Showing papers on "Fracture (geology) published in 1988"

The practical use of fracture mechanics

Abstract: 1. Introduction.- 1.1. Fracture control.- 1.2. The two objectives of damage tolerance analysis.- 1.3. Crack growth and fracture.- 1.4. Damage tolerance and fracture mechanics.- 1.5. The need for analysis: purpose of this book.- 1.6. Exercises.- 2. Effects of Cracks and Notches: Collapse.- 2.1. Scope.- 2.2. An interrupted load path.- 2.3. Stress concentration factor.- 2.4. State of stress at a stress concentration.- 2.5. Yielding at a notch.- 2.6. Plastic collapse at a notch.- 2.7. Fracture at notches: brittle behavior.- 2.8. Measurement of collapse strength.- 2.9. Exercises.- 3. Linear Elastic Fracture Mechanics.- 3.1. Scope.- 3.2. Stress at a crack tip.- 3.3. General form of the stress intensity factor.- 3.4. Toughness.- 3.5. Plastic zone and stresses in plane stress and plane strain.- 3.6. Thickness dependence of toughness.- 3.7. Measurement of toughness.- 3.8. Competition with plastic collapse.- 3.9. The energy criterion.- 3.10. The energy release rate.- 3.11. The meaning of the energy criterion.- 3.12. The rise in fracture resistance: redefinition of toughness.- 3.13. Exercises.- 4. Elastic-Plastic Fracture Mechanics.- 4.1. Scope.- 4.2. The energy criterion for plastic fracture.- 4.3. The fracture criterion.- 4.4. The rising fracture energy.- 4.5. The residual strength diagram in EPFM: collapse.- 4.6. The measurement of the toughness in EPFM.- 4.7. The parameters of the stress-strain curve.- 4.8. The h-functions.- 4.9. Accuracy.- 4.10. Historical development of J.- 4.11. Limitations of EPFM.- 4.12. CTOD measurements.- 4.13. Exercises.- 5. Crack Growth Analysis Concepts.- 5.1. Scope.- 5.2. The concept underlying fatigue crack growth.- 5.3. Measurement of the rate function.- 5.4. Rate equations.- 5.5. Constant amplitude crack growth in a structure.- 5.6. Load interaction: Retardation.- 5.7. Retardation models.- 5.8. Crack growth analysis for variable amplitude loading.- 5.9. Parameters affecting fatigue crack growth rates.- 5.10. Stress corrosion cracking.- 5.11. Exercises.- 6. Load Spectra and Stress Histories.- 6.1. Scope.- 6.2. Types of stress histories.- 6.3. Obtaining load spectra.- 6.4. Exceedance diagram.- 6.5. Stress history generation.- 6.6. Clipping.- 6.7. Truncation.- 6.8. Manipulation of stress history.- 6.9. Environmental effects.- 6.10. Standard spectra.- 6.11. Exercises.- 7. Data Interpretation and Use.- 7.1. Scope.- 7.2. Plane strain fracture toughness.- 7.3. Plane stress and transitional toughness, R-curve.- 7.4. Toughness in terms of J and JR.- 7.5. Estimates of toughness.- 7.6. General remarks on fatigue rate data.- 7.7. Fitting the da/dN data.- 7.8. Dealing with scatter in rate data.- 7.9. Accounting for the environmental effect.- 7.10. Obtaining retardation parameters.- 7.11. Exercises.- 8. Geometry Factors.- 8.1. Scope.- 8.2. The reference stress.- 8.3. Compounding.- 8.4. Superposition.- 8.5. A simple method for asymmetric loading cases.- 8.6. Some easy guesses.- 8.7. Simple solutions for holes and stress concentrations.- 8.8. Simple solutions for irregular stress distributions.- 8.9. Finite element analysis.- 8.10. Simple solutions for crack arresters and multiple elements.- 8.11. Geometry factors for elastic-plastic fracture mechanics.- 8.12. Exercises.- 9. Special Subjects.- 9.1. Scope.- 9.2. Behavior of surface flaws and corner cracks.- 9.3. Break through: leak-before-break.- 9.4. Fracture arrest.- 9.5. Multiple elements, multiple cracks, changing geometry.- 9.6. Stop holes, cold worked holes and interference fasteners.- 9.7. Residual stresses in general.- 9.8. Other loading modes: mixed mode loading.- 9.9. Composites.- 9.10. Exercises.- 10. Analysis Procedures.- 10.1. Scope.- 10.2. Ingredients and critical locations.- 10.3. Critical locations and flaw assumptions.- 10.4. LEFM versus EPFM.- 10.5. Residual strength analysis.- 10.6. Use of R-curve and JR-curve.- 10.7. Crack growth analysis.- 10.8. Exercises.- 11. Fracture Control.- 11.1. Scope.- 11.2. Fracture control options.- 11.3. The probability of missing the crack.- 11.4. The physics and statistics of crack detection.- 11.5. Determining the inspection interval.- 11.6. Fracture control plans.- 11.7. Repairs.- 11.8. Statistical aspects.- 11.9. The cost of fracture and fracture control.- 11.10. Exercises.- 12. Damage Tolerance Substantiation.- 12.1. Scope.- 12.2. Objectives.- 12.3. Analysis and damage tolerance substantiation.- 12.4. Options to improve damage tolerance.- 12.5. Aircraft damage tolerance requirements.- 12.6. Other requirements.- 12.7. Flaw assumptions.- 12.8. Sources of error and safety factors.- 12.9. Misconceptions.- 12.10. Outlook.- 12.11. Exercises.- 13. After the Fact: Fracture Mechanics and Failure Analysis.- 13.1. Scope.- 13.2. The cause of service fractures.- 13.3. Fractography.- 13.4. Features of use in fracture mechanics analysis.- 13.5. Use of fracture mechanics.- 13.6. Possible actions based on failure analysis.- 13.7. Exercises.- 14. Applications.- 14.1. Scope.- 14.2. Storage tank (fictitious example).- 14.3. Fracture arrest in ships.- 14.4. Piping in chemical plant (fictitious example).- 14.5. Fatigue cracks in railroad rails.- 14.6. Underwater pipeline.- 14.7. Closure.- 15. Solutions To Exercises.

