Dislocations and Obstacles Strengthening

From a mechanistic perspective, what transpires in the context of all of these strengthening mechanisms when viewed from the microstructural level is the creation of obstacles to dislocation motion. These obstacles provide an additional resisting force above and beyond the intrinsic lattice friction (i.e. Peierls stress) and are revealed macroscopically through a larger flow stress than would be observed in the absence of such mechanisms. Our aim in this section is to examine how such disorder offers obstacles to the motion of dislocations, to review the phenomenology of particular mechanisms, and then to uncover the ways in which they can be understood on the basis of dislocation theory. 

1 Conceptual Overview of the Motion of Dislocations Through a Field of 

As noted above, our working hypothesis concerning the various hardening mechanisms is that chemical impurities, second-phase particles and even other dislocations serve as obstacles to the motion of a given dislocation. As a result of the presence of these obstacles, the intrinsic lattice resistance tp is supplemented by additional terms related to the various strengthening mechanisms. We further assume that the flow stress can be written as 

Recall from the discussion on line tension and dislocation bow-out given in 

This equation serves as the foundation of all that we will have to say about hardening. We begin by noting that the numerator is a reflection of the interaction between a single obstacle and a single dislocation. As a result, it is something that we can expect to understand on the basis of local calculations that concern themselves only with the properties of a single such interaction. By way of contrast, the denominator reflects the statistical properties related to the distribution of obstacles. As we will see below, there are a number of different ways of 

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An example of the type of data associated with solution hardening it is the mission of our models to explain was shown in fig. 8.2(a). For our present purposes, there are questions to be posed of both a qualitative and quantitative character. On the qualitative side, we would like to know how the presence of foreign atoms dissolved in the matrix can have the effect of strengthening a material. In particular, how can we reconcile what we know about point defects in solids with the elastic model of dislocation-obstacle interaction presented in section 11.6.2. From a more quantitative perspective, we are particularly interested in the question of to what extent the experimental data permit a scaling description of the hardening effect (i.e. r oc c") and in addition, to what extent statistical superposition of the presumed elastic interactions between dislocations and impurities provides for such scaling laws. 

Solution and Precipitation Strengthening by F. R. N. Nabarro, in The Physics of Metals Vol. 2. Defects edited by P. B. Hirsch, Cambridge University Press, London England, 1975. Nabarro s article provides an interesting perspective on the thinking concerned with the interactions of dislocations with obstacles. 

Plastic deformation of metals is mainly determined by the mobility of dislocations. To design engineering materials with high strength, dislocation movement has to be impeded. In this section, we want to discuss possible mechanisms to do this by different obstacles and to see what amount of strengthening (or hardening, as it is also called) can be achieved. 

Small particles of a second phase, evenly distributed in the grains of the first phase, form a strong barrier to dislocation motion. This was previously discussed in section 6.3, and we saw there that there are two possible ways to overcome such obstacles, the Orowan mechanism and cutting of the particles. The mechanism actually occurring depends on the strength of the obstacles and on their distance. This strengthening mechanism is frequently called precipitation hardening, because the particles are usually created by a precipitation process, described below. 

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