Showing papers on "Fracture (geology) published in 1989"

The Strain Energy Release Rate of Composite Microcracking: A Variational Approach

Abstract: A variational analysis approach has been used to determine the two- dimensional thermoelastic stress state in cross-ply laminates of type [0m/90n] s and [90m/ 0n]s. The stress analysis was used to calculate the energy release rate due to formation of a new microcrack. The analysis accurately includes the effect of residual thermal stresses. When compared with experiments, the new energy release rate expressions are found to predict typical data using a single value for the critical energy release rate for microcrack ing. This critical energy release rate has a physical interpretation as a microcracking fracture toughness or as an intralaminar fracture toughness. We also used the variational solution to get an analytical expression for the longitudinal expansion coefficient of the microcracked cross-ply laminate as a function of microcrack density. Finally, variational theorems are used to show that this new microcracking fracture analysis is rigorously more accurate than previous attempts at the same problem.

Application of fracture mechanics to composite materials

Abstract: I. General Aspects. 1. Fracture mechanics of anisotropic materials (J.G. Williams). 2. Statistical concepts in the study of fracture properties of fibres and composites (H.D. Wagner). II. Fracture of Polymer Composites. IIA. Interlaminar Fracture Studies. 3. Interlaminar mode I-fracture testing (P. Davies, M.L. Benzeggagh). 4. Mode II - Interlaminar fracture of composites (L.A. Carlsson, J.W. Gillespie Jr.). 5. Relationship of matrix toughness to interlaminar fracture toughness (W.L. Bradley). IIB. Fracture of Short Fiber Reinforced Thermoplastics. 6. Microstructure and fracture mechanical performance of short fiber reinforced thermoplastics (J. Karger-Koscis). 7. The Crack layer approach to polymers and composites (A. Dolgopolsky, J. Botsis). IIC. Complex Fracture in Composite Laminates. 8. Damage mechanisms, including edge effects, in carbon fiber reinforced composite materials (K. Schulte, W.W. Stinchcomb). 9. Fracture mechanics of notched carbon/epoxy laminates (K. Kageyama). 10. Environmental effects on fracture mechanical properties of polymer composites (G. Marom). 11. Fractographic analysis of polymer composites (K. Friedrich). III. Fracture of Metallic, Ceramic and Natural Composites. 12. Fracture mechanical approach to metal matrix composites (S. Ochiai). 13. The mechanical properties and fracture behaviour of ceramic matrix composites (CMC) reinforced with continuous fibres (R.W. Davidge). 14. Fracture of whisker reinforced ceramics (R. Warren, V.K. Sarin). 15. Fracture toughness of natural composites with reference to cortical bone (W. Bonfield, J.C. Behiri). IV. Concluding Remarks. 16. Concluding remarks on the application of fracture mechanics to composite materials (F.X. de Charentenay).

Fractal Dimension of Fault Systems in Japan: Fractal Structure in Rock Fracture Geometry at Various Scales

Abstract: Based on fault maps, whether or not the fracture geometry of rocks is self-similar, was examined by using a box-counting algorithm. The statistical self-similarity (fractal structure) of the fault fracture systems holds well at the scale of about 2 to 20 km. The fractal dimension in Japan varied from 1.05 to 1.60. The fractal dimension is about 1.5–1.6 at the central part of the Japan Arc, and decreases with distance from the center. At a smaller scale, the fractal structure also holds well in the rock fracture geometry. The fractal dimension of the North Izu Peninsula fault system (branching faults) is 1.49 at the scale of 0.625 to 10 km, the fractal dimension of rock fracture geometry at the scale order of 10−1 to 10−2 meters is about 1.49–1.61. The upper limit of the fractal dimension of rock fracture geometry is about 1.6, judging from the estimation of fractal dimension on actual fracture geometry of rocks. This value may impose a restraint on modeling of faulting and the fracture process of rocks.

Inferring paleostresses from natural fracture patterns; a new method

Abstract: We introduce a method to infer the remote differential stress magnitude from the curvature of overlapping echelon fracture traces. The curving paths of overlapping echelon cracks imply the predominance of local crack-induced stresses over remote stresses during propagation. Nearly straight crack paths imply the controlling influence of a remote compressive crack-parallel differential stress. This method is used to interpret complex joint patterns mapped in sedimentary rock. It is also applied to the problem of fracture-pattern generation using computer models.

