Fracture Toughness Determinations by Indentation

A review is presented of the experimental data on subcritical crack growth in geological materials. The main parameters describing subcritical crack growth are the critical stress intensity factor Kc, the subcritical crack growth limit Ko, and the stress intensity factor-crack velocity (K-v) relationship between Ko and Kc. The K-v data are presented in terms of an equation in which the crack velocity depends on stress intensity factor raised to a power n because this is common practice in experimental studies. These data are presented as tables and in synoptic diagrams. For silicates the value of n increases as the environment becomes depleted in hyroxyl species and with increase in the microstructural complexity of the solid. Values of n as low as 9.5 have been found for tensile cracking of quartz in basic environments and as high as 170 for tensile cracking of basalt in moist air. Insufficient experimental data are available to predict subcritical crack growth behavior at depth in the earth's crust without major extrapolations of the data base. Schematic outlines are presented, therefore, of the probable influence on subcritical crack growth of some key parameters in the crustal environment. These include stress intensity factor, temperature, pressure, activity of corrosive environmental agent, microstructure, and residual strains. In addition, a discussion is presented of the likely magnitude of the subcritical crack growth limit. For stress corrosion tensile crack growth of quartz a limit of approximately 0.2 of the critical stress intensity factor is inferred from theoretical calculations. Further problems discussed with regard to the extrapolation of experimental data to crustal conditions include the choice of a suitable equation to describe crack growth and the magnitude of parameters in these equations. A brief discussion of the double torsion testing method is presented in order to aid the interpretation of experimental results because it is almost the sole method used to study subcritical cracking in rocks.

Subcritical crack growth in geological materials

Gas production from the Barnett Shale relies on hydraulic fracture stimulation. Natural opening-mode fractures reactivate during stimulation and enhance efficiency by widening the treatment zone. Knowledge of both the present-day maximum horizontal stress, which controls the direction of hydraulic fracture propagation, and the geometry of the natural fracture system, which we discuss here, is therefore necessary for effective hydraulic fracture treatment design. We characterized natural fractures in four Barnett Shale cores in terms of orientation, size, and sealing properties. We measured a mechanical rock property, the subcritical crack index, which governs fracture pattern development. Natural fractures are common, narrow (0.05 mm; 0.002 in.), sealed with calcite, and present in en echelon arrays. Individual fractures have high length/width aspect ratios (1000:1). They are steep (75), and the dominant trend is west-northwest. Other sets trend north-south. The narrow fractures are sealed and cannot contribute to reservoir storage or enhance permeability, but the population may follow a power-law size distribution where the largest fractures are open. The subcritical crack index for the Barnett Shale is high, indicating fracture clustering, and we suggest that large open fractures exist in clusters spaced several hundred feet apart. These fracture clusters may enhance permeability locally, but they may be problematic for hydraulic fracture treatments. The smaller sealed fractures act as planes of weakness and reactivate during hydraulic fracture treatments. Because the maximum horizontal stress trends northeast-southwest and is nearly normal to the dominant natural fractures, reactivation widens the treatment zone along multiple strands.

Natural fractures in the Barnett Shale and their importance for hydraulic fracture treatments

http://www.ibmc.up.pt/projectos/FJMonteiro/Researchers/AHDeAza/08_AHdeAza_Biomaterials_23%203%20937-945%202002.pdf

Crack growth resistance of alumina, zirconia and zirconia toughened alumina ceramics for joint prostheses.

The objective of this research was to show the reinforcing effects of nanofibers in an epoxy matrix and in a rubber matrix using electrospun nanofibers of PBI (polybenzimidazole). The average diameter of the electrospun fibers was around 300 nanometers, which is less than one tenth the diameter and 1/100 the cross sectional area of ordinary reinforcing fibers. The ultrafine fibers provide a very high ratio of surface area to volume. The nanofibers toughened the brittle epoxy resin. The fracture toughness and the modulus of the nanofiber (15 wt%)-reinforced epoxy composite were both higher than for an epoxy composite made with PBI fibrids (17 wt%), which are whisker-like particles. In an elastomeric matrix, The Young's modulus and tear strength of the chopped nanofiber-reinforced styrene-butadiene rubber (SBR) were higher than those of the pure SBR. Micrographs of the fracture surfaces were obtained by scanning electron microscopy (SEM).

Mechanical properties of composites using ultrafine electrospun fibers

A simple, inexpensive method for studying slow crack growth is described. The method entails measurements of load relaxation at constant displacement using a double torsion specimen. It is demonstrated that the data generated using this technique are in excellent agreement with data obtained using the more complex conventional techniques, for a range of materials - steel, titanium, glass, aluminum oxide, PMMA. These encouraging initial results suggest that additional and more detailed studies using this test procedure are merited.

D. P. Williams

Papers

A simple method for studying slow crack growth.