Free dislocations

Beyond point E, the material begins to plasticly deform, and at point Y the yield point is achieved. The stress at the yield point corresponds to the yield strength, Oy [see Eq. (5.20)]. Technically, point Y is called the upper yield point, and it corresponds to the stress necessary to free dislocations. The point at which the dislocations actually begin to move is point L, which is called the lower yield point. After point L, the material enters the ductile region, and in polycrystalline materials such as that of Eigure 5.26, strain hardening occurs. There is a corresponding increase in the stress... 

In the preheated specimens, TEM reveals many well-organized dislocation walls parallel to (100), with fewer parallel to (010) and (001), in which the dislocations are spaced at about 50 nm. Within the cells defined by these walls, the free dislocation density is about 10 cm . Small bubbles (< 300 nm in diameter) are observed in some of the walls, suggesting that the walls may be healed cracks. 

After deformation, the free dislocations climb and form low-energy networks water inclusions develop and grow at dislocation nodes. 

The types of free dislocations show that [100] slip was dominant during the high-temperature deformation, and [001] slip was dominant during the low-temperature deformation. Extrapolation of experimental data (Ave Lallement and Carter 1970) to natural deformation strain-rates suggests a transition temperature of 600 -800 C, which compares with a value of 700°-800°C inferred from the mineral assemblages. The stresses and strain-rates during the two stages of deformation can, in principle, be estimated from microstructural information, as already discussed. 

This equation considers the equilibrium of the Z dislocation. In particular, it is nothing more than a dislocation-by-dislocation statement of Newton s first law of motion, namely, = 0, which says that the total force on the dislocation is zero. The factor A is determined by the elastic moduli and differs depending upon whether we are considering dislocations of edge A = fib/27r l — v)), screw(A = fib/lit) or mixed character. The problem of determining the equilibrium distribution of the dislocations in the pile-up has thus been reduced to one of solving nonlinear equations, with the number of such equations corresponding to the number of free dislocations in the pile-up. For further details see problem 3 at the end of the chapter. 

Above there is a finite density of free dislocations, which leads to exponentially decaying translational order. 

The density of free dislocations above T translational correlation length,... 

After the various dislocation interactions, the stress needed for further plastic deformation will depend on the mean free dislocation length L. The dislocation density should be proportional to ML and thus Eq. (6.22) can be used to estimate the shear stress needed to overcome the obstacles, i.e.. 

Note It has been assumed that the ideal fiber contains no free dislocations or porosity. If it is fully graphitized, it may be expected to contain dislocations which increase Sn, S12, and S44 by a factor 3, with corresponding reductions in Cn, C,2 and C44. 3, S13, C33 and C13 would not be affected in this case. 

The variation of free dislocation densities is modeled by different creation/annihi-lation mechanisms [56,62]. In the simple case of edge dislocations, the variation equation becomes [57—60] ... 

Omphacite samples have been found to contain a range of crystal defects free dislocations, deformation twin lamellae on (100), chain multiphcity faults parallel to (010), noncrystallographic faults terminating in dislocations, APDs, low-angle... 

Mechanical (101) [101] twins have been identified in experimentally deformed hornblende single crystals, as well as dislocations on the (100)[001] slip system [333,334]. In hornblendes from naturally deformed rocks dislocations on (hkO) planes were documented, mainly [001] screws [335-338]. A systematic investigation of dynamically recrystallized hornblende from a high-temperature shear zone discovered microstructures typical of dislocation creep, with subgrain boundaries and free dislocations [313]. The primary slip system is (100)[001] consistent with experimental results. Secondary, slip systems are (010)[100] and 110)5<110>. There is evidence for cross-slip of [0 01] screws producing heUcal microstructures [Fig. 13(b)]. Amphibole structures are intermediate between pyroxenes and sheet silicates and indeed chain multiplicity faults have been described [339] and transitional structures may be facilitated by movement of partial dislocations [340]. 

The breakdown of crystalline order involves the creation of free dislocations from bound pairs (Fig. 2B). A free dislocation involves a core , which has a diameter on the order of a lattice length, and a lattice strain, which falls off as the logarithm of distance. A close-bound pair of dislocations corresponds to a short length of extra atoms or a row of missing atoms. The energy of the pair is the sum of strain and core energies, and has the form... 

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