Nucleation at crack

Later in the present chapter we will examine the application of these ideas to the study of fracture and dislocation nucleation at crack tips. For our present purposes, the key point to be made was the way in which several different modeling paradigms, namely, the use of bulk and planar constitutive models, are brought under the same roof, with the consequence that the resulting model is able to do things that neither of the constituent models can do by itself... 

Fig. 10. Deformation microstructures containing perfect dislocations (the confining pressure is 5 GPa). (a) Deformation temperature T = 293 °C (101) foil plane, weak-beam dark field (4.1g, g = 202). The dislocations nucleated at crack edges are of 1/2[1 0 i](l 11) type. These half-loops are elongated along the [3 21] direction (after Rabier and Demenet [62]). (b) In the bulk, the same dislocations tend to be aligned along several Peierls valleys < 112 > /30°, < 12 3 > /4T, and screw orientation (after Rabier et al. [62]). (c) Deformation temperature T = 150 °C. Same Peierls valleys as at room temperature some strong pinning points are indicated by arrows (after Rabier et al. [61]).

Finally, some macroscopic properties should be revisited. As an example, the brittle to ductile transition could be investigated in the light of the existence of perfect dislocations. HREM and TEM experiments should be devoted to examine the very first steps of dislocation nucleation at crack tips. Passivation treatments... 

A major factor determining the importance of ceramics lies in their usefulness at high temperatures. Two types of experimental techniques are generally used in order to determine the minimum shock required to nucleate fracture (cracking), and the amount of the damage caused by thermal shock 83 the number of quenching cycles, and strength as a function of quench temperature and crack patterns. 

Schematic diagram illustrating brittle fracture. It is typical of the temperature range below 0.87g. A crack nucleates at a pre-existing flow or craze and propagates unstably. 

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. 

The dehydration of chrome alum in vacuum [58] has an induction period, followed by nucleation at a constant rate. Surface nuclei were circular, but because the rate of bulk penetration was less than that of surface advance, the growth nuclei were flattened hemispheres. The rate of initial growth of each nucleus was exponential until a diameter of about 0.1 mm was attained and remained constant thereafter. Two fypes of nuclei were recognized [40], but in only one of these had the product undergone reorganization or recrystalhzation with the appearance of surface cracking. 

Fig. 13.3. Near vicinity of a crack tip indicating the presence of dislocations nucleated at the crack tip (courtesy of D. Clarke).

Rice J. R. and Beltz G. E., The Activation Energy for Dislocation Nucleation at a Crack, J. Mech. Phys. Solids 42, 333 (1994). 

Figure 10.10. Scanning electron micrographs of crack nucleation at a typical inclusion, high and low magnifications, respectively [15].

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. 

The stress-strain behavior of ceramic polycrystals is substantially different from single crystals. The same dislocation processes proceed within the individual grains but these must be constrained by the deformation of the adjacent grains. This constraint increases the difficulty of plastic deformation in polycrystals compared to the respective single crystals. As seen in Chapter 2, a general strain must involve six components, but only five will be independent at constant volume (e,=constant). This implies that a material must have at least five independent slip systems before it can undergo an arbitrary strain. A slip system is independent if the same strain cannot be obtained from a combination of slip on other systems. The lack of a sufficient number of independent slip systems is the reason why ceramics that are ductile when stressed in certain orientations as single crystals are often brittle as polycrystals. This scarcity of slip systems also leads to the formation of stress concentrations and subsequent crack formation. Various mechanisms have been postulated for crack nucleation by the pile-up of dislocations, as shown in Fig. 6.24. In these examples, the dislocation pile-up at a boundary or slip-band intersection leads to a stress concentration that is sufficient to nucleate a crack. 

Concerning the reinforced concrete, two t) es of failure modes are known. One is referred to as bending-mode failure. In the beginning of loading, tensile cracks are nucleated at the bottom of the moment span (a portion between loading points in the case of two-point loading) due to bending... 

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