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Interaction between optical fibre sensors and matrix cracks in cross-ply GRP laminates—part 1: passive optical fibres
Composites Science and Technology 61 (2001) 1863–1869 www.elsevier.com/locate/compscitech
Interaction between optical fibre sensors and matrix cracks in cross-ply GRP laminates—part 1: passive optical fibres E.N. Bartona, S.L. Ogina,*, A.M. Thorneb, G.T. Reedc, B.H. Le Pagea a
School of Mechanical and Materials Engineering, University of Surrey, Guildford, Surrey GU2 5XH, UK b School of Engineering in the Environment, University of Surrey, Guildford, Surrey GU2 5XH, UK c School of Electronic Engineering, Information and Mathematics, University of Surrey, Guildford, Surrey GU2 5XH, UK Received 20 December 2000; accepted 7 June 2001
Abstract The obtrusivity of a passive optical fibre embedded in the 0 ply of a model cross-ply GRP laminate has been investigated experimentally and theoretically. The experimental results show that for quasi-static loading and cyclic loads with a peak strain greater than the quasi-static cracking threshold, both the initiation and development of matrix cracks are insensitive to the presence of the optical fibre. However, for cyclic loading with a peak strain just below the cracking threshold, the matrix crack-growth rate is reduced significantly in the vicinity of the optical fibre. The reduction in the crack-growth rate can be understood in terms of a reduction in the strain-energy release rate for cracking as a consequence of the local stiffening of the 0 ply due to the presence of the optical fibre. # 2001 Elsevier Science Ltd. All rights reserved. Keywords: A. Smart materials; B. Matrix cracking; Passive optical fibres
1. Introduction This study is part of a wider programme on the use of fibre optical sensors to monitor damage in composite materials. ‘Smart structures’, consisting of sensors embedded in a composite material to monitor damage are of increasing interest. Ideally, an optical sensor should not degrade the performance of the structure and an important issue in the design of such systems is the ‘obtrusivity’ of the optical fibre. Obtrusivity refers to the mechanical interactions between the fibre and the host leading to perturbations in the stress field around the fibre. Early work in this area has shown that it is possible to minimise the perturbation in the host material, where the host is a unidirectional composite material, by choosing the optimum fibre optical sensor coating and thickness [1–3]. Recent work has shown that a similar analysis can be performed for minimising the obtrusivity of a sensor embedded within the 0 ply of a cross-ply GRP laminate [4]. Finite-element (FE) models were developed for an optical fibre (diameter 125 mm) with coatings of different * Corresponding author. E-mail address: [email protected] (S.L. Ogin).
thicknesses and different Young’s moduli, with the optical fibre located at three possible locations in the 0 ply of the laminate: near the 0/90 interface, at the centre of the 0 ply, and near the surface of the 0 ply. The main objective was to minimise the stress concentration in the host material around the fibre. It was found that the optimum choice of coating thickness and Young’s modulus was not affected by the position of the fibre. The results of the numerical modelling could be summarised in a design curve (see Fig. 1) which shows a relationship between optimum Young’s modulus and optimum thickness (a similar curve, but for a unidirectional composite has been derived previously [5,6]). In the experimental work to be described here, the obtrusivity of an optical fibre has been investigated with respect to its affect on matrix cracking in a model GRP cross-ply laminate. Matrix cracking has been used for two reasons. Firstly, matrix cracking is the predominant damage mechanism in the initial stages of mechanical degradation of laminates containing off-axis plies and the mechanics are reasonably well understood [7–9]. Secondly, if such fibres are to be used to monitor damage in smart structures, it is important that the interaction between the fibre and the host composite material, especially with regard to damage development
0266-3538/01/$ - see front matter # 2001 Elsevier Science Ltd. All rights reserved. PII: S0266-3538(01)00086-0
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Fig. 1. Design curve showing the optimum combinations of Young’s modulus and coating thickness for the minimising the obtrusivity of an optical fibre embedded in the 0 ply of a cross-ply GRP laminate near the 0/90 interface.
initiated by the fibre itself, is well understood. Hence, matrix cracking is a useful and practical tool with which to probe obtrusivity, although others have used other measures of obtrusivity such as composite strength e.g. [10], microcrack distribution in the vicinity of low velocity impact sites [11] and mode 1 fracture toughness [12]. The next section describes the fabrication of the coupons containing embedded fibres and the mechanical testing.
