Coalescence of voids

Fig. 30. Plane strain, shear fatigue fracture surface in PC. The fracture surface is oriented approximately 4S to the load direction. Fracture occurs through coalescence of voided areas within a shear band. Repnnled courtesy of MatsumotC ...

Figure 8.29 shows the mechanism of fracture according to mode B. Void formation and growth is similar to the previous mechanisms. The differences include the coalescence of voids and a singular tearing fracture initiated by a critical size of void created from coalescence. The fracture initiates from either the side or the center (mode A from the side only) and there is no rosette region. Fiber bundles are short and small in diameter. 

Fig. 6. NucleHlion, growth and coalescence of voids (a) in the necking zone (b) near cracks and notches.

The melt-spun thermoplastic fibres, nylon, polyester, polypropylene, show a quite different form of breakage. In undrawn fibres, which are unoriented or partially oriented, rupture occurs at the end of a long period of plastic extension at slowly increasing tension. In oriented fibres, which have been drawn, the stress-strain curve terminates in a short yield region, the residual plastic extension, before rupture occurs. Break starts as a crack, usually from a flaw but otherwise self-generated by coalescence of voids. Fig. 3a. The... 

So far no account has been taken of stress distributions. The experimental evidence, de.scribed in the 3rd paper in this volume (fig. 3), is that there is ductile fracture with a crack which progressively opens into a V-notch until catastrophic failure occurs when the notch covers about half the fibre cross-section. If there is a defect, usually on the surface but sometimes internally (when the V-notch becomes a double cone), the stress concentration will lead to the start of the rupture, although it has a negligible effect on the mean fibre stress at which this occurs. If there is no defect, the evidence is that an initial crack will form by a coalescence of voids that form under high stress. Variation in the degree of orientation across a fibre may well play a part. If the skin of the fibre is more highly oriented, it will reach its limiting extension before the core. 

As a result of the simulation, the widening of the A/B diffusion zone is observed and small voids start forming at the pure B/aUoy interface. In the process of a computer experiment, the voids expand, leaving between themselves the bridges of pure B. At high temperature, we observed the subsequent coalescence of voids into a single spherical void in the center of the nanoparticle (Figure 7.23). These simulation results correlate with experiments on the formation of cobalt selenides and sulfides [4, 5, 30]. 

Migration and coalescence of voids as weU as their interactions with grain boundaries (GBs) in the presence of the electric wind force is crucial for understanding the failure mechanism. The first fundamental theory of void migration was developed by Krivoglaz [34] for an isolated spherical void and was later modified by Ho [35] for voids in the vicinity of an external surface. At that, the theory of electron wind force [36, 37] was used to demonstrate a (l/R)-size dependence of void velocity. However, the interaction of a void with GBs during electromigration (EM) was not considered. 

Void velocity depends on size as weU as trapping at GBs and leads to collisions and coalescence of voids (typically, the larger the path traversed, the larger the void). 

When the material behavior is brittle rather than ductile, the mechanics of the failure process are much different. Instead of the slow coalescence of voids associated with ductile rupture, brittle fracture proceeds by the high-velocity propagation of a crack across the loaded member. If the material behavior is clearly brittle, fracture may be predicted with reasonable accuracy through use of the maximum normal stress theory of failure. Thus failure is predicted to occur in the multi-axial state of stress when the maximum principal normal stress becomes equal to or exceeds the maximum normal stress at the time of failure in a simple uniaxial stress test using a specimen of the sane material. 

Regarding the coalescence of voids, it can be simply concluded that it is not the major source of the increase of void content either, as coalescence of voids itself does not add to the total void content in the material. In fact, while coalescence transforms smaller voids into larger ones, it correspondingly reduces the number of voids. As a result, the total void content is not considerably altered. 

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