Fracture dislocation theory

The relationship of brittle fracture to plastic deformation has, of course, been elaborated in various ways with the aid of dislocation theory, e.g. nucleation of microcracks has been discussed in terms of piling-up of dislocations [124]. Davies [145] has shown that embrittlement requires the presence of islands of martensite (about 1 pm in size) and has suggested that cracks are initiated in the martensite or at the martensite-ferrite interface. 

Mathematical Theory of Dislocations and Fracture by R. W. Lardner, University of Toronto Press, Toronto Canada, 1974. This book treats a variety of interesting problems in dislocation theory without shying away from mathematically sophisticated treatments using the elastic Green function. A reference that I return to repeatedly. 

Eringen s interest in the micromorphic theory continued when he joined the faculty of Princeton University in 1966. During the early Princeton years, he concentrated on the application of this theory to turbulence, liquid crystals, polymers, suspensions, biomechanics, and composite materials. He has always kept a deep interest in questions related to the foundations of continuum mechanics and thermodynamics. In recent years, Eringen has been the most articulate and active proponent of the nonlocal theory of continua with applications to dislocation theory, fracture problems, surface physics, composite materials, and turbulence. 

By metallurgists in terms of the mechanical properties, such as modulus, fracture toughness, ultimate tensile strength. And they came up with a theory that deals with dislocation, fracture mechanic and continuum mechanics. 

A second important event was the development by Hosemann (1950) of a theory by which the X-ray patterns are explained in a completely different way, namely, in terms of statistical disorder. In this concept, the paracrystallinity model (Fig. 2.11), the so-called amorphous regions appear to be the same as small defect sites. A randomised amorphous phase is not required to explain polymer behaviour. Several phenomena, such as creep, recrystallisation and fracture, are better explained by motions of dislocations (as in solid state physics) than by the traditional fringed micelle model. 

The history of the development of the theory of low-temperature plasticity of solids resembles very much the development of tunneling notions in cryochemistry. This resemblance is not casual it is related to the similarity of the elementary act pictures this was noted by Eyring, who successfully applied the theory of absolute rates to a description of fracture kinetics [202]. Plastic deformation at constant stress (creep) is stipulated by dislocation slip... 

The subject of fracture has already arisen in several different contexts throughout the book. In chap. 2 we described the rudiments of the theory of linear elastic fracture mechanics. In addition, in the previous chapter we described the interplay of cracks and dislocations. The current discussion is aimed at elucidating yet another feature of fracture, namely, the fact that the study of fracture serves as a paradigmatic example of some of the ideas on bridging scales introduced earlier in the chapter. 

Although this is a discussion on brittle materials, such as ceramics (glass is a perfect, brittle material), several researchers have developed theories of fracture based on dislocation models. More specifically, the shear stress created by dislocation pile-ups at some obstacle, specifically grain boundaries in polycrystaUine materials, reaches a sufficient value for crack formation. The following illustrates Stroh s [52] basic concept of microcrack formation, ultimately leading to the occurrence of fracture in brittle materials. 

Similarly to Zener s model [9] of microcrack formation at a pile up of edge dislocations, Stroh [52] developed a theory of fracture based on the concept of cracks initiated by the stress concentration of a dislocation pile-up. For brittle materials in which crack growth is not damped-out by plastic flow, Stroh calculated that the conditions for crack initiation may be given by ... 

Similar contradictions in the theory of the fracture of crystalline bodies have been resolved by expanding our understanding of the role of structural defects in crystals, and in particular dislocations. 

This simple description only tests the fracture criterion at the crack tip. The CEPM brings into play the possibility of micro-de-cohesion at the head of the pile-up. A first simulation has been set up to discuss the possibility of forming a moving pile-up, due to a local softening effect and a mobile obstacle, as suggested in the model. This simulation is based on the theory of dislocations in the presence of the crack. It has to be compared to those used to study the brittle-to-ductile transition (BDT) (Roberts et al., 1993), in which the possible effects of corrosion on the dislocations is introduced. 

Various crack advance theories have been proposed to relate crack propagation to oxidation rates and the stress-strain conditions at the crack tip, and these theories have been supported by a correlation between the average oxidation current density on a straining surface and the crack propagation rate for a number of systems [12,35]. There have been various hypotheses about the precise atom-atom rupture process at the crack tip—for example, the effect that the enviromnent has on the ductile fracture process (e g., the tensile ligament theory [36], the increase in the number of active sites for dissolution because of the strain concentration [37], the preferential dissolution of mobile dislocations because of the inherent chemical activity of the solute segregation in the dislocation core [38]). 

Lardner, R. W. (1968) A dislocation model of fatigue crack growth in metals. Philos. Mag. 17, 71-82 Lardner, R.W. (1974) Mathematical Theory of Dislocations and Fracture (University of Toronto Press, Toronto)... 

Ceramics and refractories are inherently brittle materials. The reason for this behavior is that the bonding in them is predominantly ionic or predominantly covalent. For plastic deformation, which is required for ductile fracture, there should be dislocation movement. In ionic compounds, formation of dislocation itself is difficult, because, for neutrality of the material, a pair of dislocations should simultaneously form. One should carry negative charge, and the other, positive. This is a difficult thing. If at all a dislocation forms, it requires simultaneous movement of the oppositely charged dislocations. This is still more difficult. In the case of covalent bonds, they are directional and strong. There is no question of any line defect, such as a dislocation, forming. Therefore, any question of dislocation movement does not arise. Ceramic and refractory materials fail by the sudden fracture of their atomic or ionic bonds. Hence, the failiue of ceramic and refractory materials can be discussed in terms of the failure of brittle materials. In other words, the theory of brittle materials fracture can be applied to ceramics and refractories. 

---