2. Material and experimental procedure Cross-ply (0/90/0) glass/epoxy coupons were fabricated, both with and without optical fibres, by a filament-winding-wet/lay-up technique. The manufacture of laminates without optical fibres is a standard technique described elsewhere [7]. To produce laminates with optical fibres in the 0 plies, 90 fibres were first wound onto a square steel frame which was then rotated through 90 so that the optical fibres could be glued into grooves of the frame parallel to the reinforcing 0 fibre direction. The reinforcing 0 fibres were then wound around the frame and the laminate was cured in the normal way. The epoxy resin matrix used was Stag epoxy resin 300 (100 parts by weight), cured with nadic methyl anhydride (60 parts by weight) and Stag curing agent K61B (4 parts by weight). The average reinforcing fibre volume fraction for the laminates was about 0.5. Lamina ply thicknesses were about 1 mm each for the two
0 plies and the 90 ply. The optical fibres had one of the optimum combinations for minimising obtrusivity (see Fig. 1), having a polyimide coating with a thickness and Young’s modulus of 10 mm and 2 GPa respectively. The method of manufacture was found to produce specimens with the optical fibres well-aligned parallel to the reinforcing fibres and located towards the centre of the coupon, and about 25–200 mm from the 0/90 interface. The resulting laminates were optically transparent, since the refractive indices of the reinforcing fibres and the matrix are closely matched. As will be seen subsequently, the transparency of the laminates enables the interaction between the cracks and the optical fibres to be investigated readily. Aluminium end-tags were bonded to the specimens for the mechanical tests. Quasi-static tensile tests were performed using an Instron 100 kN-capacity screw-driven machine and an Instron servo-hydraulic testing machine under position or strain control. The testing speed for all tests was equivalent to 0.5 mm/min and a 50 mm gauge-length Instron extensometer was used for monitoring longitudinal strain. The extensometer knife edges rested on grooved seats, made of epoxy adhesive, to prevent the extensometer from slipping during the test. During each test, the specimens were loaded to progressively higher strain levels and unloaded for damage observations. Load and strain were measured using a data logger, while the damage state was recorded directly using transmitted light and a digital camera. Load-controlled tension–tension fatigue tests were carried out using an Instron servo-hydraulic testing machine at frequencies of 5 or 10 Hz with a sinusoidal waveform and stress ratio, R, (R=minimum stress/maximum stress) of 0.1. Peak load levels equivalent to strain levels of 0.3 and 0.45% were chosen since these correspond to loads just above and just below the static cracking threshold strain of 0.4%. A thermocouple attached to the surface of the sample confirmed that the specimen temperature did not rise as a consequence of the fatigue cycling. Subsequent to mechanical testing, specimens were sectioned and polished for optical microscopy and scanning electron microscopy (SEM); the SEM work was carried out using a Hitachi S3200 environmental scanning electron microscope.
3. Results The data obtained on crack accumulation under quasi-static loading are shown in Fig. 2. Crack density as a function of applied strain for specimens without an optical fibre are shown as the mean value for 10 tests with error bars of one standard deviation. These data are in agreement with previous work [13] showing that cracks initiate at a strain of about 0.4% and that the crack density increases with applied strain. The data for
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Fig. 2. Average crack density as a function of applied strain for coupons without optical fibres (error bars show one standard deviation) and individual results for coupons with embedded optical fibres having a polyimide coating.
specimens with an embedded optical fibre are shown in the same figure for 5 different coupons. It is clear that the results for specimens containing embedded optical fibres fall within the normal sample to sample variation of specimens without optical fibres. In particular, it is important to note that the inclusion of the optical fibre does not affect the cracking threshold. In fact, none of the cracks were initiated near the optical fibre and almost all of the cracks in all specimens were initiated at the edges of the coupons, which again is consistent with previous work [14]. The initiation of the cracks at the coupon edge, irrespective of the presence of the optical fibre, suggested that it was not necessarily the lack of obtrusivity of the optical fibre which was dominating the behaviour, but rather the tendency for cracks to initiate at the edges of cross-ply coupon with relatively thick transverse plies. This was confirmed by further tests using optical fibres with an acrylate coating having a thickness and Young’s modulus of about 62 mm and 45 MPa, repectively. This particular coating is far from optimum (see Fig. 1). The results from these tests showed a similar overlap of data between specimens with and without optical fibres (see Fig. 3). Hence, it must be concluded that for these model GRP laminates under quasi-static loading, the stress concentration caused by the inclusion of an optical fibre with an obtrusive coating (i.e. the acrylate) or with the optimum coating (i.e. polyimide) is less, in both cases, than any free edge effect with regard to crack initiation and crack accumulation. The results under fatigue loading, however, clearly indicate that the presence of the optical fibre can interact with damage development and must be taken into account. Under fatigue loading, it was found for strains both above and below the quasi-static cracking threshold, the cracks initiated at the coupon edges and not near the optical fibre. Having initiated at the edge,
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Fig. 3. Average crack density as a function of applied strain for coupons without optical fibres (error bars show one standard deviation) and individual results for coupons with embedded optical fibres having an acrylate coating.
