Thermoelastic Stress Analysis of damage mechanisms in composite materials

Composites: Part A 41 (2010) 1729–1742

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Thermoelastic Stress Analysis of damage mechanisms in composite materials T.R. Emery, J.M. Dulieu-Barton * School of Engineering Sciences, University of Southampton, Southampton SO17 1BJ, UK

a r t i c l e

i n f o

Article history: Received 23 May 2007 Received in revised form 5 August 2009 Accepted 7 August 2009

Keywords: Thermoelastic Stress Analysis A. Polymer-matrix composites (PMCs) B. Optical properties/techniques C. Damage mechanics D. Non-destructive testing

a b s t r a c t A methodology for the application of Thermoelastic Stress Analysis (TSA) in damage studies of glass reinforced polymers is established. Test specimens have been designed to promote certain damage types and the methodology applied to each. It is shown that a TSA approach can evaluate fibre breakage, matrix cracking and delamination damage. Metrics are established based on calibrated strain data obtained from the TSA. It is shown that these can be used to assess the condition of a component throughout its fatigue life. Ó 2009 Elsevier Ltd. All rights reserved.

1. Introduction The indiscriminate manner in which damage initiates and propagates in composite materials requires detection and analysis techniques that enable timely intervention and repair to prevent component failure. In metallic structures damage is often localised in the form of cracks, however, in composite materials damage accumulates throughout the structure. The mechanisms by which damage initiates and propagates have been well documented [1– 5] and are dependent on the architecture of the laminate [6,7]. This includes the stacking sequence, component geometry, loading conditions as well as the material properties of the fibre and matrix. The damage mechanisms are well known [4] and include fibre breakage, matrix cracking, debonding, transverse-ply cracking and delamination. Whilst it is possible to obtain a stress analysis of a virgin laminate, the task of modelling the laminate in the presence of damage is difficult due to the complex manner in which the different damage types interact and propagate together [8]. Furthermore, the damage mechanisms do not act in isolation or uniformly across a component and this restricts the accuracy of analytical models [7]. Of the degradation models reviewed by Tserpes et al. [9] none explicitly take into account the fundamental damage mechanisms or prescribe the dominant mechanisms that are responsible for the reduction of residual strength or how they cause final failure. The challenge of accurately predicting the failure of composite laminates has been exemplified in the detailed review of composite failure permitted by the World-Wide Failure * Corresponding author. Tel.: +44 2380 596522; fax: +44 2380 593299. E-mail addresses: [email protected] (T.R. Emery), [email protected] (J.M. Dulieu-Barton). 1359-835X/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.compositesa.2009.08.015

Exercise (WWFE) that demonstrated the difficulty in correlating theoretical predictions with experimental data [10,11]. The mechanisms underlying the failure of composites in tension, compression and shear are well understood. However, the formulations of failure criteria are still largely phenomenological. The challenge is to capture the physical mechanisms and incorporate these in computational structural failure assessment schemes. Failure theories reliant on the local stress or strain fields in the proximity of the damage are limited to simple geometries with symmetry (e.g. cross-ply laminates with cracks in the planes of symmetry) [4]. In light of the above it would be beneficial to devise an experimental approach that provides data that relates to the strain field local to the damage; a measure that can be directly related to the stress or strain will provide a route to determining the residual strength of composite laminates [12]. Full-field techniques have been used to assess damage evolution in composite structures. Examples include the application of moiré interferometry [13,14], here a cracking emanating from an open hole was studied and the output used to validate a mesh independent crack model. In [15,16] open holes were studied using a grid method. A detailed account of the methodology was provided [15] in which the grid technique provided the two components of the in-plane displacement field from which the strains were derived. Much effort focused on accurate derivation of the strain field and it was demonstrated that fitting a 17th order polynomial provided the required strain resolution that to give excellent agreement with FE simulations. Single camera Digital Image Correlation (DIC) was used in a biaxial test on carbon-carbon composites [17], where it was demonstrated that fibre and matrix damage contours could be obtained using the technique in combination with damage models. Grédiac [18] provides a comprehensive review of the use of full-field methods

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in composite characterisation. Whilst extensive effort has been focused on using full-field optical techniques to investigate the behaviour of composite materials, thermal techniques have received little attention; in [18] only three citations out of 138 mention the possibility of using a thermal technique. In the current paper a thermal technique known as Thermoelastic Stress Analysis (TSA) [19] that facilitates a full-field practical real time approach by obtaining localised strain measurements from the neighbourhood of damage in components subjected to fatigue loading. TSA is a well established technique for the evaluation of stresses in isotropic engineering components, e.g. [19–22]; the underlying theory has been summarised in a review [23]. In TSA an infra-red (IR) detector is used to measure the small reversible temperature change associated with the thermoelastic effect [24] from a component subjected to cyclic load. The detector output signal is related to the changes in the sum of the principal stresses on the surface of the material. For orthotropic materials the small temperature change (DT) is related to the changes in the stresses in the principal material directions on the surface of the material (Dr1, Dr2) by the following expression [25]:

