Digital phase-shifting grating shearography for experimental analysis of fabric composites under tension

Digital phase-shifting grating shearography for experimental

analysis of fabric composites under tension

Jung-Ryul Leea,*, J. Molimarda, A. Vautrina, Y. Surrelb

aDepartment of Mechanical and Materials Engineering, Ecole Nationale Superieure des Mines de Saint-Etienne,

158 Cours Fauriel, Saint-Etienne Cedex 2, 42023, FrancebBNM, INM/CNAM, 292 rue Saint Martin, 75141 Paris, France

Abstract

Digital phase-shifting grating shearography has been applied for the investigation of the tensile behaviour of carbon/epoxy plain-weave

fabric composite with a small waviness. Experimental analyses were performed for the two following configurations: a single lamina and an

iso-phase double laminate. The yarn crimp effects such as the tension/bending and tension/in-plane shear couplings were concentrated on the

resin rich regions for the single lamina. In the latter case, the yarn crimp effects were still significant because although the transverse shear

strain due to the local bending effect of yarns is a little constrained by the other neighboring layer, the degree of the constraint was certainly

insufficient to degenerate the local bending effect.

q 2004 Elsevier Ltd. All rights reserved.

Keywords: A. Fabrics/textiles; B. Anisotropy; C. Laminate mechanics; D. Non-destructive testing-optical full-field method

1. Introduction

Since the weaving architectures provide some beneficial

properties over the unidirectional tape laminates such as

improved resistance to impact damage or delamination,

woven composites have gained a considerable interest as

construction and repairing materials in transport industries

and civil structures. However, the in-plane properties are

reduced because of the undulating yarns. One of the

attempts to alleviate the loss of the in-plane properties is

the use of the fabric with a small waviness, which is

experimentally analysed in this paper.

As for numerical approaches, the classical laminate plate

theory is not in place for the fabric composite owing to the

yarn crimp effects and hence the analysis about the stress

distribution and deformation have been accomplished by

using finite element methods [1–5] or various theoretical

models [5,6]. In particular, Ito et al. [5] reported the

mechanical moduli and the tensile behaviour according

to the waviness of the single lamina and the iso-phase and

out-of-phase laminates using two-dimensional models in

the length and thickness directions and Woo et al. [6]

investigated the moduli of the laminate using a three-

dimensional model according to the waviness and the phase

shift between the layers. On the other hand, the complex

yarn architecture does not permit with ease any quantitative

experimental analysis even if the increasing use of woven

composites still requires a comprehensive knowledge of

their mechanical behaviours. This is because the classical

pointwise sensors are not appropriate to analyse the

complex architecture. Therefore, optical full-field methods

such as photogrammetry analysis [4] and classical moire

interferometry [7] have been utilized for this material. In the

present paper, a plain-weave fabric lamina with a very small

waviness was tested by digital phase-shifting grating

shearography and the results are compared with an iso-

phase double laminate. Grating shearography is a combi-

nation of three techniques, which are a phase-shifting

technique, shearography and diffraction grating metrology.

The introduction of a phase-shifting technique allows the

quantitative and automated measurement. The shearography

is mostly insensitive to vibration and thus there is not in

need of the stringent vibration isolation. For the purpose of

isolating strain, the shearography technique does not require

numerical differentiation because the strain is directly the

function of the displacement derivatives to be obtained by

the optical differentiation. The use of the artificial grating

provides an excellent signal-to-noise ratio (SNR) and a low

laser power requirement. The former lead to excellent

performances in the aspect of spatial resolution and the

latter make it possible the easy realization of four

1359-835X/$ - see front matter q 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/j.compositesa.2004.01.022

Composites: Part A 35 (2004) 849–859

www.elsevier.com/locate/compositesa

* Corresponding author. Tel.: þ33-4-77-42-0048; fax: þ33-4-77-42-

0249.

E-mail address: [email protected] (J.-R. Lee).

http://www.elsevier.com/locate/compositesa

illumination directions for six mechanical measurands,

which are three in-plane strains, in-plane rotation and two

directional slopes of a deformed object surface.

2. Description of digital phase-shifting grating

shearography

Fig. 1 shows grating shearography setup: a 150-mm

diameter collimated beam obtained from 10-mW He–Ne

laser (l ¼ 632:8 nm) illuminates the front surface of

the specimen covered with a diffraction grating-1200

lines/mm (pitch ¼ 833.3 nm) and a classical three-mirror

setup [8]. A screen located in front of the collimating lens1

allows only one part of the beam to pass (A, B, C or D). The

diffracted beam is focused by the lens2, and then sheared in

Michelson interferometer. The Michelson interfermeter has

a PZT-actuated mirror (3-PZT device PSH 1z NV, Piezo-

system Jena), which is capable of tilting the mirror.