crack-growth across the width of the coupon occurred at a constant rate for the higher peak strain (0.45%), as found in previous work [7,13]. However, observations of crack-growth at the lower peak strain (0.3%) suggested that in the vicinity of the optical fibres, the crackgrowth rate was reduced. Fig. 4 shows a typical result for matrix crack-growth for a coupon cycled at a peak strain of 0.3%. The crack initiates at one edge after about 18,000 cycles and then grows at a roughly constant rate until it approaches the position of the optical fibre, which for this specimen was slightly away from the mid-point of the coupon. For about 12 mm on either side of the optical fibre, the crackgrowth rate reduced significantly so that visually the crack appeared dormant. In the example shown in Fig. 4, the crack began to grow again at its original growth rate after about 10,000 cycles. Fig. 5 shows the
Fig. 4. Graph showing normalised crack length against cycle number for a matrix crack growing across the width of a coupon under cyclic loading. The crack-growth rate is reduced in the vicinity of the optical fibre for about 10,000 cycles. Normalised crack length is crack length divided by coupon width (20 mm)
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similar behaviour of another crack. Again, the growth rate was reduced for about 12 mm either side of the optical fibre: in this case for about 30,000 cycles. The relationship between the growing cracks and the optical fibres was investigated further by preparing cross sections of the cycled coupons as close to the planes of the matrix cracks as possible. All samples were potted in epoxy resin and polished down to the crack plane using standard polishing techniques. Optical and scanning electron microscopy showed that there was no debonding between the optical fibres and the rest of the composite (Fig. 6). The sectioning of the composites did reveal, however, that the position of the optical fibre could vary quite significantly in relation to the position of the 0/90 ply interface (see Figs. 7 and 8). Indeed, when the period (in cycles) of the apparent dormancy of the growing matrix crack was plotted
against the distance of the optical fibre from the 0/90 interface, a clear relationship emerged. The period of apparent dormancy of a growing crack reduces as the distance of the sensor from the 0/90 interface increases (Fig. 9); this period falls roughly by a factor of 4 for each 100 mm increase in the distance of the optical fibre from the interface.
4. Discussion The presence of the optical fibre produced no measurable effect in these laminates on the initiation and accumulation of matrix cracks under quasi-static loading and
Fig. 5. Graph showing normalised crack length against cycle number for a matrix crack growing across the width of a coupon under cyclic loading. The crack-growth rate is reduced in the vicinity of the optical fibre for about 38,000 cycles.
Fig. 7. An SEM micrograph of the cross-section of a coupon sectioned close to the plane of the crack which had shown the crackgrowth behaviour of Fig. 4.
Fig. 6. An SEM micrograph of a polished cross-section of a coupon showing that there is no debonding at the interface between the optical fibre and the rest of the composite.
Fig. 8. An SEM micrograph of the cross-section of a coupon sectioned close to the plane of the crack which had shown the crackgrowth behaviour of Fig. 5.
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the outer 0 ply and the half-thickness of the inner 90 ply. The shear-lag parameter l is given by l2 ¼
Fig. 9. The period of apparent dormancy of the growing crack (in thousands of cycles) as a function of the distance of the optical fibre from the 0/90 interface.
under fatigue loading above the quasi-static threshold strain. However, the fatigue crack-growth rate was substantially reduced in the vicinity of the optical fibre for a peak fatigue cycle strain below this threshold, in a manner which could perhaps be described as ‘benign obtrusivity’ since the crack-growth rate is reduced. It has been found in earlier work that the fatigue growth of matrix cracks in cross-ply laminates can be described using linear elastic fracture mechanics. Experimental observations on fatigue crack-growth in plies at 90 to the loading direction [7,13] as well as for a wide variety of angles [15] indicate that, as in the present case, matrix cracks grow at a constant rate once initiated. Modelling the fatigue crack-growth rate has been reduced to the problem of deriving an expression for the strain-energy release rate of a growing crack and then using a form of the Paris crack-growth law [7], i.e. da ¼ AðGÞm dN
ð1Þ
where G is the strain-energy release rate range, and A and m are constants. The exponent m in Eq. (1) was found to have a value of about 5 for thick transverse plies [7]. A consequence of the relative simplicity of this expression for the present observations is that it provides a useful starting point from which to discuss the interaction of the growing matrix cracks with the fibre optical sensor. Following [16], the strain-energy release rate for the growth of a crack which does not interact with other, neighbouring cracks, is b E2 b E0 G¼ 1þ þ T d d lE1 E2 E0
ð2Þ
In Eq. (2), E1 and E2 are the ply moduli parallel and perpendicular to the fibres, E0 is the rule-of-mixtures modulus of the (uncracked) laminate, T is the thermal stress in the transverse ply, b and d are the thickness of
3G23 ðb þ dÞ d2 bE1 E2
ð3Þ
where G23 is the out-of-plane shear modulus, although other expressions for l could also be used [17]. Inspection of Eqs. (2) and (3) shows that the expression for the strain-energy release rate has a strong dependence on E1, the modulus of the 0 plies. The local value of E1 in the vicinity of the optical fibre is enhanced because the optical fibre has replaced about 40 structural fibres and associated resin. Hence, when the growing matrix crack reaches the region immediately adjacent to the optical fibre, Eqs. (2) and (3) suggest that the energy release rate is reduced by a factor R given approximately by 1:5 0:5 E0f E1f R : E0 E1
