained constant, in agreement with the theoretical expectation that the newly formed cracks were subcritical. Only at the highest quenching temperature differences could further decreases in strength be observed; the quantitative changes, however, were masked by nonlinear deformation (evidenced by permanent crack opening). It was concluded that, although thermal shock behavior of brittle ceramics can be approximated fairly well, reliable quantitative estimates require considerably more information about strength and surface fracture energies as a function of environment, stress distribution, strain rate, and temperature and specimen size effects.

Determination of the post-failure behavior of brittle rock using a servo-controlled testing machine

Abstract: Determination of the Post-Failure Behavior of Brittle Rock Using a Servo-Controlled Testing Machine. The use of the servo-controlled testing machine to control fracture when a rock specimen is deformed beyond its peak strength is discussed. This region of deformation can not usually be examined because excess energy released by the loading system produces rapid disintegration of the specimen. In the test method described the energy release is controlled by a high frequency electronic servo-control system acting in combination with a hydraulic system of very short response time. The control causes the excess energy to be withdrawn before it can be released into the disintegrating specimen, by removing pressurized fluid from the hydraulic system. Theoretical considerations reveal that the condition for controlled fracture is determined by the ability of the hydraulic loading system to unload rapidly. This may be expressed in terms of a ‘dynamic stiffness’,K r , of the hydraulic system. For sufficiently small deformation rates and short servo-control response times the fracture process can be controlled, even though the unloading slope of the stress-strain curve of the rock specimen tends to become infinitely steep. The experimental technique is described in detail and some results obtained in studying the post-failure behavior of Tennessee Marble under uni-axial and bi-axial compression using the new system are presented.

Effect of a Reactive Environment on the Hertzian Strength of Brittle Solids

Abstract: Hertizan fracture theory, previously developed for ideal brittle solids fractured under essentially environment‐free conditions, is here modified to allow for an interaction between the growing cone crack and a reactive environment. Two alternative models, both of which account for the observed detrimental effect of an environment on the Hertzian strength but which predict slight differences in the growth of the cone crack, are offered. The first is based on a surface‐energy‐lowering concept and the second on a subcritical‐crack‐growth concept. The theoretical implications of these two models are examined in the light of Hertzian fracture experiments on abraded glass slabs in different test environments. Observations of the growth of the cone crack in fatigue experiments favor the second model for glass. The advantages of the Hertzian test as a tool for the study of environmental effects on the fracture strength of brittle solids in general are discussed in relation to more conventional fracture tests.

Velocity‐density relations

Abstract: In 1961 Birch [1961] found an empirical linear relationship between the density and the compressional velocity in rocks.

The ductile fracture of polycarbonate

Abstract: The fracture of a known ductile polymer (polycarbonate) is investigated. It is shown that polycarbonate obeys the Dugdale model of ductile yielding by comparing measured plastic-zone sizes and displacements to the theoretical predictions. Strain-energy release rates are calculated and the critical value is shown to be one or two orders of magnitude higher than critical values for brittle polymers.

On the location of fracture in brittle solids-I: Due to Static Loading

Abstract: It is shown that the Weibull treatment of brittle strength may be extended to predict the distribution of the location of fracture in brittle solids. Conversely, observations of fracture location enable conclusions to be drawn about fracture loads. Illustrations are given for the three-point bending of beams and the ring-crack of plates by spherical indenters. In the latter case the problem of multiple cracking is also considered.RésuméOn montre que la procédure suggérée par Weibull pour traiter le problème de la résistance à la rupture fragile peut être étendue à la prédiction de la localisation de la rupture dans les solides fragiles. Inversément, connaissant l'emplacement de la rupture, il est possible de tirer des conclusions sur les charges qui ont engendré celle-ci. Le raisonnement est illustré par le traitement de deux exemples: la poutre fléchie sur deux appuis par une charge concentrée, et la fissuration annulaire d'une plaque de verre sous l'effet d'une bille d'indentation. Dans ce dernier cas, on considère également le problème de la polyfissuration.ZusammenfassungEs wird gezeigt, daß das Weibull-Verfahren zur Behandlung von Problemen der Sprödbruchfestigkeit auf die Vorausbestimmung der Stelle an welcher der Bruch in spröden Wertstoffen auftritt, erweitert werden kann. Umgekehrt, ist die Bruchstelle bekannt, so ist es möglich Schlüsse über die Beanspruchung zu ziehen, welche den Bruch bewirkt hat. Diese Überlegungen werden an Hand von zwei Beispielen erläutert. Das erste bezieht sich auf den Fall eines an beiden Enden aufliegenden Trägers welcher einer Punktlast unterworfen ist, das zweite, auf den Fall von Ringrißbildung einer Platte unter Einwirkung einer Kugel. Für den letzten Fall wird auch das Problem der Mehrrißbildung in Betracht gezogen.