Therefore, we can adjust the shear distance in the xðyÞ

direction by tilting the mirror around the yðxÞ axis. The

sheared and diffracted beams generate a fringe pattern in the

image plane. The real image is focused by the lens3 on a

rotating semi-transparent glass plate to remove speckle

noise. The formed image on the glass plate is observed by a

752 £ 582 CCD camera equipped with a standard lens

system (VCL-12 YM). A temporal phase-shifting technique

is introduced for the quantitative phase determination of the

acquired intensity field with a fringe pattern. The intensity

field can be rearranged in the form of

Iði; jÞ ¼ kIl½1 þ mði; jÞcos fði; jÞ� ð1Þ

Fig. 1. Grating shearography system: (a) optical arrangement, (b) three-mirror setup, (c) diffraction grating [10].

J.-R. Lee et al. / Composites: Part A 35 (2004) 849–859850

where ði; jÞ is the pixel coordinates, kIl is the average

intensity, m is the contrast, and f is the phase map in each

load step. The phase-shifting algorithm used in this paper is

the windowed discrete Fourier transform [9]. The phase

shift is p=2 and seven phase-shifted intensity samples are

employed for the evaluation of one phase map. The resulting

form with a triangular window is represented by

tan f ¼ðI0 2 I6Þ2 3ðI2 2 I4Þ

2ðI1 þ I5Þ2 4I3

ð2Þ

The whole image processing including this phase

determination method is composed of several steps until

raw measurands. Eight phase maps at each load step are

determined by the combination between four directional

illuminations and two directional shear distances as

presented in Fig. 2. Successively, we calculate eight

phase change maps for each combination between the

reference state ðrÞ and deformed state ðdÞ; i.e. Dfx;x¼

fdx;x2fr

x;x;Df2x;x;Dfy;x;Df2y;x;Dfx;y;Df2x;y;Dfy;y;Df2y;y;

where the first index represent each direction of the

sensitivity vector ðg ¼ ko 2 kiÞ and the second one

indicates the shearing direction. This phase change map

is the raw measurand of the phase-shifting shearography.

As shown in Fig. 3, the six mechanical measurands are

next isolated at each measuring step by using the values

of the incidence angle ðu ¼ 49:418Þ; the wavelength of the

laser and the applied shear distances ðDx ¼ DyÞ: The shear

distance is a function of the relative angle between the

two mirrors inside the Michelson interferometer. The

shear distances of this Michelson interferometer-based

Fig. 2. Image acquisition and processing procedure to obtain phase change maps.

Fig. 3. Mechanical setup: tensile test machine and specimens (in mm).

J.-R. Lee et al. / Composites: Part A 35 (2004) 849–859 851

Fig. 4. Post-image processing procedure to isolate mechanical measurands.

Fig. 5. Numerical filtering: (a) correspondence between the strain map before and after filtering and the fabric mesh, (b) effect of the Gaussian and sine/cosine

separable median filtering.


shearography are precisely evaluated by a grid method

with a spatial phase-shifting technique. Practically, the

shear distances of about 100 mm are used in this paper.

More information about grating shearography can be

found in Refs. [10,11].

3. Mechanical experiment

The aim of this experimental study is to analyse

heterogeneous strain fields in fabrics under uniaxial

tension. A one-ply lamina as the fundamental construction

to stack a fabric laminate was first investigated. The

object was a T700S/M10 12K plain-weave carbon fabric

(48192, Hexcel Corporation), having the fiber and resin

tensile moduli of 230 and 3.2 GPa and the waviness

ðhy=2aÞ of 0.0078. In Fig. 3, one unit cell without its resin

for the clarity of drawing presents the mesostructure of

the fabric. A unit cell consists of two half-warp yarns and

two half-fill yarns, and the warp yarns undulate crossing

over and under the fill yarns. The size of one unit cell is

about 8 £ 8 mm2 and the inspecting zone contains six unit

cells. In the case of only one-ply fabric lamina a pure

resin region caused by loose weaving is clearly identified

Fig. 6. Tensile strain maps and strain profiles along x1- and x2-lines parallel to the loading axis.


in the middle of each unit cell. Fig. 3 also presents the

tensile test machine and the specimen. For the second

experiment, the first and the second plies in Fig. 3 were

stacked so as to have iso-phase between the layers. The

thickness of the single lamina and the iso-phase double

laminate was 0.25 and 0.52 mm, respectively. In order to

obtain the same configuration in the aspect of the yarn

architecture both specimens were cut along the boundaries

of the warp yarns. Even if the same product was used, the

sizes of unit cell were little by little different and thus

the width of specimen was a little different, 30.66 mm for

the single lamina and 29.1 mm for the double

laminate. Consequently, the applied loads were divided

by the respective widths with the aim of comparing

the two experiments. Each grating was glued in the

middle of the front surface of each specimen. A

displacement was imposed on the movable jaw in the

tensile test machine. The load was controlled using

a classical load cell and the respective specimens were

loaded in the four steps.

