Residual strain development in an AS4/PPS thermoplastic composite

measured using fibre Bragg grating sensors

Larissa Sorensen, Thomas Gmur, John Botsis*

Laboratoire de Mecanique Appliquee et d’Analyse de Fiabilite, Sciences et Techniques de l’Ingenieur,

Ecole Polytechnique Federale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland

Received 10 November 2004; revised 8 February 2005; accepted 9 February 2005

Abstract

This paper demonstrates the use of fibre Bragg grating (FBG) sensors for the measurement of residual strain development during the

consolidation of a thermoplastic composite. During the processing of the carbon fibre-reinforced polyphenylene sulphide (AS4/PPS)

laminate, FBG sensors respond to changes in material state, for example the glass-rubber transition and solid–liquid transition. The sensors

also permit the observation of wavelength shifts and spectral form changes induced by the contraction of the composite during cooling. The

experimental data are compared to a generalized plane strain, thermoelastic numerical model with temperature dependent matrix dominated

properties. The model provides solutions for two limiting cases: one where the specimen contracts freely, and one where the specimen is

restricted by perfect contact with the mould. Strain values calculated in each case are inserted into optomechanical equations, which convert

the strain state in the FBG to a corresponding change in wavelength. In this way, the modelled cases are compared to FBG wavelength shifts

during consolidation.

q 2005 Elsevier Ltd. All rights reserved.

Keywords: A. Thermoplastic resin; B. Residual/internal stress; C. Finite element analysis (FEA)

1. Introduction

The processing of thermoplastic composites may cause

significant residual strains due to their anisotropic and non-

homogeneous nature. Mismatches in coefficients of thermal

expansion of the component materials cause residual strains

on a microscopic level, while thermal mismatch between

plies of different orientations produces a similar effect on a

laminar scale. On a global level, strains may vary

throughout a laminate due to tool–part interaction and due

to thermal gradients that will vary the local material

properties. The total residual strain field in a composite

material is the combination of all of these effects.

Measurements of residual strains are often acquired by

examining the externally visible distortions of a part, such

as curvature [1,2]. Now, with the development of fibre

optic sensors, it should be possible to obtain internal,

1359-835X/$ - see front matter q 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.compositesa.2005.02.016

* Corresponding author.

E-mail address: john.botsis@epf1.ch (J. Botsis).

non-destructive measurements that indicate macroscopic

residual strain build-up in a composite laminate. It should

also be possible to vary the position of these sensors within

the composite to provide strain readings in given plies

throughout the thickness of a part. Ultimately, these sensors

could provide crucial information about the initial quality of

processed parts, followed by real-time information relating

to their health during service.

Published studies consider the response of optical fibre

sensors such as a fibre Bragg grating (FBG) to the

accumulation of residual strains in composite materials.

Most often, research focuses on monitoring the curing of

thermosetting composites where residual strains are the

result of matrix shrinkage during polymerization and

thermal shrinkage during cooling [3–7]. Results from

these studies generally show that the FBG spectra translate

towards decreased wavelengths indicating compressive

residual strains [3,7]. Some articles, including one study

on thermoplastic-metal laminates [8], present split spectra

for non-unidirectional lay-ups [4–6]. The explanation of the

split peak differs between the authors, since without

polarization control, it is impossible to verify the origin of

the peak split. Kuang et al. reason that the observed double

Composites: Part A 37 (2006) 270–281

www.elsevier.com/locate/compositesa

L. Sorensen et al. / Composites: Part A 37 (2006) 270–281 271

peaks are caused by a non-homogeneous strain field in their

cross-ply thermoplastic-aluminium laminates [8]. In con-

trast, Guemes and Menendez attribute their FBG response to

unequal transverse strains that cause birefringence in the

optical fibre core. They interpret their spectral splits using a

plane stress model of the optical fibre, thereby neglecting

the contribution of a three-dimensional stress field [4,6].

Okabe et al. provide a generalized plane-strain, thermo-

elastic model with constant material properties to show how

the strains in a cross-ply laminate after curing can create

unequal transverse strains in the fibre optic sensor, thus

causing birefringence [5]. This solution assumes that all

residual strains are solely the result of free thermal

contraction with constant material properties.

Additional progress must be made to understand three-

dimensional residual strain development and the resulting

spectral responses of embedded optical fibres, particularly

those embedded in thermoplastic composites. Conse-

quently, the first goal of this paper is to highlight the

capacities of FBG sensors for process monitoring and

measuring residual strain development in a thermoplastic

composite. By following the FBG spectral response during

the consolidation and demoulding of a composite, insight

can be gained into the ability of an FBG to follow

material and process changes. The sensor will also react

to the development of residual strains on a macroscopic

level.

