MATERIALS ENGINEERING CONCEPTS - Materials for Civil and Construction Engineers - page 18

with a dashpot. The total deformation, when d = 0 at time t = 0, is then the

sum of the deformations of these three elements:

F
M 1 +

a F
M 2

Ft
b 3

e -M 2 t

> b 2

d = d 1 + d 2 + d 3 = b 1 1 - 2 + (1.10)

The deformation-time diagram for the loading part of the Burgers model
demonstrates three distinct phases of behavior. The first phase is the in-
stantaneous deformation of the spring when the load is applied. The second
phase is the combined deformation of the Kelvin model and the dashpot. In
the third phase, after the Kelvin model reaches maximum deformation, there
is a continued deformation of the dashpot at a constant rate of deformation.
The unloading part of the Burgers model follows similar behavior.
Some materials require more complicated rheological models to repre-
sent their response. In such cases, a number of Maxwell models can be com-
bined in parallel to form the generalized Maxwell model, or a number of
Kelvin models in series can be used to form the generalized Kelvin model.
The use of rheological models requires quantifying material parameters
associated with each model. Laboratory tests, such as creep tests, can be
used to obtain deformation-time curves from which material parameters can
be determined.
Fig. SP1.4 the time-dependent response of materials, they can be used
only to represent uniaxial responses. The three-dimensional behavior of ma-
terials and the Poisson's effect cannot be represented by these models.

Sample Problem 1.4

Derive the response relation for the model shown in Fig. SP1.4 assuming that the
force F is constant and instantaneously applied.

M

d

F O F

Fig. SP1.4

Solution

For F … F o : d = F / M

For F 7 F o : movement

1.2.8 Temperature and Time Effects
The mechanical behavior of all materials is affected by temperature. Some
materials, however, are more susceptible to temperature than others. For ex-
ample, viscoelastic materials, such as plastics and asphalt, are greatly af-
fected by temperature, even if the temperature is changed by only a few