THE THREE-DIMENSIONAL DISPLACEMENT
MEASUREMENT O F SANDWICH CIRCULAR PLATES WITH A
SINGLE FULLY-POTTED INSERT USING ELECTRONIC
SPECKLE PATTERN INTERFEROMETRY
Song-Jeng Huang, Hung-Jen Yeh
Department of Mechanical Engineering, National Chung Cheng University
168 University Rd., Ming-Hsiung, Chia-Yi, 621, Taiwan, ROC
ABSTRACT
This syudy presents the construction and operation of an electronic speckle pattern interferometry (ESPI) applied to
sandwich plates with single insert (Fig.1). Proposed ESPI is a full-field and non-destructive testing that can measures
tiny out-of-plane and in-plane displacement in the elastic region. The experimental construction is to integrate out-ofplane and in-plane measurement into one optical system, to measure the three-dimens ional displacement of the
sandwich plates. The experimental result indicates that the displacement of the sandwich plate will decrease as the
core thickness is increasing. The result also indicates that the displacement will decrease as the diameter of insert is
increasing, but the strength estimated to be increas ing. For validation purpose, the analytical and FEM analysis were
introduced to compare with the result of ESPI measurements . Comparison between the results of ESPI, FEM and
analytical revealed a convincing agreement.
Introduction
In the early 1970s , Butters and Leendertz [1]; Macovski et al. [2] in vented the technique of electronic speckle pattern
interferometry (ESPI). Since then, it has been improved by many researchers. ESPI has been used to measure out of
plane displacements of the test surface, in-plane displacement, displacement gradients and also monitoring of
vibrations [3].
Sandwich structures as one of the well-known composite structures have widely been used in the aerospace,
shi pbuild ing, construction and other industries. The introduction of loads into such structural elements is often
accomplished by using fasteners or inserts, which can be of the ‘partially potted,’ ‘through-the-thickness’ or ‘fully
potted’type [4]. The present study deals with the ‘fully potted’type as shown in Figure 1, which are often employed in
aerospace sandwich plates for the transfer of severe external loads.
Thomsen et al. [4,5] introduced a high-order sandwich plate theory to derive governing equations for both sandwiches
with ‘through-the-thickness’inserts and that with ‘fully potted’inserts. Noirot et al. [6] studied the experimental and 3D
finite element model analysis to describe the breaking points of five kinds of inserts while being pulled out. Burchardt
[7] presented fatigue tests and numerical fatigue calculations in addition to the finite element method for a four-point
bending test on a sandwich beam containing an insert. It was seen from the investigation that the stiffness of the
insert material had almost no influence on the fatigue crack propagation.
Found et al. [8 ] described an experimental investigation using Mayes servo-electric test machine into the energy
absorption properties of a foam-core sandwich panel with integral fiber-reinforced plastic tubes and frusta. Conical
inserts were found to offer the most repeatable performance according to their study. Mamalis et al. [9] presented
experimental results on the compression of h ybrid sandwich composite panels reinforced with internal tube inserts by
SMG hydraulic press.
Since aforementioned experimental methods are contacting test which might destroy the specimens or affect the
stiffness of the specimen, the non-destructive testing such as electronic speckle pattern interferometry (ESPI) will be
good choice to perform the static test of sandwich containing insert. Thomsen [10] conducted experimental
investigation using a holographic interferometry technique to obtain displacement field of the loaded face of sandwich
plate. Thomsen et al. [11] meas ured very accurate out-out-plane surface displacement of loaded sandwich panels
with ply drop-offs by using ESPI. Huang et al. [12] successfully used ESPI to measure the out-of-plane displacement
of sandwich plates with single ‘fully potted’insert, which is only one-dimensional measurement.
To the authors’knowledge, there exist surprisingly few reports on ESPI meas urement of sandwich panels with insert.
The objective of this paper is to measure a full-field three-dimensional (3-D) out-of-plane and in-plane displacement
of sandwich plates with single “fully potted” inserts loaded by tensile stresses through 3-D ESPI. For validation
purpose, the experiment result is then compared with finite element method analysis and analytical solution.
Experimental technique
Construction of the 3-D ESPI system
The schematic diagram of the experimental setup is shown in Figure 2. The light beam from a He-Ne laser (10mW
output power, wavelength = 632.8 nm) is passed through a spatial filter with a 25µm pinhole and an objective (10×) to
make a d iverging beam. The light path of in-plane measurement is typified by the real line in the figure 2 , and that of
out-of-plane measurement is typified by the dashed line within the figure. The laser light beam falls on small beam
splitter (cube one), which divides it into two coherent beams of equal intensity.