Secondly, this paper attempts to better interpret the FBG

sensor output and its relationship to the far-field composite

strains by modelling the consolidation process. A numeri-

cal, thermoelastic model with temperature dependent matrix

properties investigates two limiting cases for the process: a

freely contracting composite, and a composite constrained

by perfect contact with the mould lid. These two cases are

considered due to current difficulties in precisely knowing

the mould–specimen contact behaviour. The cases

described in this work provide solutions of the strains in

the fibre sensor, which can be converted into equivalent

spectral changes and compared to experimental findings.

The model also calculates the residual stress and strain fields

throughout the composite. Finally, results from the

modelled cases are used to highlight the potential errors

that can be made when interpreting FBG spectral responses.

Fig. 1. Wavelength response of a uniform FBG to the application of a

homogeneous strain field.

2. Working principles of FBG sensors

FBG sensors are created by modulating the index of

refraction along a length of the core of an optical fibre.

When illuminated by a broadband source, it will strongly

reflect light at the Bragg wavelength according to:

lB Z 2n0L (1)

where lB is the Bragg wavelength, n0 is the effective index

of refraction and L is the grating period. As a result, sensors

with constant periods and index modulations will reflect

light at a single Bragg wavelength. Changes in the index of

refraction and the period of the grating due to strains and

temperature variations will perturb the Bragg wavelength of

an FBG. For strain and temperature fields that are uniform

along the length of the sensor, the relative shift in Bragg

wavelength is described by Sirkis [9] using the following

equations:

Dlbx

lB

Z 3z Kn2

0

2½p113x Cp12ð3z C3yÞ�CxDT (2a)

Dlby

lB

Z 3z Kn2

0

2½p113y Cp12ð3x C3yÞ�CxDT (2b)

where Dlbx,y are the shifts in Bragg wavelength for both of

the major polarization axes in the fibre, 3x,y,z are the total

principal strain components in the fibre core (3mechanicalCaDT), p11 and p12 are the strain-optic Pockel’s constants, x is

the thermo-optic constant and DT is the change in

temperature.

When the transverse strains are equal in low-birefringent

fibres (3xZ3y) the equations (2a) and (2b) become

equivalent, thus representing a single Bragg wavelength

shift. This corresponds to the case most often considered in

sensor applications and is shown in Fig. 1. The single

equation can be further reduced by assuming that the

transverse strains are related to the longitudinal strains by

the Poisson’s ratio of the glass fibre (3xZ3yZKn3z) and that

there is no temperature change:

Dlb

lB

Z ð1 KpeÞ3z (3)

where pe is the effective photoelastic constant that

incorporates the photoelastic constants pij and effective

refractive index n0. Using this equation, it is possible to

relate the measured wavelength shift to longitudinal strains

in the sensor. Although this approximation works well

in situations where uniaxial strains dominate, there are cases

when Eq. (3) is not realistic [10]. This is the case when the

transverse strains in the fibre core are not related to the

longitudinal strain by Poisson’s ratio. If a sensor is

embedded in a material that undergoes thermal contraction

L. Sorensen et al. / Composites: Part A 37 (2006) 270–281272

or chemical shrinkage, the exact state of strains transferred

to the fibre core must be considered. For an isotropic

material with a low elastic modulus, little error will be

incurred by considering the above simplification. However,

in an orthotropic composite such as a carbon-reinforced

polymer, thermal contractions in the fibre direction are

extremely small (approaching 3zZ0) compared to those in

the transverse direction. This may result in significant errors

if the simplified pe assumption (Eq. (3)) is used to relate

strains to wavelength shifts.

Unequal transverse strains will also create a response

from the FBG that cannot be interpreted using Eq. (3).

These strains deform the sensor so that its cross-section

becomes non-circular (elliptic if strains are symmetric),

and birefringence is induced in the fibre. This causes the

light to follow either the fast or slow axis, making the

sensor response polarization dependent. For each polariz-

ation axis, a different wavelength will be reflected as

predicted by the set of two equations in Eqs. (2a) and

(2b). If polarized light is sent separately along each of the

polarization axis, then two distinct peaks are distinguish-

able (Fig. 2); however, if light is sent along an arbitrary

path, then the resulting wavelength spectrum will be a

mixture of the light reflected along both axes. This dual

peak spectrum could be misinterpreted by attributing its

source to a non-uniform longitudinal strain field.

Consequently, the polarization dependence of a reflected

spectrum should be tested in order to determine the origin

of its multiple peaks.

In general, the overall strain state in the FBG sensor core

should be considered before simplifying Eqs. (2a) and (2b).

For those cases where simplification is not realistic, one is

left with a set of equations that includes three mechanical

strain components and a temperature component. The

temperature component may be removed via calibrated

temperature correlation and various other methods [11].

However, since three strain unknowns remain in the set of

two equations, additional input is required to solve the

residual strain state. This can be accomplished by creating

an appropriate model to describe the strain state in the fibre

core and then comparing it to experimental output from the

FBG sensor.

Fig. 2. Influence of unequal transverse strains on the spectral response of an

FBG.

