The concept of deformation mechanism maps was proposed by Ashby.7 6 Since different creep mechanisms operate or dominate in different stress, temperature and grain size regimes, Ashby envisioned that a deformation mechanism map would be an ideal representation of the materials consti­tutive behavior. Over the years, this concept has been extended to describe a variety of other physical phenomena such as sintering,77 wear78 and frac­ture.79 Figure 3.17 is a deformation mechanism map first reported by Ashby in 1972. The map was plotted as normalized stress (a/G) against homologous temperature (T/Tm) for a constant grain size. The map was then constructed by determining the stress or temperature boundaries where one mechanism would dominate others. To this end, the creep constitutive relations of dif­ferent mechanisms were compared and stress and temperature values where

2

to

.2!

ел

c

Л)

transitions from one mechanism to another would occur were determined. For example in Fig. 3.17, at low temperatures and low stresses, the material would resist plastic deformation and the material would behave elastically while in the later modifications this low stress regime was considered to be due to Coble creep.

However, as we continue to increase the temperature and approach higher homologous temperatures, diffusional processes become dominant. Also the applied stresses are sufficient to overcome the flow stress corresponding to that temperature and the material deforms plastically. Since diffusional creep can either be governed by Coble or N-H creep we find the map out­lining the regions where these mechanisms are dominant. As Coble creep is controlled by grain boundary diffusion, it is dominant at lower temperatures and the Coble creep field lies to the left of N-H creep on the map. Also, if we increase the stress at a given temperature, dislocation-based mechanisms come into play. Depending upon the homologous temperature, the defor­mation can be controlled by dislocation climb or glide. At low homologous temperatures dislocation climb is suppressed and hence dislocation glide becomes the dominant deformation mechanism; this is not to be confused
with the viscous glide creep discussed earlier which occurs along with climb creep in class-A alloys. For the sake of the reader, we present a small exam­ple of how the temperature and stress boundaries of different mechanisms can be determined in a given material. If we assume Coble creep and N-H creep as competing mechanisms for a given grain size, then Coble creep will be dominant when

^Coble > £N-H. [3.45]

From the relevant equations for Coble and N-H creep mechanisms, this would imply

Bc DB8B <°l dl oQ

> Bu.

П d3kT d2 kT

Cancelling the common terms we obtain

Db > Kl

Dl d

where K5 is a constant. At a constant grain size, and after expanding Db and Dl, the above equation will turn out to be

Dob (~Qb/rt)> ^

> Kc

Dol (-QlRT)

where K5 is a constant. Clearly the transition from Coble to N-H creep is temperature dependent and independent of stress. The transition is only dependent on the activation energies for grain boundary and lattice diffu- sivities. The temperature dependence of this cross-over is captured by the map where we can observe that a line parallel to the stress axis separates the Coble creep and N-H creep fields.

An alternate way of representing the deformation mechanism maps was proposed by Mohamed and Langdon.80 Since grain size is an important factor which governs the deformation behavior of materials, the mecha­nism map can also be plotted for normalized grain size (d/b) against nor­malized stress (a/G) for a given temperature (Fig. 3.18). As the plot shows, smaller grain sizes are favorable for Coble creep and as we increase the grain size N-H and H-D creep mechanisms become dominant. Since dis­location creep is independent of grain size, transitions from dislocation creep to other mechanisms are represented by lines parallel to the grain size axis. The climb-glide mechanisms are noted for larger grain sizes with

108

106

$ t5

105 104 103

climb occurring at lower stresses; this plot did not consider the climb region at the higher stress-end as described earlier. Also missing is the GBS that is expected between viscous and dislocation creep mechanisms.