Mechanisms of Creep

There are several basic mechanisms that may contribute to creep in materials (and 

A short summary of the above contributions to creep follows  

Vacancies must be located at a site where climb is supposed to occur, to enable climb by means of a vacancy-atom exchange. As the temperature increases, atoms gain thermal energy and the equilibrium concentrations of these vacancies in the metals increase exponentially. In Chap. 3, Sect. 3.2.1, the number of vacancies, n, was given by Eq. (3.9), which may be rewritten (see, for example, Damak and Dienes [7]) as  

And again, as given in Chap. 3, N is the number of lattice sites and Ep is the energy of vacancy formation. The activation energy, Q, for the jump rate, J, is given by the sum of the energy of vacancy formation and the vacancy s energy for 

Jo represents the respective entropies. The diffusion coefficient, D, may be given as  

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There are two mechanisms of creep dislocation creep (which gives power-law behaviour) and diffusiona creep (which gives linear-viscous creep). The rate of both is usually limited by diffusion, so both follow Arrhenius s Law. Creep fracture, too, depends on diffusion. Diffusion becomes appreciable at about 0.37 - that is why materials start to creep above this temperature. 

Mechanisms of creep, and creep-resistant materials 189, Climb... 

In the last chapter we saw how a basic knowledge of the mechanisms of creep was an important aid to the development of materials with good creep properties. An impressive example is in the development of materials for the high-pressure stage of a modern aircraft gas turbine. Here we examine the properties such materials must have, the way in which the present generation of materials has evolved, and the likely direction of their future development. 

An understanding of the mechanism of creep failure of polymer fibres is required for the prediction of lifetimes in technical applications. Coleman has formulated a model yielding a relationship similar to Eq. 104. It is based on the theory of absolute reaction rates as developed by Eyring, which has been applied to a rupture process of intermolecular bonds [54]. Zhurkov has formulated a different version of this theory, which is based on chain fracture [55]. In the preceding sections it has been shown that chain fracture is an unlikely cause for breakage of polymer fibres. 

For creep in the absence of radiation the rate of deflection at a given time increases linearly with the applied stress. This relationship is also observed during irradiation. One can infer that the basic mechanism of creep in the two instances is likely to be the same. 

Creep and fracture in crystals are important mechanical processes which often determine the limits of materials application. Consequently, they have been widely studied and analyzed in physical metallurgy [J. Weertmann, J.R. Weertmann (1983) R.M. Thomson (1983)]. In solid state chemistry and outside the field of metallurgy, much less is known about these mechanical processes [F. Ernst (1995)]. This is true although the atomic mechanisms of creep and fracture are basically independent of the crystal type. Dislocation formation, annihilation, and motion play decisive roles in this context. We cannot give an exhaustive account of creep and fracture in this chapter. Rather, we intend to point out those aspects which strongly influence chemical reactivity and reaction kinetics. Illustrations are mainly from the field of metals and metal alloys. 

Understanding of the mechanism of creep failure of polymeric fibres is required for the prediction of lifetimes in technical applications (Northolt et al., 2005). For describing the viscoelastic properties of a polymer fibre use is made of a rheological model as depicted in Fig. 13.103. It consists of a series arrangement of an "elastic" spring representing the chain modulus ech and a "shear" spring, yd with viscoelastic and plastic properties... 

H. E. Evans, Mechanisms of Creep Fracture, Elsevier Applied Science Publishers, London, U.K., 1984. 

In all expressions the Einstein repeated index summation convention is used. Xi, x2 and x3 will be taken to be synonymous with x, y and z so that o-n = axx etc. The parameter B will be temperature-dependent through an activation energy expression and can be related to microstructural parameters such as grain size, diffusion coefficients, etc., on a case-by-case basis depending on the mechanism of creep involved.1 In addition, the index will depend on the mechanism which is active. In the linear case, n = 1 and B is equal to 1/3t/ where 17 is the linear shear viscosity of the material. Stresses, strains, and material parameters for the fibers will be denoted with a subscript or superscript/, and those for the matrix with a subscript or superscript m. 

A. Saxena, Mechanics and Mechanisms of Creep Crack Growth, in Fracture Mechanics Microstructure and Micromechanisms, eds. S. V. Nair, J. K. Tien, R. C. Bates, and O. Buck, ASM Materials Science Seminar, ASM International, OH, 1987, pp. 283-334. 

As the shear stress reaches some value, xSchW(, the region of slow viscoplastic flow, known as Schwedov s region (Fig. IX-24, region II ), is observed in the system with almost undestroyed structure. In this region the shear strain is caused by fluctuational process of fracture and subsequent restoration of coagulation contacts. Due to the action of external pressures this process becomes directed in a certain way. Such mechanism of creep may be described analogously to the mechanisms of fluid flow, the description of which was developed by Ya.B. Frenkel and G. Eiring. 

Figure 3.21. Relationship between volume strain AF/F and longitudinal strain for creep of a high-impact ABS resin, showing mechanism of creep as a function of strain at five different stresses. (Bucknall and Drink water, 1973.)...

Mechanisms of creep in FRP materials are related to the progressive changes in the internal balance of forces within the materials resulting from the behaviour of the fibre, adhesion and load transfer at the resin—fibre interface, and from the deformation characteristics of the matrix. Thus any factors which either directly or indirectly cause changes to any of these key areas will affect the creep process. 

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