3. Experimental method

3.1. Characterization and preparation of the fibre Bragg

grating sensors

This study used polyimide-coated, low-birefringent,

single mode FBG sensors with a cladding diameter of

125 mm. All fibres were annealed at 320 8C for 2 h in order

to stabilize their optical response during the high-

temperature processing cycle [12]. Both 3 and 22 mm

gauge length sensors were used during testing, all operating

at a wavelength of approximately 1300 nm. The 3 mm

sensor provided strain measurements after specimen

consolidation. The 22 mm sensors were used to follow

wavelength evolution during processing. These long gauge

length sensors also had the benefit of narrow bandwidths:

less than 0.03 nm for the full width, half maximum of their

spectra. Such narrow bandwidths provided a clear distinc-

tion of any splits in the spectral form that may have been

caused by load-induced birefringence both during and after

the consolidation process.

Before embedding, the region around the FBG grating

was stripped of its polyimide coating using hot sulphuric

acid. The sensors were rinsed with alcohol and then treated

with Silquest RC-2 silane that generates a strong interface

between glass fibres and polyphenylene sulphide (PPS)

polymer [13]. The fibres were dried for a minimum of 1 h at

120 8C after the silane treatment.

Reference spectra were measured for all FBG sensors

before embedding and their equivalent photoelastic constant

pe was measured by hanging calibrated weights on the ends

of the optical fibres. The measured peZ0.29 corresponded

well to that calculated using p11 and p12 provided by

Springer and van Steenkiste [14]. All other fibre optic

properties can be found in Table 1. Fibre Bragg gratings

were also characterized with respect to their temperature

sensitivity by matching their wavelength shifts to that of

250 mm diameter type K thermocouples. This allowed their

temperature-induced response to be separated from their

mechanical response.

3.2. Specimen preparation

Four specimens were fabricated from Cytec’s AS4/PPS

(carbon fibre—polyphenylene sulphide) Fiberite composite

prepreg. The prepreg was cut into 200 mm by 50 mm strips,

with a consolidated ply thickness of approximately 130 mm.

Table 1

Properties for the optical fibre and FBG

Mechanical properties Optical properties

Ef 70 GPa p11 0.17 [14]

nf 0.16 p12 0.36 [14]

af 0.5!10K6 1/8C n0 1.45

Fig. 3. (a) Composite laminate schematic, showing position of FBG sensor and thermocouple. (b) Micrograph showing the distribution of consolidated

composite around the embedded 125 mm diameter FBG sensor.

L. Sorensen et al. / Composites: Part A 37 (2006) 270–281 273

The strips were cleaned with a damp alcohol rag, air dried

and stacked into a matched-metal mould in a unidirectional

configuration [0]28. Each specimen included an FBG sensor

that was centrally located either between the middle plies, or

between the 3rd and 4th outer plies. Each sensor was

correctly positioned in the x-direction by passing it through

slits centred in either end of the mould and the exiting

portions of the fibre were protected by PTFE tubing to

prevent fracture. Long gauge length FBG specimens also

included thermocouples that were embedded in an adjacent

ply to provide a means for temperature compensation. A

schematic of the specimen configuration and a micrograph

of an embedded FBG are shown in Fig. 3(a) and (b) and a

list of the four specimen configurations is provided in

Table 2.

3.3. Composite mechanical properties

Mechanical properties of the AS4/PPS composite were

obtained using a mixed numerical–experimental identifi-

cation method based on modal analysis [15] and key values

were confirmed with both manufacturers data [16] and

independent tensile tests. Temperature dependent transverse

moduli trends were measured using a Rheometrics Solids

Analyzer (RSAII) which performed dynamic mechanical

thermal analysis (DMTA) in three point bending at 1 Hz.

Table 2

List of specimen characteristics

Specimen FBG gauge

length (mm)

FBG

location

Compensating thermo-

couple location

U1 3 Middle None

U2 22 Middle Adjacent ply

U3 22 Outer Adjacent ply

U4 22 Middle Adjacent ply

Table 3

Room temperature properties for AS4/PPS composite

Longitudinal modulus, E11 128 GPa

Transverse modulus, E22 10 GPa

Shear modulus, G12 5.7 GPa

Longitudinal Poisson’s ratio, n12 0.30

Transverse Poisson’s ration, n23 0.49

Longitudinal coefficient of thermal expansion, a11 1!10K6 1/8C

Transverse coefficient of thermal expansion, a22 28!10K6 1/8C

These transverse moduli were then multiplied by a factor of

1.18 to bring the room temperature modulus in line with

accepted values since the DMTA can provide accurate

trends but not necessarily accurate absolute values [2].

Where required, shear moduli were assumed to follow the

same temperature trend as the transverse modulus.

Coefficients of thermal expansion (CTE) in the

transverse direction were measured up to 270 8C using a

Perkin Elmer thermomechanical analyser (TMA7). This

technique was not sensitive enough to measure the

extremely small CTE in the fibre direction, therefore, the

embedded FBG’s were used to provide this information.

