Creep polycrystals

As the stress is reduced, the rate of power-law creep (eqn. (19.1)) falls quickly (remember n is between 3 and 8). But creep does not stop instead, an alternative mechanism takes over. As Fig. 19.4 shows, a polycrystal can extend in response to the applied stress, ct, by grain elongation here, cr acts again as a mechanical driving force but, this time atoms diffuse from one set of the grain faces to the other, and dislocations are not involved. At high T/Tm, this diffusion takes place through the crystal itself, that... 

Mass diffusion between grain boundaries in a polycrystal can be driven by an applied shear stress. The result of the mass transfer is a high-temperature permanent (plastic) deformation called diffusional creep. If the mass flux between grain boundaries occurs via the crystalline matrix (as in Section 16.1.3), the process is called Nabarro-Herring creep. If the mass flux is along the grain boundaries themselves via triple and quadjunctions (as in Sections 16.1.1 and 16.1.2), the process is called Coble creep. 

Figure 16.5 Deformation mechanism map for Ag polycrystal a = applied stress, p = shear modulus, grain size = 32 pm, and strain rate = IGF8 s 1. The diffusional creep field is divided into two subfields the Coble creep field and the Nabarro-Herring creep field. From Ashby [20].

Consider the diffusional creep of the idealized two-dimensional polycrystal illustrated in Fig. 16.4 and discussed in Section 16.2. Each boundary will be subjected to a normal stress, an, and a shear stress, as, as illustrated in Fig. 16.11. Suppose that all boundaries shear relatively slowly at a rate corresponding to... 

The creep rate is therefore proportional to the applied stress, and the polycrystal acts effectively as an ideally viscous material. 

According to the equation, the diffusional creep rate of a polycrystal may be enhance by reducing the crystal size cl, and by increasing the boundary diffusivity I. Nanoceramics are therefore expected to exhibit enhanced diffusional creep for two reasons first, the reduction of the crystal size from about 10 pm to -10 nm enhances the creep rate by a factor of 109, and second, the enhanced boundary diffusivity may increase the creep rate by 103, so that the total enhancement is 1012. 

F. W. Crossman and M. F. Ashby, The Non-Uniform Flow of Polycrystals by Grain Boundary Sliding Accommodated by Power Law Creep, Acta Metall., 23, 425-440 (1975). 

The temperature dependence of a was obtained in experiments on copper polycrystals [ ]. From Cu creep curves, values of a were determined in the temperature range 1.4 to 4.2 K for a constant r of 24 MPa. Figure 2 shows a plotted against temperature. From the logarithmic creep theory, based on the thermally activated creep assumption [ one expects the linear- and temperature-proportional behavior of the a factor to be... 

Table I shows that 0, in all the cases, is about OATd (the Debye temperature), consistent with Natsik s theory. In addition, experiments revealed a qualitatively similar nature of creep in single and polycrystals of metals.

At r <, creep in single and polycrystals of the studied f.c.c. and h.c.p. metals appears to be due to quantum fluctuation surmounting of crystal lattice barriers by dislocations by way of zero oscillations of dislocation segments. 

Figure 7.5 In polycrystals, diffusional creep may occur by diffusion through the grains (diffusivity D ) or along the grain boundaries (diffusivity D ). The two possible atom diffusion paths are shown by the arrows. (Adapted from Cook and Pharr, 1994, reproduced eourtesy of VCH Publishers, Weinheim, Germany.)...

At 1750°C, the steady-state creep rate of AljOj is approximately four orders of magnitude faster in the polycrystal compared to the single crystal. Explain the source of this difference. Would you expect the activation energy to be the same for both forms of the material ... 

In diffusional creep of polycrystals, vacancies flow from grain boundaries under tension to those under compression. True or False ... 

Although the findings described above regarding creep in fine-grained polycrystals have been limited to oxides, it is anticipated that analogous effects are possible for non-oxide ceramics. For example, certain additives and second-phase particles (e.g., Ti, C, and B4C) enhance the creep strength of polycrystalline SiC, while others (e.g., B and Al) degrade it (recall Chapter 3). The mechanisms, however, are not understood. 

Depending on which of the above factors dominates during deformation, the accommodation mechanism may be regarded as viscous flow, solution-precipitation, or cavitation creep. In general, cavitation creep can be discarded as an accommodation mechanism for superplasticity, as the strain-to-failure afforded by this mechanism is rather small. Therefore, only viscous flow and solution-precipitation mechanisms are important. Obviously, too, whether these mechanisms apply depends on the presence or absence of a liquid phase. Solution-precipitation requires a liquid phase to envelop the grains, while viscous flow is facilitated by the fast diffusion path of the liquid, although it may also occur in a dry polycrystal via diffusional creep. 

The asymmetry between tensile and compressive creep is a typical feature of other systems, such as SiC-based and Al203-based ceramics. In fact, this is common in ceramic systems in which an easily deformable glassy phase located at the grain boundaries is present. In contrast, single-phase ceramics such as pure alumina polycrystals and YTZP are reported to be symmetric under both tension and compression. 

Figure 6.62 shows the polycrystalline data plotted as a log (s. Td exp Q/kT) versus log a to normalize the temperature and grain-size dependence. Q is taken as 5.7 eV. Data from other experiments are included in the plot, which shows that the creep resistance of single crystals is better than that of ZrOa polycrystals having a similar composition under all stresses <100 MPa. From the best fit of the data, a slope of n = 4.1 may be obtained. In single crystals, p = 0. At lower temperatures, n rises to 7.5 and Q is 7.5 eV which is greater than its value at high... 

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