The detailed mechanisms responsible for creep tend to be complex. However, they almost always involve diffusion of some sort. This is how the time-dependence arises, since diffusional processes are progressive with time. Further information about the fundamentals of diffusion is available in the Diffusion TLP.
Creep deformation is caused by the deviatoric (shape changing) component of the stress state applied to a sample – the von Mises stress. The hydrostatic component has no effect, meaning that during creep deformation occurs at constant volume. However, whilst the overall deformation is in response to the deviatoric stress, local variations in in hydrostatic stress do affect creep behaviour, as will be outlined below.
Creep deformation often involves various defects, particularly dislocation cores or grain boundaries. These may simply act as fast diffusion paths, or play a larger role in creep mechanisms (some of which are beyond the scope of this TLP), depending on factors such as dislocation density, grain size, grain shape and temperature. The shape change experienced by the sample may arise simply from atoms becoming redistributed by diffusion. When this occurs on the scale of a grain, with the diffusion occurring mainly via grain boundaries, then this is commonly referred to as Coble Creep. The simulation below shows how this tends to cause the sample to extend under an applied load.
Note: Coloured atoms are no different from those in the bulk, but merely allow each atom to be identified easily.
It can be seen that raising the applied stress accelerates the rate of deformation. The driving force for this net migration of material (from the “equatorial” regions of grains to the “polar” regions) is that an applied tensile stress like this creates hydrostatic compression in the equatorial regions and hydrostatic tension in the polar regions. The hydrostatic tension can be thought of as arising from the applied tensile stress, where the compression arises from the lateral contraction of the sample (due to volume conservation). The atoms then tend to move from the more “crowded” to the more “open” regions. The diffusive flux can be considered as a migration of vacancies in the opposite direction to the motion of atoms, although the concept of vacant sites is less well-defined in a grain boundary than in the lattice. We could equally imagine how hydrostatic compression could arise in the “polar” regions, and hydrostatic tension could arise in the “equatorial” regions, via the application of a compressive stress to the sample. Hence diffusive flux would be in the opposite direction, and the sample would deform in the opposite fashion, with the grains becoming “squashed” by the compressive stress.
It’s also clear that raising the temperature increases the creep rate. This is simply due to the rates of diffusion becoming higher as a consequence of the Arrhenius dependence (click here for details). The activation energy for grain boundary diffusion is low, and the cross-sectional area available for diffusion along grain boundaries is much less than for diffusion through the bulk. Therefore this type of creep is often the dominant one at relatively low temperatures and for samples with a fine grain size.
A similar type of creep deformation to that described above can occur with the diffusion being predominantly within the interior (crystal lattice) of the grains, rather than in the grain boundaries. This is often termed Nabarro-Herring creep (N-H creep). It is depicted in the simulation below.
A similar dependence on temperature and stress is observed to that for Coble creep. The diffusion of atoms in one direction can be more easily pictured as the diffusion of vacancies in the other direction during N-H creep. There is a considerably greater sectional area available via crystal lattice paths, particularly if the grains are relatively large. On the other hand, the activation energy is higher, so diffusion rates tend to be low, particularly at low temperature. This type of creep tends to dominate over Coble creep at relatively high temperature, and with large grains or single crystals.
Purely diffusional creep (Coble and Nabarro-Herring) is fairly simple, and does occur under certain conditions - usually with relatively low applied stresses. With higher stresses, it is common for a type of creep to occur that involves motion of dislocations, particularly in metals, where dislocation densities tend to be high. Provided the stress is below the yield stress, conventional macroscopic plasticity, occurring predominantly via dislocation glide, should not occur. However, with stresses that are starting to approach the yield stress, and are maintained for extended periods, progressive dislocation motion, and hence macroscopic plastic deformation, can occur, often facilitated by extensive climb (absorption or emission of vacancies at the core) of individual dislocations. It should be noted that climb does not refer only to vertical motion of the dislocation, and can refer to horizontal motion too. One of the ways dislocation creep can occur via climb is shown in the simulation below:
In this example, the shear stress provides the driving force for diffusion into the dislocation core, rather than hydrostatic compression or tension as in the case of Coble or N-H creep. In detail, there are several different ways in which combinations of dislocation glide and diffusion in the vicinity of dislocations can promote creep. Some of these have been given specific names, but these often relate to observed dependences on the main variables (e.g. temperature or grain size), rather than being clear about the precise mechanisms involved. In general, they all involve some combination of dislocation climb and glide, although, in particular cases, factors such as the presence of obstacles (e.g. fine precipitates), the ease of cross-slip etc. may affect the observed behaviour. Dislocation density may also affect the behaviour. However, at the high homologous temperatures at which creep typically occurs, the dislocation density may decrease somewhat with time, or could indeed drop sharply if recrystallization were to occur. It might be imagined that this would reduce the rate of deformation. However, in practice the associated decrease in the yield stress might well promote the onset of conventional plasticity - ie extensive dislocation glide - such that the rate of deformation increased.