Specimens were placed in a freezer and the temperature

drops read by the embedded thermocouples were compared

to the wavelength shifts. Wavelengths were then related to

the strain state using Eqs. (2a) and (2b). The thermally

induced strains in the fibre were also calculated analytically

by assuming the generalized plane strain case of a

cylindrical inclusion in an infinite host used by Sirkis

[10]. By combining this solution with Eqs. (2a) and (2b) and

assuming room temperature material properties and the

previously measured transverse CTE, it was possible to

extract the value of the longitudinal CTE. This value was

assumed to remain constant for all temperatures due to the

domination of the carbon fibres. Room temperature values

of all material parameters are provided in Table 3, given a

fibre volume fraction of 60%.

3.4. Specimen consolidation and data acquisition

Specimens were consolidated in a matched-metal mould

placed in a Fontijne hot-press under pressure and

temperature control, as shown in Fig. 4. The processing

profile represented by Fig. 5 was chosen to coincide with

those suggested by the prepreg manufacturer [17]. They

Fig. 4. Cross-section of the specimen in the matched-metal mould.

Fig. 5. Processing cycle parameters, including the mould temperature and the platen pressure applied on the mould.

L. Sorensen et al. / Composites: Part A 37 (2006) 270–281274

allowed the thermoplastic to completely melt and then

solidify into the mould form upon cooling.

Each FBG sensor was characterized before and after

consolidation with a tunable laser-based system capable of

polarization control. Additionally, specimens with 22 mm

long gauge lengths were monitored throughout the

consolidation process. During processing, a tunable laser

and photodetector were coupled to the FBG sensor fibre to

provide continuous measurements of the reflected spectra.

The temperatures of the embedded thermocouple and of a

thermocouple inserted into the mould (Fig. 3) were

measured concurrently via a temperature data acquisition

system.

The available optical monitoring system used during

fabrication did not posses sufficiently fast polarization

control, thus spectral measurements were taken with

arbitrary and possibly changing polarization states. The

monitored Bragg wavelength was consequently defined by

either the maximum of a single or multiple-peak spectrum,

or by the maximum of the rightmost peak in a double-peak

spectrum. The requirement for this arbitrary standardization

stemmed from the tendency of the spectra to change form

and centre of gravity due to load-induced birefringence.

When possible, peak separation due to birefringence was

measured during processing in order to complete the

spectral data from these tests.

4. Experimental results

During the heating portion of the consolidation process,

Bragg wavelength shifts and spectral forms provided

qualitative indications of changes in the surrounding

composite prepreg. The magnitude of spectral shifts and

their forms depended on the contact between the optical

fibre and the composite. For example, when the sensor was

placed between the prepreg sheets and pressure applied on

the mould, the measured spectra transformed from a single

peak into multiple peaks due to the non-uniform contact

stress between the rigid, curved prepreg plies and the optical

fibre [18]. Later in the process, around the glass-transition

temperature (Tg) of 90 8C, the polymer matrix softened

allowing for better contact with the FBG. As a result, the

spectra presented a double peak after this transition. They

did not return to a single peak form because of the mould

pressure which was pressing the fibre into an elliptic shape

causing birefringence as described by Eqs. (2a) and (2b)

when 3xs3y. The deformed shape can be assumed due to

geometric and loading symmetry.

Another indication of the passage through Tg was

given by the magnitude of the Bragg wavelength. In

Fig. 6, the temperature corrected wavelength shifts showed

a sharp jump around Tg. A similarly marked step in Bragg

wavelength was observed at the melting temperature (Tm),

of 280 8C. This jump was also followed by a change in

the spectral forms, from double peaks to single peaks.

This transformation was explained by the liquid state of the

polymer matrix that permitted viscous flow of the composite

around the fibre optic sensor creating equal transverse

strains.

Later in the melt state of the process, two step pressure

increases were applied. During each of these pressure steps,

there were corresponding increases in Bragg wavelength

due to the increased pressure in the mould. If one considered

that the FBG and polymer were now in perfect contact, then

it would be possible to model these instantaneous

wavelength shifts using a low transverse modulus for the

composite as described later in this paper.

After solidification, the FBG sensor was considered to have

perfect adhesion with the matrix, and consequently wave-

length shifts and spectral forms then represented strains

transferred from the surrounding composite specimen into the

core of the optical fibre. During cooling, the Bragg wavelength

followed the contraction of the composite plate (Fig. 6).

Fig. 6. Typical changes in the wavelength peak (right peak if split) during processing.

L. Sorensen et al. / Composites: Part A 37 (2006) 270–281 275

Some fluctuations were observed in the wavelength measure-

ments corresponding to the on/off water cooling process. After

viewing video recordings of the specimen and mould during

processing, it was evident that this on/off sequence caused

significant movement and pressure changes that would explain

the periodic wavelength fluctuations. The video recording also

indicated that the matrix retained the capacity for viscous flow

until temperatures around the recrystallization temperature

(TcZ235 8C) published for PPS [19].

