Page 59 - Mechanical Behavior of Materials

60 Chapter 2 Structure and Deformation in Materials

σ σ

time
0
ε =
ΔL/L ε creep recovery
ε e
ε e
t
0
Figure 2.25 Accumulation of creep strain with time under constant stress, and partial
recovery after removal of the stress.

σ

atm.
vac.

Figure 2.26 Mechanism of creep by diffusion of vacancies within a crystal grain.

2.5.3 Creep Deformation

In addition to elastic and plastic deformation as already described, materials deform by mechanisms
that result in markedly time-dependent behavior, called creep. Under constant stress, the strain varies
with time, as shown in Fig. 2.25. There is an initial elastic deformation ε e , and following this, the
strain slowly increases as long as the stress is maintained. If the stress is removed, the elastic strain
is quickly recovered, and a portion of the creep strain may be recovered slowly with time; the rest
remains as permanent deformation.
In crystalline materials—that is, in metals and ceramics—one important mechanism of creep is
diffusional flow of vacancies. Spontaneous formation of vacancies is favored near grain boundaries
that are approximately normal to the applied stress and is disfavored for parallel ones. This
results in an uneven distribution of vacancies and in vacancies diffusing, or moving, from regions
of high concentration to regions of low concentration, as illustrated in Fig. 2.26. As indicated,
movement of a vacancy in one direction is equivalent to movement of an atom in the opposite
direction. The overall effect is a change in the shape of the grain, contributing to a macroscopic
creep strain.
Some other creep mechanisms that operate in crystalline materials include special dislocation
motions that can circumvent obstacles in a time-dependent manner. There may also be sliding of