Flow and tracer transport in a single fracture: A stochastic model and its relation to some field observations

Abstract: Calculations for the flow and solute transport through a single rough-surfaced fracture were carried out. The fracture plane was discretized into a square mesh to which variable apertures were assigned. The spatially varying apertures of each single fracture were generated using geostatistical methods, based on a given aperture probability density distribution and a specified spatial correlation length. Constant head boundary conditions were assumed for the flow in the x direction of a single fracture with no flow boundaries in the y direction. The fluid potential at each node of the discretization mesh was computed and the steady state flow rates between all the nodes were obtained. Our calculations showed that fluid flow occurs predominantly in a few preferred paths. Hence, the large range of apertures in the single fracture gives rise to flow channeling. The solute transport was calculated using a particle tracking method. Both the spatial and time variations of tracer breakthrough results are presented. The spatial variation of tracer transport between a line of injection points and a line of observation points are displayed in contour plots which we labeled “transfer matrix.” Our results indicate that such plots can give information on the spatial correlation length of the heterogeneity in the fracture. The tracer breakthrough curve obtained from a line of point measurements is shown to be controlled by the aperture density distribution and is insensitive to statistical realization and spatial correlation length. These results suggest the importance of making line measurements in the laboratory and the field. Sensitivity of our results on parameter variations was also investigated.

Why are mammalian tendons so thick

Abstract: The maximum stresses to which a wide range of mammalian limb tendons could be subjected in life were estimated by considering the relative cross‐sectional areas of each tendon and of the fibres of its muscle. These cross‐sectional areas were derived from mass and length measurements on tendons and muscles assuming published values for the respective densities. The majority of the stresses are low. The distribution has a broad peak with maximum frequency at a stress of about 13 MPa, whereas the fracture stress for tendon in tension is about 100 MPa. Thus, the majority of tendons are far thicker than is necessary for adequate strength. Much higher stresses are found among those tendons which act as springs to store energy during locomotion. The acceptability of low safety factors in these tendons has been explained previously (Alexander, 1981). A new theory explains the thickness of the majority of tendons. The muscle with its tendon is considered as a combined system which delivers mechanical energy: the thickness of the tendon is optimized by minimizing the combined mass. A thinner tendon would stretch more. To take up this stretch, the muscle would require longer muscle fibres, which would increase the combined mass. The predicted maximum stress in a tendon of optimum thickness is about 10 MPa, which is within the main peak of the observed stress distribution. Individual variations from this value are to be expected and can be understood in terms of the functions of the various muscles.