Itwasalsonoticed that thespectralpeaksplit returnedinthe

vicinity of this Tc; however, it was difficult to pinpoint the

exact temperature where this occurred due to the lack of

polarization control during processing. It is likely that the

mould–composite interaction during thermal contraction

caused the birefringence leading to a peak split. At the end

of cooling, the mould was released from the press, resulting in

a wavelength step increase but no peak split change. The same

type of wavelength jump was again observed when the

specimen was removed from the mould. These step increases

in wavelength were related to the release of constraints caused

by mould contact; however, since the peak split did not

Fig. 7. Spectral measurements of U3 before and after consolidation. The

two right-hand peaks represent the two major polarization axes.

change, the ratio of transverse strains was considered

constant.

After demoulding, it was possible to measure the complete

spectral response of the embedded FBG sensors with a

polarization controlled laser using 1 pm scan steps. Fig. 7

shows a typical wavelength response before embedding (left)

compared to the spectra obtained after consolidation (right).

All spectra exhibited uniform single-peak forms, indicating

uniform longitudinal strain fields. However, since the two

right-hand spectra were obtained from the same specimen

simply by adjusting the polarization angle of the light by 908,

this indicated that the dual peaks were caused by strain-

induced birefringence in the embedded fibre. By combining

Eqs. (2a) and (2b), transverse strain differences in the core of

the optical fibre were calculated using the wavelength

separation between the two peaks:

3x K3y Z2

n20ðp12 Kp11Þ

� �lbx Klby

lB

(4)

The separations between lbx and lby were measured with

the polarization controlled system, and then inserted into

Eq. (4) toobtaincorresponding transversestraindifferencesas

listed in Table 4. Measurements taken during processing are

provided later in the paper; however, it is interesting to note

that the removal of the composite specimen from the mould

and from the press caused no change in the transverse strain

difference (peak split), even though significant jumps were

observed in the overall wavelength. This led to the conclusion

Table 4

Differences between the wavelengths of the two major polarization axes

caused by transverse strain differences

Specimen Peak split (nm) Strain difference (mm/m)

U1 0.040 154

U2 0.071 273

U3 0.038 146

U4 0.030 116

L. Sorensen et al. / Composites: Part A 37 (2006) 270–281276

that the forms of strain distributions were ‘frozen’ into place

during processing, and then proportionally released upon

removal from the mould. For measurements taken during

processing, the lack of polarization control would not permit

the visualization of peak splits less than approximately 30 pm

due to the bandwidth of the original spectra. The resolution

was also limited to G5 pm due to the laser step spacing.

Although the experimental configuration gave overall

wavelength shift and peak split data, they were insufficient

to completely describe the three dimensional strain state if

longitudinal strains are small compared to transverse strains.

For this reason, a model of the consolidation process must

be used to solve for the strain field in the FBG.

5. Numerical modelling

5.1. Description of the numerical modelling

A generalized plane strain thermoelastic model is used to

calculate the strain field both in the centre of the optical fibre

and in the surrounding composite. This incremental model

follows the cooling portion of the consolidation cycle so that

residual strain development can be calculated starting from

the solidification of the composite laminate. The strain data

are then inserted into Eqs. (2a) and (2b) and the resulting

wavelength shifts compared to experimental data.

Considering the symmetry of the specimen geometry and

the applied loads, only one quarter of the specimen is

analyzed. The specimen is subjected to two sets of boundary

conditions in order to show the effect of the loading pressure

and mould–specimen contact. In the first case, the model is

described as ‘unconstrained’ since it represents a freely

contracting specimen without mould contact. Although, this

situation does not match reality, it is chosen as a reference

state. A second ‘constrained’ boundary condition set is

chosen to provide the limiting solution where the contact

between the specimen and the mould lid is assumed perfect.

These two sets of boundary conditions, subsequently

referred to as the ‘unconstrained’ model and the ‘con-

strained’ model, are shown in Fig. 8.

The numerical analysis of these two cases is performed in

ABAQUS 6.4 using an incremental thermoelastic model

Fig. 8. (a) Unconstrained model boundary conditions, (b) constrained model bound

scale).

with quadratic, generalized plane strain elements

(CPEG8R). The radius of the optical fibre is 0.065 mm

compared to the specimen half thickness of 1.82 mm and in

the constrained case, the mould lid thickness of 15 mm.

Since the fibre optic region is the area of interest, the mesh is

refined to provide appropriately small elements around the

FBG sensor. For the unconstrained model this includes 14,

599 elements and 44,439 nodes. The constrained model uses

14,974 elements and 45,646 nodes.

