Engineering, 2
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g
Copyright © 2
0
Fa
t
ABSTRA
C
In order to a
n
accordance
w
Models of th
e
software for s
t
obtained. The
was found th
a
ble to suffer f
r
Keywords: P
e
1. Introdu
c
Instrumented
p
rovide inter
m
accomplished
modeling ex
p
for up to 12
screw techni
q
quickly spre
a
rection and r
e
treatment, an
d
though many
biomechanic
a
search has b
e
thoracolumba
r
alloys have g
r
biomaterials
f
their radiogra
p
[5,6]. This p
a
ture of thorac
o
2. Fixed St
r
2.1. Thorac
o
The titanium
a
TC4
p
late ha
s
good fatigue
p
chloride, hyd
r
terial propert
i
MPa of Elast
i
013, 5, 292-29
6
g
/10.4236/eng.
2
0
13 SciRes.
t
igue L
i
Scho
o
C
T
n
alyze the fati
g
w
ith the anti-f
a
e
fixed structu
r
t
atic analysis.
fatigue life w
a
t the stress at
r
o
m
fatigue.
e
dicle Screw;
c
tion
spinal fusio
n
m
ediate stabil
. The natural
p
oses
t
he met
a
months post
o
q
ue was first
u
a
d to trauma,
e
construction
d
many othe
r
studies have
a
l aspects of
p
e
en seen wor
k
r
fixed struct
u
r
adually repla
c
f
or lumbar s
p
p
hic safety an
d
a
per analyzed
t
o
lumba
r
p
edic
r
ucture an
d
o
lumbar Fi
x
a
lloy TC4
p
la
t
s
such featur
e
p
erformance.
I
r
oxide and s
u
i
es of titaniu
m
i
c Modulus, 0
.
6
2
013.510B060
P
i
fe Ana
l
Thor
a
T
o
o
l of Mechanica
l
g
ue life of th
e
a
tigue test re
q
r
e with two b
a
The maximu
m
as then calcul
a
the middle of
Stress; Fatigu
e
n
constructs
a
l
ity until biol
o
rate of bone
a
llic construc
t
o
perative
p
er
i
u
sed in spond
y
degeneration,
after resectio
r
disease trea
t
been done
f
p
edicle screw
s
k
ing on the fa
t
u
re. Recently,
c
ed stainless s
t
p
inal applicati
d
better
p
hysi
c
t
he fatigue of
le screw usin
g
d
Static M
o
x
ed Structur
e
t
e was chosen
e
s as lightnes
s
I
t is also corro
u
lfide enviro
n
m
alloy TC4
a
.
3 of Poisson
R
P
ublished Onlin
e
l
ysis of
a
colum
b
o
ng Yang,
K
l
Engineering,
H
k
Rece
e
posterior th
o
q
uirements sp
e
a
rs and four b
a
m
and minimu
m
a
ted using rel
e
the crossbea
m
e
Life
a
re designed
t
o
gical fusion
healing and r
t
to duty cycl
e
i
od [1]. Pedic
y
lolisthesis, a
n
deformity c
o
n of the tum
o
t
ments [2].
A
f
ocusing on t
h
s
[3,4], few r
t
igue life of t
h
t
itanium and
i
t
eel as preferr
e
ons because
o
c
al performan
c
the fixed stru
g
FEM metho
d
o
del
e
for calculatio
s
, high strengt
sion resistant
i
n
ment. The m
a
a
re: 1.13 × 1
0
R
atio, 875 M
P
e
October 2013
Fixed
S
b
ar Pe
d
K
ai Chen, Y
o
H
angzhou Dian
z
k
.
ive
d
July 2013
o
racolumbar fi
x
e
cified by A
S
a
rs were built
m
stresses of
r
e
vant mathem
a
m
between the
t
o
is
e-
e
s
c
le
n
d
or
-
o
r
A
l-
h
e
e-
h
e
i
ts
e
d
o
f
c
e
c-
d
.
n.
t
h,
in
a
-
0
5
P
a
of Yie
l
the fix
e
1 cons
i
p
endic
u
of the
usuall
y
lumbar
structu
r
fixed c
o
2.2. S
t
Thorac
spine
t
throug
h
Some
r
p
atient
s
[7,8].
I
p
edicl
e
as an
i
dimen
s
The
structu
r
is first
made
o
thylen
e
inserte
d
b
lock
w
terial t
e
thorac
o
(http://www.sc
i
S
truct
u
d
icle Sc
r
o
nggui Lv
z
i University, H
a
.
cn
x
ed structure,
S
TM Standar
d
by 3D softw
a
r
isk nodes und
e
a
tical formula
o
two bars is la
r
l
d Stress, 925
e
d structure o
f
i
sts of two
be
u
lar ba
r
, and
w
beam is 6
m
y
used in the t
r
fixation sur
g
r
e can be ext
e
o
nnections fo
r
t
atic Model
olumbar fixe
d
t
hrough pedic
l
h
the fixed st
r
r
esearches de
m
s
is higher if
I
n order to m
e
e
screws and t
h
i
ntegral
p
art i
n
s
ional model i
s
normal fatig
u
r
e is as follo
w
screwed into
o
f UHMWPE
e
module), sh
o
d
into the U
H
w
ith the chuc
k
e
sting machi
n
o
lumbar fixed
rp.org/journal/
e
u
re of P
o
r
ew
a
ngzhou, China
a loading mo
d
F1717-04.
T
a
re (UG), and
i
e
r different lo
a
o
f S-N curve
a
r
ger than the s
u
MPa of Yiel
d
f
the pedicle s
c
e
a
m
s that are
w
ith screws at
t
m
m and its le
n
r
eatment of th
e
g
ery. If need
e
e
nded to less
t
r
wider applic
a
d
structure is
p
l
e screws. Th
r
ucture to pro
m
onstrated tha
t
the spinal in
t
e
sh and calc
u
h
eir host stru
c
n
this model.
s
shown in Fi
g
u
e test for th
e
w
s: the thoraco
the prepared
(ultra high m
o
o
wn in Fi
g
ure
H
MWPE mo
d
k
of the fixin
g
n
e. The UHM
W
structure ne
e
e
ng)
o
sterio
r
del was estab
l
T
wo three-di
m
i
mported into
a
ds and mom
e
a
nd Goodman
u
rroundings a
n
d
Limit. In th
i
c
rew shown i
n
connected wi
t
t
he ends. The
d
n
gth is 105
m
e
two or three
e
d, the lengt
h
t
han 410 mm
a
tions.
p
unctured int
o
e force is tra
n
tect the brok
e
t
the fusion r
a
t
ernal fixatio
n
u
late convenie
n
c
ture are char
a
The simplifi
e
g
ure 2.
e
thoracolum
b
lumbar fixed
s
plate fixatio
n
o
lecular weig
h
3. A pair of
m
d
ule connects
g
apparatus on
W
PE module
e
d to be repl
a
ENG
r
l
ished in
m
ensional
ANSYS
e
nts were
curve. It
n
d is lia-
i
s pape
r
,
n
Figure
t
h a per-
d
iameter
mm
. It is
thoraco-
h
of the
through
o
human
n
smitted
e
n spine.
a
te of the
n
is used
n
tly, the
a
cterized
e
d three-
b
ar fixed
s
tructure
n
module
h
t polye-
m
etal bar
the test
the ma-
and the
a
ced for

