TRADUCCION Y NORMALIZACION LINGÜISTICA

When the shear stress fields associated with both edge and screw dislocations are resolved

into their normal stress components (figure) ,note that the absolute magnitude of the shear stress is equal to the normal stress; of importance, however, is the fact that the sign of the normal stress is reversed along the 450 _{directions. It follows that the shear stress field surrounding a screw}

dislocation is distortional (i.e., stretched in one direction and compressed in the other), whereas the edge dislocation contains both distortional and dilatational components.

The potential interaction between an edge or screw dislocation with a solute atom depends

on the stress field associated with the solute atom. For example, if an atom of chromium were to substitute for an atom of FCC nickel or BCC iron, the host lattices would experience a symmetrical (hydrostatic) misfit stress associated with difference in size between solute and solvent atoms.29

Lattice distortion would be felt equally in all direction, with the strengthening contribution being

proportional to the magnitude of the misfit  such that

da

dc



where a = lattice parameter

c = solute concentration

The hydrostatic stress field of a substitution solute atom interacts with the hydrostatic

stress field associated with edge dislocations but not with the distortional stress field surrounding screw dislocations in the lattice. The level of hardening also depends on how much the local

modulus G of the crystal was altered as a function of solute content (i.e., G-1_(dG/dc).

A much greater solute atom-dislocation interaction occurs when the stress field associated with the solute atom interacts with both edge and screw dislocations. The stress fields associated with the four lattice defects shown in Figure. satisfy this requirement in that they are nonsymmetrical and, as such, will interact with the nonsymmetrical stress components of both edge and screw dislocations. The defect type shown in Figure . identifies one of the octahedral interstitial sites within the BCC iron lattice where carbon and / or nitrogen atoms are located. The size of this octahedral interstitial site along any edge in the BCC lattice (or its equivalent location in the middle of each cube face) is not symmetrical and provides insufficient room for carbon and nitrogen atoms in the 100 direction30_{; this arises from the fact that the site size is 0.38 and 1.56 A}o _.

In the 100 and 110 directions, respectively, whereas the diameter of the carbon atom is 1.54 Ao .

Theoretical considerations as well as experimental findings have shown that steel alloys strength

increases rapidly at small carbon concentrations with a relationship of the from  c . Such alloy

strengthening is of great commercial interest to the steel industry. The insufficient amount of space available for the carbon atom in the BCC lattice also accounts for the very limited solid solubility of carbon in BCC iron (approximately 0.02%)

Figure: Nonsymmetrical strees fields in crystals. (a) octahedral interstitial site in BCC crystal









Figure: Alloy strength dependence on solute content. Greater strengthening associated with non symmetrical defect site. (Reprinted with permission from K.M. Ralls, T.H. Courtney and J. Wulff, Introduction to Materials Science and Engineering, Wiley, New York (1976)

And leads to the development of a body – centered – tetragonal lattice in high carbon

Martensite rather than the body – centered – cubic crystal form for pure iron. It should be noted that the octahedral interstitial site in FCC iron is symmetrical and provides space for an atom whose diameter is as great as 1.02 A. since the extent of lattice distortion in the FCC lattice is much less than that found in the BCC form, the strengthening contribution of carbon in FCC iron (i.e., austenite) is low. (At the same time, the solubility limit of carbon in FCC iron is in excess of 2% - more than 100 times greater than that associated with carbon in the BCC ferrite phase). To summarize, the strengthening potential for carbon in FCC iron is much less than that for carbon in BCC iron since the strain field surrounding the interstitial atom site is symmetrical in the FCC lattice; solute atom interaction with screw dislocations is then much weaker than for the placement of carbon atoms in the non symmetrical interstitial site in the BCC lattice.

Other non symmetrical defects are shown in figure. The substitution of a divalent ion in a monovalent crystal requires that two monovalent ions be replaced by a single divalent ion; this is necessary to maintain charge balance. The divalent ion and the associated vacancy have an affinity for one another which establishes a nonsymmetrical stress field in the 110direction figure. Interstitial atom pairs such as those resulting from irradiation damage in an FCC crystal

produce a stress field in the 100 direction. Finally, the collapsed vacancy disk in an FCC lattice

produces a dislocation loop with asymmetry in the 111 direction.

From the above discussion, it is seen that the relative strengthening potential for a given solute atom is determined by the nature of the stress field associated with the solute atom. When the stress field is symmetrical, the solute atom interacts only with the edge dislocation and solid

solution strengthening is limited. Example of such symmetrical defects are shown in table. In sharp contrast, when the stress field.

TABLE: Dislocation-solute Interaction Potential

Surrounding the solute atom is nonsymmetrical in character, the solute atom interacts strongly with both edge and screw dislocations; in this instance, the magnitude of solid solution strengthening is much greater (table). Note that the degree of solid solution strengthening depends on whether the solute atom possesses a symmetrical or nonsymmetrical stress field and not whether it is of the substitutional or interstitial type. Examples of solid solution strengthening in both symmetrical (Pd or Pt in Cu) and asymmetrical distortional stress fields (C in Fe and N in Nb) are shown in figure. Finally, it is interesting to note that the addition of a given amount of solute atoms to the host metal may, in some instances, lead to solid solution hardening at one temperature and solftening at another. It has been suggested that this contrasting response is due to complex temperature-dependent interactions of screw dislocations with Peierls and solute misfit strain fields.

2. Precipitation hardening?