Fracture-surface analysis of dental ceramics

Abstract: This study demonstrated that quantitative fractography can be used to study failed aluminous and glass-ceramic central porcelains. Fracture surfaces of DICOR and Vitadur-N core porcelain modulous-of-rupture bars were studied to identify fracture mirror features useful in (1) locating the source of fracture and (2) calculating the stress at fracture in clinically failed restorations. The morphology of fracture surfaces results from events related to the initiation and propagation of the crack front during failure. Modulus-of-rupture testing was performed in four-point bending. Fracture surfaces were studied by scanning electron microscopy. The mean fracture stress for the Vitadur-N porcelain was 94.7 +/- 12.4 MPa (13,730 psi); for DICOR the fracture stress was 55.4 +/- 10.6 MPa (8,030 psi). The standard quantitative fractography relationship between in mirror radius and ln fracture stress was followed for both materials. This quantitative fractography relationship was used to calculate the in vivo stress at failure in a clinically fractured DICOR molar crown. Five clinically failed DICOR crowns were seen to fail from the internal surface.

Flow channeling in a single fracture as a two-dimensional strongly heterogeneous permeable medium

Abstract: The void space of a rock fracture is conceptualized as a two-dimensional heterogeneous system with variable apertures as a function of position in the fracture plane. The apertures are generated using geostatistical methods. Fluid flow is simulated with constant head boundary conditions on two opposite sides of the two-dimensional flow region, with closed boundaries on the remaining two sides. The results show that the majority of flow tends to coalesce into certain preferred flow paths (channels) which offer the least resistance. Tracer transport is then simulated using a particle tracking method. The apertures along the paths taken by the tracer particles are found to obey a distribution different from that of all the apertures in the fracture. They obey a distribution with a larger mean and a smaller standard deviation. The shift in the distribution parameters increases with increasing values of variance for the apertures in the two-dimensional fracture. Provided that the correlation length is no greater than one fifth of the scale of measurement, the aperture density distributions of tracer particle paths remain similar for flow in two orthogonal directions, even with anisotropy ratio of spatial correlation up to 5. These results may be applicable in general to flow and transport through a two-dimensional strongly heterogeneous porous medium with a broad permeability distribution, where the dispersion of the system may be related to the parameters of the permeability distribution along preferred flow channels.

Transport of fluid and electric current through a single fracture

Abstract: One expects the hydraulic and electrical conductivities of rock to be related, since there is an analogy between the differential equations describing each process. Fractures in rock are commonly described by the parallel plate model, where the fracture surfaces are smooth and parallel with a separation or aperture of /ital d/. For this model the hydraulic conductivity is proportional to /ital d//sup 3/, whereas the electrical conductivity is proportional to /ital d/. Deviations from the parallel plate model are expected, since real fracture surfaces are rough and in partial contact. Computer simulations of fluid flow and conduction of electricity were performed on simulated fractures composed of rough surfaces generated with a fractal algorithm. The finite difference method was used to calculate the volume flow rate and electric current. This solution was used in the parallel plate model to get an effectie hydraulic aperture /ital d//sub h/ and electric aperture /ital d//sub e/. The electric and hydraulic apertures are nearly the same when the surfaces are widely separated. However, /ital d//sub e/ is always smaller than /ital d//sub h/, with the difference increasing as the fracture closes. Additionally, the local directions of fluid flow and electric current are not the same.more » Thus contrary to the common assumption, the actual path length of a fluid particle as measured by the tortuosity is different for each process. The results of these simulations are consistent with the ''equivalent channel model,'' which shows that by introducing the tortuosity of the fluid flow or electric current paths, one can relate the microscopic physics of the transport properties to the macroscopic behaviors described by Darcy's and Ohm's laws. /copyright/ American Geophysical Union 1989« less

Fracture spacing and its relation to bed thickness

Abstract: Using examples from the Gulf of Suez and southeastern France, the distribution of tension tectonic joints as well as shear tectonic joints in continuous profiles is shown to fit a Gamma distribution. The parameters of this distribution are determined using the maximum likelihood method. Apparent fit with negative exponential distribution in photointerpretation analysis results from lack of resolution. The average joint spacing is directly proportional to bed thickness; it decreases when the degree of rock consolidation increases.

