Viscous creep

Viscous creep takes place when the ceramic contains a glassy phase. This phase softens and flows when temperature is raised to a high value. Out of many mechanisms proposed, three are the most notable. 

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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. 

Diffusion creep (giving linear-viscous creep)... 

Figures 5 and h show how the shape of the creep curve is modified by changes in the constants of the model. The values of the constants are given in Table I. Curve I is the same as shown in Figure 4, curve II shows onlv a small amount of viscous creep, and in curve 111, viscous flow is a prominent part of the total creep. The same data were used in Figures 5 and 6, but notice the dramatic, change in the shapes of the curves when a linear time scale is replaced by a logarithmic time scale. In the model, most of the recoverable creep occurs "Within about one decade of the retardation time.

Figure 5.10 Strain response for a material that exhibits a combination of elastic and viscous creep behavior when a constant stress is applied for a time i.

Several empirical models have been suggested for creep. Andrade was the hrst to consider creep in 1914. He considered creep to be the superposition of transient and viscous creep terms (discussed in the next section dealing with creep in polycrystalline materials). Since creep is a thermally-activated process, the minimum secondary-creep rate may be described by an Arrhenius equation (see McLean [15]) as ... 

The term viscous creep is often used for creep at high temperatures with low stresses. Two mechanisms have been proposed to describe such creep in polycrystalline materials. The one known as Nabarro-Herring creep conceives of a stress-directed, diffusional migration of vacancies, while the other, originally suggested by Mott and subsequently elaborated by Weertman, is based on a dislocation-climb model [66]. Extensive experimental evidence also exists to support a dislocation-climb model . 

If Y is the distance across which coulombic attraction could pull a particle to the bubble surface in the available time of passage, it can be shown that the particle must be within a distance of (2) of the path of the center of the bubble in order for it to attach to the bubble as it passed (see Fig. 17.2-2). This capture volume is v h, where h is the distance the bubble rises. This analysis is based on small bubbles which are within the viscous creeping flow regime. 

The transition from power-law creep with a stress exponent of about seven to a viscous creep regime occurs at a stress of about one below 30 MPa at 700°C. Any extrapolation from the power-law creep regime to stresses below 30 MPa may lead to serious underestimation of the creep rate and therefore overestimation of lifetime based on the Dyson nucleation law (Eq. (6.5)) which is accounted for in the lifetime prediction. As the strain rates measured at low stress are used as inputs of the Riedel model (Eq. (6.6)), the long-term creep lifetimes are more correctly predicted (Fig. 6.30(a,b)) and the experimental data are within the predicted scatter bounds. 

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