Biomedical Engineering Reference
In-Depth Information
Fig. 3.7
Time-dependent viscoelastic material behavior (left Creep; right Relaxation)
and thus viscoelastic. The stress-strain curves #7, #8 and #9 illustrate their time-
dependent behavior as shown.
Creep. The stress-strain curve #7 in Fig.
3.5
depicts creep behavior which can
be described in a strain-time diagram, Fig.
3.7
, as follows. If the material is exposed
to sudden constant loading r
0
,attimet
¼
0(sudden loading refers to a process that
takes place within a time span where no measurable deformation occurs and the
process is slow enough that inertia forces can be neglected), the strain suddenly
increases (elastic or spontaneous straining) to e
0
and then further increases over
time. Depending on the material and the deformation, creep rupture may occur at
point B. Three regions can be distinguished: primary creep, secondary creep and
tertiary creep. An elastic material would rest at point A of the r-e-diagram
(cf. Fig.
3.7
) which corresponds to a constant path of e
0
(cf. dashed line in Fig.
3.7
).
Relaxation. According to the stress-strain curve #8, relaxation can be descri-
bed in the stress-time and strain-time diagram as follows (cf. Fig.
3.7
). If the
material is exposed to sudden constant straining e
0
at time t
¼
0, the stress
response suddenly increases to r
0
(elastic or spontaneous reaction) and decreases
with increasing time. Depending on the material, the stress may either converge to
a constant value or decrease to zero. An elastic material would respond with a
constant r
0
(cf. dashed line in Fig.
3.7
).
Retardation. According to the stress-strain curve #9, deformation-relaxation
can be described in the stress-time and strain-time diagram as follows (cf.
Fig.
3.7
c). If the constant stress r
0
during a creep process at point B at time t
0
is
suddenly reduced to zero (in this context, suddenly reduced refers to a process that
takes place within a time span where no measurable deformation occurs and the
process is so slow that inertia forces can be neglected), the deformation is reduced