For the out-of-plane measurement, the two beams illuminate the two rough surfaces (specimen and reference plane),
which are coated with magnesium oxide for improved reflection. The light beam from the laser is divided by the cube
beam splitter, then the other beam splitter (circular one with 7cm diameter) is employed to recombine the beams
reflected from the reference arm and specimen. The two reflected beams come out of the circular beam splitter, and
then interfere at the detector plane. In this out-of-plane configuration, the mirror 1 is used to reflect the laser beam
and the black plate is put to stop the second light beam come from laser.
For the in-plane measurement, the same euuipements are installed as the out-of-plane configuration, except that the
mirror 2 is used to reflect the laser beam and the black plate is removed to let the second light beam coming from
laser pass through mirror 4 then incident into specimen. In this configuration, the reference plate is not used and
previous mirror 1 is tilted becoming mirror 2.
The CCD camera (881 (H)×508 (V), NTSC-interlaced scanning type) with Optem Zoom 70 micro-lens was adjusted
so that the image of the object substantially filled the whole area of the CCD. Eventually the interference pattern can
be observed on the computer by image subtracting of software Matrox Inspector. To avoid the effects of external
vibrations, which are extremely detrimental to ESPI, the entire sys tem is placed on an optical table (DAEIL DVIO-I2412E-200t (700h)) in our laboratory.
Out-of-plane ESPI fringe formation
The total intensity Ic at a given point P（x,y）in the im age plane must be proportional to the square of the sum of E1
and E2 i.e.,
I c (x , y) = I1 + I 2 + 2 (I1 I 2 ) cosϕ
(1)
where I1 (=E1E* 1) and I2 (=E2E*2) are the intensity distributions of the two speckled wavefronts, and, ϕ ( = ϕ1 − ϕ 2 ) is
their phase difference.
The specim en surface S is now deformed by some mechanical or thermal disturbance, while surface R is left
′
′
undisturbed. (E2 can be considered as the ‘object’ wavefront, and E1, the ‘reference’ wavefront.). Let d ( x , y ) shown
in Figure 3 be the displacement of any given point of surface S to the surface normal (known as out-of-plane motion).
Assuming that a is the incident angle, and ß is the reflective angle, the phase difference caused by out-of-plane
displacement becomes
∆ϕ (d ) = ∆L ×
2π 2π
=
d (cosα + cos β )
λ
λ
(2)
Using Eq.(2), the interference conditions mean
nλ

 (cosα + cos β )

d=
 ( 2n + 1)λ

 2(cosα + cos β )
dark fringes
bright fringes
n=0, 1, 2 …
(3)
, where d is the out-of-plane displacement and n is the fringe order.
In the present study, a is set to be 10 degrees and ß is set to be -10 degrees. Hence the displacement difference of
two adjacent fringes is 0.3213 µm. The zero fringe order is located at the circumference of the exposed free area of
the specimen.
In-plane ESPI fringe formation
If two incident lights E1 and E2 from the same source, having same intensities (A1 = A 2 = A ) and same light pathes,
the intensity before deformation becomes
I before = A 2 + A 2 + 2A 2 cos(φ1(x,y) - φ 2(x,y) )
= 4A 2
.
(4)
After deformation of the object, the combined light intensity including light path differences δ L and δ R (see Figure 4)
becomes
E ′ = E ′1 + E ′2 = A(e j2π (L +δ R )/λ + e j2 π (L+δ L )/λ )
(5)
where δ R = d in sinα + dout cosα , δ L = -d in sinβ + dout cosβ .
The intensity after deformation can be expressed as
I after = A 2 [2 + e
j 2π ( δ L - δR )
λ
j 2π ( δ R - δ L )
+e λ
2π (δ R - δ L )
= 2A 2 [1 + cos
]
λ
]
(6)
If we substract the intensity after deformation from that beformation, we can obtain their deformation difference:
I fr = I after - I before = 2A 2 [1 - cos
= 2A 2{1 - cos
2π (δ R - δ L )
]
λ
2π
[d in (sin α + sinβ ) + d out (cosα - cosβ )]}
λ
(7)
If both incident angle a, and reflective angle ß is zero, Eq. (7) becomes:
2π
[d in (2sin θ )]}
λ
4π sinθ
= 2A 2 [1 - cos(
d in )]
λ
I fr = 2A 2 {1 - cos
(8)
Using Eq. (8), the interference conditions mean
(2n + 1) λ bringht fringes
4sin θ
nλ dark fringes
=
2sin θ
⇒ d in =
⇒ d in
(9)
n=0, 1, 2…
(10)
Both from Eq. (9) and Eq. (10), there between two adjacent fringes existing in-plan displacement:
∆d in =
λ
2sinθ
(11)
The subtracted image usually results in a speckled-fringe distribution, and is dis played on the computer monitor.
