Composite structures are also susceptible to damage from accidental impact or cyclic loading (tension, compression, shear, bending, etc.) during service, storage, and routine maintenance.18,19 This damage is mainly in the form of delamination failure and matrix microcracking. In particular, invisible delamination may occur in the interlayer resin-rich region, which results in a drastic drop in the load-carrying capacity of the composite structure;20,21 this is the key failure mode limiting the service life of a composite.
where KI is the Stress Intensity Factor (SIF) for each of the fracture mode. The use of SIFs assumes that the singular stresses dominate the stress field near the crack front, thus neglecting higher order terms of the Williams series. It can be easily seen that the stress field shows a singularity when r tends toward zero.
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Dependency of fatigue analysis location and initial crack length in fretting fatigue lifetime. (a) Von Mises stress contour showing the high stress gradient present in fatigue phenomena. (b) and (c) Schematic representation of the influence of fatigue analysis location in the crack initiation cycle prediction (Ni) and the influence of initial crack length in the propagation cycle estimation (Np), respectively.
The experimental results for transport flow path aperture, permeability, and porosity are listed in Table 2. Figure 3(a) shows the variation of with confining pressure, where tends to increase systematically with confining pressure. Figure 3(b) shows the flow path aperture calculated from as a function of confining pressure. The flow path aperture decreases with increasing confining pressure for all samples, although the flow path apertures are considerably smaller for the sample treated at 400C. This suggests that thermal damage due to the α- to β-quartz transition results in significant crack opening.
For a medium in which permeation occurs through interconnected and randomly distributed thin cracks, the following model has been used [28, 29]:where is the crack radius and is the aspect ratio (), which is assumed to be constant at . The constant is dimensionless and depends on the tortuosity of the crack network and shape factor as follows [30, 31]: . Tortuosity was calculated by inserting the measured values of and into Eq. (6), to evaluate the relevance of to . Tortuosity decreased with decreasing permeability, ranging from 17 to 3 (Figure 8). Pore connectivity is related to the reciprocal of the tortuosity squared [32]. Thus, the tortuosity reduction corresponds to increasing crack network connectivity. Our results indicate that the connectivity increases with decreasing porosity due to the closure of cracks. Details of the calculation are given in the next section.
Gueguen and Dienes [32] showed that permeability can be expressed as follows:where is the fraction of cracks that contribute to the flow, which is zero when the probability of crack intersection is below the percolation threshold [34]. Note that differs from the crack network connectivity described in the previous section. If decreases, the network connectivity invariably decreases, but can increase if decreases more than . is the ratio of interconnected cracks to the total cracks and can be expressed as follows:where is the probability that a path from one site passing through an adjacent site will be interrupted (Gueguen and Palciauskas, 1994). This suggests that the connectivity factor represents flow paths that belong to the infinite cluster and propagate in various directions. However, we determined the permeability from the flow rate in the axial direction of the sample (Figure 11). Therefore, the permeability obtained in this study needs to be expressed by a connectivity factor that is different from .
This indicates that although the connectivity in the flow path network is significantly reduced with decreasing permeability, the fraction of cracks that contribute to flow in the axial direction of the sample increases; consequently, fluid flow is mostly dominated by a specific path in a relatively impermeable medium (Figure 13). The existence of preferential flow paths has been proposed based on numerical simulations of two-dimensional heterogeneous systems, which have been used as an analog for pore geometry in porous rocks [35, 36]. Our experimental results for thermally cracked granite suggest that permeability is dependent not only on porosity and flow path aperture but also on the fraction of cracks that contribute to flow.
We investigated the relationship between permeability and pore characteristics by taking into account the fraction of hydraulically connected cracks that contribute to flow in the axial direction under confining pressure. The variable appears to be required for the case where fluid flow occurs in a specific direction in the subsurface (e.g., the production of geothermal energy by fluid flow in the direction between the inlet and outlet wells).
We have presented experimental data for the permeability, porosity, and flow path aperture of thermally cracked granite under hydrostatic conditions. Using the gas breakthrough method, we measured the crack aperture of samples subjected to elevated pressure. In all experiments, the confining pressure increased as permeability decreased, due to the closure of cracks. Based on the relationships between permeability, porosity, and flow path aperture, permeability is inferred to be controlled mainly by variations in the crack aperture as follows: . A comparison of the obtained equation with the permeability model [32] indicates that fluid flow is more concentrated on a specific path with decreasing permeability. To obtain a more detailed permeability model, quantitative analysis of the effects of geometric factors, such as the crack network and aperture, at hydrostatic pressures is required. 2ff7e9595c
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