Nucleation of voids

Homogeneous nucleation may be described by assuming that critical-size nuclei will be formed from ideal vapor (water or air) at a rate, I, given by classical nucleation theory [4]. The equation is 

P = water vapor pressure, air pressure, or total mixture pressure (water plus air) M = molecular weight of the vapor phase 

The free energy barrier AF and the critical nucleus size r are given by [4] 

It is far more likely that heterogeneous nucleation plays the governing role in nucleation of voids. The effect of a particle or substrate is to lower the free energy barrier AF. Thus, Equations 6.1 and 6.3 remain unchanged, and Equation 6.2 takes on the new form 

Equation 6.1 provides the rate at which stable nuclei will form. It also demonstrates the clear rate dependence on the temperature, surface energy, and transition enthalpy. 

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The craze nucleation in bulk polymers results from nucleation of voids in the plane strain region of the sample to relieve the triaxial constraints. 

It seems reasonable to assume that crazing is a process which can occur quite naturally in any orientation hardening material, which exhibits plastic instability at moderate strains and in which the yield stress is much higher than the stress required for the nucleation of voids (cavitations). 

Table 3.13 shows that the kinetic factor A increases with temperature. This fact cannot be explained without knowing the concrete mechanism of formation of the holes in the foam bilayer. A possible explanation is the occurrence of hole nucleation on preferred sites, for example along line defects (such as domain boundaries) in the bilayer. A similar preferential nucleation of voids on structural defects is known to occurs in crystals [422], If the density N0 of these preferred sites in the bilayer decreases with increasing temperature, according to Eq. (3.125). A will increase with Tprovided oKT) dependence is not significant. 

Fig. 2a—c. Schematic drawing of several postulated microscopic steps in craze nucleation a Formation of a localized surface plastic zone and buildup of significant lateral stresses, b Nucleation of voids in the zone to relieve the triazial constraints, c Further deformation of polymer ligaments between voids and coalescence of individual voids to form a void network... 

Craze nucleation appears controlled by the nucleation of voids in localized regions undergoing large unstable plastic deformation. The sensitivity of this process to the nature of the flaw structure of the surface makes a detailed comparison of data between different experimental groups or between experiment and theory very difficult. 

Fig. 16. Schematic of crack development in crazes I. stress direction and craze orientation in a CT-specimen, 2 Growth of individual crazes, 3. Nucleation of voids and their coalescence for crack formation (A), 4. Crack through craze acceleration (B), 5. Lateral coalescence of crazes with tendency to quasi-homo-geneous deformation and subcritical crack progress...

The nucleation of voids produce a decrease of the macroscopic response of the material, by continuing deformation, they growth and coalesh as a result of strain localization causing small increments, at every cycle, of crack tip extension. 

Figure 2. Dark-field weak beam TEM images of Si/SiGe/Si structures which were in-situ implanted with Ge and furnace annealed at 600 °C (a), 650 C (b), 700 C (c) or 750 C (d) for 10 min in a dry N2 [5]. Note that the main nucleation of voids and annealing of as-implanted defects take place in the temperature range 650-750 "C.

The swelling rate as a function of dose is negligible below an incubation dose, followed by a rapid acceleration (transient regime) after which the sweUing rate tends toward a constant value. The incubation dose is sensitive to a number of parameters such as temperature, dose rate, chemical composition/microstructure, and gas content (in particular He produced by transmutation). Indeed it has been shown that the presence of gases stabilizes the three-dimensional geometry for small vacancy clusters and thus promotes the nucleation of voids [44,45]. 

Due to the effect of gases (He and possibly H) on the nucleation of voids, it is stiU an open issue whether FM will retain their swelling resistance at high doses in a fusion environment. 

For modeling purposes, plastic strain-controlled nucleation of void has been used, and is given by ... 

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