Mechanical properties - Orthopaedic Biomaterials in Research and Practice - page 63

of improving creep behavior (reducing creep rates or increasing creep
rupture strength) and vice versa. However, other factors, including envi-
ronmental interactions, may also act, and thus it is extremely difficult to
predict creep behavior from fundamental considerations.

Stress relaxation Stress relaxation is, in a sense, the opposite of creep: reduction of inter-

nal stress while a constant strain, below ε y , is maintained. It is character-
ized by an early rapid release of stress followed by a rate that is constant
with the logarithm of time (Figure 3.5). There is no third stage, compa-
rable to tertiary creep, since the final condition is not rupture but simply
the loss of all internal stress. As is suggested by the initial strains present
in creep experiments, the initial values of stress, such as σ 0 ,

σ 0 , and so ′

on, are the elastic consequences of deformation (= ε 0 E ).
As is the case with creep, the rates of stress relaxation increase with
increasing initial stress, deformation, σ 0 , and increasing temperature.
Stress relaxation rates are usually not listed in handbooks directly.
However, the interrelationship with creep rates is obvious. The constant
(later) stress relaxation rate may be calculated, with some difficulty,
from the secondary creep rate. However, the direct comparison between
the two behaviors is easy: a higher secondary creep rate is always associ-
ated with a higher steady-state stress relaxation rate.
Note that if both creep and stress relaxation data are plotted on
a linear time (horizontal) scale, they appear to reach a limit fairly
rapidly for many materials. This is apparent but not real; the vast
majority of materials under most conditions lack a real limit to either
phenomenon.
The primary evidence for stress relaxation effects in orthopaedic
applications is the early reduction of internal elastic stress in internal
fixation devices, particularly preloaded hardware, as is used in long bone
(internal) fracture fixation (Figure 3.6). The loss in stress at the fracture
site, which has been demonstrated in experimental models, is due to a
combination of creep of bone at screw contact points and internal stress
relaxation in bone and other tissues secondary to the external application
of the plate with an initial tensile stress. In addition, creep deformation

σ ´´

ε 0

σ

σ ´

σ 0

1 min 1 h 1 day 1 month 1 year 10 year

Time (log scale)

FIGUre 3.5 stress relaxation curves.