Small-scale crack bridging and the fracture toughness of particulate-reinforced ceramics

Abstract: T heoretical analyses of small-scale bridging of crack surfaces by elastic-ideally plastic springs are presented and applied to the study of the fracture toughness of ceramics reinforced by small particles. The dependence of toughening on particle size, concentration, strength, and ductility is explored, and relations between toughening and bridge length at fracture are given. Available experimental information is examined in the light of the analyses.

Deformation and fracture processes and the physical metallurgy of WC–Co hardmetals

Abstract: Deformation and fracture processes have been examined in WC–Co tool materials, still the most commonly used hardmetal. The relevant microstructural parameters are described in detail and an assessment is made of their effects on strength and fracture tests at ambient temperature, for the constituent phases separately and in combination. The results of properties more relevant to service behaviour, such as fatigue and creep, are summarised. Finally, recommendations are made with regard to the need for further fundamental research.

Fracture testing of silicon microelements in situ in a scanning electron microscope

Abstract: Fracture testing of silicon cantilever beams (thicknesses 10–20 μm) was performed in situ in a scanning electron microscope by means of an equipment specially designed for this purpose. Beams of various sizes and orientations (〈011〉 and 〈001〉) were manufactured in Si (100) wafers by two different micromachining procedures. The beams were tested by simple bending to fracture, and a number of fundamental fracture parameters were determined from an analytical model of elastic fracture. To verify its validity, the model was utilized to evaluate an experimental E modulus, which was found to agree well with previous results. Fracture limits, fracture strains, and initiating flaw sizes were determined. The maximum fracture limit was very high; about 10 GPa. The strengths of different beams scattered from this value down to practically zero strength, with an average close to 4 GPa. The corresponding fracture strains and initiating flaw sizes were 6% and 3 nm, respectively (maximum strength), and 2% and 17 nm (ave...

Fluid percolation through single fractures

Abstract: Large deviations from "cubic-law" dependence of laminar fluid flow through fractures on the apparent mechanical aperture of a fracture can be explained by assuming: 1) cubic-law dependence of flow on the actual local aperture at the microscopic level; 2) conservation of rock volume when deforming the fracture; and 3) macroscopic flow properties are dominated by the critical neck (the smallest aperture along the path of highest aperture through the fracture).

Rising Fracture Toughness from the Bending Strength of Indented Alumina Beams

Abstract: The analytical function of crack extension to a fractional power is used to represent the fracture resistance of a vitreous-bonded 96% alumina ceramic. A varying flaw size, controlled by Vickers indentation loading between 3 and 300 N, was placed on the prospective tensile surfaces of four-point bend specimens, previously polished and annealed. The lengths of surface cracks were measured by optical microscopy. Straight lines were fitted to the logarithmic functions of observed bending strength versus indentation load in two series of experiments: (I) including the residual stress due to indentation and (II) having the residual stress annealed out at an elevated temperature. Within the precision of measurement these lines have the same slope, being about 32% less than the -1/3 slope which a fracture toughness independent of crack extension would indicate. Considering the criteria for crack extension and specimen failure, the fracture mechanics equations were solved for the conditions of the two series of experiments. Approximately the same values of fracture toughness, rising as a function of indentation flaw size, were obtained from both series of experiments.

Fractal and geostatistical methods for modeling of a fracture network

Abstract: The modeling of fracture networks is useful for fluid flow and rock mechanics studies. About 6600 fracture traces were recorded on drifts of a uranium mine in a granite massif. The traces have an extension of 0.20–20 m. The network was studied by fractal and by geostatistical methods but can be considered neither as a fractal with a constant dimension nor a set of purely randomly located fractures. Two kinds of generalization of conventional models can still provide more flexibility for the characterization of the network: (a) a nonscaling fractal model with variable similarity dimension (for a 2-D network of traces, the dimension varying from 2 for the 10-m scale to 1 for the centimeter scale, (b) a parent-daughter model with a regionalized density; the geostatistical study allows a 3-D model to be established where: fractures are assumed to be discs; fractures are grouped in clusters or swarms; and fracturation density is regionalized (with two ranges at about 30 and 300 m). The fractal model is easy to fit and to simulate along a line, but 2-D and 3-D simulations are more difficult. The geostatistical model is more complex, but easy to simulate, even in 3-D.

