Mesoscale Simulation of Grain Boundary Diffusion Creep in the Presence of Grain Growth

Grain-boundary (GB) diffusion creep (Coble creep) is the dominant deformation mechanism for the fine-grained materials under low stress and at elevated temperature [1]. From the classical Coble creep formula [1], the strain rate is proportional to the external stress, and inversely proportional to the cube of the grain size: 3 ~ − d σ ε& . During creep deformation the grains become elongated in the tensile direction because of atoms diffusion along GBs from places in compression to those in tension. Consequently, the GB diffusion rate depends on the normal stress gradient along the boundaries. Over the last two decades there have been a lot of experimental and theoretical research studies aimed at the fundamental understanding of the role of GB migration during Coble creep [2,3]. It is widely accepted that the GB migration generally plays two important roles during Coble creep: one leading to the decrease of the creep rate due to the increase of the grain size by GB migration mediated grain growth and the other one leading to the relaxation of the stress concentrations along the GBs and at the triple junctions [4,5]. In this study we use mesoscopic simulations to investigate the influence of the external stress and grainboundary migration (static grain growth) on creep deformation of polycrystalline materials. Our simulation methodology is based on the variational principle of dissipated power [4]. Figure 1 shows three snapshots of the evolving microstructure during Coble creep accommodated by GB migration. Interestingly, our simulations show that in the presence of GB migration the grains remain relatively equiaxed with very little distortion even after substantial deformation of the microstructure. This is in strong contrast with the large morphological changes in a microstructure in which the role of GB migration is strongly diminished [5]. In general both the static and dynamic grain growth are present during Coble creep deformation. Moreover, it is known that the externally applied stresses can have strong effect on the grain growth. Figure 2 shows our simulation results of the influence of stress on grain growth. This clearly shows that the average grain size decreases with stress at the same strain level. One can rationalize this result by noticing that the deformation time required to reach the same strain level is shorter at higher stresses which in turn leads to smaller effect of the time dependent static grain growth. This result is somehow counterintuitive considering that higher stresses enhance the grain boundary diffusion and therefore accelerate the rates of GB switching and the disappearance of small grains (the so called dynamic grain growth). However, one can reconcile this apparent contradiction by noticing that the dynamic grain growth is responsible for only a small percent (about 30%) of the total ε =0% ε = 20% ε = 100% Figure 1 Three snapshots of the evolving microstructure at different strains level in the presence of both Coble creep and GB migration. The normalized external stress is GB d γ σ σ / = , where  = the actual stress, d = the average grain size and GB = GB energy.