DT ¼ 

T

qC p

ða1 Dr1 þ a2 Dr2 Þ;

ð1Þ

where a1 and a2 are the coefficients of linear thermal expansion relative to the principal material axes, q is the density, Cp is the specific heat at constant pressure and T is the absolute temperature of the surface. DT is observed from the surface of the component of interest using a staring IR detector which enables the full-field measurements. In the present work a DeltaTherm 1400 [26] is used to record the thermoelastic data; the IR detector incorporated in the system is a 256  256 pixel array capable of resolving a temperature change of 4 mK. The thermoelastic signal is processed digitally and allows the data to be recorded in a matter of seconds. This rapid processing enables data collection in practically real-time, providing clear benefit in damage propagation studies, as the system allows the component to be inspected at regular intervals through its life, under the actual fatigue load. In previous work [27] conducted with the SPATE (Stress Pattern Analysis by Thermal Emission) system much longer inspection times were required and the risk of damage propagation during inspection meant the application of very low applied loads during TSA data collection. To obtain the stress change from the IR detector output the usual approach is to calibrate in terms of stress. The DeltaTherm system is not radiometrically calibrated so a measurement of DT is not available. Moreover, it has been shown [28] that the variation in the material properties render a simple measurement of DT inaccurate and that a calibration approach that incorporates the material properties is necessary for quantitative TSA. Techniques for calibrating isotropic materials are well established; some common approaches have been described and assessed in [28]. However, the complexities of measuring or calculating the direct surface stresses from a laminated orthotropic material has meant that a generalised calibration routine for composites has been elusive. Recent work by the authors [29] has developed a means of calibration that allows the evaluation of the strain change in a laminated composite structure. This means that during damage evolution a quantitative measure of the strain distribution can be made. A brief overview of the calibration approach is provided in the present paper. Aside from the calibration, a further complication in the analysis of the thermoelastic data is that as damage evolves heat is generated local to the damage site. Inspection of Eq. (1) shows that changes in the absolute temperature will effect the magnitude of DT and in turn the thermoelastic signal; in [30] the effects of tem-

perature were reported to have a dramatic influence on the thermoelastic data recorded using the DeltaTherm and prohibited quantitative analysis of the stress redistribution local to the damage. In response to these findings a means for correcting for an absolute temperature increase has been devised by the authors [31] that decouples the absolute temperature response from the response associated with the stress change. In this paper a methodology is presented that firstly accounts for the absolute surface temperature variation and secondly calibrates the corrected thermoelastic signal in terms of strain. It is shown that the data can be quantified in terms of strain and provides an insight into the way the combined damage mechanisms result in final failure of a laminated composite component. Therefore, the paper reports an important first step in developing TSA into a means of comparison and evaluation of existing failure theories such as those described by Daniel [11]. The experimental objective of the present work is to demonstrate the application of the damage assessment methodology on laminated specimens representative of those found in engineering components. In the work damage propagation in three types of glass reinforced epoxy test specimens is investigated. The specimens are subject to a fatigue loading to generate damage. It is expected that when the component damages the stress will redistribute around the damage site; it is intended that the TSA analysis will present data that allows a visualisation of the redistribution in a quantitative manner directly related to the strain in the component. The considerations of the effect of the damage evolution on the mechanical properties of the test specimens is considered and incorporated into the testing programme. The test programme described in the paper covers a number of damage initiation mechanisms and will demonstrate that the fullfield nature of TSA can be exploited to monitor distributed damage as it propagates throughout a structure. The application of TSA to such problems has a major benefit over existing single point measurements, as strain gauges cannot accurately identify the inception of damage nor follow its growth in a structure. Furthermore, despite the need for calibration and temperature correction, it offers advantages over other the other full-field techniques described in [13–18]. Most importantly specimen preparation is minimal; there is no need for a grid or application of a painted speckle pattern. Further the measurement obtained requires little manipulation – it is a measure directly related to the strain. Therefore, the difficulties reported in [15] resulting from differentiating displacement reading values to derive the strain are eliminated as the thermoelastic response is a stress/strain metric. There are limitations such as the necessity for a cyclic load (although current work is addressing this) and the measurement cannot provide the individual coordinate direct strains, although effort is also being targeted at resolving this limitation [21]. In the work in this paper, holes are introduced in test specimens as stress raisers. Although the stress concentration at cut-outs (such as holes) are known to generate a detrimental stress state and initiate damage, the complexity of this three dimensional problem has limited analytical solutions [32]. Thereby the work in this paper will also demonstrate the usefulness of TSA as an experimental tool in damage and stress analysis of complex composite components. 2. Damage assessment methodology To date the standard approach in thermoelastic studies of composite materials has been to use the following equation [13]:

A S ¼ ða1 Dr1 þ a2 Dr2 Þ 

ð2Þ

where A is a calibration constant [22] and S is the thermoelastic signal.

