Download - Dr R. Moulart, Prof. F. Pierron
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Moulart, Pierron, Hallett, Wisnom - SEM 2009 Albuquerque 1
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rs High strain rate photomechanics on composites:
use of a ultra high speed camera and
the virtual fields method
Dr R. Moulart, Prof. F. PierronArts et Métiers ParisTechChâlons-en-Champagne, France
ACCIS, Aerospace Engineering, University of Bristol, UK
Dr S.R. Hallett, Prof. M.R. Wisnom
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Moulart, Pierron, Hallett, Wisnom - SEM 2009 Albuquerque 2/19
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Perform full-field deformation measurements with a ultra high speed camera
Evaluate performances (quantitative measurements)
Process the deformation data to identify stiffnesses
Use of acceleration maps to make up for the lack of force
data
Objectives
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Moulart, Pierron, Hallett, Wisnom - SEM 2009 Albuquerque 3/19
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rsTest set-up
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Moulart, Pierron, Hallett, Wisnom - SEM 2009 Albuquerque 4/19
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rsTest set-up
Quasi-isotropic lay-up: [-452/902/452/02]s
Input tensile wave
y
x
Thickness: 2
16
50
Ø = 3.17
20
Cross-line grid: 200 m pitch Transferred onto specimen Displacements obtained by spatial phase shifting
Test specimen: glass-epoxy composite
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Moulart, Pierron, Hallett, Wisnom - SEM 2009 Albuquerque 5/19
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rsTest set-up
Ultra high speed camera: Cordin 550-62
Time resolution: 3.3 s (300.000 fps) – light issues Maximum frame rate: 4 Mfps!
Spatial resolution: 1 Mpixel
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Moulart, Pierron, Hallett, Wisnom - SEM 2009 Albuquerque 6/19
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Grey level images
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Moulart, Pierron, Hallett, Wisnom - SEM 2009 Albuquerque 7/19
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Problem of bias caused by sensor positions
Need for a first set of 62 still images
Phase maps obtained sensor by sensor
Final resolution: 5 m (2.5% of grid pitch)
Ux in m
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Moulart, Pierron, Hallett, Wisnom - SEM 2009 Albuquerque 8/19
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Longitudinal displacement
Ux in m
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Moulart, Pierron, Hallett, Wisnom - SEM 2009 Albuquerque 9/19
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Acceleration maps: double temporal differentiation 4th order polynomial fit over time Sliding window of 9 images Resolution: between 1 and 2.105 m.s-2
m.s-2
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Moulart, Pierron, Hallett, Wisnom - SEM 2009 Albuquerque 10/19
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Strain maps: spatial differentiation Local smoothing (diffuse approximation) Resolution: 10-3
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Moulart, Pierron, Hallett, Wisnom - SEM 2009 Albuquerque 11/19
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Strain rate maps (s-1): temporal differentiation Calculated through point to point finite difference Resolution: about 400 s-1
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Moulart, Pierron, Hallett, Wisnom - SEM 2009 Albuquerque 12/19
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The virtual fields method
V
x Fdydz
x
y
F-F
L
LFdxdydzV
x Integrate over x
t
FLdxdy
S
x Plane stress
t
FLdxdy)QQ(
V
yxyxxx
Linear elastic isotropy
t
FLdxdyQdxdyQ
S
yxy
S
xxx Homogeneous material
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Moulart, Pierron, Hallett, Wisnom - SEM 2009 Albuquerque 13/19
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Principle of virtual work
V V V
*** dVu.adSu.TdV:
No force measurement In “static”:
V
* 0dV:
Only stiffness ratios ()
0QA
No force measurement In dynamic
V V
** dVu.adV:
Acceleration forces: distributed volumic load cell!
1 VF: 1 linear equation
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Moulart, Pierron, Hallett, Wisnom - SEM 2009 Albuquerque 14/19
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Choice of virtual fields: field 1
0u
)Lx(xu*y
*x
0
0
Lx2
*s
*y
*x
S
x
S
yxy
S
xxx dSa)Lx(xdxdy)Lx2(Qdxdy)Lx2(Q
Spatial differentiation of Ux
Spatial differentiation of Uy
Double time differentiationof Uy
x
y
L
0dSu.TV
*
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Moulart, Pierron, Hallett, Wisnom - SEM 2009 Albuquerque 15/19
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Choice of virtual fields: field 2
y)Lx(xu
0u*y
*x
y)Lx2(
)Lx(x
0
*s
*y
*x
BQA Linear system
S
y
S
sxxy
S
syxx
dSya)Lx(xdxdyy)Lx2(21)Lx(xQ
dxdyy)Lx2(21)Lx(xQ
www.camfit.fr
x
y
L
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Moulart, Pierron, Hallett, Wisnom - SEM 2009 Albuquerque 16/19
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Results
0
5
10
15
20
25
6,67 10 13,33 16,67 20 23,33 26,67 Mean
Young’s modulus (GPa)
Time (s)
Reference: 24.5 GPa
Mean: 17.2 GPa
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Moulart, Pierron, Hallett, Wisnom - SEM 2009 Albuquerque 17/19
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Results
0
0,05
0,1
0,15
0,2
0,25
0,3
0,35
6,67 10 13,33 16,67 20 23,33 26,67 Mean
Poisson’s ratio
Time (s)
Reference: 0.35
Mean: 0.28
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Moulart, Pierron, Hallett, Wisnom - SEM 2009 Albuquerque 18/19
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rs Measurements Use of a UHS speed camera Quantitative data obtained (novel) Quality can be improved
Increase frame rate (limit: 4 Mfps)
Improve lighting, improve spatial resolution (grid pitch)
Understand origin of bias and noise
Identification Quantitative data obtained Use of acceleration forces (novel) Huge future potential: no need for Hopkinson bar setup Need for better (and cheaper) cameras Need for new test designs
CONCLUSION
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Moulart, Pierron, Hallett, Wisnom - SEM 2009 Albuquerque 19/19
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Grant EP/G001715/1 for sabbatical of R. Moulart
Access to the Cordin camera through the EPSRC pool of instruments
ACKNOWLEDGEMENTS
Engineering and Physical Sciences Research Council