Failure Analysis of a Fin Design for
the Micro-Mechanical Fish
By Michael Petralia
December 12, 2006
Fin Design by Kyla Grigg
Wood MicroRobotics Laboratory
Harvard University
Division of Engineering and Applied Sciences
Eng-Sci 240: Solid Mechanics
Professor Zhigang Suo
Design of the fin
The final design will look like a fish fin, but to prototype the mechanical system,
square elements are being used.
Goal
Harvard University
Division of Engineering and Applied Sciences
Prototype Design
Eng-Sci 240: Solid Mechanics
Professor Zhigang Suo
Design of the fin
Shape Memory Alloy
(SMA)
Silicone Rubber
Glass Fiber Laminas
Carbon Fiber Tendon
Brass Plate
Harvard University
Division of Engineering and Applied Sciences
Eng-Sci 240: Solid Mechanics
Professor Zhigang Suo
Forces acting on the fin
FSMA
FTendon
FRubber
FSMA
Harvard University
Division of Engineering and Applied Sciences
Eng-Sci 240: Solid Mechanics
Professor Zhigang Suo
Forces acting on the fin
FSMA
FTendon
FRubber
Case 1: Maximum Deflection
FSMA
The SMA’s provide a maximum pull of,
FSMA = 1.47 N
Assuming the rubber stretches at most 1 mm,
θmin = 6.5o
The horizontal force from the SMA to the
rubber will be,
FSMA
θmin
Frubber = 2FSMAsin(θmin) = 0.333 N
Assuming this load is equally distributed over
the right edge of the fin,
Frubber / A = 0.2641 N/mm2
Harvard University
Division of Engineering and Applied Sciences
Eng-Sci 240: Solid Mechanics
Professor Zhigang Suo
Forces acting on the fin
FSMA
FTendon
FRubber
Case 2: Maximum Force
FSMA
The maximum angle is,
FSMA
θmax = 22o
Though this would mean the fin has not moved, let’s
take this as our worst case scenario. The maximum
horizontal force from the SMA will be,
θmax
Fmax = Frubber = 1.10 N
Again, assuming this load is equally distributed
over the right edge of the fin,
Frubber / A = 0.8740 N/mm2
Harvard University
Division of Engineering and Applied Sciences
Eng-Sci 240: Solid Mechanics
Professor Zhigang Suo
Forces acting on the fin
FSMA
FTendon
FRubber
Force from the Tendon
FSMA
The force in the tendon is the force necessary to keep the fin in place during
swimming. It will be the horizontal force from the SMAs for a given angle.
Because the deflection will be relatively small, it should be safe to assume the
force in the tendon will act parallel to the surface of the fin.
Although it would mean there was no deflection of the fin, let’s use the
maximum horizontal force provided by the SMA for analysis.
Ftendon = 1.10 N
Harvard University
Division of Engineering and Applied Sciences
Eng-Sci 240: Solid Mechanics
Professor Zhigang Suo
Properties of glass fiber
According to Chou* unidirectional lamina can be treated as a homogeneous,
orthotropic continuum. Additionally, for circular cross-section fibers
randomly distributed in the unidirectional lamina, the lamina can be
considered transversely isotropic.
The result is that we only have five
independent material constants:
E11, E22, v12, G12, v23
These values of these constants were
provided by the manufacturer:
*Chou,
+This
E11 (GPa)
E22 (GPa)
v12
G12 (GPa)
v23+
50
7
0.33
5
0.33
Microstructural Design of Fiber Composites (1992)
value was not provided by the manufacturer, but it was necessary to assume a value in order to please ABAQUS.
Harvard University
Division of Engineering and Applied Sciences
Eng-Sci 240: Solid Mechanics
Professor Zhigang Suo
Orientation of the glass fiber
+
Horizontal Fibers
=
Vertical Fibers
Harvard University
Division of Engineering and Applied Sciences
Crossed Fibers
Eng-Sci 240: Solid Mechanics
Professor Zhigang Suo
List of Analyses
The following situations were analyzed for the cases of maximum deflection
and maximum forces. To look at the worst case scenario, the tendon force
was included in each analysis.