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For laminated composite structure it is necessary to derive the stress change in the surface ply by obtaining a host of mechanical properties and applying classical laminate theory [33]. Ref. [29] demonstrates that this is feasible but time consuming. An alternative would be to use manufactures’ material property data, but the resulting accumulation of error makes this approach impractical. A generalised form of Eq. (2) can be presented in terms of the change in surface ply strains as follows:

A S ¼ ða1 Q 11 þ a2 Q 12 ÞDe1 þ ða1 Q 12 þ a2 Q 22 ÞDe2

ð3Þ

where De1 and De2 are the strains in the surface ply in the principal material directions and Qij are the reduced stiffness terms [33]. The strain in the surface ply fibre direction can be related to the strain in the laminate principal material directions (i.e. L and T directions) with the expression:

½e1;2 ¼ ½T ½eL;T

ð4Þ

where [T] is the standard transformation matrix [33]. By substituting Eq. (3) into Eq. (4) and assuming a uniform strain through the thickness of the laminate (e.g. for an in-plane loading) a thermoelastic equation is obtained in terms of the laminate longitudinal, L, and transverse, T, strains, i.e.:

 A S ¼ ½ða1 Q 11 þ a2 Q 12 Þm2 þ ða1 Q 12 þ a2 Q 22 Þn2 DeL þ ½ða1 Q 11 þ a2 Q 12 Þn2 þ ða1 Q 12 þ a2 Q 22 Þm2 DeT þ ½ða1 Q 11 þ a2 Q 12 Þmn  ða1 Q 12 þ a2 Q 22 ÞmnDcLT g

ð5Þ

where m = cos h, n = sin h (h is the angle between the axes of the surface ply (1, 2) and those of the laminate (L, T)). Eq. (5) appears at first sight to be far more complicated than Eq. (2). However, it can be seen that the laminate strains could be measured (e.g. from a specimen loaded in uniaxial tension) and these related to the thermoelastic signal measured from such a test. It is possible to group the material constants into a ‘calibration constant’ and obtain this from a tensile test; full details are provided in [29]. An interesting and beneficial finding of the work described in Ref. [29] was that the thermoelastic response did not emanate from the orthotropic surface ply but from the isotropic resin-rich surface layer. The resin-rich layer was around 25 lm thick and was produced as a consequence of the use of ‘peel-ply’ in the manufacturing process. The existence of the resin-rich layer considerably simplifies the analysis. As the resin surface layer responds with the underlying orthotropic material it will act as a ‘strain witness’ and deform in the same way as the orthotropic material. However, the thermoelastic response from this strain witness layer will be that of the isotropic resin, assuming that there is no heat transfer through the resin. This enabled a new calibration constant to be devised, B, as follows [29]:

DeL ð1  mLT Þ A ð1  mR Þ ¼ ¼ B S a R ER

ð6Þ

where mR is the major Poisson’s ratio of the resin-rich layer, aR is the coefficient of thermal expansion of the resin-rich layer, ER is the

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Young’s modulus of the resin-rich layer and mLT is the major Poisson’s ratio of the laminate. B can be derived from a strip of material loaded uniaxially where DeL is measured using an extensometer, mLT is obtained from longitudinal and transverse strain measurements and S is obtained from the thermoelastic measurement. Before it is possible to calibrate the thermoelastic data it is also necessary to ensure the data is not subject to the influence of variation in the absolute surface temperature. As a global ‘calibration’ cannot account for this local behaviour it has been necessary to develop the temperature correction approach to operate in a point-by-point manner [31]. The procedure is based on the measurement of the thermoelastic response from a specimen at a known temperature. In [31] gradient of log-log plots of response against temperature were used to derive a correction index, n. A correction factor was developed of the form R ¼ ðT 0 =T m Þn where R is the correction factor and T0 is the initial temperature of the surface. Fig. 1 shows the methodology for analysing damage using TSA. The procedure is implemented using a MATLAB program that is applied to the data array obtained from the DeltaTherm software and presents the output in a full-field manner. It incorporates both the temperature correction procedure [31] and the strain calibration procedure [29]. Firstly thermoelastic data, S0, and absolute temperature, T0, are obtained from the undamaged specimens. The S0 data is used to obtain the calibration constant B and the T0 data is used as the baseline for the temperature correction. A damaging load is applied to the specimen and thermoelastic data, Sm, and the temperature, Tm, are obtained at various stages throughout the component life. Tm is also used in the temperature correction in the form ðT 0 T m Þ9:8 [31]. (It is important to note the index 9.8 has been established experimentally [31] for the DeltaTherm 1400 system and the lens used in this work.) Sm is corrected using this quantity and a data set is obtained that is temperature corrected in a point-by-point fashion. The resulting output from this Sc is then calibrated as follows:

