Dorn equation

The creep strength of AljNb is comparatively low - a stress of 10 MN/m produces 1 % strain in only 500 h and fracture in 2300 h - whereas the yield stress compares favorably with the superalloys. This illustrates the fact that the difference between the yield stress and the creep strength is much more pronounced for intermetallics than for conventional alloys. Creep of Al3Nb is controlled by dislocation climb which is accompanied by subgrain formation. The observed creep behavior corresponds to that of conventional disordered alloys and the creep rates are described by the known constitutive equations. This will be discussed in more detail with respect to NiAl (Sec. 4.3). The secondary creep rate follows the power law, i.e. Dorn equation for dislocation creep... 

The creep behavior of the ternary B2 phase (Ni,Fe)Al was studied in detail as a function of stress, temperature, composition, and grain size (Rudy and Sauthoff, 1985 Rudy, 1986 Jung etal., 1987). At high temperatures, e.g. 60% of the melting temperature or higher, the secondary creep at rates between about 10" s" and 10" s exhibits power law behavior, i.e. the observed secondary creep rates are described by the familiar Dorn equation for dislocation creep [Eq. (2)] (Mukherjee etal., 1969). 

The strain-time creep curves of alumina based fibers exhibit a steady state (or secondary) e-t linear domain, the corresponding strain rate, e, depending on the applied stress, a the grain size, a and the test temperature, T, according to the Dorn equation. 

In an earlier chapter, reference was made to a relation called the Mukheijee-Bird-Dorn equation for superplastic deformation (in metals), reproduced here as ... 

Concerning the above-mentioned critical quantities the authors have in fact established (i) that irrespective of stress level damage is apparently initiated at a critical creep strain ec of 3 to 3.5% (ii) that a notable deviation of creep data from the potential law starts just at this strain level and (iii) that although the strain rate dev/df is a function of stress, the minimum in the Sherby-Dorn plot also occurs (for the tubular specimens) at ec. The postulated changes in sample morphology at about the time when the strain values started to deviate from Findley s equation, were in fact seen by these and other authors [42,52], who detected in U PVC deformed micro-cavities later... 

The second approach is the use of the dynamic nuclear polarization (DNP) detection principle. Dorn and co-workers have pioneered the application of this technique [9,10], Whereas the NOE enhancement of 13C nuclei in the conventional 13C H recording is dependent upon the 7h/7c ratio (NOE = Th/ Tc = 2 1), the DNP enhancement relates to the ye/yuc ratio (2640 1). In an electron-nucleus spinsystem, the electron-electron transitions are saturated by microwave irradiation and magnetization transfer from electron to nucleus (Overhauser effect) occurs via a scalar and/or dipolar mechanism. The DNP enhancement, A, is described by the following equation ... 

Exact relationships between creep rate and diffusion coefficients have been proposed, such as the Bird-Dorn-Mukherjee equation ... 

For details concerning the basis of these and other equations, and discussions of specific plant problems, the reader is referred to Fundal (1979), Miller (1980), and Puertas and others (1988), and more recently, du Toit (1996a and 1996b), the latter also using an hydrochloric acid dissolution method to determine Cj g. Dorn... 

Becker was the first to suggest, in 1925, [2] that the deformation rate could be expressed by an Arrhenius-type equation. His concept was developed from the recognition of an identity between deformation and chemical reactions. The rate theory of thermally activated processes and, in general, the principles of deformation and fracture were established by Eyring [3], Orowan [4], and J. Frenkel [S]. In the latter part of the 20th century, these principles were further developed for polymers by Krausz and Eyring [6], Dorn [7], Zhurkov [8] and his collaborators [9], Kausch [10], and many others [11-14]. 

Mindel and Brown [54] performed a Sherby-Dorn type analysis on data for the compressive creep of polycarbonate. Superposition was achieved using an equation of the form of Equation (11.33) with an activation volume of 5.7 nm, which was very close to the values of the activation volume obtained from measurements of the strain rate dependence of the yield stress (Section 12.5.1). 

As discussed in Section 11.3.1, Eyring and collaborators had already considered the application of activated rate theory to the creep of polymers. For polymethyl methacrylate, Sherby and Dorn [68] showed that the creep rate could be fitted to an equation of the form... 

The potential differences caused by the movement of particles through a liquid have only been investigated very rarely and rather superficially. The technique is difficult and it is not to be expected that the experiments will give additional information to the results of the other electrokinetic phenomena. We mtntion here the experiments of Dorn S Billxter Maxelt and Stock the last of which could confirm Von Smolu-CHOWSKi s equation for this phenomenon. 

In Eq. (10), V is the atomic vibration frequency, p is the dislocation density, a is the area swept out by a dislocation during an event, b is the Burgers vector, and Q is the activation energy. [A mistake in the reference has been corrected in Eq. (10).] Following the development of the Dorn creep equation, Eq. (10) can be generalized to... 

---