In developing these numerical models various factors

should be considered. For the AS4/PPS composite system,

with a high melting point of 280 8C, the laminate thermal

contraction is considered to have the most influence on

residual strain development. Mould contact and pressure are

also considered significant due to the development of

birefringence in the experimental results, which implies

unequal transverse strains. Global strains caused by thermal

gradients are neglected due to the small temperature

differences recorded between the inner, outer and mould

thermocouples during cooling. Crystallization development

is also omitted from the model due to the difficulty of

performing tests to accurately quantify its evolution and due

to an uncertainty in its importance as discussed by Sonmez

and Eyol [20]. The recrystallization temperature, is

however, considered an important reference point, since

above Tc the matrix is so soft that no significant residual

strains are expected to accumulate.

The simulations of this consolidation process use

constant elastic, isotropic material properties in the fibre

optic (Table 1) and in the steel mould. The modulus of steel

is 200 GPa, its Poisson’s ratio 0.3 and its coefficient of

thermal expansion 12 mm/8C. In the composite region the

material is elastic, transversely isotropic, and the fibre

dominated properties (E11, a11) and Poisson’s ratios are

considered constant with temperature (Table 3). In order to

better model the stress and strain development due to

consolidation, the temperature dependence of the matrix

dominated composite properties (E22, G12, a22) is taken into

account as shown in Fig. 9. By applying temperature

dependence, it is assumed that such an incremental elastic

model sufficiently describes the process without the need for

an experimentally and numerically expensive viscoelastic

model [1,2,21]. The use of temperature dependent moduli

ary conditions where the mould is perfectly attached to the composite (not to

Fig. 9. Temperature dependent transverse modulus E22 and CTE a22, with piecewise constant steps shown only on the modulus curve. (G12 follows the same

trend as E22.)

L. Sorensen et al. / Composites: Part A 37 (2006) 270–281 277

that are very low, close to Tm, also means that no significant

residual stresses will accumulate before Tc.

In the numerical model, transverse modulus, shear

modulus and transverse CTE are considered piecewise

constant by step, corresponding to thirteen temperature

increments calculated in both models. As shown in Fig. 9,

temperature increments have different magnitudes depend-

ing on the rate of change of the transverse modulus in a

given temperature range. In temperature ranges where the

modulus varies quickly, the steps are smaller, whereas, the

entire process below Tg is considered in one step.

Calculations are performed at each temperature incre-

ment using the corresponding material properties to solve

for the incremental stress–strain state in the specimen. At

any point in the cooling process, the total stresses and strains

are the sums of the temperature-induced stresses and strains.

In the constrained case, the moulding pressure is also

applied at each temperature step; thus the total accumulated

strains include the current pressure-induced strains in

addition to the sum of the temperature-induced strains.

The strains calculated at each increment of the

unconstrained model are verified using an analytical

generalized plane strain model for a fibre in an infinite

orthotropic matrix subjected to thermal contraction [9].

Both the numerical and analytical calculations provide

identical results for strains at the fibre core.

6. Results of numerical analysis

6.1. Optical fibre core

In Fig. 10, results from the two numerical models are

compared with experimental measurements taken during the

cooling portion of the consolidation process. This graph

shows the experimental evolutions of the rightmost peak

shift compared to the modelled Bragg wavelengths for the x-

axis of polarization. The experimental results are set to a

reference point corresponding to zero strain at 235 8C

following video observations of matrix behaviour (Section

4). It is assumed that the viscous composite will not retain

any significant residual strain above Tc. At solidification,

(TmZ280 8C) the results from the constrained and uncon-

strained models differ due to the addition of the moulding

pressure as a boundary condition in the constrained model.

While the specimens cool in the mould, the peak shifts

closely follow the constrained model results. When they are

released from the mould, the experimental wavelengths

jump towards the results predicted by the unconstrained

model. This implies that the specimen–tool interaction

contributes significantly to strain development during

cooling.

This specimen–tool interaction can be further investi-

gated by looking at the birefringence induced in the

experiments compared to that predicted by the models. In

the fibre core, transverse strains in the unconstrained model

develop to be equally compressive, thus this model does not

explain the peak splits observed during and after consolida-

tion (Fig. 11). In contrast, due to tool–part contact in the

constrained model, the transverse strains diverge signifi-

cantly during cooling. The small difference in strains upon

application of moulding pressure does not cause any

measurable peak split, supporting the single peak observed

in FBG measurements.

In Fig. 12, the separations of the transverse strains (3xK3y) are compared to the experimental strain differences

measured via Eq. (4). While the unconstrained model does

not predict any birefringence, the perfect mould–specimen

Fig. 10. Evolution of wavelength shift (rightmost peak when required) during cooling: experimental and modelled.

L. Sorensen et al. / Composites: Part A 37 (2006) 270–281278

contact assumed in the constrained model clearly introduces

excessive birefringence. It does, however, provide a

plausible explanation for the origin of the experimentally

observed peak splits. A solution considering realistic

frictional contact between the mould and the composite

would be required to provide the intermediate solution that

better follows the experimental results.