DðeL þ eT Þ ¼ B ð1  mLT ÞSc

ð7Þ

The output of the procedure is a measure that is related to the strain sum change in the damaged component that occurs purely as a result of the stress distribution in the component. 3. Test specimens and procedure Three laminate panels were manufactured from 13 layers of a unidirectional (UD) E-glass epoxy (SE84) pre-impregnated (prepreg) material. A ‘cross-ply’ (laminate (i)), a ‘quasi-isotropic’ (laminate (ii)) and an ‘angle-ply’ (laminate (iii)) panel were produced by orientating the pre-preg as specified in Table 1. The panels were consolidated under vacuum pressure for one hour and then cured for four hours at a temperature of 80 °C. After curing, end tab strips were bonded to both sides of the panel using an adhesive film. Specimens were cut from each panel that were 40 mm wide and had an approximate length of 180 mm and thickness of 3.5 mm, as illustrated in Fig. 2a. In specimens (i) and (ii) an 8 mm hole

Fig. 1. Damage assessment methodology.

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Table 1 Test specimens. Laminate

Lay-up

Laminate type

Illustration

(i) (ii) (iii)

[(0/90)3, 0, (90/0)3] [(0, ±45, 90)2s] [(+45/45)3,+45, (45/+45)3]

Cross-ply Quasi-isotropic Angle-ply

Fig. 2b Fig. 2b Fig. 2a

was introduced in the centre of the specimens as shown in Fig. 2b. A modified drill bit that minimised tearing of the surface plies was used to produce the holes, where the drill was ground with small flats on both the cutting edges so the bit cut with a scraping action. The three laminate types were chosen so that different damage mechanisms could be obtained during fatigue loading. It should be noted that all the laminates are symmetric and hence there is no coupling between in-plane loading and out of plane deformation. In laminates (ii) and (iii) there will be bending–torsion coupling but this is only important when the loading causes a bending moment. The damage progression expected for the laminates have been characterised in the literature using conventional nondestructive techniques such as radiography or microscopic examination of surface replicas [34]. In a cross-ply test laminate (i.e. (i)) the dominant damage mechanism is matrix cracking caused by the large mismatch of mechanical properties between the layers [35]. The damage takes the form of small longitudinal cracks in the transverse ply and splits in the longitudinal ply between the fibre and the matrix. Delamination initiates where these two mechanisms intersect in a laminate stack [36]. It is often assumed that the cracking spans either the width or the length of the plate. However, transverse cracking only occurs where the applied strain

exceeds the failure strain of the matrix material [4]. The quasi-isotropic type (ii) configuration was chosen as cross-ply laminates are not extensively used in engineering applications. Quasi-isotropic laminates such as type (ii) are more widely used [37] and the damage mechanisms are well known [34,38,39]. The stress field in a multidirectional laminate is more complicated than cross-ply laminates because the damage evolution is more progressive as the stress discontinuities ply-by-ply are less severe. However, matrix cracking occurs in the off axis plies and delaminations develop in a similar manner to those in cross-ply laminates. The third angle-ply laminate is used to produce specimens that are loaded in the direction of bisectors of reinforcement angles. In this configuration all the laminae in the stack will experience an almost identical stress field [40]; the only difference is the direction of the shear stresses. Therefore, in-plane failure can initiate in any lamina with equal probability with matrix crack accumulation occurring parallel to the fibre direction [41–43]. In the laminates it is expected that the damage will accumulate and cause stress transfer to the remaining intact plies until a stress state is generated that causes gross failure of the laminate through the failure of the fibre or matrix across the width of the test specimen. In specimens type (i) and (ii) laminates the large stress gradient at the edges will tend to peel successive plies and result in delamination at the ply interfaces. The ability to withstand this is matrix related and thus damage will be initiated below the expected failure strength of the fibre reinforcement. Therefore, edge stresses will initiate localised matrix cracking damage and will tend to propagate into the laminate under the fatigue loading. The magnitudes of the stresses generated at the free edges are a function of the in-plane stresses and therefore will be accentuated in areas

Fig. 2. Specimens.

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of higher in-plane stress. The type (i) and (ii) specimens both contain a hole and it is expected that damage will initiate from the free edge at the hole boundary as a result of the stress concentration. The anisotropic stress concentration around discontinuities in composite components can be obtained from a consideration of anisotropic elasticity theory for infinite and homogeneous plates [37]. For finite width specimens experimental observation of the stress and strain concentration factors have been developed for typical composite laminates [33,37]. For the two specimens with holes it is possible to estimate the influence of the hole in damage accumulation. In the type (i) specimen the stress gradient is high at the hole boundary and a stress concentration of approximately five has been obtained for a boron reinforced epoxy laminate [33]. The stress distribution around a hole in a type (ii) laminate has be shown to be similar to that of an isotropic plate [33] and the stress concentration for a glass-epoxy laminate has been demonstrated experimentally to be approximately 3.5 [37]. The strength reduction as a consequence of the introduction of a hole is a function of the radius; for the 8 mm hole in the type (ii) laminate a reduction of 40% of the strength should be expected [33]. The introduction of a hole in angle-ply laminates does not produce the same magnitude of stress concentration as in the type (i) and (ii) laminates due to a lower ratio between the longitudinal and transverse stiffnesses. In the first two examples it is anticipated that damage would propagate from the hole notch. The hole is a high stress concentration area with the associated free-edge complexities and as such is the prime area at which the damage assessment can be targeted. However, a known initiation site is uncommon in laminated composite structures and the study in the ±45 exemplifies why a full-field assessment is required. Therefore, it was decided to test the angle ply specimen without a hole and without any known damage or weaknesses.