A theory of snow slab failure

Abstract: Existing theories of snow slab failure emphasize failure either in the tensile zone of the slab or along the slab base. The tensile zone theories do not explain measured fracture angles or the observed fact that a necessary condition for extensive fracturing is weakness in the basal plane. On the other hand, the basal theories do not explain where the tensile stress originates and why brittle failure commences in the tensile zone and propagates into the basal plane. A new model is proposed wherein the critical value of the maximum principal stress evaluated at the tensile zone is coupled to the inability of the slab to sustain basal stress. A scale analysis of the equilibrium equations shows that this model predicts the measured fracture angles and large values for the maximum principal stress.

A theory of brittle creep in rock under uniaxial compression

Abstract: Scholz's theory of brittle creep is rejected. A new theory based on Charles's theory of the subcritical growth of pre-existing cracks in the specimen by stress-aided corrosion is put forward. It is a successful explanation of new experiments on the creep of Pennant sandstone and Carrara marble under uniaxial compression at room temperature.

The fracture of titanium carbide under static and sliding contact

Abstract: Under static loading, crack formation in titanium carbide is shown to obey Auerbach's law for hemispherical indenters. From the results, using the Frank and Lawn theory of 1967, an estimate of the surface energy of TiC is obtained. In the case of sliding contact the load to fracture varies markedly with the coefficient of friction. A reasonable estimate of the sliding load to fracture is obtained by assuming that the fracture stress, as calculated using the analysis of Hamilton and Goodman in 1966, is the same as in the case of static loading for the same indenter. This is at some variance with the Lawn's 1967 predictions.

On fracture path stability in the compact tension test

Abstract: A simple criterion based on the engineers' theory of bending is suggested for the determination of the stability of fracture path in the compact tension test.

Fracture surface of polystyrene: Mackerel pattern

Abstract: Characteristic markings of concentric bands are formed on the fracture surface of tensile specimens under certain loading conditions. The marking form in the fast crack growth region of the mirror area of fracture. Optical and electron optical microscope techniques have been used to study the morphology of the markings. It is shown that in this region the crack propagates along the interface between the craze, in which the crack nucleated, and the bulk material. The mackerel pattern is caused by the crack jumping from one craze–matrix interface to the other.

Process for horizontally fracturing subsurface earth formations

Abstract: Horizontal fractures are formed in a subsurface earth formation which tends to fracture vertically at the naturally occurring formation temperature by a process which includes the steps of extending at least one well borehole into the formation, generating a vertical fracture by pressurizing said borehole, injecting hot fluid into at least one borehole to heat the formation, continuing the injection of hot fluid until thermal stressing of the formation matrix material causes the horizontal compressive stress in the formation to exceed the vertical compressive stress therein at a location selected for a second well, extending the borehole of the second well into the formation, and hydraulically fracturing the formation through this second well borehole to form a horizontal fracture extending therefrom into the formation.

The Brittle Fracture of Amorphous Thermoplastic Polymers

Abstract: The brittle fracture properties of polyphenylene oxide, polysulfone, polycarbonate, and poly(methyl methacrylate) thermoplastic polymers were investigated over a wide range of temperatures Fracture energy measurements were made using double edge-notched tensile samples Tensile strength, tensile strain, and initial elastic modulus were measured for calculation of the fracture energy and further analysis of the polymer behavior It was found that mechanical transitions in the tensile properties corresponded reasonably well with transitions in the fracture energy in the temperature range investigated Fracture surface photographs permitted visual analysis of the fracture process It was found that the roughest fracture surface corresponded to the maximum in the fracture energy for a given polymer A theory for prediction of polymer tensile yield strain is presented, based on the volume dilation concept The implications of this theory are discussed in terms of the crack tip flow process leading to brittle fracture

Uses of electron paramagnetic resonance in studying fracture

Abstract: The uses of electron paramagnetic resonance (EPR) in studying aspects of polymer fracture are discussed. The sensitivity of EPR is such that all phases of fracture are not amenable to investigation by these means. This paper attempts to define those areas where the authors' experience would indicate that success might or might not be expected. A discussion of the difference between the tensile fracture of drawn polymer fibers, in which strong signals are obtained, and cast and molded materials is given.

A comparison of reaction rate models for the fracture of solids

Abstract: The application of the theory of reaction rates to the fracture of solids is reviewed. Four different models are compared and shown to exhibit three basic differences in formulation. The evidence appears to favor bond rupture, as opposed to bond slippage, as the basic mechanism leading to fracture of certain polymer systems. It is shown that other differences in the models cannot be resolved by a comparison with existing experimental data.

Dynamic fracture by spallation in metals

Abstract: Material responses and fracture criteria relevant to the description of spallation phenomena are reviewed. The state of the material at the instant of fracture is an important part of a fracture criterion. The stress state associated with plane strain is described, and the effect of the initial conditions and the time dependent conditions of the material on spallation are discussed. The important quantities in any fracture criterion are the applied stress state, the size of the critically stressed region, the critical value of stress at which fracture begins, and the critical crack velocity. Stress gradient and cumulative damage spall-criteria are discussed in relation to these more fundamental quantities. Finally, some experiments are suggested that would isolate important parameters of the spallation process.