In-Situ Microtomographic Characterization of Single-Cavity Growth During High-Temperature Creep of Leaded Brass
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TRODUCTION
THE active damage mechanism of metals deformed at high temperatures depends strongly on the rate of deformation.[1] At low strain rates, when the corresponding stress levels are relatively low, failure is supposed to occur by the diffusive growth of grain boundary (GB) cavities. At rather high strain rates, however, failure is dominated by power law creep of the material.[1] Cavity growth by diffusion of matter from the cavity surface along the grain boundaries (GBs) was first proposed by Hull and Rimmer.[2] Their model was later extended in various ways to account for different nonequilibrium cavity boundary conditions,[3,4] [5,6] and elastic deformations of adjoining shapes, grains.[7] The influence of plastic flow on damage during high-temperature creep is indirectly suggested by the empirical Monkman–Grant law[8] and indicates that the mechanism of creep damage was related to the creep mechanism itself, which determines the steady-state creep rate. Plastic-creep controlled cavity growth models were developed by many authors: Hancock,[9] Edward and Ashby,[10] as well as Cocks and Ashby, the latter including the case of multiaxial stresses, too.[11,12] Since void growth by power-law creep alone cannot explain the observed times or strains to fracture, Beere and
A. ISAAC, Researcher, formerly with the Helmholtz-Zentrum Berlin fu¨r Materialien und Energie GmbH, 14109 Berlin, Germany, is now with the Brazilian Synchrotron Light Laboratory, Campinas, SP 13083-970, Brazil. Contact e-mail: [email protected] K. DZIECIOL, Postdoctor, and A. BORBE´LY, Professor, formerly with the Max-Planck-Institut fu¨r Eisenforschung GmbH, 40237 Du¨sseldorf, Germany, are now with the E´cole Nationale Supe´rieure des Mines de Saint-E´tienne 158, Cours Fauriel F-42023 Saint-E´tienne, Cedex 2, France. F. SKET, Associated Researcher, formerly with the MaxPlanck-Institut fu¨r Eisenforschung GmbH, is now with the IMDEA Materials Institute, 28040 Madrid, Spain. Manuscript submitted January 15, 2011. Article published online July 20, 2011 3022—VOLUME 42A, OCTOBER 2011
Speight[13] suggested a cavity growth model accounting for both mechanisms of diffusion and plastic creep. They assumed that each cavity is surrounded by a spherical shell of effectively noncreeping material within which the Hull–Rimmer diffusive process takes place, and the shells are embedded in a matrix deforming uniformly. The model of Beere and Speight[13] was further refined by Edward and Ashby,[10] who specified the range of stress, strain rate, and temperature where the coupled mechanism becomes important. An accurate solution of the coupled problem was obtained by Needleman and Rice[14] using a variational principle incorporating both processes of GB diffusion and nonlinear viscous creep. Needleman and Rice[14] revealed that coupling between these mechanisms can be expressed in terms of a length parameter L, which is a function of material properties, temperature, and applied stress. Coupled plastic creep and diffusion effects become important when L is nearly equal to
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