Growth Velocities

The theoretieal fraeture parameters in (8.22) and (8.23), based on a model assuming an inherent power law fracture flaw distribution and a constant fracture growth velocity, can be determined with the strain rate dependent fracture data in Fig. 8.11 (Grady and Kipp, 1980). Using the fracture data for oil shale provides a value of m = 8 and a fracture stress dependence on strain... 

The energy release rate (G) represents adherence and is attributed to a multiplicative combination of interfacial and bulk effects. The interface contributions to the overall adherence are captured by the adhesion energy (Go), which is assumed to be rate-independent and equal to the thermodynamic work of adhesion (IVa)-Additional dissipation occurring within the elastomer is contained in the bulk viscoelastic loss function 0, which is dependent on the crack growth velocity (v) and on temperature (T). The function 0 is therefore substrate surface independent, but test geometry dependent. 

In Eq. (76) we neglect the kinetic effects, that is, the dependence of the interface temperature on the growth velocity v . The approximation holds at sufficiently small undercoolings and velocities. 

Eqs. (74-78) contain two dimensional parameters, and D, and two dimensionless parameters, A and e. This means that any characteristic length scale i and growth velocity v of the possible structures can be presented in the form... 

The patient will present with reduced growth velocity and delayed skeletal maturation. 

K Linear pellet growth velocity in V Mean pellet volume... 

In the classical Lauritzen-Hoffman theory for the mechanism of polymer crystal growth [106], it is assumed that the observed lamellar thickness corresponds to those crystallites that happen to have the largest growth velocity. However, this picture is hard to reconcile with the experimental observation that the thickness of polyethylene single crystals can be modulated by varying the temperature at which they are grown [117,118]. In fact, simulations by Doye et al. [119,120] suggest that the observed lamellar thickness does... 

In the dense regime, the superficial current density i and the growth velocity can be related to one another by a material balance around the growth front [12, 13], If the rate of deposition is imposed by a constant applied current density, and all of the metal in solution is consumed by the passing growth front, the ratio of deposition rate to metal ion concentration C fixes the velocity. 

TABLE 57-3 Expected Growth Velocities in Term Infants and Children ... 

Values of 6a/p are 1 for spheres and cubes and 0.816 for octahedra and typical values of the mean linear growth velocity, // (= 0.5 Gd) for crystals 0.5-1 mm growing in the presence of other crystals are given in Table 15.4 which is taken from Mullin(3). 

A simple correlation was noticed by Donnay and Harker, (10) between the interplanar spacing of a crystallographic plane, d, and its area on an average crystal. A similar correlation holds between d and the frequency with which the plane (hkl) appears in an ensemble of crystals. Since an area of a plane is roughly proportional to the inverse of its (linear) growth velocity R, the Donnay-Harker law is equivalent to stating that R 1/dj. 

Reduction in growth velocity Closely follow the growth of adolescents taking corticosteroids, and weigh the benefits of corticosteroid therapy and asthma control against the possibility of growth suppression. 

Figure 5.9 shows the time evolution of the radii of selected 2D spherulites from Fig. 5.8. We observe that the process is non-linear and accelerated, (fR/df > 0. It is also interesting to notice that, at a given time, the radial growth velocity Ur = dR/dt (slope) is nearly the same for all spherulites, which implies that it depends on the deposition time and certainly not on the radius of the spherulites. In the case discussed here the thickness of the film is increasing with time because of continuous exposure to the molecular beam. The non-linearity is more pronounced at the beginning of the experiment (roughly between 250 and 350 s) and the velocity nearly tends towards an asymptotic value, so that 2D spherulites that are formed last show almost linear growth.

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