ð4Þ
where E0f is the Young’s modulus of the cross-ply laminate with an optical fibre and E1f is the Young’s modulus of the 0 plies with an optical fibre. Eq. (4) enables an upper limit for the effect of the optical fibre to be obtained by assuming that the whole of each 0 ply has the same Young’s modulus as the sensor. In that case Eq. (4) suggests that the strain-energy release rate, G, would be reduced by about 30%. A better model for the effect on the strain-energy release rate requires that a local change in stiffness due to the optical fibre is taken into account. A complete three-dimensional solution of this problem has not been attempted here, but an existing two-dimensional finite element analysis under generalised plane strain conditions has been modified [18]. To preserve the symmetry, one-half of the optical fibre was added either side of the 90 -ply so that, overall, the stiffening due to the optical fibre is equivalent to the experimental situation. The geometry used here enables the strain-energy release rate to be calculated only for the situation where the crack is, in effect, passing the equator of the optical fibre because in this two-dimensional model, the properties of the optical fibre are introduced as two sheets of material with a combined thickness equal to the optical fibre diameter (Fig. 10). Although an obvious limitation, the value of this model is that the distance of the optical fibre from the 0/90 interface can be varied easily. Hence, the variation in G with the distance of the optical fibre from the 0/90 interface can be determined and is shown in Fig. 11 as a function of this distance. The strain-energy release rate increases from a value of about 203 J m2 when the optical fibre is immediately adjacent to the interface, to a value of about 218 J m2 when the optical fibre is distant from the interface, a change in the strain-energy release rate of about 7%. Fig. 11 also shows the experimentally
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ply, the obtrusivity of an optical fibre embedded in the 0 ply near the 0/90 interface is not large enough, even with a poorly optimised coating, to affect the site of matrix crack intiation or subsequent crack accumulation under quasi-static loading. Under fatigue loading, crack initiation was again insensitive to the presence of the optical fibre. However, the presence of an optical fibre inhibited significantly the fatigue growth of transverse ply cracks at low peak cyclic strains. The influence of the optical fibre on crackgrowth falls away rapidly with the distance of the optical fibre from the 0/90 interface. The reduction in the fatigue crack-growth rate of the matrix cracks in the vicinity of the optical fibre can be understood in terms of the effect on the strain-energy release rate of a local stiffening of the 0 ply. Fig. 10. Schematic diagram showing the geometry of the finite element model used, with one half of the optical fibre positioned at equal distances either side of the 90 ply.
Acknowledgements The authors are grateful for the support of the EPSRC and MOD in the form of a research fellowship for E. Barton. We would like to thank Dr. P Lloyd of the DERA (Farnborough) for helpful discussions and Mr. Reg Whattingham for technical assistance.
References
Fig. 11. Calculated strain-energy release rates and measured matrix crack-growth rates as a function of the distance of the optical fibre from the 0/90 interface.
measured matrix crack-growth rates when the cracks are growing in the vicinity of the optical fibres. The matrix crack-growth rate in the vicinity of the optical fibre is very difficult to measure experimentally since the growth rates are very small. The crack-growth rates shown in Fig. 11 are calculated using data of the type shown in Figs. 4 and 5. To obtain a crack-growth rate, the distance over which the growth rate is reduced (i.e. about 1 mm) has been divided by the number of cycles over which the crack appears dormant. Fig. 11 shows that both the crack-growth rate and the strain-energy release rate increase with the distance of the optical fibre from the interface, in agreement with Eq. (1), although the measurements of the crack-growth rates in the vicinity of the optical fibre are too uncertain to establish the value of the exponent, m.
5. Conclusions The experimental work shows that for a model GRP cross-ply composite laminate having a thick transverse
[1] Dasgupta A, Sirkis JS. Importance of coating to optical fibre sensors embedded in ‘smart’ structures. AIAA 1992;30(5):1337– 43. [2] Hadjiprocopiou M, Reed GT, Hollaway L, Thorne AM. Optimization of fibre coating properties for fibre optic smart structures. Smart Mater Struct 1996;5:441–8. [3] Carman GP, Averill RC, Reifsnider KL, Reddy JN. Optimization of fiber coating to minimize stress concentrations in composite materials. J Comp Mater 1993;27(6):589–612. [4] Barton E, Ogin SL, Thorne AM, Reed GT. Optimisation of a coating of a fibre optical sensor embedded in a cross-ply GFRP laminate Composites Part A (in press). [5] Case SW, Carman GP. Optimization of fiber coatings for transverse performance. An experimental study J Comp Mater 1994; 28(25):1452–66. [6] Carman GP, Reifsnider KL. Analytical optimization of coating properties for actuators and sensors. Journal of Intelligent material Systems and Structures 1993;4:89–97. [7] Boniface L, Ogin SL, Smith PA. Strain-energy release rates and the fatigue growth of matrix cracks in model arrays in composite laminates. Proc R Soc Lond A 1991;432:427–44. [8] Nairn JA. The stress energy release rate of composite microcracking: a variational approach. J Comp Mater 1989;23:1106–29. [9] McCartney LN. Stress transfer mechanics for ply cracks in general symmetric laminates. NPL report 1996 CMMT(A)50. [10] Roberts SSJ, Davidson R. Mechanical properties of composite materials containing embedded fibre optic sensors. SPIE 1991; 1588:326–41. [11] Sirkis JS, Chang CC. Low velocity impact of optical fibre embedded laminated graphite/epoxy panels. J Comp Mater 1994; 28(16):1532–52.