T. YANG ET AL. 293
Figure 1. A typical thoracolumbar fixed structure.
Figure 2. Simplified 3-D model with beam and bar structure.
Figure 3. Fatigue test apparatus for thoracolumbar fixed
structure.
each fatigue test.
According to the above described prototype of the fa-
tigue test and the actual behavior of human vertebral
body bending and lateral bending movement, a compres-
sive load, a tensile load, a bending moment and a lateral
load were added respectively for FEM analyses, as
shown in Figure 4. Compressive loads and tensile loads
of 100 N, 140 N, 180 N, 200 N and 220 N were used for
the first run of calculation, bending moments of 200
Nmm, 300 Nmm, 400 Nmm and 500 Nmm were used for
the second run of calculation, and lateral loads of 20 N,
40 N, 60 N and 80 N, were used for the third run of cal-
culation.
Figure 4. Four loading methods: (a) Compressive load; (b)
Tensile load; (c) Bending moment; (d) Lateral load.
3. FEA and Fatigue Calculation
The finite element analysis (FEA) by ANSYS software
was carried out for the type of thoracolumbar fixed struc-
ture with four corresponding loads. The fatigue lives of
each load type were then calculated and listed in tables
for comparison.
3.1. The Finite Element Mesh Model
The simplified three-dimensional model was created us-
ing the 3-D solid-building software UG (Version 6.0).
Then the 3-D model was imported into Workbench stat-
ics analysis module of ANSYS. The whole-size control
method was used for grid partition. The mesh unit sol-
id185 is a small, six-degree freedom tetrahedron. The
two beams and one bar were controlled with 1 mm unit
size and the rest was controlled with 1.2 mm unit size.
Automatic grid partition with same solid185 unit was
applied on two UHMWPE holding blocks, screws, bar
and beams. The meshing result was shown in Figur e 5.
3.2. FEA Results
Four different loading methods were applied for cal- cu-
lation after grid generation: a pair of compressive loads,
a pair of tensile loads, a pair of bending moments and a
single lateral load were added on UHMWPE holding
blocks respectively, as shown in Figure 3. Some results
of the calculated stress clouds for the four loading types
were shown in Figures 6-9.
From Figures 6, 7 and 9, it can be seen that higher
stress is distributed in the connection area of the beam
and bar when the structure is loaded with compressive
force, tensile force and lateral force. When the structure
is loaded with bending moment, higher stress locates in
the area of the middle of the beam, as shown in Figure 8.

