THE OUT-OF-PLANE STRAINS MEASUREMENT IN SANDWICH
PLATES WITH SINGLE FULLY-POTTED INSERT BY USING DIGITAL
SPECKLE PATTERN SHEAROGRAPHY
1, 2
Song-Jeng Huang1, Yu-Tan Lin2
Department of Mechanical Engineering, National Chung Cheng University
168 University Rd., Ming-Hsiung, Chia -Yi, 621, Taiwan, ROC
1
[email protected], 2 [email protected]
ABSTRACT
The construction and operation of digital speckle pattern shearography (DSPS) applied to sandwich plates with single
fully-potted insert has been presented in this paper. Proposed DSPS has advantages of full-field and non -destructive
testing that can measure tiny out-of-plane strain in the elastic region without wasting specimen. For validation
purpose, the analytical solution analysis (ASA) stemmed from reference [11] was conducted. By comparing the
results of DSPS and ASA strain fields throughout the sandwich surface that a convincing agreement is revealed, thus
showing successfully the full-field stains measurement of the single fully-inserted sandwich plates using DSPS.
Introduction
Sandwich plates have widely been used in the aerospace, shipbuilding, construction and other indus tries. 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 [1]. The present study deals with the ‘fully potted’
type (see Figure 1), which are often employed in aerospace sandwich plates for the transfer of severe external loads.
Thomsen et al. [1,2] 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. [3] studied the experimental and 3D
finite element model analysis to describe the breaking points of five kinds of inserts while being pulled out. Burchardt
[4] 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 his investigation that the stiffness of the
insert material had almost no influence on the fatigue crack propagation. Since aforementioned experimental
methods are contacting test which might destroy the specimens or affect the stiffness of the specimen, the nondestructive testing such as electronic speckle pattern interferometry (ESPI) or digital shearographic (DS) technique
will be good choice to perform the static test of sandwich containing insert.
specimen
Q
θ
z
r
r
fixture
Figure 1. Sandwich plate with single fully -potted insert
Figure 2. Fixture for sandwich specimen
The technique of ESPI was invented in the early 1970s (Butters and Leendertz [5]; Macovski et al. [6]). 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. A digital speckle pattern
s hearographic (DSPS) technique is a tool well-established for precision strain measurement and is also a
nondestructive testing technology [7-8]. Because a speckle fringe pattern is not observed readily on a TV monitor,
there has been much consideration of how to obtain the information of derivative displacement fields quantitatively
from the fringe pattern.
Hung [9] conducted experimental investigation using a digital shearography to obtain strain measurement, material
characterization, residual stress evaluation, vibration studies and 3-D shape measurement of composite structures.
Huang et al. [10] measured accurate out-out-plane surface displacement of loaded sandwich panels with single fullypotted insert by using ESPI. To the authors’knowledge, there exist surprisingly few reports on DPSS strains
meas urement for sandwich panels with insert. The objective of this paper is to measure a full-field out-of-plane strain
(
∂w
) of sandwich plates with single “fully potted” inserts loaded by tensile stresses through DPSS. For validation
∂r
purpose, the experiment result is then compared with analytical solution analysis (ASA) results stemmed from the
method proposed by Huang et al. [11].
Digital speckle pattern shearography
In digital speckle pattern shearography, the phase change is the phase difference between two shearing points on
the test object surface, as shown in Figure 3. The object is illuminated by an expanded He–Ne laser beam at an
S ( xS , yS , zS )
O (x O , y O , z O )
incidence angle θ. Points
and
represent the position of the light source and the position
P
(
x
,
y
,
z
)
of observation, respectively. Consider a point 1
on the surface of the object and a neighbouring
point P2 (x + δ x , y , z ), which is a small distance δx in an x direction from P1 ( x , y , z ) . Assuming that the amount of
shearing is δx on the object surface, the rays from the points P1 and P2 pass through the shearing device and
interfere with each other on the CCD target in the image plane. Through some calculations of points P1’s and P2’s
light paths before and after deformations, the following equations could be obtained:
2π
(1)
φ1 =
δ L1
λ
φ2 =
2π
δL2
λ
(2)
where φ1 andφ2 are the relative phase changes related to δL 1 and δL2, respectively; δL1 and δL 2 are the light path
changes between the light source S to the camera at O via point P1 and P2 , and that between the light source S to
the camera at O via point P1’ and P2’, respectively.
Through some mathematical manipulations , we can obtain:
2π
λ
∆
where X
∆
X
=
δu
δv
δw 