E.N. Barton et al. / Composites Science and Technology 61 (2001) 1863–1869 [12] Choi C, Seo DC, Lee JJ, Kim JK. Effect of embedded optical fibres on the interlaminar fracture toughness of composite laminates. Composite Interfaces 1998;5(3):225–40. [13] Tong J, Guild FJ, Ogin SL, Smith PA. On matrix crack-growth in quasi-isotropic laminates-1. Experimental investigation. Comp Sci Tech 1997;57:1527–35. [14] Crocker LE, Ogin SL, Smith PA, Hill PS. Intra-laminar fracture in angle-ply laminates. Composites Part A 1997;28A:839–46. [15] Crocker, LE. Mixed mode intra-laminar fracture in glass/epoxy laminates. PhD thesis, University of Surrey, 1998.
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[16] Boniface L, Smith PA, Rezaifard AH, Bader MG. Transverse cracking in cross-ply CFRP laminates-initiation or propagation controlled? J Comp Mater 1997;31:1008–112. [17] Lee JW, Daniel IM. Progressive transverse cracking of cross-ply composite laminates. Journal of composite materials 1990;24: 1225–43. [18] Le Page BH, Barton E, Ogin SL, Thorne AM, Reed GT, Smith PA. (to be published).
Interaction between optical fibre sensors and matrix cracks in cross-ply GRP laminates—part 1: passive optical fibres E.N. Bartona, S.L. Ogina,*, A.M. Thorneb, G.T. Reedc, B.H. Le Pagea a
School of Mechanical and Materials Engineering, University of Surrey, Guildford, Surrey GU2 5XH, UK b School of Engineering in the Environment, University of Surrey, Guildford, Surrey GU2 5XH, UK c School of Electronic Engineering, Information and Mathematics, University of Surrey, Guildford, Surrey GU2 5XH, UK Received 20 December 2000; accepted 7 June 2001
Abstract The obtrusivity of a passive optical fibre embedded in the 0 ply of a model cross-ply GRP laminate has been investigated experimentally and theoretically. The experimental results show that for quasi-static loading and cyclic loads with a peak strain greater than the quasi-static cracking threshold, both the initiation and development of matrix cracks are insensitive to the presence of the optical fibre. However, for cyclic loading with a peak strain just below the cracking threshold, the matrix crack-growth rate is reduced significantly in the vicinity of the optical fibre. The reduction in the crack-growth rate can be understood in terms of a reduction in the strain-energy release rate for cracking as a consequence of the local stiffening of the 0 ply due to the presence of the optical fibre. # 2001 Elsevier Science Ltd. All rights reserved. Keywords: A. Smart materials; B. Matrix cracking; Passive optical fibres
1. Introduction This study is part of a wider programme on the use of fibre optical sensors to monitor damage in composite materials. ‘Smart structures’, consisting of sensors embedded in a composite material to monitor damage are of increasing interest. Ideally, an optical sensor should not degrade the performance of the structure and an important issue in the design of such systems is the ‘obtrusivity’ of the optical fibre. Obtrusivity refers to the mechanical interactions between the fibre and the host leading to perturbations in the stress field around the fibre. Early work in this area has shown that it is possible to minimise the perturbation in the host material, where the host is a unidirectional composite material, by choosing the optimum fibre optical sensor coating and thickness [1–3]. Recent work has shown that a similar analysis can be performed for minimising the obtrusivity of a sensor embedded within the 0 ply of a cross-ply GRP laminate [4]. Finite-element (FE) models were developed for an optical fibre (diameter 125 mm) with coatings of different * Corresponding author. E-mail address: [email protected] (S.L. Ogin).
thicknesses and different Young’s moduli, with the optical fibre located at three possible locations in the 0 ply of the laminate: near the 0/90 interface, at the centre of the 0 ply, and near the surface of the 0 ply. The main objective was to minimise the stress concentration in the host material around the fibre. It was found that the optimum choice of coating thickness and Young’s modulus was not affected by the position of the fibre. The results of the numerical modelling could be summarised in a design curve (see Fig. 1) which shows a relationship between optimum Young’s modulus and optimum thickness (a similar curve, but for a unidirectional composite has been derived previously [5,6]). In the experimental work to be described here, the obtrusivity of an optical fibre has been investigated with respect to its affect on matrix cracking in a model GRP cross-ply laminate. Matrix cracking has been used for two reasons. Firstly, matrix cracking is the predominant damage mechanism in the initial stages of mechanical degradation of laminates containing off-axis plies and the mechanics are reasonably well understood [7–9]. Secondly, if such fibres are to be used to monitor damage in smart structures, it is important that the interaction between the fibre and the host composite material, especially with regard to damage development
0266-3538/01/$ - see front matter # 2001 Elsevier Science Ltd. All rights reserved. PII: S0266-3538(01)00086-0
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Fig. 1. Design curve showing the optimum combinations of Young’s modulus and coating thickness for the minimising the obtrusivity of an optical fibre embedded in the 0 ply of a cross-ply GRP laminate near the 0/90 interface.
initiated by the fibre itself, is well understood. Hence, matrix cracking is a useful and practical tool with which to probe obtrusivity, although others have used other measures of obtrusivity such as composite strength e.g. [10], microcrack distribution in the vicinity of low velocity impact sites [11] and mode 1 fracture toughness [12]. The next section describes the fabrication of the coupons containing embedded fibres and the mechanical testing.