Necessary contrast enhancement and smoothing were also performed by the software Matrox Inspector version 3.1.
Specimens for test
The sandwich plates specimens with different inserts’diameters (d out=0.95cm, din=0.49 cm ; d out=1.10cm, d in=0.58cm;
and d out=1.18cm, din=0.74cm; where d out and dincm are as indicated in Figure 5) combined with different core
thicknesse (1.16 cm, 1.76 cm and 2.46 cm ) for the experiment were rectangular sandwich plates characterized by the
mechanical and geometric quantities shown in Table 1.
Loads are applied at the inserts of single-inserted sandwich specimen (see Figure 1), which range from 0 to 20 kg
with suitable loading velocity. A test fixture was made to hold the specimen and expose a free circular area 70 mm in
diameter. Therefore the sandwich plate rests on the circular hole to reproduce simply supported boundary conditions
at the circumference (r = 70 mm).
Experimental results
By the aforementioned 3-D ESPI method with image processing, we applied several loads to the sandwich specimen,
and for each load, recorded two images by the CCD, one before and the other after the load is applied. Later
s ubtraction is performed pixel by pixel on the personal computer. The results of out-of-plane and in-plane
displacement from such a subtraction and image processing are shown in Figure 7 and Figure 8, respectively. The
core thickness effect on out-of-plane displacement under loading is shown in Figure 9. It can be oberved that the
displacement of the sandwich plate will decrease as the core thickness is increasing. The insert diameter effect on
out-of-plane displacement under loading is shown in Figure 10. It can be oberved that the displacement will decrease
as the diameter of insert is increasing, but the strength estimated to be increasing.
Finite element model and analytical model
A finite element method (FEM) model of the sandwich plate with ‘fully potted’inserts is generated using the finite
element package ANSYS. The model consists of thin plate four-node element with six degrees of freedom in each
node for the face sheets; and cubic solid eight-node elements with three degrees of freedom in each node for the
core, insert and potting material. The faces are assumed as isotropic materials and operate according to the
Kirchhoff-Love hypothesis. The core is assumed as an orthotropic body which can resist only transversal forces.
Therefore the material properties of the core remain only three, i.e. Ez , GL and Gw. The insert and potting material
are isotropic materials. The film adhesive layers of sandwich plate are neglected in this model due to their very small
thickness. The total number of elements in this FEM model is ranging from 8000 to 10000, which depends on the size
of potting materials and the spatial interval of two inserts. The insert geometry for FEM analysis is simplified as
shown in Figure 6. The mechanical and geometric quantities of calculation of sandwich plate with insert are the same
as those shown in Table 1 for FEM analysis, as well as analytical analysis.
The analytical modeling method propoesd by Huang et al. [13] is used for present analytical study.
Comparative results and conclusions
Figure 11 shows the in-plane displacement comparison between the results of ESPI, FEM and analytical. The
comparison between the results revealed a convincing agreement, which verifies the accuracy of the present 3-D
ESPI.
The proposed 3-D ESPI is a excellent tool to measure out-of-plane and in-plane displacement. That is a full-field and
non-destructive testing method and without wasting specimen during testing.
References
1.
Butters, J. N., Leendertz, J. A., “Holographic and video techniques applied to engineering measurements ,” J
Meas Control, 4, 349 (1971 ).
2.
Macovski, A., Ramsy, D., and Schaefer, L. F.,
“Time-laps-interferometry and contouring using television
systems,” J Appl Optics, 10, 2722-2727 (1971).
3.
Sirohi, R. S., Speckle Metrology. New York: Marcel Dekker, Inc. ; 1993.
4.
Thomsen, O. T. “Sandwich plates with ‘through-the-thickness’ and ‘fully potted’ inserts: evaluation of
differences in structural performance,” Compos Struct, 40,159– 174 (1988).
5.
Thomsen, O. T., Rits, W., “Analysis and design of san dwich plates with insert-a high-order sandwich plate
theory approach,” J Compos Part B, 29B, 795– 807 (1998 ).
6.
Noirot, F., Ferrero, J. F., Barrau, J. J., Castanie, B., and Sudre, M. “Analyse d’inserts pour les structures
sandwich compos ites ,” J Mech Ind, 1, 241–249 (2000).
7.
Burchardt, C., “Fatigue of sandwich structures with insert,” Compos Struct, 40, 201– 211 (1998).
8.
Found, M. S., Robinson, A. M., and Carruthers , J. J., “The influence of FRP inserts on the energy absorption of
a foam -cored s andwich panel,”Compos Struct, 38, 373–381 (1997).