Evoluton of Polygonal Fracture Patterns in Lava Flows

Abstract: Cooling-induced fractures, also known as columnar joints, divide basaltic lava flows into prismatic columns with polygonal cross sections. The regularity and symmetry of the fracture patterns have long fascinated naturalists. In view of the recent selection of two candidate nuclear waste sites in areas where polygonally fractured volcanic rocks are located, a better understanding of the fracture patterns is required. Field data indicate that the tetragonal networks at flow surfaces evolve systematically to hexagonal networks as the joints grow inward during solidification of lava. This evolution occurs by the gradual change of most orthogonal intersections to nonorthogonal intersections of about 120 degrees. The surface features and intersection geometries of columnar joints show that joint segments at any given level form sequentially yet harmoniously.

Characterizing Jointed Systems by Azimuthal Resistivity Surveys

Abstract: Anisotropy, directional connectivity, and porosity of fracture systems can be estimated from surface azimuthal electrical resistivity surveys. Azimuthal resistivity surveys utilize conventional resistivity equipment and are performed by rotating a Wenner array about a fixed center point and measuring apparent resistivity as a function of azimuth. The depth of investigation is determined by the electrode spacing which is generally limited by practical considerations to approximately 70 m. The azimuthal survey generates an apparent resistivity ellipse from which the properties of a subsurface joint system can be determined. Theoretically the major axis of the resistivity ellipse will coincide with strike of the primary joint set. The ratio of major axis to minor axis of the ellipse defines the coefficient of anisotropy associated with the joints, and from this coefficient, secondary porosity can be calculated. Application of azimuthal surveys at 60 sites in bedrock and clayey till throughout Wisconsin generally yielded joint strikes within a few degrees of direct observations. Porosities calculated for jointed bedrock are within a few percent of values determined by other methods. The absolute values of porosities calculated for the tills appear unreliable due to conduction effects along the surface of clay minerals. Although the theoretical foundation for this technique is based on idealized jointing, the field results indicate that the method is effective in media with multiple joint sets. When mean joint length exceeds the electrode spacing, azimuthal resistivity peaks closely coincide with the mean strikes of observed joint sets. When joint lengths are less than the electrode spacing, the major ellipse axis indicates the most conductive path through the joint system. In both cases, ellipse shape indicates the direction (s) having the greatest joint connectivity, which are also the directions of greatest aquifer permeability.

Shear fracture

Abstract: The material aspects of mode II and III fracture in adhesively bonded joints were elucidated for a range of adhesives using DCB type test specimens and scanning electron microscopy. The adhesive thickness was varied from as little as a small fraction of the natural crack tip damage zone to a value large enough to expose the bulk fracture behavior.

Effect of Temperature and Humidity on Fracture Energy of Concrete

Abstract: Fracture experiments were conducted at temperatures from 20 to 200 C (68 to 392 F) to determine the dependence of the Mode I fracture energy of concrete on temperature as well as the specific water content. The fracture energy values were determined by testing geometrically similar specimens of sizes in the ratio 1:2:4:8 and then applying Bazant's size effect law. Three-point bend specimens and eccentric compression specimmns are found to yield approximately the same fracture energies, regardless of temperature. To describe the temperature dependence of fracture energy, a recently derived simple formula based on the activation energy theory (rate process theory) is used and verified by test results. The temperature effect is determined both for concrete predried in an oven and for wet (saturated) concrete. By interpolation, an approximate formula for the effect of moisture content on fracture energy is also obtained. This effect is found to be small at room temperature but large at temperatures close to 100 C (212 F).

Feldspar-influenced rock rheologies

Abstract: Progressive fracture, subsequent cataclasis, and syntectonic alteration of feldspar to phyllosilicates transformed a massive granite into a quartz-mica phyllonite during early Tertiary deformation in a 20-30-m-wide shear zone in southeastern Arizona. The ductile deformation proceeded at temperatures and pressures approximating, middle to upper crustal levels. Most of the deformation was taken up by the feldspar and its alteration products. Quartz deformed by both brittle fracture and crystal plastic mechanisms. These results show that under certain temperature-pressure-strain rate conditions feldspars are weaker than quartz. The observed deformation mechanisms indicate that the brittle to ductile transition in fault zones is not simply a function of the onset of temperature-activated plastic deformation in quartz nor of the frictional behavior of rocks, as inferred in the familiar strength vs. depth curves. It is more likely that the transition is complex and depends on a variety of parameters. One such factor delineated in this study is the fracture and fracture-facilitated syntectonic alteration of feldspar under hydrated conditions.

