Page 196 - Mechanical Behavior of Materials

Section 5.2 Models for Deformation Behavior 197

Figure 5.5 Rheological models having time-dependent behavior and their responses to a
stress–time step. Both strain–time and stress–strain responses are shown. Model (a) exhibits
steady-state creep with elastic strain added, and model (b) transient creep with elastic strain
added.

stress dependence can be used, as described later in Chapter 15. However, the simple linear models
will suffice here to illustrate some of the gross features of creep behavior.
For the model of Fig. 5.5(a), the response during 1–2 is given by adding the elastic and creep
components of the strain:

σ
ε = ε e + ε c = + ε c (5.11)
E 1
The rate of creep strain is related to the stress by the dashpot constant:

dε c σ
˙ ε c = = (5.12)
dt η 1
This represents a very simple differential equation that can be solved for ε c by integration, and
combined with Eq. 5.11 to give the strain–time response:

σ σ t
ε = + (5.13)
E 1 η 1
This is the equation of the linear ε-t response during 1–2 as shown in Fig. 5.5(a). After removal of
the stress, the elastic strain disappears, but the creep strain accumulated during 1–2 remains as a
permanent strain.