5.9 Consider the constant stress rate history
!
“=#t
(a) determine an expression for the corresponding strain history in terms of a general
creep compliance J(t). Sketch a typical plot of ε vs. t.
(b) Show that the plot of
!
” #
vs.
!
” #
is independent of β
(c) Show that the slope of the plot in part (b) is
!
1 J ” #
( )
.
(d) Plot
!
” #
vs.
!
” #
, indicating its slope at small and large values of
!
” #
.
SOLUTION
(a) Given the stress history, the strain history is found from
!
!
!
!
!
!
˙
“ (t) =#J(t)
The creep compliance and the slope of the
!
“
vs.
!
t
plot increases with time.
(b) Since
“(t) =#t
, then
t=” #
. Then
!
“ # =J(s)ds
0
$ #
%
!
!
!
(c) From part (b)
!
d” #
( )
(d) From the above, the plot of
!
” #
vs.
!
” #
has the form
!
!
5.10 Consider a linear viscoelastic solid subjected to the stress history shown in
Figure-Problem 5.10.
(a) derive an expression for the strain history in terms of an arbitrary creep
compliance J(t).
(b) Discuss the
!
” # t
graph for large and small values of
!
“
. Does the strain
always decrease with time?
Figure-Problem 5.10
SOLUTION
(a) The stress history is
The term
“oJ(t)
is the creep response to the step stress history. The term
“# J(x)dx
0
t
$
is