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Showing papers on "Fracture (geology) published in 1977"


Journal ArticleDOI
TL;DR: In this article, a general expression for the failure probability of a brittle material is developed by using the properties of flaw size distribution and the stress necessary to fracture an inclined crack, and a comparison is made with Weibull analysis.
Abstract: A general expression for the failure probability of a brittle material is developed by using the properties of flaw size distribution and the stress necessary to fracture an inclined crack. A comparison is made with Weibull analysis and an expression for the Weibull modulus, which is known to be an empirical material constant, is related to the properties of the flaw size distribution of a material. Limitations in the application of Weibull analysis are also discussed.

634 citations


Journal ArticleDOI
TL;DR: Triangular and prismatic quadratic isoparametric elements, formed by collapsing one side and placing the mid-side node near the crack tip at the quarter point, are shown to embody the (1/√r) singularity of elastic fracture mechanics and the ( 1/r)-singularity of perfect plasticity as discussed by the authors.
Abstract: Triangular and prismatic quadratic isoparametric elements, formed by collapsing one side and placing the mid-side node near the crack tip at the quarter point, are shown to embody the (1/√r) singularity of elastic fracture mechanics and the (1/r) singularity of perfect plasticity. The procedure of performing the fracture analysis for the case of small scale yielding is discussed, and the finite element results are compared with theoretical results. The proposed elements have wide application in the fracture analysis of structures where ductile fracture is investigated. They permit a determination of the relationship between crack tip field parameters, loading, and geometry. And for a given fracture criterion can be applied to the prediction of fracture in structures such as pressure vessels under in service conditions.

563 citations


Journal ArticleDOI
TL;DR: In this article, it was shown that the work performed in the end region at the tip of a crack, where the fracture process takes place, is considered the essential work of fracture, and a constant for a particular sheet thickness.
Abstract: In a ductile material, the total work of fracture is not a material constant and linear fracture mechanics is inappropriate. The work performed in the end region at the tip of a crack, where the fracture process takes place, is considered the essential work of fracture, and a constant for a particular sheet thickness. It is shown that this essential work can be estimated from deep edge notched tension specimens by extrapolating the straight line relationship between the work of fracture and ligament length to zero ligament length.

439 citations


Journal ArticleDOI
Richard Hey1
TL;DR: In this article, the propagation rift model was used to explain the oblique trends of the fracture zones in the Juan de Fuca spreading center, and it was shown that the overall trend of the en echelon fracture zones are oblique to the Blanco transform fault, and the strike of each individual fracture zone is quite different, and is compatible with transform motion between the rigid Pacific and Juande Fuca plates.

267 citations



Journal ArticleDOI
TL;DR: In this article, the effect of cracks initially present in a rock was studied by measuring the full tensor of the coefficient of thermal expansion on two rocks with anisotropic crack distributions.

120 citations


Journal ArticleDOI
TL;DR: In this paper, the authors examined the effect of the induced dilatant volume formed by microcracking in relation to critical crack density models of creep rupture and found that the magnitude of inelastic strain at the onset of tertiary creep appears to be related to fracture strength and rock type.
Abstract: During uniaxial compression creep tests at 24°C, quartzite and granite specimens were subjected to stresses ranging from 73% to 95% of their uniaxial fracture strengths. Fracture times ranged from 10 to 1.6×106 s. Strains both parallel (ez) and perpendicular (er) to the maximum stress direction were recorded continuously in order to compute volumetric strain. Tertiary creep is signified by a continuous increase of strain rate in either direction. The amount of time spent in tertiary creep prior to failure was different for the two rock types. Inelastic volumetric strain at the onset of tertiary creep was computed and found to be nearly constant, independent of stress level. The magnitude of inelastic strain at the onset of tertiary creep appears to be related to fracture strength and rock type. For quartzite the value is about 3×10−3, and for the granite it is about 1×10 −3. The hypothesis that the tertiary creep onset is dependent upon the induced dilatant volume formed by microcracking is examined in relation to critical crack density models of creep rupture.

118 citations


Journal ArticleDOI
TL;DR: The use of linear elastic fracture mechanics for modeling the fracture of rock is discussed and compared to Griffith theory in this article, where fracture toughness is measured for single-edge-notch specimens of Indiana limestone as a function of hydrostatic pressure.