9.
Mamalis, A. G., Manolakos , D. E., Ioannidis, M. B., Papapostolou, D. P., Kostazos, P. K., Konstantinidis, D. G.,
“On the compression of hybrid sandwich composite panels reinforced with internal tube inserts: experimental,”
Compos Struct, 56, 191–199 (2002).
10.
Thomsen, O. T., “Theoretical and experimental investigation of local bending effects in sandwich plates,”
Compos Struct, 30, 85– 101 (1995).
11.
Thomsen, O. T., Rits , W., Eaton, D. C. G., Dupont, O.,and Queekers, P., “Ply drop-off effects in
CFRP/honeycomb sandwich panels - experimental results ,” J Compos Sci and Technol, 56, 423– 437, (1996).
12.
Huang, S. J., Lin, H. L., “Electronic Speckle Pattern Interferometry Applied to the Displacement Measurement
of Sandwich Plates with Single ‘Fully Potted’Insert,” J Mech, 20(4), 273– 276 (2004).
13.
Huang, S. J ., Chiu, L. W., Kao, M. T., “Structural Analysis of Sandwich Plates with Inserts – Five Layers
Theory,” 2004 AASRC (Aeronautical and Astronautical Society of the Republic of China) / CCAS Joint
Conference, Taichung, Taiwan, Dec. 11 (2004).
Table 1. Mechanical properties and geometric quantities
Geometry:
rectangular plates with length 100 mm and width 100 mm for single-inserted
sandwiches, having simply supported boundary conditions at the circumference (r =
70 mm) of the fixture hole;
Faces:
HYSOL Al-2024-T3, thickness = 0.16 mm, E1 = E 2 = 69000 N mm 2 , υ1 = υ 2 = 0 .33 ;
Aluminum A: SP7314-1-0-3-12 (dout=0.95cm, d in=0.49 cm)
B: SP7314-2-0-3-12 (dout=1.10cm, d in=0.58cm )
C: SP7314-8-0-3-12 (dout=1.18cm, d in=0.74cm ),
Insert:
E1 = E2 = 72300N mm2 , υ 1 = υ 2 = 0 .33 , geometry is shown in Figure 5;
Potting material:
Core:
3M DP-460, E3 r = 83 N mm2 , G3 rz = G3θ z = 31 N mm2 , ? = 0.4, dp = 19 mm;
5052 Hexagonal aluminum honeycomb CR3.250-5052-004N-7, thickness = 1.16 cm,
1.76 cm and 2.46 cm, E = 0. 36 N mm 2 , G = G = 0.075 N mm 2 ;
3r
Film adhesive:
3rz
3θz
3M 299-947-320 TY I, E = E = 3.1 N mm2 , υ = υ = 0. 4;
4
5
4
5
where E, the Young’s modulus; ?, the Poisson’ ratio; G L, the shear modulus in the
length direction; and Gw, the shear modulus in the width direction.
Q
θ
z
r
r
FIGURE 1. Sandwich plate with single fully-potted
insert
FIGURE 2. ESPI experimental setup for 3-D displacement
measurements
X
Z
P, before deformation
P’
P’, afterdeformation
FIGURE 3. Out -of-plane displacement of specimen
surface
FIGURE 4. In-plane displacement of specimen surface
FP
din
dout
,QVHUW
FP
FP
FIGURE 5. Insert
FP
FIGURE 6. Measured area by 3-D ESPI
FIGURE 7. Out -of-plan fringe pattern under 2 kg subtracted
by 0 kg image
FIGURE 8. In-plan (x axis) fringe pattern under 2 kg
subtracted by 0 kg image
Out-of-plane displacement of the insert :
core thickness= 24.6 mm
insert diameter = 11.0 mm
5
insert diameter = 9.5 mm
Load (kg)
20
0
0
0 2 4 6 8 10 12 14 16 18 20
insert diameter = 11.8 mm
16
core thickness= 11.6 mm
10
8
core thickness= 17.6 mm
12
core thickness= 24.6 mm
15
4
35
30
25
20
15
10
5
0
Displacement (μm)
Displacement (μm)
Out-of-plane displacement of the insert :
insert diameter= 11.0 mm
Load (kg)
FIGURE 9. Out -of-plan displacement with changing core
thickness
FIGURE 10. Out-of-plan displacement with changing insert
diameter
In-plane displacement distribution: core thickness =
24.6 mm
displacement (μm)
30
20
10
Experimental result
0
Analytical result
FEM result
-10
-20
-30
-4
-3
-2
-1
0
1
2
3
4
x-axis (cm)
FIGURE 11. In-plane displacement comparison between the results of ESPI, FEM and analytical