6.2. Strains in the composite

Next, one must consider that the strains measured by an

FBG represent the strains in the fibre core and not

necessarily those in the surrounding composite material.

The numerical analysis used in this section provides insight

into the stress and strain distribution throughout the

composite specimen, by considering the FBG to be

embedded in a homogeneous laminate. Fig. 13 shows that

all residual stresses remain low or zero in the far-field

composite of both models, except for the transverse stresses

(x-direction, constrained model) which surpass half of

Fig. 11. Evolution of strains in the optical fibre core during cooling as

calculated by the unconstrained and constrained models.

the matrix fracture strength [22]. The origin of these high

stresses (sx) is the thermal expansion mismatch between the

steel mould and the 908 direction of the composite. During

cooling, the steel mould restricts the contraction of the

composite, thus causing tensile stresses in the x-direction.

These tensile stresses would significantly reduce the

resistance of the composite to transverse matrix cracking.

Examining the plot of strain distribution in Fig. 14 one

observes large compressive through-thickness strains both

around the optical fibre and in the far-field composite. At the

fibre interface these compressive strains reach 3%, which in

tension represents the failure strain reported for the PPS

matrix. Interestingly, the optical fibre disturbance of the

strain field becomes negligible at a distance of approxi-

mately three fibre radii from the FBG. Although, the cases

investigated herein represent two extreme situations of the

consolidation process (unconstrained and constrained), the

actual residual strain distribution should fall between

the results presented in Fig. 14. Consequently, the strains

Fig. 12. Evolution of transverse strain difference in the fibre core during

cooling: modelled and experimental.

Fig. 14. Strains along the y-axis after cooling as calculated by the unconstrained and constrained models.

Fig. 13. Stresses along the y-axis after cooling as calculated by the unconstrained and constrained models.

L. Sorensen et al. / Composites: Part A 37 (2006) 270–281 279

in the far-field composite can be estimated to be

approximately K2%.

Fig. 15. Evolution of relative strain error derived from wavelengths

calculated using the unconstrained model results, and then worked

backwards into strains using the pe assumption.

6.3. Potential interpretation error due to pe assumption

Although, it may seem obvious that one should avoid

simplifying the optomechical equations when considering a

birefringent signal, single-peak responses may sometimes

be misinterpreted. When the transverse strains are large

relative to the longitudinal strain, and thus do not follow the

Poisson’s ratio relationship (3xs3ysKn3z), Eq. (3) will

produce significant error in the measured 3z. In the case of

the freely contracting composite modelled in this investi-

gation, the pe simplification causes 180% relative error in

the measured longitudinal strains and about 110% error in

the transverse strains (Fig. 15).

L. Sorensen et al. / Composites: Part A 37 (2006) 270–281280

By studying the residual strain cases modelled in this

paper, it is clear that one must carefully consider the type of

strain field in the core of an FBG sensor before interpreting

its signal. In cases where uniaxial loads are applied to a

specimen, Eq. (3) should provide adequate correlations.

When materials like carbon fibre-reinforced polymers

undergo thermal shrinkage, the fibre-direction strains are

close to zero due to the negative coefficient of thermal

expansion of the carbon fibres. This creates a strain state that

may be difficult to interpret without additional information

or modelling.

7. Conclusions

The FBG sensors used in this study demonstrate their

ability to follow pressure and material changes in a

thermoplastic composite during the consolidation process.

After consolidation, the birefringence of the FBG sensors is

verified using a polarization controlled system, and the dual

peak spectra are attributed to unequal transverse residual

strains. Since the interrogation of a single polarization axis

produces only one peak, the residual stress and strain field

must be constant along the length of the sensor.

The combination of FBG measurement with numerical

modelling can serve as a good tool for measuring residual

strain accumulation. Further comparison of the FBG

response and the modelling indicates that the specimen–tool

interaction plays a significant role in the development of

residual strains in the unidirectional composite. In the case

of the constrained model, the calculated transverse stress

(sx) is about 50% of the matrix fracture strength.

Modelling the consolidation process is a challenging

problem because of the need to realistically describe the

material behaviour, to accurately measure material proper-

ties, and to define appropriate boundary conditions. This

investigation uses a model with temperature dependent

material properties and two types of boundary conditions

that provide limiting solutions to the consolidation process.

In order to improve the accuracy of the calculated residual

strain fields, it is very important to identify appropriate

contact conditions between the mould and the specimen;

however, such an experimental task is very difficult at

present. Thus, in conjunction with accurate and precise

experimental data from FBG, various specimen–mould

contact conditions should be simulated to find a narrow

range of realistic solutions for particular material/processing

conditions.

Acknowledgements

The authors would like to acknowledge the financial

support of the Swiss National Science Foundation, Grant no.