2. Material and experimental procedure Cross-ply (0/90/0) glass/epoxy coupons were fabricated, both with and without optical fibres, by a filament-winding-wet/lay-up technique. The manufacture of laminates without optical fibres is a standard technique described elsewhere [7]. To produce laminates with optical fibres in the 0 plies, 90 fibres were first wound onto a square steel frame which was then rotated through 90 so that the optical fibres could be glued into grooves of the frame parallel to the reinforcing 0 fibre direction. The reinforcing 0 fibres were then wound around the frame and the laminate was cured in the normal way. The epoxy resin matrix used was Stag epoxy resin 300 (100 parts by weight), cured with nadic methyl anhydride (60 parts by weight) and Stag curing agent K61B (4 parts by weight). The average reinforcing fibre volume fraction for the laminates was about 0.5. Lamina ply thicknesses were about 1 mm each for the two
0 plies and the 90 ply. The optical fibres had one of the optimum combinations for minimising obtrusivity (see Fig. 1), having a polyimide coating with a thickness and Young’s modulus of 10 mm and 2 GPa respectively. The method of manufacture was found to produce specimens with the optical fibres well-aligned parallel to the reinforcing fibres and located towards the centre of the coupon, and about 25–200 mm from the 0/90 interface. The resulting laminates were optically transparent, since the refractive indices of the reinforcing fibres and the matrix are closely matched. As will be seen subsequently, the transparency of the laminates enables the interaction between the cracks and the optical fibres to be investigated readily. Aluminium end-tags were bonded to the specimens for the mechanical tests. Quasi-static tensile tests were performed using an Instron 100 kN-capacity screw-driven machine and an Instron servo-hydraulic testing machine under position or strain control. The testing speed for all tests was equivalent to 0.5 mm/min and a 50 mm gauge-length Instron extensometer was used for monitoring longitudinal strain. The extensometer knife edges rested on grooved seats, made of epoxy adhesive, to prevent the extensometer from slipping during the test. During each test, the specimens were loaded to progressively higher strain levels and unloaded for damage observations. Load and strain were measured using a data logger, while the damage state was recorded directly using transmitted light and a digital camera. Load-controlled tension–tension fatigue tests were carried out using an Instron servo-hydraulic testing machine at frequencies of 5 or 10 Hz with a sinusoidal waveform and stress ratio, R, (R=minimum stress/maximum stress) of 0.1. Peak load levels equivalent to strain levels of 0.3 and 0.45% were chosen since these correspond to loads just above and just below the static cracking threshold strain of 0.4%. A thermocouple attached to the surface of the sample confirmed that the specimen temperature did not rise as a consequence of the fatigue cycling. Subsequent to mechanical testing, specimens were sectioned and polished for optical microscopy and scanning electron microscopy (SEM); the SEM work was carried out using a Hitachi S3200 environmental scanning electron microscope.
3. Results The data obtained on crack accumulation under quasi-static loading are shown in Fig. 2. Crack density as a function of applied strain for specimens without an optical fibre are shown as the mean value for 10 tests with error bars of one standard deviation. These data are in agreement with previous work [13] showing that cracks initiate at a strain of about 0.4% and that the crack density increases with applied strain. The data for
E.N. Barton et al. / Composites Science and Technology 61 (2001) 1863–1869
Fig. 2. Average crack density as a function of applied strain for coupons without optical fibres (error bars show one standard deviation) and individual results for coupons with embedded optical fibres having a polyimide coating.