(3)
+ C2
+ C3
 C1
δ x
δ x
δ x
δ x 

(= φ2 − φ1) is the relative phase change before and after deformation; and coefficients can be expressed
by:
C1 =
x − xO x − x S
y − yO y − y S
z − z O z − zS
+
, C2 =
+
, C3 =
+
,
RO
RS
RO
RS
RO
RS
1
2
2
2
2
RO =  ( x − x O) + ( y − yO ) + ( z − zO )  ,


RS =  ( x − xS ) + ( y − yS

2
) + ( z − zS )
2
2
1
 2.

(4)
After deformation
Before deformation
O
p2
p1
'
p1' p2
x
y
S
z
Figure 3. Scheme for optical paths in digital shearography; Coordinates of the points :
'
p1: p1 ( x , y, z) , p2 : p 2 ( x + δx, y, z) , p1' : p1' ( x + u, y + v, z + w) , p 2 : p'2 ( x + δx + u + δ u, y + v + δ v, z + w + δw) ,
O:
O( x0 , y 0 , z0 ) , S: S( xs , ys , z s ) .
Hence, if we put source S and observation O on the same x-z plane, also set the incidence angle of source and
reflective angle to observation both equal to zero, equation (4) could be simplified to be:
∂w
λ
= −
∆
∂x
4π δ x
= −
x
nλ
2δ x
(5)
∂w
where n is the fringe order of dark fringe. If we use DSPS, the whole-field strain ( ∂x ) may be obtained by substitute
n and δx into equation (5).
If we use the polar coordination as shown in Figure 1, the x variable in equation (5) can be replaced by r variable,
yielding:
∂w
λ
= −
∆
∂r
4πδ r
r
= −
nλ
2δ r
(6)
Construction of the DSPS system
Geometric configuration of single-inserted sandwich specimen for tes t is shown in Figure 5. A test fixture was made
to hold the specimen and expose a free circular area 70 mm in diameter, referring Figure 2. Therefore the sandwich
plate rests on the circular hole to reproduce simply supported boundary conditions at the circumference (r = 70 mm).
Loads are applied at the inserts of single-inserted sandwich specimen, which range from 0 to 6 kg with suitable
loading velocity.
The schematic diagram of the experimental setup is shown in Figure 6. The system consists of a He-Ne laser (10mW
output power, wavelength = 632.8 nm), 2 mirrors, a beam splitter (7cm diameter) used as shearing device, a mirror
for reflecting the laser light to specimen, CCD camera, and personal computer (PC). The image shearing is
generated by tilting one of the mirrors, and these two beams are recombined onto the CCD. The interference of these
two beams gives the information about the optical phase difference between the two neighbouring points on the
specimen.
insert
upper face
upper adhesive
core
potting material
lower adhesive
lower face
(a) Cross section of sandwich plate with single fully-potted insert
1.791cm
1.588cm
0.102cm
0.381cm
0.038cm
1.811cm
8cm
(b) Geometric size of sandwich plate with single fully-potted insert
Figure 5. Geometric cross-sectional configuration of circular sandwich specimen for experiments
CCD camera
specimen
computer
screen
beam splitter
r
z
mirror
loading system
mirror
mirror
sp atial filter
laser
Figure 6. DSPS experimental setup for out -of-plane strain measurements
Results and discussions
The fringe patterns obtained by DSPS when the specimen is loaded up to 2, 4, and 6 kg are shown in Figure 7. The
fringe orders in the patterns are easy to be determined. Plots in Figure 8 show the comparison of out-of-plane
∂w