Formation and geometry of fractures, and related volcanism, of the Krafla fissure swarm, northeast Iceland

Abstract: During the past 12 yr, a major volcano-tectonic episode occurred in the Krafla fissure swarm at the divergent plate boundary in north-east Iceland. This swarm is an 80-km-long and as much as 10-km-wide zone of tension fractures, normal faults, and volcanic fissures. The average length of 1,083 measured tectonic fractures is about 350 m, the maximum length being 3.5 km, and the average estimated depth is of the order of 102 m. Most fractures strike north to north-northeast, with widths as much as 40 m and throws of as much as 42 m. Pure tension fractures are most common, but as they grow they commonly change into normal faults. Most fractures gradually thin out at their ends, but several exceptionally wide tension fractures end in tectonic caves, several tens of meters long, only a few meters beneath the surface. The total dilation measured in 5 profiles across the Krafla swarm reaches a maximum of at least 80 m and decreases from south to north along the swarm. Some 20 intrusive events and 9 eruptive events occurred during this volcano-tectonic episode. New lavas covered many old fractures, but several new fractures were also formed and many old ones grew. New lava flowed into some of the major fractures in the area, presumably forming pseudodikes. Locally, magma used a part of a pre-existing fracture as a pathway to the surface. Small width: length ratios of the normal faults, as compared with such ratios of the tension fractures, are attributed to the tendency of tension fractures to close as they develop into normal faults. It is concluded that divergent plate movements with dike intrusions, or pressure changes in a deep-seated changes in a deep-seated magma reservoir, are viable models for formation of the fractures.

Fracture evaluation using reflected Stoneley-wave arrivals

Abstract: We use the low-frequency reflected Stoneley-wave mode to locate permeable fractures intersecting a borehole and to estimate their effective apertures. Assuming a model in which the average aperture of the fracture is roughly constant, theoretical work relates the magnitude of the Stoneley-wave reflectivity to an effective fracture width. We treat both the case of a horizontal fracture and the case of a fracture crossing the borehole at an angle.Laboratory experiments verify the analytic solution for the case of a horizontal fracture. Full-waveform array sonic data were also acquired in a wellbore with a long recording time (25.5 ms) in order to capture the late Stoneley-wave arrivals. The data processing involves computation of the Stoneley-wave reflectivity response using the measured direct and reflected Stoneley-wave arrivals. A least-squares fit to the arrival time of the reflected-wave arrivals is used to estimate the locations of permeable fractures, and the effective width of the fractures is estimated by comparing the computed Stoneley-wave reflectivity to the theoretical response from a parallel-plate model. Test-well results are consistent with a borehole televiewer analysis.

On the mechanics of crack closing and bonding in linear viscoelastic media

Abstract: The mechanics of quasi-static crack closing and bonding of surfaces of the same or different linear viscoelastic materials is described. Included is a study of time-dependent joining of initially curved surfaces under the action of surface forces of attraction and external loading. Emphasis is on the use of continuum mechanics to develop equations for predicting crack length or contact size as a function of time for relatively general geometries; atomic and molecular processes associated with the healing or bonding process are taken into account using a crack tip idealization which is similar to that used in the Barenblatt method for fracture. Starting with a previously developed correspondence principle, an expression is derived for the rate of movement of the edge of the bonded area. The effects of material time-dependence and the stress intensity factor are quite different from those for crack growth. A comparison of intrinsic and apparent energies of fracture and bonding is made, and criteria are given for determining whether or not bonding can occur. Examples are given to illustrate use of the basic theory for predicting healing of cracks and growth of contact area of initially curved surfaces. Finally, the effect of bonding time on joint strength is estimated from the examples on contact area growth.