106 citations


Journal ArticleDOI
TL;DR: In this paper, the authors combined fracture mechanics with fracture surface analysis to analyze brittle failure of glass bars which were tested relative to the direction of grinding and found that the fracture mirror radius, r, occurs at a constant stress-intensity level independent of flaw geometry.
Abstract: Fracture mechanics is combined with fracture surface analysis to analyze brittle failure of glass bars which were tested relative to the direction of grinding. Grinding essentially produces two sets of flaws from which failure occurs. In the most severe set, formed basically parallel to the grinding direction, the ratio of the average depth (a) to the half-width (b) is 0.5. In the less severe set, formed perpendicular to the grinding direction, the average a/b ratio is 1.6. In both sets the most severe flaws are generally associated with a particularly deep grinding groove or gouge. The strength reduction resulting from testing perpendicular to the grinding direction results from the larger flaw size and slightly higher stress-intensity factor resulting from the greater ellipticity of the flaws formed parallel to the grinding grooves and perpendicular to the tensile axis. Detailed analysis of these 2 sets of flaws causing failure of appropriately oriented specimens shows that (1) the fracture mirror radius, r, occurs at a constant stress-intensity level independent of flaw geometry; (2) unsymmetric fracture mirrors result from unsymmetric, irregular flaws leading to unsymmetric stress-intensity distributions; (3) is constant for semielliptical flaws; and (4) fracture energy calculated from an expression including mirror constants, the flaw-to-mirror size ratio, and the flaw geometry agrees with measured values over a wide range of a/b values.

106 citations


01 May 1977
TL;DR: In this paper, the authors used a three dimensional finite-element elastic stress analysis to calculate the stress-intensity factors for center-crack tension, single and double edge-cracks, and compact fracture specimens with through-the-thickness cracks.
Abstract: The stress-intensity factors for most of the commonly used fracture specimens (center-crack tension, single and double edge-crack tension, and compact), those that have a through-the-thickness crack, were calculated using a three dimensional finite-element elastic stress analysis. Three-dimensional singularity elements were used around the crack front. The stress intensity factors along the crack front were evaluated by using a force method, developed herein, that requires no prior assumption of either plane stress or plane strain. The calculated stress-intensity factors from the present analysis were compared with those from the literature whenever possible and were generally found to be in good agreement. The stress-intensity factors at the midplane for all specimens analyzed were within 3 percent of the two dimensional plane strain values. The stress intensity factors at the specimen surfaces were considerably lower than at the midplanes. For the center-crack tension specimens with large thickness to crack-length ratios, the stress-intensity factor reached a maximum near the surface of the specimen. In all other specimens considered the maximum stress intensity occurred at the midplane.

101 citations


Journal ArticleDOI
TL;DR: In this article, the authors carried out a systematic experimental study of fracture in materials which contain hard second phase particles and found that the growth of cavities in the grain boundaries was the rate limiting step in the fracture process.
Abstract: We have carried out a systematic experimental study of fracture in materials which contain hard second phase particles. The principal variables in this study were the average size and spacing of the second phase particles, grain size, temperature, and the strain rate. Polycrystalline copper containing a dispersion of silica particles was the material used in these experiments. Three modes of fracture were observed: transgranular necking fracture, fracture by the propagation of intergranular cracks initiated at the surface, and intergranular fracture by grain boundary cavitation throughout the entire specimen cross-section. The transition between the fracture modes was shown to shift systematically with temperature, strain rate, and the microstructure. The intergranular fracture mode was studied in detail. The growth of cavities in the grain boundaries was determined to be the rate limiting step in the fracture process. It was determined that in the range of 10-4 to 10-7 s-1 in strain rate, the dominant growth mechanism of the cavities was power-law creep rather than diffusional transport. The ductility of the material in the intergranular mode of fracture was found to be strongly dependent on the area fraction of the second phase in the grain boundary and on the strain rate sensitivity of the material; it was weakly dependent on the grain size. A theoretical lower bound and a practical upper bound of the ductility in the intergranular fracture mode were established. The results are in qualitative agreement with the data on nickel-base alloys and other materials published in the literature.

