Creep at very low rates
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A LAND-BASED turbine may have a life of 40 years. If a total creep strain of 1 pct is permissible, the creep rate is about 10⫺11 s⫺1. Extrapolation to this rate from rates measurable in the laboratory is perilous, and we need to understand the physical processes involved. These processes are usually classified as diffusional creep, Harper–Dorn (H-D) creep, and grain boundary sliding. In diffusional creep, the concentration of vacancies close to a grain boundary normal to an applied tensile stress is greater than that in the unstressed material in equilibrium. The excess vacancies diffuse to the grain boundaries parallel to the tensile axis, where they are absorbed. This leads to a plastic deformation in which the applied stress does work. At high temperatures, the vacancies diffuse through the bulk of the grain, leading to Nabarro–Herring (N-H) creep, according to the analyses of Nabarro[1] and Herring.[2] At lower temperatures, diffusion is mainly along the grain boundaries, Coble (C) creep, as analyzed by Coble.[3] In H-D creep, vacancies diffuse from the edges of dislocations with Burgers vectors parallel to the tensile axis to the edges of dislocations with Burgers vectors normal to the tensile axis. There is again a distinction between the high temperature process in which diffusion occurs in the bulk (H-D creep), and the process at lower temperatures in which diffusion occurs along the channels of the dislocation network which act as pipes for diffusion (H-DP). In a polycrystal, the grain boundaries are regions of weak cohesion, and deformation may occur by the sliding of one grain over another (grain boundary sliding). Since the grain F.R.N. NABARRO, Professor, is with the Materials Physics Institute, University of the Witwatersrand, WITS 2050, Johannesburg, South Africa, and the Division of Manufacturing and Materials Technology, CSIR, Pretoria 0001, South Africa. This article is based on a presentation made in the workshop entitled “Mechanisms of Elevated Temperature Plasticity and Fracture,” which was held June 27–29, 2001, in Dan Diego, CA, concurrent with the 2001 Joint Applied Mechanics and Materials Summer Conference. The workshop was sponsored by Basic Energy Sciences of the United States Department of Energy. METALLURGICAL AND MATERIALS TRANSACTIONS A
boundaries are not smooth and intersect at the lines where three grains meet, this sliding can produce strains greater than the elastic strain only if there is accommodation by the diffusion of vacancies. Again, this diffusion may occur through the bulk of the adjacent grains or along the grain boundary. The theory of grain boundary sliding is less well developed than those of N-H, C, and H-D creep. A polycrystal cannot remain coherent if any one of these processes occurs alone. When two processes occur simultaneously, one or the other may determine the rate of the combined process, but the rate-determining process will not necessarily provide the major component of the strain. (For example, in the model of Spingarn and Nix[4] for plastic def
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