One Layer:
Horizontal fiber direction
Vertical fiber direction
Two Layers:
Horizontal fiber direction
Vertical fiber direction
Crossed fiber direction
Harvard University
Division of Engineering and Applied Sciences
Eng-Sci 240: Solid Mechanics
Professor Zhigang Suo
A Note on the Results
The maximum tensile and compressive stresses and strains in the
1 and 2 directions were compared to the maximum allowable
values as provided by the manufacturer.
The orientation of the fibers was considered, and the graphs are
based on the stresses and strains with respect to the fiber
orientation, not with respect to the fin orientation.
Because of this, in the cross fiber analyses, the front and back
square were considered separately.
Harvard University
Division of Engineering and Applied Sciences
Eng-Sci 240: Solid Mechanics
Professor Zhigang Suo
or
La
ye
rH
iz
er
ti
V
ca
lM
ax
ca
lM
ax
rc
e
Fo
n
ct
io
n
2
70
Fo
rc
o
La
e
nt
a
ye
l
M
rs
ax
H
or
Fo
2
iz
La
rc
o
e
nt
ye
al
rs
M
Cr
ax
os
Fo
se
d
rc
M
e
2
a
La
x
D
ye
ef
rs
le
Cr
ct
io
os
n
se
d
M
ax
Fo
rc
e
U
lti
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at
eS
he
ar
1
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ye
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ti
ef
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D
ct
io
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ef
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D
D
n
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io
ef
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D
40
2
ta
lM
ax
on
iz
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or
H
al
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ca
lM
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ca
lM
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20
1
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ye
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iz
o
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V
or
La
ye
rH
La
ye
rs
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ti
La
ye
rV
30
2
1
2
1
(MPa)
Maximum value of σ12
80
68
63
60
50
34
36
23
17
18
11
18
13
15
10
0
ca
lM
ax
rc
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Fo
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iz
0.0034
2
Fo
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on
e
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H
Fo
o
riz
2
rc
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ta
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Cr
ax
os
Fo
se
rc
d
e
M
2
ax
La
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ye
ef
rs
le
ct
Cr
io
os
n
se
d
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ax
Fo
rc
e
U
lti
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at
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he
ar
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ti
V
or
La
ye
rH
La
ye
rs
ca
lM
ax
n
ct
io
ef
le
D
ct
io
ef
le
D
n
ct
io
ef
le
0.014
1
2
er
ti
La
ye
rV
ta
lM
ax
on
iz
D
n
ct
io
ef
le
D
0.004
or
H
al
M
ax
nt
ca
lM
ax
ca
lM
ax
0.008
1
La
ye
rs
iz
o
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ti
V
or
La
ye
rH
La
ye
rs
er
ti
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ye
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0.006
2
1
2
1
Maximum value of ε12
0.016
0.0136
0.0130
0.012
0.010
0.0068
0.0071
0.0045
0.0035
0.0023
0.0036
0.0026
0.0030
0.002
0.000
Vertical Fibers - Max Deflection
Deformation Scale Factor =100
σt,max = 58.5 MPa
σc,max = 65.3 MPa
Harvard University
Division of Engineering and Applied Sciences
Eng-Sci 240: Solid Mechanics
Professor Zhigang Suo
