Fractures propagation

Lee, W.S. "Fracture Propagation Theory and Pressure Decline Analysis with Langrangian Formulation for Penny-Shaped and Perkins-Kern Geometry Models," SPE paper 17151, SPE Formation Damage Control Symposium, Bakersfield, February 8-9. 

A fracture propagating perpendicular to the fibers can be considered as having many energy dissipative component mechanisms all of which add up to provide the fracture toughness of the material. 

Figure 2. Ageing temperature influence on average rate of slowing down fracture propagation in water ...

Research by Battelle also shows that the Charpy V-notch energy required to prevent ductile fracture propagation can be calculated by the following equation ... 

Usually the radius of curvature p at the sharp notch of the crack is determined by the atomic sizes and is very small. It is immediately evident that the stress concentration at the sharp notches of the microcracks can become extremely large due to the above stress intensity factor, and the fracture should start propagating from there. Although this analysis indicates clearly where the instabilities should occur, it is not sufficient to tell us when the instability does occur and the fracture propagation starts. This requires a detailed energy balance consideration. 

Typically, the kinetic energy Ek of fracture propagation can be estimated as... 

The above results are all for a perfect solid under stress, with a single microcrack inside. For randomly disordered solids, the appropriate modification of the above Mott formula has not been developed yet. However, some quantitative features of the fracture propagation process in extremely disordered solids, like the percolating solid near its percolation threshold, are quite obvious and interesting. Although the (equilibrium) strength erf of the solid vanishes near the percolation threshold Pc erf (Ap) ), the... 

As mentioned earlier, although the fracture propagation velocity can theoretically approach the transverse sound velocity in the solid, in practice... 

Fig. 3.19. Molecular dynamic simulation results for the fracture propagation in amorphous structures (with Lennard-Jones potential) show that the average fracture velocity crosses over to a higher value (ufinai from Uinitiaij indicated by the dotted lines) at the late stages of growth, as the crack size exceeds the typical size (correlation length) of the voids in the network. The inset shows that a corresponding crossover in the fractured surface roughness exponent also occurs along with the crossover in the fracture velocity (from Nakano et al 1995).

Such behaviour of fracture propagation can clearly be of extreme importance for practical purposes. For example, the fraction r, from the measurement of the sound velocity ratio of compressional and shear waves, can indicate the proximity of the imminent macroscopic failure or fracture of... 

As the fracture propagates, the elastic energy released due to the micro-fractures occurring within the sample can be measured. This ultrasonic emission due to micro-fracture aftershock relaxation has recently been measured for various laboratory samples. Petri et al (1994) measured the ultrasonic emission amplitude distribution in a large number of stressed solid samples under different experimental conditions. A power law decay for the cumulative energy release distribution n Er) with the released energy amplitude Er was observed in all cases n Er) E (see Fig. 3.21). This is indeed very similar to the Guttenberg-Richter law for the frequency distribution of earthquakes, as discussed briefly in Chapter 1, and will be discussed in detail in the next chapter. 

The role of disorder, in particular of the fractal structure of the earthquake faults (discussed in Section 4.4), are not clearly understood. As discussed in an earlier chapter (Section 3.8), the dynamics of fracture in disordered solids also indicate similar (Guttenberg-Richter type) power law behaviour in the power spectrum of the ultrasonic emission from such solids, as the fracture propagates. No doubt the understanding of the connections between the dynamics of fracture in disordered solids and the dynamics of earthquakes will become much clearer in the near future, because of the intensive efforts which are being made currently. 

Clemens J. D. and Mawer C. K. (1992) Granitic magma transport by fracture propagation. Tectonophysics 204, 339-360. 

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