Total Life
Given:
•
A high cycle fatigue power law, with the coefficients
A
and
b
obtained from
experiments on the alloy.
b
f
n
N
A
S
)
(
=
a)
Engineers run SN tests (in repeated loading, periodically from 0 to S
n
) to
find that N
f
=1 x 10
5
cycles for S
n
=800 MPa, N
f
=1 x 10
7
cycles for S
n
=510 MPa.
What are the coefficients
A
and
b
?
N
f
= # of cycles to failure, S
n
= Stress range.
Given the equation above, a and b are as follows:
MPa
a
E
a
b
b
E
A
MPa
E
A
MPa
b
b
2463
)
5
1
(
800
0977
.
0
2
510
800
log
)
7
1
(
510
)
5
1
(
800
0977
.
0
=
=

=

=
=
=

b)
Find the stress life for an unetched neck (no stress concentration).
Assume that the neck is cyclically loaded during daily activity to the maximum
stress computed in part (b) above. Choose (justify) an appropriate minimum
stress.
In Part. 1, Static Analysis, you were told that the force is some multiple of the body
weight, α.
As determined from gait analysis, the maximum load that occurs is about 4x
body weight.
Hence, you solve for the maximum load (P
maz
) with α=4.
The maximum
stress at point A and point B are tensile and compressive, respectively.
Since the
stresses at point B are compressive, we are not concerned with the stress range there.
What remains to be determined is the minimum stress at point A. The minimum could be
tensile or zero.
Generally, during walking α is about zero. I accepted either of these two
assumptions, but for simplicity, the solutions here assume α=0). From Part I,
∆σ @ A =
348 MPa.
Substituting back into the equation:
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Cycles
E
Nf
Nf
8
0977
.
0
10
9
.
4
)
(
2463
348
=
=

c)
If the device is required to survive for 3 x 10
7
cycles (assuming an
unetched surface and no endurance limit), will the device fail?
Since the number of cycles to failure is greater than 3 x 10
7
cycles, the device will not
fail.
d)
As given in the case study, the device failed after 43 months post
operatively.
If the patient loaded the implant for 1 x 10
6
cycles/year, what was the
total number of cycles to failure?
What would the stress concentration factor
from
the laser etching have to have been to cause failure at 43 months?
Total number of cycles to failure:
62
.
1
348
564
564
)
6
58
.
3
(
2463
6
58
.
3
)
6
1
(
12
43
0977
.
0
=
=
=
=
=

SCF
MPa
E
S
year
cycles
E
year
cylces
E
months
Months
etched
e)
If laser etching has to be included in the design, how might the neck
design (geometry, materials, implantation) be changed to allow the etching but
still meet the 3 x 10
7
cycles life requirement?
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 Spring '11
 prof
 Stress concentration, Fracture mechanics, kic, crack length

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