Elif Temiz, 030070195, 11th Week Definitions-Bonus Words-Part3

4-Grain Boundary Strengthening

New Definition (Material) (Better)

Metals normally contain huge numbers of randomly oriented grains, or crystals, separated by grain boundaries. Whereas a single crystal has a free surface and can deform by dislocation glide on a single active slip system,  grains in a polycrystal with differing orientations of their lattice and slip systems are forced to conform to the overall strain. In general, for a given plastic strain the dislocation density will be higher in a polycrystal than in a single crystal due to the presence of geometrically necessary dislocations (Fig. 3.1) that result from nonuniform strain in the polycrystal. A polycrystal is deformed by disassembling it into its constituent grains and allowing each to slip according to Schmid's law, thereby introducing statistical dislocations . When the crystals are subsequently reassembled, they no longer "fit" together (Fig. 3.1b). In some areas adjacent grains have moved apart.,leaving a gap, whereas in other areas grain overlap occurs. To shift metal from the overlapped regions to the gaps, geometrical dislocations, in the form of prismatic loops, tilt boundaries, and so on, may be imposed on the structure (Fig. 3.1c) until the grains again fit together as shown in Fig. 3.1d. The number of dislocations required to put the polycrystal back together should be roughly proportional to the strain times the grain size (i.e., the displacement) times a "geometrical constant."

Figure 3.2 compares the stress—strain behavior of single crystal and polycrystalline Al tensile specimens. Curves 1 to 4 were measured from polycrystalline specimens with various grain sizes, and these display generally greater strength than curves 5 to 7, which were measured from single-crystal specimens with various orientations. Although the general form of curves 1 to 4 is similar, the coarser-grained samples work-hardened substantially less than the finer-grained samples. Crystal 6 is typical of single crystals deforming on several slip systems, and its strength falls somewhat short of the coarsest polycrystalline sample. The soft orientation of crystal 7 has a much lower work-hardening capacity than that of any of the polycrystalline samples because it slips predominantly on one slip plane and dislocation interactions are minimal. Curiously, crystal 5 (oriented with its tensile axis nearly parallel to the [111] direction) hardens even more rapidly than polycrystalline samples, probably because this particular orientation is especially favorable for the formation of Lomer-Cottrell dislocation locks.

The higher strength of line-grained polycrystalline specimens (curves 1 to 4 in Fig. 3.2) was first quantified by Hall (1951) and Fetch (1953) in the now familiar Ha11—Petch relationship: 

where σ₀ is the friction stress, d the average grain size, and k_y the stress intensity for plastic yielding across polycrystalline grain boundaries. This behavior (Fig. 18.19) is typical also of other types of boundaries, such as second-phase particles, mechanical twins, and martensite plates. In general, more closely spaced barriers to dislocations produce greater strength. A complete and fundamental understanding of the mechanisms behind the Halt—Petch equation still eludes materials scientists. Two types of theories have been proposed to explain Hall—Petch strengthening in metals. One invokes dislocation pile-ups, and the other could be called a grain boundary source model.

(Alan M. Russell,Kok Loong Lee, Structure-Property Relations In Nonferrous Metals, pp.28,30)

Previous Definition

In fcc lattices the dislocat,ons glide in (111) planes which do end at grain boundaries . If there are large orientation differences between neighbouring grains a group of moving dislocations in grain 1 will be stopped at the boundary and the deformation in the neighbouring grain 2 can continue only after another dislocation has been nucleated in that grain . This stress concentration is proportional to the external stress multipled by the number of dislocations in the pile-up . the latter depends on the external stress and the grain size .


(Structure and structure development of Al-Zn alloys ; Hans Löffler, D. Bergner ; pg 163 , 1995)