specimens with an embedded optical fibre are shown in the same figure for 5 different coupons. It is clear that the results for specimens containing embedded optical fibres fall within the normal sample to sample variation of specimens without optical fibres. In particular, it is important to note that the inclusion of the optical fibre does not affect the cracking threshold. In fact, none of the cracks were initiated near the optical fibre and almost all of the cracks in all specimens were initiated at the edges of the coupons, which again is consistent with previous work [14]. The initiation of the cracks at the coupon edge, irrespective of the presence of the optical fibre, suggested that it was not necessarily the lack of obtrusivity of the optical fibre which was dominating the behaviour, but rather the tendency for cracks to initiate at the edges of cross-ply coupon with relatively thick transverse plies. This was confirmed by further tests using optical fibres with an acrylate coating having a thickness and Young’s modulus of about 62 mm and 45 MPa, repectively. This particular coating is far from optimum (see Fig. 1). The results from these tests showed a similar overlap of data between specimens with and without optical fibres (see Fig. 3). Hence, it must be concluded that for these model GRP laminates under quasi-static loading, the stress concentration caused by the inclusion of an optical fibre with an obtrusive coating (i.e. the acrylate) or with the optimum coating (i.e. polyimide) is less, in both cases, than any free edge effect with regard to crack initiation and crack accumulation. The results under fatigue loading, however, clearly indicate that the presence of the optical fibre can interact with damage development and must be taken into account. Under fatigue loading, it was found for strains both above and below the quasi-static cracking threshold, the cracks initiated at the coupon edges and not near the optical fibre. Having initiated at the edge,
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Fig. 3. Average crack density as a function of applied strain for coupons without optical fibres (error bars show one standard deviation) and individual results for coupons with embedded optical fibres having an acrylate coating.
crack-growth across the width of the coupon occurred at a constant rate for the higher peak strain (0.45%), as found in previous work [7,13]. However, observations of crack-growth at the lower peak strain (0.3%) suggested that in the vicinity of the optical fibres, the crackgrowth rate was reduced. Fig. 4 shows a typical result for matrix crack-growth for a coupon cycled at a peak strain of 0.3%. The crack initiates at one edge after about 18,000 cycles and then grows at a roughly constant rate until it approaches the position of the optical fibre, which for this specimen was slightly away from the mid-point of the coupon. For about 12 mm on either side of the optical fibre, the crackgrowth rate reduced significantly so that visually the crack appeared dormant. In the example shown in Fig. 4, the crack began to grow again at its original growth rate after about 10,000 cycles. Fig. 5 shows the
Fig. 4. Graph showing normalised crack length against cycle number for a matrix crack growing across the width of a coupon under cyclic loading. The crack-growth rate is reduced in the vicinity of the optical fibre for about 10,000 cycles. Normalised crack length is crack length divided by coupon width (20 mm)
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similar behaviour of another crack. Again, the growth rate was reduced for about 12 mm either side of the optical fibre: in this case for about 30,000 cycles. The relationship between the growing cracks and the optical fibres was investigated further by preparing cross sections of the cycled coupons as close to the planes of the matrix cracks as possible. All samples were potted in epoxy resin and polished down to the crack plane using standard polishing techniques. Optical and scanning electron microscopy showed that there was no debonding between the optical fibres and the rest of the composite (Fig. 6). The sectioning of the composites did reveal, however, that the position of the optical fibre could vary quite significantly in relation to the position of the 0/90 ply interface (see Figs. 7 and 8). Indeed, when the period (in cycles) of the apparent dormancy of the growing matrix crack was plotted
against the distance of the optical fibre from the 0/90 interface, a clear relationship emerged. The period of apparent dormancy of a growing crack reduces as the distance of the sensor from the 0/90 interface increases (Fig. 9); this period falls roughly by a factor of 4 for each 100 mm increase in the distance of the optical fibre from the interface.
4. Discussion The presence of the optical fibre produced no measurable effect in these laminates on the initiation and accumulation of matrix cracks under quasi-static loading and
Fig. 5. Graph showing normalised crack length against cycle number for a matrix crack growing across the width of a coupon under cyclic loading. The crack-growth rate is reduced in the vicinity of the optical fibre for about 38,000 cycles.
Fig. 7. An SEM micrograph of the cross-section of a coupon sectioned close to the plane of the crack which had shown the crackgrowth behaviour of Fig. 4.
Fig. 6. An SEM micrograph of a polished cross-section of a coupon showing that there is no debonding at the interface between the optical fibre and the rest of the composite.
Fig. 8. An SEM micrograph of the cross-section of a coupon sectioned close to the plane of the crack which had shown the crackgrowth behaviour of Fig. 5.
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the outer 0 ply and the half-thickness of the inner 90 ply. The shear-lag parameter l is given by l2 ¼
Fig. 9. The period of apparent dormancy of the growing crack (in thousands of cycles) as a function of the distance of the optical fibre from the 0/90 interface.