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4. Fatigue loading and application of TSA The requirement for cyclically loading specimens during TSA is a major consideration when applying the technique to components subject to damage. As the damage accumulates the elastic properties of the material will change [3], resulting in changes in the laminate strains for the same given load. This in turn causes a modification to the surface stresses and hence a change in the thermoelastic response. To ensure that the readings obtained from TSA are as a result of the stress/strain redistribution due to the damage, a constant displacement load was applied to the test specimens during the TSA data collection to maintain a uniform level of strain in the laminate. This means that as the material elastic properties deteriorate (particularly the longitudinal modulus) the load applied reduces in proportion to the reduction in the stiffness. The material elastic property changes were monitored to establish a link between them and the damage evolution. To establish the effect of the damage from the specimens at stages during their fatigue life a test procedure was developed as shown in Fig. 3. Starting with the virgin test specimen the elastic properties of the specimen are obtained, the thermal and thermoelastic data are then obtained followed by the application of a fatigue load that results in damage. The procedure is repeated and results in a number of ‘fatigue steps’ being applied to each specimen that could be related to life of the specimen. At the start of each step the longitudinal and transverse stains were recorded from a quasi-static tension test over a 0–5 kN range with a ramp-rate of 1 kN/min using clip gauge extensometers. The load applied during the quasi-static test was used to obtain the global secant Young’s modulus, EL, for the specimens. The purpose of calculating the modulus was to provide a metric with which to compare the TSA data by establishing the residual stiffness of the specimens after N cycles. The Poisson’s ratio was also obtained at

Fig. 3. Fatigue test method.

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Table 2 Cyclic loading. Laminate

(i) (ii) (iii)

TSA

Fatigue

Displacement (mm)

Frequency (Hz)

Load (kN)

Frequency (Hz)

Cycles

Number of steps

0.167 0.178 0.44

10 10 10

14 ± 12 12 ± 11 8±6

2 2 2

3000 3000 3000

17 17 10

this stage from the strains derived by both extensometer readings. The extensometers, used to obtain the strains, remained attached to the specimen during the TSA constant displacement testing to obtain the longitudinal strain change, DeL to monitor the strain during the collection of the TSA data. The test specimens were loaded in an Instron 8802 test machine and subject to cyclic displacement at a frequency of 10 Hz; it has been shown [24] that this frequency is sufficient to generate adiabatic conditions in the type of specimens used in this work. The cyclic displacements in the TSA tests are detailed in Table 2. The thermal, T, and thermoelastic, S, data were recorded using a DeltaTherm system with a 25 mm lens that meant the detector was positioned at a stand-off distance of 500 mm from the specimen surface to obtain a full-field of view the specimen, which resulted in a thermoelastic data spatial resolution of about 0.5 mm. The S and T data are the inputs for the thermoelastic procedure illustrated in Fig. 1. The specimen surface, from which the thermoelastic signal was recorded, was unpainted and left in the manufactured state as the epoxy surface provides a sufficiently high emissivity (i.e. no significant reflections noted in the thermal images) for thermoelastic studies [19]. It was estimated, from values given in [29] and using the manufacturer’s quote of a 4 mK minimum resolvable temperature difference, for a UD material the minimum strain change that can be detected is of the order of 0.0001. Glass/epoxy is transparent, so a visual inspection of the specimen can provide an insight into the types of damage occurring in the specimens. Fig. 3 shows the visual inspection taking place at the end of the procedure when gross damage had evolved. The visual inspection was made by using a macroscope and illuminating from the underside of each specimen. It should

be noted that in practice this would not be possible as in-service structures would normally be coated in an opaque finish. It was not possible to record the TSA data at the amplitude of the fatigue load as the servo-hydraulic test machine could not achieve the required displacements at the frequency required for TSA. Therefore, the specimens were fatigued by applying a cyclic load over a period of cycles. A constant load was selected as it has been shown [34] that it is impossible to fail angle-ply specimens in constant strain cycling. Table 2 provides the applied displacements used in the TSA data collection, the fatigue load used to produce the damage and the number of fatigue steps to produce gross damage; each fatigue step comprised of 3000 cycles. The applied displacements were chosen so that it was below the spatial resolution of the data but sufficient to generate nominal thermoelastic response of around 0.05 K. 5. Results and discussion Data relating to each of the processes presented in Fig. 3 were collected for each step, however, the results presented here are restricted to those that show significant interest in the redistribution of strain due to damage. Inspection of the thermal data recorded simultaneously with the thermoelastic data showed significant thermal variations during the tests so it was necessary to correct the thermoelastic signal for temperature variations [31] in a point-by-point manner. An example of the temperature distribution is illustrated in Fig. 4 for the type (i) laminate at the beginning and end of the fatigue testing; a point increase of 12 K is evident local to the damage, with an increase of 5 K away from the damage. From the temperature sensitivity relationship presented in Ref.