T. YANG ET AL. 294
Figure 5. Mesh model.
Figure 6. Stress cloud for compressive load of 50 N.
Figure 7. Stress cloud for tensile load of 50 N.
Figure 8. Stress cloud for bending movement of 150 Nmm.
Figure 9. Stress cloud for lateral load of 60 N.
Table 1 lists the maximum stress of different compres-
sive and tensile loads. It can be seen that the maximum
stress is approximately the same for same loads of com-
pressive and tensile methods, and approximately in-
creases linearly with the loading force.
3.3. Calculation of Fatigue Life
The classic stress fatigue theory relates the stress (S) with
the fatigue life (N) by the S-N curve formula:
m
SN C

 
where m and C are the parameters associated with ma-
terial properties, stress ratio, and the corresponding load-
ing method.
m can be calculated by taking two points of the high
cycle fatigue S-N curve for TC4 [9], as shown in Figure
10, using the following formula:



10
10
1
log2
2
log1
NN
mSS


and C is calculated with:
11
m
CNS

 
where (N1, S1) and (N2, S2) are any of two points on the
S-N curve.
Goodman Curve follows the following relationship:
1
1
am
u
SS
SS


 




where Sa is the average stress, Sm is stress amplitude, S-1
is stress cycling characteristics of the stress at cycle for
symmetry, Su for material fatigue limit.
Combining the S-N curve and Goodman curve, the cir-
cle life N the cervical steel plate can be calculated by the
following steps:

T. YANG ET AL. 295
Figure 10. High cycle fatigue S-N curve for TC4.
Table 1. Different compressive and tensile loads and their
highest stress.
Load
Max Stress (MPa)
Compressive Tensile
50 N 48.4 48.9
100 N 97.6 97.7
140 N 136.7 136.6
200 N 195.3 195.4




max min
max min
0.6
2
2
1/
us
a
m
a
mu
m
SS
SS
S
SS
S
S
Sa SS
C
NSa
 



 

 

 






where Smax is the maximum work stress of the plate under
loads, Smin the minimum work stress under load, Ss the
tensile strength for TC4, S_a the cyclic stress corres-
ponding to the stress ratio R = −1.
The fatigue circle life N was calculated for the type of
the thoracolumbar fixed structure under four loading
methods. The results were listed in Table 2.
From Table 2 it can be seen that the maximum stress
increases with the increasing load, while the fatigue life
decreases. US standard ASTM F1717-13 [1] requires a
fatigue life of 5 million times without any damage, while
China’s domestic requirement is 1 million times without
any damage. Under the compressive load of 200N, or the
bending moment 500N, or the lateral load of 60N, the
fixed structure has fatigue life larger or close to 5 million
times. When the body side bends, its lateral load is small.
As the load increases, the fatigue life number decreases
dramatically. When the compressive load is lager than
195.3 N or the lateral load is lager than 80 N, the fatigue
Table 2. The fatigue life of thoracolumbar fixed structure.
Compressive load (N)Max stress(MPa) Fatigue circle life (106)
100 97.6 400
140 136.7 50
180 175.7 14.7
200 195.3 5.0
220 214.3 2.6
Bending moment
(N.mm) Max stress (MPa) Fatigue circle life (106)
200 19.2 4.18×106
300 28.7 4.53×105
400 38.3 9.02×104
500 47.9 2.55×104
Lateral load (N) Max stress (MPa) Fatigue circle life (106)
20 53.311 1.39×104
40 106.62 237
60 159.93 18.7
80 213.25 2.72
life is less than 5 million but greater than China’s domes-
tic requirement.
4. Conclusion
The FEM analyses of thoracolumbar fixed structure were
carried out in this study. The stress distribution of the
fixed structure was studied under four different types of
loads: compressive loads, tensile loads, bending moment
loads and lateral loads. The FEM results show that the
most fragile part under bending moment is the central
part of beam. When the fixed structure was loaded with
compressive load, tensile load and lateral load separately,
the most fragile part is the connection area between beam
and bar. The fatigue life numbers were calculated through
S-N curve and Goodman curve after FEM analyses under
different types and different values of loads. The calcula-
tion results show that the fatigue life decreases rapidly as
the value of the load increases. The type of thoracolum-
bar fixed structure meets the China’s domestic require-
ment of 1 million time under the compressive or tensile
loads of 100 - 220 N, bending moment loads of 400 - 500
Nmm or lateral loads of 20 - 80 N.
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T. YANG ET AL. 296
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