4. Post-image processing

During the tensile test, the grating will act as a sensor

because the surface deformation of the specimen induced

by external load is digitized in the form of a phase change

corresponding to the change of the attached grating. Due to

the feature of the excellent SNR of grating shearography,

the phase change maps can be directly converted into the

six displacement derivative maps of Fig. 4 without

filtering. This is possible due to the quasi-plane wavefront

diffracted from the grating and the optical temporal

filtering by the use of a semi-transparent rotating glass

plate. The displacement derivative maps are next filtered

and unwrapped. As shown in Fig. 4, the four-displacement

Fig. 7. Local bending effect induced by the stretch of the undulating warp yarn.

Fig. 8. Local x- and y-slope maps at 8 N/mm load step.


derivative maps are directly converted into the four

mechanical measurands, tensile strain, transverse strain,

x- and y-slope maps. The other two measurands are

isolated by the combination of the two remaining

displacement derivative maps, ›u=›y and ›v=›x:

As for filtering, the two-dimensional low-pass filter with

a Gaussian kernel is applied to the six-displacement

derivative maps because Gaussian kernel is more efficient

than a box kernel in the aspects of the high frequency

rejection, the preservation of spatial resolution and the small

distortion of signal. The energy of the displacement

derivative maps is primarily concentrated on its low-

frequency components because the mechanical behaviour

of the specimen induces the high spatial correlation among

neighboring pixels. On the other side, the energy of such

degradation causes of phase map as wideband random

Fig. 9. Transverse strain maps and strain profiles along y0-line perpendicular to the loading axis.


optical and electronic noise or speckle noise is typically

more spread out over the frequency domain. By cutting off

the high-frequency components while preserving the low-

frequency signal, this Gaussian low-pass filtering sup-

presses a large amount of noise at the expense of reducing a

small amount of signal. A separable median filter with a

horizontal n £ 1 kernel and a vertical 1 £ n kernel is also

applied if a filtered image still has some salt-and-pepper

noise, because it can remove efficiently the impulsive noise

without distortion for the local linear data in the one-

dimensional kernel. The salt-and-pepper noise should be

removed before the step of the phase unwrapping,

because it makes the unwanted phase jump during the

line-by-line unwrapping process used in this study.

Although the line-by-line unwrapping process is the

simplest algorithm, it is enough to unwrap the measurand

map due to its excellent SNR. Another advantage of the

linear line-by-line processing conserves the spatial resol-

ution of the wrapped image.

For example, the tensile strain map in the case of the

single lamina obtained by these post-image processing

procedures is shown in Fig. 5a, which also shows the

correspondence between the strain map and the fabric mesh.

Fig. 5b shows the filtering effect on a cross-section along x0-

line in Fig. 5a. The dominant strain information was not

changed. Finally, all mechanical measurands post-pro-

cessed in both experiments for the single lamina and the

iso-phase double laminate have the spatial resolution of

Fig. 10. Shear strain maps and strain profiles along x3- and x4-line parallel to the loading axis.


about 0.8 mm. This means the measuring area comprises

about 600 pieces of three-elements stacked rosette with the

gage area of 0.8 £ 0.8 mm2.

5. Results

First, we here outline the results of the experimental

analysis of the single lamina. Fig. 6 presents the post-

processed tensile strain map at each load step. The tensile

strain of the fill yarn in the matrix dominant direction is

higher than the value of the warp yarn in the fiber dominant

direction. Two crescent-shape strain concentration regions

occur between the vertical centerline of the fill yarn and its

vertical borders. The two tensile strain concentration

regions on the fill yarn are represented in the line profile

graphs of Fig. 6 by two peaks. However, tensile strain

decreases significantly from the beginning line of the warp

yarn, which is the beginning of the fiber dominant region.

The lowest tensile strain value occurs not in the middle of

the warp yarn but in the resin rich region. Such a result on the

warp yarn gives rise to two valleys in the line profile

graphs. This is due to the local bending effect induced by

the stretch of the warp yarn. The tension/bending coupling

effect caused by the local bending effect of the undulating

yarns is quite significant when dealing with one-ply woven

composites because there is no adjacent ply, which can

constrain the flexural deformation. Fig. 7 provides a rough

schematic view of the local bending effect in the single

lamina. In isolating the average tensile strain, the strain

induced by local flexural deformation is compressive at the

zone D–E and tensile at the zone E–F. Both the C–D and

F–G zones existing visibly in the fabric with a large unit

cell remain unchanged before and after deformation. The

effect is more remarkable since the regions where the local

bending effect occurs are resin rich regions. Therefore, two

peaks and two valleys appear on the fill yarn and on the warp

yarn, respectively, as already shown in Fig. 6.