Fig. 4. Calibrated temperature map from the first and last data set of crossply.

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Fig. 5. Strain sum in crossply.

[31] this would give rise to a 30% increase in the thermoelastic signal, therefore, justifying the inclusion of the point-by-point temperature correction procedure in the damage assessment methodology. 5.1. Cross ply laminate (type (i)) The strain sum distribution was recorded at the start of the test (Fig. 5), at fatigue step 14 (Fig. 5) and from the final data set (Fig. 5). The data shown as red around the hole in the image given in Fig. 5 occurs as a consequence of the test specimen motion. This is a well-known phenomenon in TSA and is most pronounced at edges. The effect of motion causes the thermoelastic signal to ‘blur’. Observation of the affected area through the fatigue history shows motion becomes more of significant as the stiffness reduces locally to the hole. A robust method of compensating thermoelastic data for motion is not available with the present system hence the decision to reduce the displacement level during the TSA data collection. As the single detector data collection area (i.e. the spatial resolution) is much greater than the applied displacement

this was considered only to be significant close to the hole. Therefore, in this work the effect of motion is neglected as the only significant effects are restricted to the vicinity of the hole edge and are clearly identified in the full field data. As the areas affected are very pronounced in the data and have no apparent deleterious affect on the readings away from the hole it was unnecessary to mask the data as might be done in say image correlation techniques. To inspect the damage propagation that has caused the redistribution of strain around the hole the specimen was imaged using a macroscope and the result is shown in Fig. 6. As predicted the fatigue loading has initiated localised damage around the hole. The mismatch in the Poisson’s ratio between the 0° and 90° produce an interlaminar shear which produces strains sufficient to cause cracking of the epoxy matrix. There is matrix cracking in the transverse plies where the matrix cracks (the short dark horizontal lines in the image) appear to be restricted to the areas of the specimen subject to a tensile strain. Longitudinal splits have occurred in the 0° plies, running vertically and parallel with the 0° fibres; these are most severe at the edge of the hole. The dark areas with diffuse edges between the longitudinal splits indicate delaminations. As

Fig. 6. Macroscope image of damage in crossply.

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the concentration of matrix cracking increases to a saturation point, for a constant loading (fatigue) scenario, the stress is redistributed at the local level into the unbroken constituents. In the cross ply laminate this means transfer of the stress into to the 0° ply. As there are large stress concentrations at the hole, of the order of five in cross ply (see above), fibre breakage is initiated at the edge of the hole. Although not visible in the image shown in Fig. 6, fibre breakage occurred in the form of cracks extending (in a discontinuous manner) from the hole towards the edge of the specimen; the positions of the cracks are marked with a dotted line in Fig. 6. A comparison of the line of the cracks with the TSA data shown in Fig. 5, shows that the strain has redistributed as a consequence of the cracks and the strain ‘concentration’ has moved to the tip of the crack. A more detailed examination of the localised data is provided later in the paper. Prior to this a comparison of the global response of the specimen to that of the strain sum derived by the TSA is made. To make a concise comparison of the all of the collected thermoelastic data an analysis routine was developed so that strain sum was analysed at each stage of the fatigue loading. Three metrics were established. The maximum strain sum which is a single point reading easily identified in the data and two globally averaged values: the percentage of the image area that gave a strain sum of greater than 0.001, the percentage of the image area that gave a strain sum of less than 0.001 and the maximum strain sum. The value of 0.001 was chosen as it is approximately 10 times the strain resolution and twice the nominal strain. The lower image area metric provides an indication of the reduction in strain in certain areas as the load carrying capacity reduces; the upper limit provides an indication of the strain redistribution as a result of the damage. The expectation is that these two metrics will change at the same rate and provide an indication that the collected data is mechanically compatible. All the data is normalised to the undamaged specimen value and is plotted in Fig. 7 along with the percentage decrease in the measured Young’s modulus of the specimen. Fig. 7 shows that in the early stages of the fatigue loading (up to step 8) the decrease in Young’s modulus is more rapid than the strain redistribution indicated by the TSA data. In fact there is no change in the maximum strain until fatigue step 8. This is because

