Grain boundaries Hall-Petch

Since the grain boundaries essentially act as barriers to slip in adjacent crystals (see Figure 5.14), it makes sense that the yield strength should depend on grain size. This is indeed the case, and the Hall-Petch relationship shows an inverse square-root dependence of yield strength on grain size, d ... 

Movement of dislocations is a primary mechanism for plastic deformation. A dislocation s motion is impeded when they encounter obstacles, causing the stress required to continue the deformation process to increase. Grain boundaries are one of the obstacles that can impede dislocation glide, so the number of grain boundaries along a slip direction can be expected to influence the strength of a material. In the early 1950s, two researchers, Hall (1951) and Petch (1953),... 

It has been proposed by others that this B segregation produces disorder at grain boundaries, thus facilitating slip transmission across them. This view is supported by a Hall-Petch type analysis of flow stress data as a function of the grain size. There are observations on disordered grain boundary layers which indicate the formation of the y-Ni-Al phase at the grain boundaries. This is not improbable since the A1 content of Al-deficient NijAl is near the solubility limit, and in the case of the LI 2 phase CU3 Au it has been found (Tichelaar et al., 1992) that the order-disorder transition is preceded by the formation of disordered layers at the interfaces. However, such disordered layers have also been found in NijAI without B, and have not been found in many ductile NijAl alloys with B (see also Lin et al., 1993 Sun and Lin, 1993). 

Figures 15 and 16 show that Hq in Eq. (7) decreases rapidly with increasing temperature up to about 600°C, while Ky decreases substantially with temperature only above 600°C. Since //q is a combination of the intrinsic hardness of WC and Co (see Eq. (8)) and Ky a combination of the Hall-Petch coefficients of Eqs (1) and (2) (see Eq. (9)), Figs 15 and 16 suggest that the softening of WC-Co with increasing temperature is due to the intrinsic softening of the component phases up to about 600°C but is controlled by the ease of slip transfer across grain boundaries and interfaces above that temperature.

Many measurements in polycrystalline Cu, Au and Al wires have shown that the yield stress Oy varies as shown in Fig. 21 with the reciprocal square root of the grain size. This relation between yield stress and grain size d, usually referred to as the Hall-Petch relationship, expresses the strengthening effect of the grain boundaries. 

Dense nanostructured monoliths are of interest for a range of applications where materials experience extreme conditions of pressure and temperature. In this case, hardness must be pursued and grain boundaries can enhance such properties, for instance, by the Hall-Petch effect. The management of thermal and electrical behaviors at the same time is also of prime importance in thermoelectricity, for which devices often rely on monolith-shaped materials. In this case, incorporation of grain boundaries may be a mean to fine-tune thermal conductivity independent of electrical conductivity. In both cases, the design of nanostructured monoliths may represent a significant advance in the respective fields. 

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