Mode-II Interlaminar Fracture of Composites

Abstract: This chapter will present fracture mechanics and experimental mechanics approaches used to characterize mode-II interlaminar fracture of composites. This chapter is organized into four major sections: background, analytical, numerical, and experimental results. The first section documents from an historical viewpoint, the various mode-II specimen geometries that have been proposed prior to the emergence of the end notch flexure (ENF) specimen as the most frequently used test method to characterize mode-II interlaminar fracture toughness. The second section focuses on analytical approaches to model the ENF specimen that includes shear deformation beam theory, shear deformation plate theory where the crack-tip singularity is introduced as a surface traction and a higher-order beam theory. Specimen design procedures to maintain linear elastic response and to minimize geometric non-linearities and friction between crack surfaces are presented. The third section reviews numerical results. Compliance, strain energy release rates, delamination offset from the mid-plane and frictional effects are investigated. Results are compared to analytical solutions. The last section reviews experimental mechanics techniques used to characterize the static mode-II interlaminar fracture toughness of composites.

A three‐dimensional hydraulic fracturing simulator

Abstract: The propagation of non-planar hydraulic fractures is modelled using a three-dimensional numerical simulator. This paper describes the different components of the model (stress/displacement analysis, fluid-flow analysis, propagation criterion) with an emphasis on the numerical techniques used. A few examples of out-of-plane fracture geometries are provided.

Relationship of Matrix Toughness to Interlaminar Fracture Toughness

Abstract: The relationship of resin fracture toughness to delamination fracture toughness is considered in this chapter. The resin toughness is seen to play a dominant role in the interlaminar fracture of composite materials. In situ observations of fracture in the SEM indicate that increasing the ductility and decreasing the yield strength of the matrix resin increase the delamination fracture toughness by increasing the plastic (or non-linear viscoelastic) zone size ahead of the crack tip, giving greater load redistribution away from the crack tip and more crack-tip blunting. The low efficiency of translation of resin fracture toughness into delamination fracture toughness for very ductile resins is the result of constraint provided by the fibers in the adjacent plies to the development of a larger plastic zone. The surprisingly high mode-II delamination toughness observed in composites made with brittle resins is due to the nature of the fracture process; namely, the formation of sigmodial shaped microcracks over a considerable distance ahead of the crack tip, giving significant load redistribution.

Fracture Toughness of Polycrystalline Ceramics in Combined Mode I and Mode II Loading

Abstract: The present investigation of the fracture of alumina and zirconia polycrystalline ceramic specimens of precracked-disk type, in diametral compression, evaluated fracture toughness in pure mode I, combined mode I/mode II, and pure mode II, depending on the alignment of the center crack relative to the loading diameter. The mixed-mode fracture-toughness envelope thus obtained exhibits significant deviation to higher fracture toughness in mode II, relative to the predictions of linear elastic fracture mechanics theory. Crack-surface resistance due to grain-interlocking and abrasion are identified as the primary sources of increased fracture resistance in mode II loading of the polycrystalline ceramics.

Size Effects on Strength, Toughness, and Ductility

Abstract: Strain localization for slabs in tension and curvature localization for beams in flexure are associated with the fracture toughness of the material. Even if no initial cracks are supposed to exist in the sturcture, the concepts of fracture mechanics are applicable. Size‐scale and slenderness are demonstrated to have a fundamental influence on the global structure behavior, which can range from ductile to brittle when softening is taken into account. Whereas in classical plasticity and damage theory geometrically similar structures exhibit congruent behavior since only energy dissipation per unit volume is allowed, when energy dissipation per unit area is also considered (strain or curvature localization), the global brittleness becomes scale‐dependent. A limit analysis for beams in flexure is proposed, taking into account the cohesive forces developing between the two opposite crack surfaces. Such a simple approach shows a clear trend toward brittle behavior and catastrophic events for large size and slen...

Mechanisms for rate effects on interlaminar fracture toughness of carbon/epoxy and carbon/PEEK composites

Abstract: The objective of this study was to investigate strain-rate dependent energy absorption mechanisms during interlaminar fracture of thermosetting (epoxy) and thermoplastic (PEEK) uni directional carbon fibre (CF) composites. A simple model addressing the translation of matrix toughness to mode I and mode II interlaminar toughness of the composite is presented, in conjunction with a fractographic examination of the fracture surfaces and the fracture process. The observed rate dependency of composite fracture toughness is attributed to the rate dependent toughness of the viscoelastic matrix and the size of the process zone around the crack tip. Other important factors identified are the roughness of the fracture surface and fibre bridging.