Void nucleation

Evidence suggests that there is a threshold tensile stress at which void nucleation occurs and spall fracture initiates. Materials subject to transient internal tensions can support tensile stresses significantly in excess of this threshold level, however. Such behavior is a consequence of kinetics and inertia associated with the nucleation and growth of voids during spall. A fairly large body of experimental and theoretical literature on spall phenomena exists and many aspects of the effect are reasonably well understood. Review articles on spall (Curran et al., 1977 Davision and Graham, 1979 Curran, 1982 Meyer and Aimone, 1983 Novikov, 1981) provide access to most of the literature on the subject. 

A void nucleation and growth fracture model embedded in a general viscoelastic-plastic material model is representative of approaches to ductile dynamic fracture (Davison et al., 1977 Kipp and Stevens, 1976). Other approaches include employing the plastic strain as a damage variable (Johnson and Cook, 1985) so that both spall and large strain-to-failure can be treated. 

We consider conditions where there is no significant island or void nucleation on the terraces, and surface mass transport is associated with the addition and removal of material from the preexisting surface steps. This provides an important simplification since the number of steps is now a conserved quantity and we do not have to deal with problems arising from the annihilation of steps of different sign. 

For pure water voids, void nucleation is instantaneous. For air-water voids, air void nucleation or entrapment has already occurred during lay-up or at the beginning of the cure cycle. 

The second ramp portion of this cure cycle is critical from a void nucleation and growth standpoint. During this ramp, the temperature is high, the resin pressure can be near its minimum, and the volatile vapor pressure is high and rising with temperature. These are the ideal conditions for void formation and growth. 

Fig. 7.10 (a) Schematic illustration of void nucleation from grain boundary sliding, (b) TEM micrograph taken from the fatigue crack tip (R = 0.15, T = 1400°C, and vc = 0.1 Hz) showing the formation of the void in the alumina/SiC composite. From Han and Suresh, MIT. 

Note the meniscus of the glass phase within the triple-junction cavity.) Quantitative estimation of the conditions of void nucleation due to the negative pressure of a constrained fluid has been given in Refs. 16 and 60. 

The escape of CO gas at the reaction site can occur via diffusion through the reaction products. However, if CO diffusion through the reaction products is slow, the CO partial pressure can increase to levels sufficiently high to cause void nucleation and cracking. The development of cracks greatly accelerates the outward diffusion of CO and also inevitably degrades the mechanical properties of the composite. 

Similar craze breakdown morphologies have been observed for dust-free films of polymethylmethacrylate (PMMA), poly(a-methylstyrene) (PaMS) and poly(styrene-acrylonitrile) (PSAN) Large pear-shaped voids nucleate at the craze-bulk polymer interface, never in the craze mid-rib, and thus this mode of craze breakdown seems to be a dominant one for all glassy polymers. 

Currently, the best ODS Fe3Al spalls more readily than commercial ODS FeCrAl alloys. This is attributed to more rapid interfacial void nucleation and growth in the case of ODS Fe3Al. 

The role of the POE phase is more complex. As many elastomers, it undergoes extensive cavitation when it is hydrostatically loaded within the interphase layers and the isolated nodules. However, it is often seen in the micrograph (especially after stress triaxiality has been released by void nucleation) that POE is capable to undergo considerable stretching without further damage. The net effect could thus be to reduce volume strain. 

A vacancy is created in the metal phase, which can be aimihilated by operations of structural defects, disorientation, and misfit dislocations [116, 117]. Prolonged sulfidation also can cause void nucleation and cavity growth at the interface. In the case of sulfidation by liquid sulfur, the separation of sulfide and metal by cavities could be avoided by applying a pressure on the growing sulfide [13-18]. 

The adsorbed hydrogen-induced model is based on the fact that the adsorbed atoms weaken interatomic bonds at crack tips and thereby facilitate the injection of dislocations (alternate slip) at crack tips. Crack growth occurs by alternate slip the crack tips, which promotes the coalescence of cracks with small voids nucleated ahead of the cracks. 

More examples can be found in two textbooks, Shaw (2004), which takes the view that fracmre (void nucleation) is more important than adiabatic shear for the initiation of serrated chip formation, and Trent and Wright (2000), which considers secondary shear (stick-sUp motion between the chip and tool) as additionally influencing behavior, and one research mmio-graph (Tonshoff and Hollmann 2005). 

Gurson, A. L. (1977) Continuum theory of ductile rupture by void nucleation and growth part I - yield criteria and flow rules for porous ductile media, J. Eng. Mater. Technol., 99, 1-15. 

In this section we will use a slightly different trick to solve the nucleation problem. This trick is particularly useful for solving very complex nucleation problems on a computer. While we have previously used this trick, which is more powerful than that of McDonald, to solve the problem of void nucleation in nuclear reactors (discussed in Section 6), it has never been fully explained in the literature. We will do so now. The exposition in this section, combined with the further explanation of using this trick in Section 5, will enable the reader to solve almost any complex nucleation problem without having to find a closed-form expression for the nucleation rate as was done in the previous section using McDonald s trick. 

There was one problem with this program. Various experiments suggested that the voids in the neutron (reactor) irradiated materials contained helium. Helium is formed rapidly during neutron irradiation as a decay product. Harkness et had shown that the swelling is a nucleation-controlled process. As the accelerator ion bombardment experiments, intended to mimic the reactor neutron bombardments experiments, do not produce helium within the sample, it is important to ask what effect helium has on the void nucleation problems. 

---