strain ∂r between DSPS and ASA under the same loading conditions, and their amount of shearing is 0.9 mm. It is
observed that the strains increase with increasing loading. When the loading is smaller, the error between DSPS and
ASA seems bigger. The biggest strains occurred at the vicinity of the boundary edge, not at the edge itself. The
reason for error might be the uncertainties from experimental procedure and determination of fringe order. Generally
speaking, a convincing agreement between DSPS and ASA is revealed (Table 1 through 3).
(a) 2kg
(b) 4kg
(c) 6kg
Figure 7. DSPS fringe patterns of sandwich as specimen is loaded up to (a) 2kg (b) 4kg (c) 6k g
(a) 2kg
(b) 4kg
(c) 6kg
Figure 8. Comparison of out -of-plane strain ∂w between DSPS and ASA as specimen is loaded up to (a) 2kg (b) 4kg (c) 6k g,
∂r
and shearing is 0.9 mm
Table 1. Comparison of out-of-plane strain between DS PS and ASA, as specimen is loaded up to2kg and shearing is 0.9
mm.
Loaded up to 2kg
r, mm
Fringe order
∂w
（DSPS）
∂r
∂w
（ASA）
∂r
error（％）
-15.3
-5.5
0
5.6
15.5
1
0.5
0
-0.5
-1
3.48×
10-4
1.71×
10-4
0
-1.7×
10-4
-3.53×
10-4
3.04×10-4
1.77×10-4
0
-1.76×10-4
-3.07×10-4
14
3
0
3
15
Table 2. Comparison of out-of-plane strain between DS PS and ASA, as specimen is loaded up to 4kg and shearing is 0.9
mm.
Loaded up to 4kg
r, mm
Fringe order
∂w
（DSPS）
∂r
∂w
（ASA）
∂r
error（％）
-23.9
-19.7
-15.1
-11.2
-6.5
-3.8
0
3.3
6.3
9.1
15.8
19.9
25.4
1
1.5
2
1.5
1
0.5
0
-0.5
-1
-1.5
-2
-1.5
-1
3.84×
10-4
5.33×
10-4
7.01×
10-4
5.42×
10-4
3.58×
10-4
2.02×
10-4
0
-1.75×
10-4
-3.63×
10-4
-5.27×
10-4
-6.86×
10-4
-5.34×
10-4
-3.55×
10-4
4.28×
10-4
5.73×
10-4
6.2×
10-4
6.12×
10-4
3.95×
10-4
2.28×
10-4
0
-1.82×10-4
-3.89×10-4
-5.43×10-4
-6.11×10-4
-5.75×10-4
-3.74×10-4
10
7
13
11
9
11
0
4
7
3
12
7
5
Table 3. Comparison of out-of-plane strain between DS PS and ASA, as specimen is loaded up to 6kg and shearing is 0.9
mm.
Loaded up to 6kg
r, mm
Fringe order
-26.6
-24.3
-21
-14.6
-10.4
-6.5
-3.3
-1.8
0
1.9
3.8
6.3
1
1.5
2
2.5
2
1.5
1
0.5
0
-0.5
-1
-1.5
∂w
（DSPS）
∂r
3.72×10-4
5.24×10-4
6.93×10-4
8.91×10-4
6.81×10-4
5.36×10-4
3.29×10-4
1.57×10-4
0
-1.58×10-4
-3.34×10-4
-5.11×10-4
∂w
（ASA）
∂r
4.01×10-4
5.03×10-4
6.82×10-4
7.66×10-4
7.44×10-4
4.97×10-4
3.02×10-4
1.48×10-4
0
-1.49×10-4
-3.08×10-4
-4.87×10-4
error（％）
7
4
2
16
8
8
9
6
0
6
8
5
9.1
14.7
22.1
25.6
29.5
-2
-2.5
-2
-1.5
-1
-7.14×10-4
-8.87×10-4
-6.83×10-4
-5.22×10-4
-3.57×10-4
-7.69×10-4
-7.63×10-4
-6.22×10-4
-4.79×10-4
-3.85×10-4
7
16
10
10
7
Conclusions
A study of the strains measurement of sandwich circular plate with single fully-potted insert was undertaken using the
DSPS. The proposed DSPS has the superiority of full-field, non-contacting, non-destructive testing and flexibility to
adjust the light path of the setup. It was found that the greatest strains occurred at the vicinity of the boundary edge,
not at the edge itself. The DSPS experimental results were compared with the ASA results to show the consistence of
the strains tendency under loading in the elastic region. This study shows the excellence of using DSPS to measure
out-of-plane strain of sandwich structure.
References
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