Mechanism maps

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).

Alternatively, in Bonella and Coker s derivation [118,119] the difference between the two classical Hamiltonians in Eq. (116) arises from a different H-dependence in the semiclassical limit > 0. To illustrate the idea, the quantum-mechanical mapping Hamiltonian (112) is rewritten by introducing... 

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].

Figure 16.10 Sintering mechanism map for silver powder of radius 100 pm plotted...

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

Tse et al. (41) BM-MNC 8 Transendocardial— guided by electro mechanical mapping 58 11 40-ml BM Regional wall motion and perfusion increased angina reduced... 

A survey of the load-deformation curves for linear polymers at different temperatures is given in Fig. 25.1A. Each mechanism is further illustrated by a schematic diagram (Figs. 25.1B-E). The mathematical equations for the different mechanisms were given in the Chaps. 13-15. Based on the respective equations Ahmad and Ashby designed Failure Mechanism Maps. The most important of these are reproduced here as Fig. 25.2A-D. 

Fig. 1.3 A proposed mechanism map that distinguishes Class I and Class II behavior.

Fig. 1.23 A mechanism map representing the various modes of interface response.

Fig. 2.14 Fracture mechanism map for uniaxially fiber-reinforced ceramic composites under tensile loading.72...

G. D. Quinn and W. R. Braue, Fracture Mechanism Maps for Advanced Structural Ceramics, Part 2, Sintered Silicon Nitride, /. Mater. Sci., 25, 4377-4392 (1990). 

The experimental results described above can be explained within the basic fracture mechanism map after detailed consideration of the processes necessary to generate a craze at the interface. The criterion lfb > ocmze is a necessary condition for the formation of stable craze fibrils. However, it is not sufficient for the formation of a craze at an interface. Craze initiation is believed to occur by a meniscus instability process that happens within a yield zone (an active zone) at a... 

With this in mind, it is useful to represent the expected fracture mechanisms at the interface with maps. For individual connectors, the fracture mechanisms map can be presented as a function of 2/2 and N/Ne. This normalization then takes into account two important material parameters of the bulk polymers which will influence the fracture mechanisms map the crazing stress acmze (contained in 2 ) and the entanglement density (contained in Ne). 

Fig. 53. Fracture mechanisms map for interfaces between glassy polymers reinforced with connecting chains. Failure mechanisms are represented as a function of normalized degree of polymerization N/Ne and normalized areal density of connectors 1/1 ...

A similar fracture mechanisms map can also be drawn for interfaces effectively broadened by a buffer layer. In this case we assume that the buffer layer is laterally homogeneous. As shown in Fig. 54, several different fracture mecha-... 

We have shown that the fracture toughness of interfaces between polymers is dependent on the molecular structure at the interface as well as on the bulk properties of the polymers on either side of the interface. This relationship is now relatively well established for glassy polymers and the main results are summarized in Figs. 53 and 54, as well as in Sects 3.2-3.5. However, these results should be used with caution when the polymers on either side of the interface are rubbery or semicrystalline. The stress-transfer mechanisms, and in particular the role of the entanglements, will be very different from those observed for the glassy polymers and only preliminary data are currently available on those systems. In principle, fracture mechanisms maps analogous to those depicted in Figs. 53 and 54 could be drawn for these systems but the relevant parameters are not yet as clearly identified. 

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]. 

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