Journal ArticleDOI
TL;DR: In this paper, it was found that the observed linear magnetic minima are caused by a combination of a fault graben and the oxidation of magnetite to hematite, and the alteration process (martitization) was shown on a susceptibility-Q-value diagram.

Journal ArticleDOI
TL;DR: Theoretical fringe loops were generated for a crack of length 2a in a semi-infinite plate with biaxial loading as discussed by the authors, and these fringe loops are used to compare the three analysis methods and to determine the accuracy of each method.
Abstract: Two-parameter methods of fracture analysis for determining the stress-intensity factor from photoelastic isochromatic-fringe data were critically reviewed. The methods of Irwin, Bradley and Kobayashi, and Smith were developed in detail and differences in the three approaches were noted. Theoretical fringe loops were generated for a crack of length 2a in a semi-infinite plate with biaxial loading. These fringe loops were used to compare the three analysis methods and to determine the accuracy of each method.

Journal ArticleDOI
TL;DR: In this paper, experimental curves relating the crack propagation velocity vs the stress intensity factor K 1 were established for a micrograined (1-4 μm) limestone (micrite) and for a fine-grained marble (100-300 μm).


Book ChapterDOI
TL;DR: In this paper, an experimental procedure is described for accurately establishing the dynamic fracture initiation properties of structural metals at extremely high loading rates, where a 1-in-diameter round bar specimen with a prefatigued circumferential notch is loaded to failure by the rapidly rising tensile pulse resulting from an explosive detonation.
Abstract: An experimental procedure is described for accurately establishing the dynamic fracture initiation properties of structural metals at extremely high loading rates. The apparatus is an adaptation of the Kolsky pressure bar(split-Hopkinson bar) in which a 1-in.-diameter round bar specimen with a prefatigued circumferential notch is loaded to failure by the rapidly rising tensile pulse resulting from an explosive detonation. Using the standard Kolsky technique, the average stress at the fracture site is measured as a function of time. Crack opening displacement is measured by optical means, as a function of time, thus yielding a complete load-displacement record for each test. From the data the critical value of the crack-tip stress intensity factor, K I c , at loading rates, K I in excess of 10 9 psi √in./s may be obtained. This is nearly two orders of magnitude faster than has been achieved by other standard techniques. Results are presented for dynamic tests conducted on SAE 4340 steel and 1020 cold-rolled steel, and these are compared to results from static tests performed on specimens of similar shape.

Journal ArticleDOI
TL;DR: In this article, the impact fracture behavior of notched specimens of polycarbonate has been studied for a range of notch tip radii, and a comparison of results for two molecular weight grades shows that the behaviour is molecular weight-dependent.
Abstract: The impact fracture behaviour of notched specimens of polycarbonate has been studied for a range of notch tip radii. For razor-notched specimens a simple fracture toughness analysis is appropriate, as shown by previous workers. Very blunt notches also give constant fracture toughness values, but at a much higher level, corresponding to a different mode of failure. For intermediate notch tip radii the situation is much more complex, and comparison of results for two molecular weight grades shows that the behaviour is molecular weight-dependent. Analysis of these results has been discussed either in terms of a combination of plane strain and plane stress fracture modes, or in terms of a critical stress at the root of the notch, which appears to be appropriate in certain cases.

Journal ArticleDOI
TL;DR: In this article, a stochastic theory for concrete fracture under simple loading is presented, in which, not only the structural characteristics, but also the statistical stress distribution due to material defects are taken into consideration.

Journal ArticleDOI
01 Jun 1977-Wear
TL;DR: In this paper, the authors described the range of fracture processes which may occur beneath Vickers indentations in sintered tungsten carbide-cobalt composites and the mode of fracture may be altered by changing the conditions of loading.

Journal ArticleDOI
TL;DR: In this article, the authors derived the fracture toughness of the bulk alloy is composed of a trans-crystalline portion pt = (1 − pi) and an inter-crystaline portion pi and can be derived from the partial fracture toughness KICi, and kICiKIC = KIciPt + (1−Pi)KICi.