under fatigue loading above the quasi-static threshold strain. However, the fatigue crack-growth rate was substantially reduced in the vicinity of the optical fibre for a peak fatigue cycle strain below this threshold, in a manner which could perhaps be described as ‘benign obtrusivity’ since the crack-growth rate is reduced. It has been found in earlier work that the fatigue growth of matrix cracks in cross-ply laminates can be described using linear elastic fracture mechanics. Experimental observations on fatigue crack-growth in plies at 90 to the loading direction [7,13] as well as for a wide variety of angles [15] indicate that, as in the present case, matrix cracks grow at a constant rate once initiated. Modelling the fatigue crack-growth rate has been reduced to the problem of deriving an expression for the strain-energy release rate of a growing crack and then using a form of the Paris crack-growth law [7], i.e. da ¼ AðGÞm dN
ð1Þ
where G is the strain-energy release rate range, and A and m are constants. The exponent m in Eq. (1) was found to have a value of about 5 for thick transverse plies [7]. A consequence of the relative simplicity of this expression for the present observations is that it provides a useful starting point from which to discuss the interaction of the growing matrix cracks with the fibre optical sensor. Following [16], the strain-energy release rate for the growth of a crack which does not interact with other, neighbouring cracks, is b E2 b E0 G¼ 1þ þ T d d lE1 E2 E0
ð2Þ
In Eq. (2), E1 and E2 are the ply moduli parallel and perpendicular to the fibres, E0 is the rule-of-mixtures modulus of the (uncracked) laminate, T is the thermal stress in the transverse ply, b and d are the thickness of
3G23 ðb þ dÞ d2 bE1 E2
ð3Þ
where G23 is the out-of-plane shear modulus, although other expressions for l could also be used [17]. Inspection of Eqs. (2) and (3) shows that the expression for the strain-energy release rate has a strong dependence on E1, the modulus of the 0 plies. The local value of E1 in the vicinity of the optical fibre is enhanced because the optical fibre has replaced about 40 structural fibres and associated resin. Hence, when the growing matrix crack reaches the region immediately adjacent to the optical fibre, Eqs. (2) and (3) suggest that the energy release rate is reduced by a factor R given approximately by 1:5 0:5 E0f E1f R : E0 E1
ð4Þ
where E0f is the Young’s modulus of the cross-ply laminate with an optical fibre and E1f is the Young’s modulus of the 0 plies with an optical fibre. Eq. (4) enables an upper limit for the effect of the optical fibre to be obtained by assuming that the whole of each 0 ply has the same Young’s modulus as the sensor. In that case Eq. (4) suggests that the strain-energy release rate, G, would be reduced by about 30%. A better model for the effect on the strain-energy release rate requires that a local change in stiffness due to the optical fibre is taken into account. A complete three-dimensional solution of this problem has not been attempted here, but an existing two-dimensional finite element analysis under generalised plane strain conditions has been modified [18]. To preserve the symmetry, one-half of the optical fibre was added either side of the 90 -ply so that, overall, the stiffening due to the optical fibre is equivalent to the experimental situation. The geometry used here enables the strain-energy release rate to be calculated only for the situation where the crack is, in effect, passing the equator of the optical fibre because in this two-dimensional model, the properties of the optical fibre are introduced as two sheets of material with a combined thickness equal to the optical fibre diameter (Fig. 10). Although an obvious limitation, the value of this model is that the distance of the optical fibre from the 0/90 interface can be varied easily. Hence, the variation in G with the distance of the optical fibre from the 0/90 interface can be determined and is shown in Fig. 11 as a function of this distance. The strain-energy release rate increases from a value of about 203 J m2 when the optical fibre is immediately adjacent to the interface, to a value of about 218 J m2 when the optical fibre is distant from the interface, a change in the strain-energy release rate of about 7%. Fig. 11 also shows the experimentally
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ply, the obtrusivity of an optical fibre embedded in the 0 ply near the 0/90 interface is not large enough, even with a poorly optimised coating, to affect the site of matrix crack intiation or subsequent crack accumulation under quasi-static loading. Under fatigue loading, crack initiation was again insensitive to the presence of the optical fibre. However, the presence of an optical fibre inhibited significantly the fatigue growth of transverse ply cracks at low peak cyclic strains. The influence of the optical fibre on crackgrowth falls away rapidly with the distance of the optical fibre from the 0/90 interface. The reduction in the fatigue crack-growth rate of the matrix cracks in the vicinity of the optical fibre can be understood in terms of the effect on the strain-energy release rate of a local stiffening of the 0 ply. Fig. 10. Schematic diagram showing the geometry of the finite element model used, with one half of the optical fibre positioned at equal distances either side of the 90 ply.
Acknowledgements The authors are grateful for the support of the EPSRC and MOD in the form of a research fellowship for E. Barton. We would like to thank Dr. P Lloyd of the DERA (Farnborough) for helpful discussions and Mr. Reg Whattingham for technical assistance.
References
Fig. 11. Calculated strain-energy release rates and measured matrix crack-growth rates as a function of the distance of the optical fibre from the 0/90 interface.
measured matrix crack-growth rates when the cracks are growing in the vicinity of the optical fibres. The matrix crack-growth rate in the vicinity of the optical fibre is very difficult to measure experimentally since the growth rates are very small. The crack-growth rates shown in Fig. 11 are calculated using data of the type shown in Figs. 4 and 5. To obtain a crack-growth rate, the distance over which the growth rate is reduced (i.e. about 1 mm) has been divided by the number of cycles over which the crack appears dormant. Fig. 11 shows that both the crack-growth rate and the strain-energy release rate increase with the distance of the optical fibre from the interface, in agreement with Eq. (1), although the measurements of the crack-growth rates in the vicinity of the optical fibre are too uncertain to establish the value of the exponent, m.
5. Conclusions The experimental work shows that for a model GRP cross-ply composite laminate having a thick transverse
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