Initial crack velocity

Fig. 10.5 (a-f) Normalized crack growth velocity A a/K] l versus normalized crack extension A = ball for transient SSC crack growth under constant / loading based on a model for crack growth by grain boundary cavitation (taken from Ref. 45). The parameters K, r A0, and Ass are normalized values of, respectively, the stress intensity factor (which is held constant), the crack growth initiation time, the initial crack velocity, and the steady-state crack velocity. 

Fig. 3.17. Molecular dynamic simulation results for the onset of fracture growth instablity in a triangular lattice network with Lennard-Jones potential, having an initial crack at the left-side boundary, (a) Initial stages of growth, and (b) late stage unstable growth with large propagation velocities (Abraham et al 1994).

The second term k (t) is a dynamic correction function that was determined in a model experiment by the evaluation of caustics. These result in a set of dynamic correction functions, which in a normalised form are called Dynamic Key Curves (DKC). A dynamic key curve has been established for a specimen having a relative initial crack length a/W = 0.30 0.02, relative specimen length L/W = 5.50 0.10, and relative support span S/W = 4.0-4.2. For the range of tf addressed in this paper (tf<9.2 W/Ci where Ci is the longitudinal wave velocity in the specimen) the dynamic key curve is given by the following approximation... 

Although we do not measure crack velocity pier se, friilure during the rather short tip>-particle contact (typically 35 ms) requires a minimum crack velocity and thus a minimum K. The exponential dep>endence of crack velocity on crxy in Eq. (2) ensures that the majority of crack growth will occur when axy is close to the p>eak shear stress, starter cracks of lei th c in Eq. (2). Under these conditions, we exprect Gc to be propx>rtional to c. ... 

However, real solids contain many flaws, which become stress raisers and initiate cracks at loads much below those required for the separation of an ideal body, even if only tensile forces are applied. The stressed system is unstable and cracks expand rapidly, accelerating to high propagation velocities only the bonds at the crack tips are breaking at any instant. 

The lifetime of a structure, under a constant load or stress, can be calculated if we know (i) The initial crack size and location, (ii) the Kj versus crack length relationship and (iii) the variation in the crack velocity V with Ki. This will be illustrated for an elliptical-shaped surface crack at the bore of an HDPE pipe under internal pressure p. The crack plane is normal to the hoop stress cth, while its ellipse minor axis a is perpendicular to, and major axis b parallel to, the bore. The stress intensity factor of such a crack is given by Ewalds and Wanhill (1984) as... 

Comparable damage can occur through the repeated impact of drops or liquid jets at high velocity. After the deformability has become exhausted in tough materials, initial cracks appear that develop into breaks and progress to deep Assuring. This wear, known as drop impingement, depends on the impact. 

The features described above can be generated by either a slowly or a rapidly moving crack. There is, however, a class of features called mist and velocity hackle that are produced only when the crack velocity approaches that of acoustic waves in the material. Figure 9.7 is a micrograph of a fracture surface in glass with examples of mist and velocity hackle. This fracture initiated at the point marked O and grew... 

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