Deformation mechanism maps

The various creep mechanisms discussed so far differ in their temperature dependence because the activation energy of the mechanisms is different. Furthermore, they differ in their stress-dependence. The creep exponent takes values 

At low external stresses and low temperatures, the material deforms elastically. At higher temperatures, diffusion creep starts, being stronger at small stresses than dislocation creep because of its lower creep exponent. Because of the lower activation energy for grain boundary diffusion, this mechanism is more important than bulk diffusion at low temperatures. Since the creep exponent is the same in both cases, the two regions are separated by a vertical line. 

At even higher stresses, time-independent plastic deformation begins. If the stress level reaches about one tenth of the shear modulus, the theoretical strength of the material is reached. 

Since creep processes are time-dependent, the dominant mechanism also depends on the strain rate. This can also be represented in the diagrams as shown in figure 11.12. At high strain rates i.e., high stresses, diffusion creep becomes less important in comparison to dislocation creep. 

Adding ceramic whiskers in volume fractions above the percolation threshold has been found to improve creep resistance, often increasing the creep resistance by two orders of magnitude. One would expect a similar effect with fibers but, in some cases, the fibers have such a small grain size (for high strength) that they can show very poor creep resistance. Other important factors that can affect the creep rate of a material are composition, stoichiometry, defect density and environment, often through their dependence on diffusivity. 

The emphasis to this point has been on steady-state creep but clearly information is also needed on creep rupture. For ceramics, an empirical approach suggested by Monkman and Grant is often used (see Wiederhorn, 1992). In this approach the failure time is given as a power function of the steady-state creep rate e, i.e., 

For a given material, different creep mechanisms may dominate in different temperature and stress regions. This information can be conveniently given in the form of a deformation mechanism map, as shown schematically in Fig. 7.12. This 

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H. J. Frost and M. F. Ashby, Deformation Mechanism Maps, Pergamon Press, New York, 1982. 

Frost, H.J. and Ashby, M.F. (1982) Deformation-Mechanism Maps The Plasticity and Creep of Metals and Ceramics (Pergamon Press, Oxford). 

The various densification mechanisms at different temperatures can be modelled and displayed in HIP diagrams, in which relative temperature is plotted against temperature normalised with respect to the melting-point (Arzt el al. 1983). This procedure relates closely to the deformation-mechanism maps discussed in Section 5.1.2.2. 

Figure 5.5. Deformation-mechanism maps for MAR-M200 superalloy with (a) 100 pm and (b) 10 mm grain size. The rectangular box shows typical conditions of operation of a turbine blade, (after Frost and Ashby 1982). (c) A barchart showing the range of values of expansion coefficient for generic materials classes. The range for all materials spans a factor of almost. 3000 that for a class spans, typically, a factor of 20 (after Ashby 1998).

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].

M.F. Ashby. A first report on deformation mechanism maps. Acta Metall., 20(7) 887-897, 1972. 

Competition between the various mechanisms can be described by so-called deformation-mechanism maps, as shown in Fig. 1.17 for pure W with a grain size of 10 pm [1.35,1.66]. In industrial practice these maps, however, are of limited use, because the predominance areas for the respective mechanisms alter significantly with changes in microstructure (grain size, subgrain size, grain aspect ratio), which may even occur during deformation [1.64],... 

FIGURE 1.17, Deformation-mechanism map of pure tungsten with grain size of 10 pm (p = 4 x 10 cm ) normalized tensile stress refers to the shear modulus (p) is the melting point [1.65]. 

Fig. 7.7. Deformation mechanism map for Ni (adapted from Frost and Ashby (1982)).

In chap. 7 we laid the foundations for the analysis of mass transport in solids. In the current section, our aim is to examine the ways in which mass transport can assist the deformation that occurs in a given material. As a preliminary, we remind the reader of one of the key features of the deformation mechanism map introduced in fig. 7.7. We refer to the fact that in many instances for stresses well below the putative yield stress, permanent deformation is still observed. Such deformation usually occurs at temperatures which are larger than, say, 0.37, ... 

The deformation behavior at elevated temperature is assumed by using the deformation mechanism map [6, 7] proposed by Ashby. In order to estimate the... 

Depending on the temperature and the stress, different microscopic processes are important in determining creep behaviour. These will be discussed in this section. We will see that different processes are important at different temperature and stress values a fact that can be visualised using so-called deformation mechanism maps. 

So-called deformation mechanism maps allow to read off the dominant mechanism under different conditions. Figure 11.9 shows a schematic deformation mechanism map. In the diagram, the temperature and the external... 

Fig. 11.10. Deformation mechanism maps (after [35]). The grain size is 32pm in both cases...

Fig. 11.11. Deformation mechanism map of silver as function of the grain size (after [35])...

Fig. 11.12. Ideahsed deformation mechanism map at different strain rates (after [26])...

Diagrams like this can be compiled for different materials and material states. Figure 11.10 shows the deformation mechanism maps of aluminium and tungsten at a grain size of 32 pm. Although both maps have the same overall structure as the schematic map from figure 11.9, they nevertheless differ in the size and exact shape of the different regions. 

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