Hardness and fracture toughness of semiconducting materials studied by indentation and erosion techniques

Abstract: In recent years, the growing field of semiconductor micromechanics has created an increasing demand for strength data on semiconductors and for adequate tests and evaluations of their mechanical properties. In a recently published paper, the present authors have demonstrated that the solid particle erosion rate can be taken as a simple and highly reproducible statistical measure of the susceptibility of silicon and GaAs to contact damage in the micron range. In the present work the scope is broadened to include several new crystal orientations (and one new doping level), as well as three other materials: germanium, InP and InAs, for which the hardness and fracture toughness K Ic values are determined by means of the indentation technique. K Ic values are also derived from erosion data by means of a recently reported brittle fracture model, based on non-lateral spalling in single-crystal semiconductors. These values are compared with results obtained by the indentation technique and conventional test methods reported in the literature. Fracture surface energies are deduced from the experimental K Ic results. The materials tested are ranked with respect to elastic properties, microhardnesses, fracture toughnesses, and sensitivities to contact damages in general. The influence of crystallographic orientation on room temperature microfracture properties is clearly established, but the corresponding influence on microhardness is found to be rather limited. The influence of doping on the room temperature mechanical properties is noticeable but small.

A finite element analysis of continuum damage mechanics for ductile fracture

Abstract: A finite element formulation of an anisotropic theory of continuum damage mechanics for ductile fracture is presented. The formulation is based on a generalized model of anisotropic continuum damage mechanics of elasticity and plasticity proposed earlier by the authors. The validity of the proposed anisotropic damage model and finite element formulation is verified by comparing the predicted fracture load of center-cracked tension specimen made of thin aluminium alloy 2024-T3 with those determined experimentally and excellent agreement is achieved. The proposed finite element analysis can thus provide an important design tool to solve practical problems of engineering significance which may have hitherto been found difficult using the conventional fracture mechanics concept.

The rheological and fracture properties of Gouda cheese

Abstract: The rheological and fracture behaviour of Gouda cheese was studied. Methods for determining these properties of visco-elastic materials are described. Application of the theory of fracture mechanics, after modification and expansion, to visco-elastic materials with a low or no yield stress is discussed. For such materials, of which Gouda cheese is an example, the flow properties greatly affect the fracture behaviour. From the effect of variation in composition (fat, water, NaCl and Ca content, pH) and maturation on the behaviour of Gouda cheese, it may be concluded that this cheese may be considered as a composite material. Fat particles act as a filler in a swollen protein matrix. The amount of fat and the rigidity of the fat particles affect the rigidity of the cheese. Factors like pH, water and NaCl content, that change the properties of the protein matrix, clearly affect the -rheological and fracture behaviour, e.g. the rigidity and the shortness, of the cheese. The trends of these changes on the protein matrix are similar to those on rennet and acid skimmilk gels under various conditions . As an example of the importance of the experimental results for cheese manufacturing, the relation between the pH of cheese and eye or slit formation was studied.

Delayed unions and nonunions of stress fractures in athletes

Abstract: From 1971 to 1985, 369 athletes presented to us with stress fractures. Of these patients, 10% (37) were treated for development of delayed unions or nonunions. Twenty-seven of the patients were male and 10 were female. Their mean age was 23.1 years (range, 17 to 39). About half of the athletes were involved in endurance sports. The diagnostic criteria for a delayed union or nonunion were clinical and radiological evidence. There was a diagnostic delay of about 3.5 months in the series. Plain radiographs, tomography, and isotope scans were used in the diagnosis. Special radiographic views were also used. In 15 cases (10 hallux sesamoid bone fractures, 1 midtibial shaft fracture, 1 metatarsal V base fracture, 1 tarsal navicular fracture, 1 olecranon fracture, and 1 proximal tibial shaft fracture) nonoperative treatment was used. Operative treatment was used 22 times (5 sesamoid fractures, 5 midtibial fractures, 5 metatarsal V base fractures, 3 tarsal navicular fractures, 3 olecranon fractures, and 1 proximal tibial shaft fracture). Results were good or excellent in 32 cases (86.5%), moderate in 4 cases, and poor in 1 case.