We study the effect of concentration of stresses near grain-boundary voids on their growth rate for the diffusion mechanism of growth. For this purpose, we use the boundary-value problem of diffusion posed earlier on the basis of the thermodynamic analysis of a two-phase metal-void system with vacancies. To obtain its solution in the analytic form, we apply a simplified geometric scheme in which the voids are regarded as infinite tubes in the planes of grain boundaries. The results of numerical calculations demonstrate that if we ignore the effect of concentration of stresses, then we obtain (1.5-2)-times underestimated values both of the void growth rate and of the time to fracture of the grain boundary.The process of formation of grain-boundary voids in structural steels is one of the main ways of their high-temperature degradation. This stage of the evolution of damage to a material terminates by the coalescence of grainboundary voids and formation of intergranular cracks. Quite often it occupies the major part of the service life of engineering structures operating at high temperatures. For this reason, the evaluation of the rate of growth of grainboundary voids along grain boundaries is also very important for the prediction of the residual life of these structures.Under the indicated conditions, the principal mechanisms of degradation of metals are connected with grainboundary diffusion [1,2]. This is explained by the fact that, in this case, admissible stresses are computed from the condition of elimination of dislocation creep. At the same time, these stresses are sufficient for the nucleation of vacancies on grain boundaries as a result of migrations of grain-boundary dislocations [3,4]. Note that the diffusion of vacancies along grain boundaries is much more intense under these conditions than bulk diffusion through the bodies of grains, i.e., D << Db [2], where D and Db are the coefficients of diffusion of vacancies in the bulk of the grain and on the grain boundary, respectively. Therefore, the vacancies appearing on grain boundaries diffuse along them to grain-boundary voids. Finally, they are absorbed by these voids and increase their volume. The coaiescence of a vacancy with a grain-boundary void is regarded as an elementary act of growth of grain-boundary voids according to the diffusion mechanism.The absence of significant viscous flows (due to the inhibition of the dislocation mechanism of creep) and the fact that the process of grain-boundary degradation is controlled by grain-boundary diffusion enable us to formalize the problem of degradation and reduce it to a one-dimensional problem of diffusion. In some special cases, the latter can be solved in a closed form, which is quite important for engineering purposes. Several types of dependences of this sort for the rate of grain-boundary growth of voids are known from the literature [5][6][7][8][9][10].At the same time, in order to obtain the required relations in the analytic form, the researchers often make serious simplifications. Thus, the m...
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