transverse matrix cracking is occurring in the 90° plies only during these fatigue steps. As little of the stress is carried by these plies it has a small effect on the global strain and has a less pronounced effect on the strain sum data collected by the TSA; this was noted by Cunningham et al. [30] who showed that simulated cracks in transverse lamina in cross ply could not be detected in TSA data. Fig. 8 shows a close up of the TSA data in the undamaged state and a close up of the macroscope image. Here it can be seen that the transverse matrix cracks are restricted to the areas of tensile strain observed in the undamaged TSA image (bounded by the dashed line). Between fatigue steps nine and ten there is a large decrease in Young’s modulus of 5%. Inspection of the specimen revealed the initiation of breakage of the 0° fibres at the hole and explains the step change in stiffness at this stage. At fatigue step 9 there is a change in all three TSA strain data sets. At step 9 there is an increase in the maximum strain and at 10 there is a decrease. Fig. 9 shows the TSA data at steps 9 and 10. There is a large strain sum concentration at the hole edge at step 9 which is reduced at step 10. At step 11 a crack was visible. As cracks are arrested by fibre reinforcement the increase between step 8 and 9 indicates some crack growth, which is arrested in steps 10 and 11. Here the reduction in the maximum strain could be attributed to the prominent mode being delamination (see quasi isotropic specimen). At step 11 more fibre breakage occurred and the crack started to grow progressively, with fibre breakage being the prominent failure mode, hence the rapid increase in the maximum strain. At step 11 the area metrics also start to increase/decrease more rapidly. The initial increase and then reduction because of crack arrest and delamination becoming the prominent mode could provide an indicator of the rapid failure seen in the following fatigue steps when the crack occurred. Fig. 9 shows the strain concentration at the crack tip at fatigue step 13. The large changes noted in the TSA data are not present in the modulus data, which simply shows a steady decrease throughout the fatigue life. The TSA data is indicating that significant damage is present at step 9 and at step 12 failure is imminent. Although further validation studies are necessary, this initial work clearly shows that TSA data can has the potential to be used as a damage assessment tool.

Fig. 7. Strain metrics and mechanical properties for crossply.

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Fig. 8. Transverse cracking in crossply.

5.2. Quasi-isotropic laminate (type (ii)) The quasi-isotropic laminate was tested in an identical manner to the previous specimen. The strain sum data obtained from the TSA are shown in Fig. 10 again for the beginning, middle and end of the fatigue damage process. The distribution on the surface shows that the strain concentration at the hole reduces as fatigue damage propagates within the laminate. In Fig. 11 macroscope image is shown from the end of the test. The Poisson’s ratio mismatch between the four ply orientations has caused matrix cracking; this cracking is evident in Fig. 11 in the +45° and 45° plies (the dark lines in the ±45° orientations) and also in the 0° plies as longitudinal splitting. (It is assumed transverse cracks have occurred in the 90° plies although these cannot be observed in the macroscope image.) It can be seen that there are delaminated areas around the hole; the delamination appears as the dark areas with diffuse edges. From inspection of Fig. 11 it can be seen that the area of the delamination is bounded by the area of ±45° matrix cracking. The extensive delamination occurring in this laminate is a result of the shear mismatch between the plies (there is no shear mismatch in the cross ply laminate).

The axial loading develops an interlaminar shear stress that prevents the angle plies from deforming in opposing directions. In quasi-isotropic materials the stress concentration at the hole is less than that in the cross ply. Therefore, delamination occurs preferentially, instead of fibre breakage at the hole, as a result of the through-thickness direct stress. The delaminations result in a reduction in the load carrying capability and the strain concentration maxima occurring locally through the horizontal centre-line evident at the start of the test disperses and decreases during the test. Fig. 12 shows the stiffness degradation in the component through the fatigue steps; both the Young’s modulus and major Poisson’s ratio decrease. This stiffness reduction is attributed to the cracking in the ±45° plies. The Poisson’s ratio variation is slightly more complex; the decrease is interrupted at stages through the fatigue life. This can be attributed to an effect reported in Ref. [7] where longitudinal splitting had the effect of reducing the transverse stiffness of a laminate and in turn increasing the Poisson’s ratio. As with the cross ply laminate it was decided to present the strain sum data in three forms: i.e. area of strain sum above

Fig. 9. Strain sum evolution due to fibre breakage.

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Fig. 10. Strain sum evolution in quasi-isotropic specimen.

0.001, area below 0.001 and the maximum strain sum. The maximum strain sum decreases by 31% over the course of the fatigue steps. In Fig. 12 it is evident that the TSA is insensitive to the early stages of fatigue. At fatigue step 5 there is a large change in the TSA data. The full-field strain sum data in Fig. 13 shows fatigue steps 5 and 6. There is a clear reduction in the strain concentration as a result of the delamination and most importantly the occurrence of a longitudinal split at step 6. As with the cross ply simply monitoring the elastic properties does not indicate the onset of the delamination, as the trend in this data is a steady decrease, even though a longitudinal split should cause an increase in Poisson’s ratio. After the first split, which is clearly insufficient to case a major reduction in the load carrying capacity of the specimen, the TSA area data remains constant until step 11 when both data sets start to increase or decrease markedly. The maximum strain sum data shows a slight decrease up to step 9 and then another decrease at step 10 and then remains constant. Fig. 13 shows the data at fatigue steps 11 and 12 with no discernable difference between the two. 5.3. Angle-ply laminate (type (iii)) For the angle-ply laminate the experimental set-up and the procedure was the same as the previous two specimen types.