Actually, as presented in the local x- and y-slope maps in

Fig. 8, warp yarns go down and fill yarns go up by reason of

stretching the specimen. To characterize the local slope

behaviours within the fabric cells, the global slopes

Fig. 11. In-plane shear deformation of the warp and the fill yarns.

Fig. 12. Local x- and y-slope maps of the iso-phase double laminate at 8 N/mm load step.


(averaged values) were subtracted from the original maps.

The sudden changes of the behaviours occur at the

horizontal and vertical crossings of the warp and the fill

yarns. The fundamental interest of the slope mapping is

clearly enlightened by this analysis.

If the previous analyses about the tensile strain and local

slope maps were reasonable, there should be considerable

transverse tensile strain against Poisson’s effect on the

ascended fill yarn. As shown in Fig. 9, the fill yarns are in

tension. The line profiles on the warp yarn at each step are

also shown in Fig. 9 and there are two distinct valleys on the

warp yarn. The flexural deformation induced by the local

bending effect and the resin rich region can also explain the

heterogeneity of transverse strain maps even if they differ

from the tensile strain maps in that the compression by

Poisson’s effect governs the transverse strain maps.

Fig. 10 presents the in-plane shear strain maps and their

line profiles along the x3- and x4-line parallel to loading

axis. It is shown that shear strains reach high magnitudes in

the vicinity of the six-pure resin regions. This is the tension/

in-plane shear coupling effect induced by the local bending

effect. In focusing now on the upper fill yarn, it is clear that

the two diagonally opposite corners, which correspond to

pure resin regions, undergo positive shear strains while the

other two corners sustain negative shear strain values. It is

easy to get a qualitative outline of the global shear

behaviour of the yarns when the fabric is loaded in tension

along the orthographic axes. Fig. 11 displays some basic

results. In both the warp and fill yarn, the local areas with no

shear are naturally located on the symmetry axes and are

symbolized as squares surrounded by zeros while the non-

zero areas are located in the corners. The diagonally

opposite corners of each yarn are the same sign. Signs of the

four corners in the warp yarn have the reverse signs as

compared with the fill yarn.

6. Discussions

6.1. Comparison with the iso-phase double fabric laminate

The x- and y-slope maps in Fig. 12 show that the local

bending effect such as in the single lamina still exists in the

iso-phase double laminate because its configuration allows

the up and down movement of the yarns. Fig. 13 presents the

comparison in the in-plane strain maps between the two

cases at the same surface tensile strain of 1290m1; which

was obtained by averaging over the six unit cells,

respectively. In the tensile strain maps, the two peaks and

the two valleys that have been in the fill and warp yarns of

the single lamina smoothened in the iso-phase double

laminate. Similarly, the strain concentrations in the

transverse and shear strain maps were also dispersed.

These alleviations of the tension/bending and the tension/in-

plane shear couplings are because two neighboring layers

constrain on each other. It should be here noted that

Fig. 13. Comparison of the in-plane strain maps between the single lamina

and the iso-phase double laminate at the same averaged surface tensile

strain of 1290m1.


the respective measurands after post-image processing in

both experiments were controlled so as to have the same

spatial resolution.

7. Conclusion

Digital phase-shifting grating shearography has been

applied for the investigation of the elementary behaviour of

carbon/epoxy plain-weave fabric composite with large unit

cells under uniaxial tension. Experimental analyses have

been performed on the surfaces of a single lamina and an

iso-phase double laminate. We begun to perform the

experimental analysis with the single lamina as a basic

element and then the results were compared and discussed

with the second results about the iso-phase double laminate.

The final measurands in each specimen, i.e. the surface

slopes and in-plane strain fields made it possible to catch an

in-depth understanding of the mechanical behaviour of the

fabrics under tension. In both cases the tension/bending and

tension/in-plane shear coupling effects revealed and their

cause was the local bending effects of the undulating yarns

caused from their configurations allowing the transverse

shear strain ð1zxÞ: As for the number of the layers, the

tension/bending and tension/in-plane shear coupling effects

smoothened in the iso-phase double laminate because the

other layer works as the boundary condition of one side of

the first layer.

It should be noted that these measurements were possible

because the 0.8-mm spatial resolution was small enough to

follow these yarn crimp effects. Further experimental works

are planned to understand the configurations of an out-of-

phase double laminate and multi-layer laminates.

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Digital phase-shifting grating shearography for experimental analysis of fabric composites under tension

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