Horizontal Fibers - Max Deflection
σt,max = 53.2 MPa
σc,max = 52.3 MPa
Harvard University
Division of Engineering and Applied Sciences
Eng-Sci 240: Solid Mechanics
Professor Zhigang Suo
Vertical Fibers - Max Deflection
σt,max = 25.5 MPa
σc,max = 32.6 MPa
Harvard University
Division of Engineering and Applied Sciences
Eng-Sci 240: Solid Mechanics
Professor Zhigang Suo
Horizontal Fibers - Max Deflection
σt,max = 26.7 MPa
σc,max = 26.1 MPa
Harvard University
Division of Engineering and Applied Sciences
Eng-Sci 240: Solid Mechanics
Professor Zhigang Suo
Crossed Fibers - Max Deflection
Front Square:
σt,max = 27.5 MPa
σc,max = 33.1 MPa
Back Square:
σt,max = 38.9 MPa
σc,max = 48.2 MPa
Harvard University
Division of Engineering and Applied Sciences
Eng-Sci 240: Solid Mechanics
Professor Zhigang Suo
Vertical Fibers - Max Deflection
σt,max = 25.5 MPa
σc,max = 32.6 MPa
Harvard University
Division of Engineering and Applied Sciences
Eng-Sci 240: Solid Mechanics
Professor Zhigang Suo
Vertical Fibers - Max Force
Deformation Scale Factor =100
σt,max = 175.2 MPa
σc,max = 62.7 MPa
Harvard University
Division of Engineering and Applied Sciences
Eng-Sci 240: Solid Mechanics
Professor Zhigang Suo
Horizontal Fibers - Max Forces
σt,max = 60.2 MPa
σc,max = 59.3 MPa
Harvard University
Division of Engineering and Applied Sciences
Eng-Sci 240: Solid Mechanics
Professor Zhigang Suo
Vertical Fibers - Max Force
σt,max = 45.5 MPa
σc,max = 30.7 MPa
Harvard University
Division of Engineering and Applied Sciences
Eng-Sci 240: Solid Mechanics
Professor Zhigang Suo
Horizontal Fibers - Max Force
σt,max = 28.6 MPa
σc,max = 28.4 MPa
Harvard University
Division of Engineering and Applied Sciences
Eng-Sci 240: Solid Mechanics
Professor Zhigang Suo
Crossed Fibers - Max Force
Front Square:
σt,max = 31.6 MPa
σc,max = 37.7 MPa
Back Square:
σt,max = 37.5 MPa
σc,max = 44.8 MPa
Harvard University
Division of Engineering and Applied Sciences
Eng-Sci 240: Solid Mechanics
Professor Zhigang Suo
Vertical Fibers - Max Force
σt,max = 45.5 MPa
σc,max = 30.7 MPa
Harvard University
Division of Engineering and Applied Sciences
Eng-Sci 240: Solid Mechanics
Professor Zhigang Suo
Table of Maximum Principal Stresses and Strains
σc,max
εt,max
εc,max
Number of Layers
Fiber Direction
1
Vertical
58.5
65.3
0.0044
0.0059
Horizontal
53.2
52.3
0.0064
0.0051
25.5
32.6
0.0022
0.0063
Horizontal
26.9
26.1
0.0032
0.0067
Crossed - Front
27.5
33.1
0.0017
0.0027
Crossed - Back
38.9
48.2
0.0017
0.0027
Vertical
175.2
62.7
0.0133
0.0025
Horizontal
60.2
59.3
0.0063
0.0031
45.5
30.7
0.0034
0.0033
Horizontal
28.6
28.4
0.0032
0.0018
Crossed - Front
31.6
37.7
0.0019
0.0016
Crossed - Back
37.5
44.8
0.0019
0.0016
Vertical
2
1
Vertical
2
Case
σt,max
Max Deflection
Max Force
Harvard University
Division of Engineering and Applied Sciences
Eng-Sci 240: Solid Mechanics
Professor Zhigang Suo
Conclusions
• As was previously thought, it is necessary to employ two layers
of glass-fiber.
• The crossed-fiber configuration provides lower strains in the
the 2 direction, but the horizontal stresses will approach the
limit of the material in the vertical-fiber square.
• Despite the higher strains, the 2 layer, horizontal-fiber
configuration does not experience any stresses or strains
greater than 50% of the maximum allowable value.
• It is recommended that the fin be constructed using two
horizontal-fiber squares.
Harvard University
Division of Engineering and Applied Sciences
Eng-Sci 240: Solid Mechanics
Professor Zhigang Suo
Questions?
Harvard University
Division of Engineering and Applied Sciences
Eng-Sci 240: Solid Mechanics
Professor Zhigang Suo