Proceedings ArticleDOI
L.B. Salz1
TL;DR: Fracture stimulation data have been analyzed in conjunction with reservoir pressure buildup surveys to investigate the relationship between pore pressure and fracture propagation pressure in the geopressured Vicksburg Formation in S. Texas as discussed by the authors.
Abstract: Fracture stimulation data have been analyzed in conjunction with reservoir pressure buildup surveys to investigate the relationship between pore pressure and fracture propagation pressure in the geopressured Vicksburg Formation in S. Texas. The empirical relationship derived from the data can be used to improve well control and planning during drilling or workover and aid in stimulation design in partially depleted geopressured zones. Although limited to a specific formation and geographic area, application to other geopressured provinces may be made if substantiated by field data.

Journal ArticleDOI
TL;DR: In this paper, the authors show that the assumption that the probability of survival is the product of the probabilities of survival of the structure for the principal stresses applied individually is generally unconservative and therefore the approximation serves as a lower bound to the failure probability.
Abstract: A frequently used approximate treatment of fracture statistics for polyaxial stress states assumes that the probability of survival is the product of the probabilities of survival of the structure for the principal stresses applied individually. The present paper shows that this assumption is generally unconservative and therefore the approximation serves as a lower bound to the failure probability. A simple technique is given for finding an upper bound in cases of biaxial tension provided the uniaxial fracture behavior is described satisfactorily by Weibull's two-parameter formula. The upper bound is a good approximation when in high stress regions the stresses are equibiaxial, or nearly so, as in laterally loaded or spinning disks.

Journal ArticleDOI
TL;DR: In this paper, a precipitation hardening Al-Zn-Mg-alloy was used to define the conditions under which a quantitative model for grain size dependence of fracture toughness can be applied in precipitation hardened alloys.

Journal ArticleDOI
TL;DR: In this paper, the authors investigated the fracture properties of small flexural specimens with notches of lengths up to 25 mm and found that both mortar and concrete are notch sensitive materials although not as sensitive as neat cement paste.

Proceedings ArticleDOI
TL;DR: In this paper, a model for the transient pressure behavior of vertical fractures was modified to include the effects of well-bore storage and fracture damage, and the results showed flat, almost horizontal lines that later become concave upward curves approaching the curve for undamaged fractures.
Abstract: A model recently presented by Cinco et al. for the transient pressure behavior of wells with finite conductivity vertical fractures was modified to include the effects of well-bore storage and fracture damage. An infinitesimal skin was considered around the fracture and it was handled as a dimensionless factor defined as (pi/2)(w/sub d//x/sub f/)(k/k/sub d/ - 1). It was found that the well behavior is importantly affected by the fracture damage. When plotted as a function of log p/sub wD/ vs. log t/sub D/ for short times, results show flat, almost horizontal lines that later become concave upward curves asymptotically approaching the curve for undamaged fractures. This behavior is shown even by slightly damaged fractures. Also, it was found that important information about the fracture characteristics may not be determined when well-bore storage effects are present. (24 refs.)


Journal ArticleDOI
TL;DR: In this paper, a review of the micromechanical events involved in composite fracture is given, and a critical appraisal is made of various analytical contributions that have appeared in the literature.


BookDOI
01 Jan 1977

Journal ArticleDOI
TL;DR: In this article, the authors used plate impact techniques and laser interferometry instrumentation to obtain continuous one-dimensional compression wave data through states of loading and unloading on Blair dolomite in the stress range of 0 to 6.5 GPa.
Abstract: Plate impact techniques and laser interferometry instrumentation were used to obtain continuous one-dimensional compression wave data through states of loading and unloading on Blair dolomite in the stress range of 0 to 6.5 GPa. These data are used to infer the dynamic stress--strain response. Both the character of the wave propagation and a comparison with quasi-static uniaxial strain data obtained by other workers suggest substantial strain rate dependence in this rock. The dynamic yield stress of 2.5 GPa determined from the wave propagation data was approximately a factor of 10 higher than that observed in the quasi-static data. Wave propagation below 2.5 GPa is suggestive of viscoelastic response, and a nonlinear Maxwell constitutive equation fitted to these data provides a characteristic relaxation time of 0.01 ..mu..s. Comparison of dynamic and quasi-static loading data suggests that the large difference in observed yield stress could be the result of a transition from failure by brittle fracture to failure by intracrystalline plastic flow.