However, to ensure the fatigue damage propagated to failure in a timely fashion, the fatigue load was set so it represented a substantial amount of the ultimate failure load of the coupon. The specimen was fatigue loaded over a series of 10 increments before gross failure occurred and prevented any further testing. Fig. 14 shows the thermoelastic strain sum data obtained from the specimen at four load steps. Fig. 14 shows the first load step and it is clear that there is some initial damage in the specimen. It should be noted that the data shown was taken from the central area of the specimen and not close to either of the test machine grips. As the loading progress the strain concentrations increase and the damage progresses. Fig. 14 shows an optical image of the specimen in the failed condition and the position of the wires holding the two extensometers. In the TSA data the data from the wires has been removed; this is evident in the plots of Fig. 14 by the presence of discontinuities in the data. Fig. 14 shows distributed strain concentrations throughout the laminate corresponding to areas of matrix cracking. The matrix cracking is evident in the visual image of the surface of the component in Fig. 14, indicated by the lighter areas that follow the fibre direction. As the cracking accumulates both on the surface and subsurface for any given transverse section where the cracking occurs there is less in tact material to carry the load. There will be a reduction in the strain in these sections evidenced by the strain

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Fig. 11. Macroscope image local to damage.

Fig. 12. Strain metrics and mechanical properties for quasi-isotropic specimen.

reduction and hence increase in the darker areas in the TSA data. The growth of the darker areas corresponds to the progression of the matrix cracking between the fibres and evolves in the ±45° directions. An identical procedure to that used in the previous two specimen types was used to produce Fig. 15. Here the TSA area data shows a sharp increase/decrease between steps 3 and 4 and then returns to a nominally constant level. The maximum strain sum in-

creases steadily throughout the fatigue steps, in much the same way as the modulus decreases. This indicates that when matrix plays a significant role in the integrity of the specimen, unlike the previous two cases, the thermoelastic response is sensitive to the matrix cracking. Here matrix cracking is the dominant failure mode and therefore the TSA data is monitoring matrix cracking damage progression. This is supported by the fact that the maximum strain indicator simply mirrors the monotonic decrease in

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Fig. 13. Strain evolution due to delamination.

Fig. 14. Strain sum evolution in angle ply.

stiffness. Therefore, the maximum strain changes cannot provide such a clear indicator of gross failure as that seen with fibre breakage and delamination. To quantify how the strain has evolved over the course of the fatigue a ‘damage analysis’ macro has been developed in MATLAB that provides a percentage change in the strain sum between undamaged and damaged data. The strain data is processed for each pixel, a threshold is set that accounts for noise in the data. If the change in the data is below the threshold the data from that pixel is rejected from the analysis. For pixels that are subject to a percentage change above the threshold the ratio of the strain in the damaged and undamaged state is calculated and displayed on a corresponding full-field plot. This process was carried out for the strain results from the type (iii) laminate. The plots in Fig. 16 demonstrate the distributed nature of the matrix cracking

in the direction of the fibre axes. This clearly shows how the damage is increasing in the specimen without the distraction of the initial damage shown in Fig. 14.

6. Conclusions It has been shown that TSA can be used in a quantitative manner to obtain the strain distribution in the neighbourhood of damage in laminated glass reinforced fibre composites. Three types of damage have been studied: 1. Fibre breakage. 2. Delamination. 3. Matrix cracking.

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Fig. 15. Strain metrics and mechanical properties in angle ply.

Fig. 16. Full field damage map.

The damage types occurred together but specimens were designed so that a single damage type was the prominent cause of failure. Damage metrics have been developed based on the thermoelastic response throughout the fatigue life. The experimental work described in the paper has shown that these could be used as a damage indicator that is directly related to the level of fatigue damage to which the specimen has been exposed.

The work represents an important initial step in which a methodology for damage assessment has been established. The methodology using TSA accounts for changes in surface temperature due to damage evolution and incorporates a calibration procedure so that the data is presented in terms of strain. To apply this more widely further work is required on different materials, different ply lay-ups and different loading configurations. At present TSA is a laboratory based technique, current work is investigating

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possibilities of taking the technique away from the laboratory hence extending dramatically the possible applications of the work described in this paper.

Acknowledgements The thermoelastic data collected in this work was obtained using a DeltaTherm 1400 system borrowed from the UK Engineering and Physical Sciences Research Council (EPSRC) loan pool.

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