2000-068279. They also thank their partners in this grant,

the Advanced Photonics Laboratory, BIOE, EPFL, for their

continued support on optics issues. Finally, they wish to

thank Cytec Industries Inc. for the composite material used

in this investigation and the Laboratoine de technologie des

composites et polymers, IMX, EPFL for the use of their hot

press.

References

[1] Jeronimidis G, Parkyn AT. Residual-stresses in carbon fiber-

thermoplastic matrix laminates. J Compos Mater 1988;22(5):401–15.

[2] Barnes JA, Byerly GE. The formation of residual-stresses in

laminated thermoplastic composites. Compos Sci Technol 1994;

51(4):479–94.

[3] Dewynter-Marty V, Ferdinand P, Bocherens E, Carbone R,

Beranger H, Bourasseau S, Dupont M, Balageas D. Embedded fiber

Bragg grating sensors for industrial composite cure monitoring.

J Intell Mater Syst Struct 1998;9(10):785–7.

[4] Menendez JM, Guemes JA. Bragg grating-based multiaxial strain

sensing: its application to residual strain measurement in composite

laminates. In: Smart structures and materials 2000: sensory

phenomena and measurement instrumentation for smart structures

and materials, SPIE, Newport Beach, CA, USA, vol. 3986; 2000. p.

271–81.

[5] Okabe Y, Yashiro S, Tsuji R, Mizutani T, Takeda N. Effect of thermal

residual stress on the reflection spectrum from fiber Bragg grating

sensors embedded in CFRP laminates. Compos Part A 2002;33(7):

991–9.

[6] Guemes JA, Menendez JM. Response of Bragg grating fiber-optic

sensors when embedded in composite laminates. Compos Sci Technol

2002;62(7-8):959–66.

[7] Lawrence CM, Nelson DV, Spingarn JR, Bennett TE. Measurement of

process-induced strains in composite materials using embedded fiber

optic sensors. In: Smart structures and materials 1996: smart sensing,

processing, and instrumentation, SPIE, San Diego, CA, vol. 2718;

1996. p. 60–8.

[8] Kuang KSC, Kenny R, Whelan MP, Cantwell WJ, Chalker PR.

Residual strain measurement and impact response of optical fibre

Bragg grating sensors in fibre metal laminates. Smart Mater Struct

2001;10(2):338–46.

[9] Sirkis JS. Unified approach to phase-strain-temperature models for

smart structure interferometric optical fiber sensors: part 1,

development. Opt Eng 1993;32(4):752–61.

[10] Sirkis JS. Unified approach to phase-strain-temperature models for

smart structure interferometric optical fiber sensors: part 2,

applications. Opt Eng 1993;32(4):762–73.

[11] Patrick HJ, Williams GM, Kersey AD, Pedrazzani JR, Vengsarkar A

M. Hybrid fiber Bragg grating/long period fiber grating sensor for

strain/temperature discrimination. IEEE Photonics Technol Lett 1996;

8:1223–5.

[12] Douay M, Fertein E, Xie WX, Bernage P, Niay P, Bayon JF,

Georges T. Thermal hysteresis of Bragg wavelengths of intra-core

fiber gratings. IEEE Photonics Technol Lett 1993;5(11):1331–4.

[13] Jang J, Kim Hak S. Performance improvement of glass fiber-

poly(phenylene sulfide) composite. J Appl Polym Sci 1996;60(12):

2297–306.

[14] Springer GS, van Steenkiste RJ. Strain and temperature measurement

with fiber optic sensors. Lancaster: Technomic Publishing; 1997.

[15] Cugnoni J, Gmur T, Schorderet A. Inverse method based on modal

analysis for characterzing the constitutive properties of thick

composite plates. Accepted for publication in Comput Struct.

[16] Leach D. Cytec Industries Inc.. Private communication, Lausanne;

2003.

[17] LWilliams L. Quality assurance test method for laminate preparation

in a one press process. Cytec Fiberite Inc. MP-128, Rev. A; 1991.

L. Sorensen et al. / Composites: Part A 37 (2006) 270–281 281

[18] Sorensen L, Gmur T, Botsis J. Long FBG sensor characterization of

residual strains in AS4/PPS thermoplastic laminates. In: Smart

structures and materials 2004: smart sensor technology and

measurement systems, SPIE, San Diego, vol. 5384; 2004. p. 267–78.

[19] Weteringe BJ, Bersee HEN, and Beukers A. Characterization of

microcracking in PPS laminates. In: 23rd International European

Chapter SAMPE Conference, Paris; 2002. p. 225–36.

[20] Sonmez FO, Eyol E. Optimal post-manufacturing cooling

paths for thermoplastic composites. Compos Part A 2002;33(3):

301–14.

[21] Wang C, Sun CT. Experimental characterization of constitutive

models for PEEK thermoplastic composite at heating stage during

forming. J Compos Mater 1997;31(15):1480–506.

[22] Ticona, Fortron 0214 - Data Sheet, Ticona (Cleanese AG), 2000.