Grain growth of a superplastic 7475Al alloy
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in the grain boundary, DB is the diffusivity there, and kT has the usual meaning. Eventually, the smaller grain disappears, and the surrounding grains enlarge. Assuming that u .~ Od/at, where t is the time, we have the following grain growth rate: d = mBF = mB(f~/6) [ 2 y / d ]
D.J. SHERWOOD and C.H. HAMILTON The 7000 series aluminum alloys were developed by the aerospace industry for high strength and corrosion resistance.[~] The alloy 7475A1,121 in particular, possesses these qualities and improved fracture toughness, m 7075A1t31 is a material very similar to 7475A1. An important alloy addition to 7475 and 7075A1 is chromium, a well-known grain refiner in AI-Mg-Zn alloys that also forms an undissolvable compound with aluminum, Cr2Al7, as well as several other precipitated species, t4-8~ Superplastic forming o f 7475A1 was achieved by stabilizing a fine grain structure. I3,61 Ghosh I61 attributes grain stability to a large volume fraction (1.5 pct) o f very small Cr2Al9 dispersoids (0.1 /~m). Submicron-sized AI~sMg3Cr2 dispersoids have also been detected in both 7075 and 7475A1 in triangular, spherical, and rodlike morphologies,tT~ Paton et al. I8J reviewed the thermomechanical process for developing a fine grain size in 7075A1. They o f f e r evidence that very small ( ~ 0 . 1 /zm) insoluble dispersoids are responsible for pinning the grain boundaries. Rao and Mukherjee 19,~°1 annealed 7475A1 at 530 °C for 24, 72, and 144 hours and obtained grain sizes o f 14, 25, and 30 /xm, respectively. 11°1 No indication o f dispersoid coarsening, a convenient explanation for grain growth in particle-containing materials, was observed even after the 144-hour anneal.ll°l W e will present and discuss here the grain growth kinetics obtained from annealing a similar 7475A1 alloy. These grain growth kinetics must be understood before the deformation-enhanced grain growth that the material exhibits I61 can be addressed. The "driving force" for grain growth must be attributable to grain boundary surface tension, tll] y, a quantity associated with the fact that atoms in a grain boundary are acted upon by forces that tend to move them into lattice positions associated with the regions on either side of the boundary.[~2] Local surface tension equilibrium can be achieved in a stack o f regular tetrakaidecahedra, a polyhedron comprised o f eight hexagons and six squares for a total o f 14 faces, if the hexagonal faces are doubly curved,l~21 Let d be the distance between the square faces; then all o f the edges are o f length d/2X/-2.L~21 Assuming that the radius o f curvature, p, o f the square face in a tetrakaidecahedra is approximately equal to d and that the face borders a smaller grain that is able to disappear, a chemical potential (per atom) across the boundary o f Atz = l~(2y/p) ~ l ) ( 2 y / d ) exists, where I~ is the atomic volume, l~3~ A "driving force" across the grain boundary width 6 o f F = A t z / 6 = (1~/6) (2 y / d ) "propels" atoms from the smallergrain into the tetrakaidecahedra at a rate o f v = m~F, where mB = D ~
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