**1. Introduction**

At temperatures above 0.4 of the absolute melting temperature *T*m, materials are exposed to a slow plastic deformation called creep. For steel 0.4 *T*m is about 500°C. The slow deformation takes place also at constant stress. Many important technical units operate at such high temperatures. This applies, for example, to fossil fired power plants that produce most of the world's electric power. Another example is gas turbines in aircrafts where the maximum metal temperature exceeds 900°C.

Due to creep the total strain in the material gradually increases. At the same time the microstructure can also change. For example the strength of many materials used at high temperatures is based on the presence of fine particles that slow down the deformation. There is a thermodynamic driving force for coarsening of the particles, since this will reduce the total surface area of the particles and thereby the surface energy. The deformation of the material and changes in the microstructure will decrease the strength of the material and this is referred to as the formation of creep damage. When the creep damage has reached a certain level, failure takes place.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Polycrystalline materials consist of regions with a specific lattice orientation called grains and the boundaries between them grain boundaries. During the creep deformation, small voids called creep cavities are formed at the grain boundaries. The size for the cavities is of the order 1 μm. The creep cavities are continuously nucleated so their number increases with time. Each individual cavity also grows so their radii increase. The driving force is the same as for coarsening of particles, that is, a reduction of the surface energy. In this way, there is a gradually increasing fraction of the grain boundaries that is cavitated. When the area fraction of cavities has reached a critical value, the cavities join and eventually form cracks that make the material fail.

The fact that creep rupture is mainly controlled by the development of grain boundary cavities has created a large technical interest in cavitation. This interest increased even more in the 1980s, when it was recognised that the appearance of the cavitation could be used to estimate the residual life time of fossil fired power plants. The service time of many power plants were approaching the design life and operators were asking whether it would be safe to continue running the plants. Neubauer found that by observation of the cavitation with the help of the replica technique, the residual lifetime could be estimated [1, 2]. The cavitation was subdivided into four classes (and one for undamaged material): individual cavities to a small extent, individual cavities to a large extent, stringers of cavities and finally microcracks. Replicas were taken at welds, pipe bends and other critical positions. The basic idea was that if damage of one class was detected, the damage did at most correspond to the next class at the next inspection. The method was very successful when it was applied to low alloy steels such as 0.5Cr0.5Mo0.25V and 2.25Cr1Mo, which represented the body of materials of the plants at the time. Unfortunately the method is less applicable to today's materials such as 9 and 12Cr steels, because cavitation appears only at a late stage of life and does not provide the necessary early warning.

The successful technical use of observations of cavitation stimulated a lot of scientific work. This was dominated by empirical approaches to describe the development of the creep damage. The first and perhaps most well-known approach was set up by Kachanow and Rabotnov [3–5]. They simply assumed that the cavities represented voids that reduced the loading capacity. The most interesting feature of the method is that it is consistent with behaviour of creep strain during the tertiary creep, that is, the final stage before rupture [6, 7]. This dependence is nowadays referred to as the omega method [8].

We will now concentrate on basic models for cavitation. Traditionally cavity nucleation has been modelled either as a process of rupturing atomic bonds or of atomic vacancy condensation. For the former approach the estimated threshold stress is orders of magnitude higher than the applied stress, which makes it physically unrealistic because high stresses will be reduced quickly in a creeping material [9]. The condensation of vacancies can be treated with the help of the classical nucleation theory [10]. It is shown that cavity nucleation would be a very rare event at low stresses but becomes frequent above a certain threshold stress [11]. High stress concentration can be formed at grain boundary ledges, grain boundary triple points and particles. Cavity nucleation at particles can be a result of decohesion of particles from the matrix. In practically all models that have been presented, a high stress concentration is needed. A threshold stress and an incubation time are essential to form a cavity [10, 12]. Contrary to these suggestions nucleation frequently takes place at low stresses and is controlled by strain rather than stress. In agreement with statements in the literature it can be concluded that theories of cavity nucleation have not been fully successful in earlier work [13, 14]. In both these papers excellent reviews are given.

For modelling cavity growth the situation was different but not entirely unproblematic. A diffusion controlled cavity growth was formulated by Hull and Rimmer [15]. The model was later improved in particular by Beere and Speight [16]. It was soon realised that the model gave much larger growth rates than observed experimentally in many cases. Dyson proposed that the cavities should not be able to grow faster than the creep deformation of the surrounding material [17]. This is referred to as constrained cavity growth. Rice developed an explicit model for constrained growth [18]. The idea of constrained growth is now fully accepted. However, the model still tends to overestimate the growth rates. It is now believed to be due to the assumptions in Rice's derivation. This will be analysed in the present paper.

It is evident from the summary above that the modelling of formation and growth of cavities has met considerable difficulties in the past. In recent years important new developments have taken place. With the help of these developments fundamental quantitative modelling of both nucleation and growth of creep cavities has now been possible to set up. In addition some of the difficulties that have been encountered in the past can be understood. It is the purpose of this paper to review these new developments.
