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Use of heat emitted by broken optic fibers: A new approach for damage detection in composites
Engineering Failure Analysis 12 (2005) 860–874 www.elsevier.com/locate/engfailanal
Use of heat emitted by broken optic fibers: A new approach for damage detection in composites q Pavel Pevzner *, Tanchum Weller, Avraham Berkovits Faculty of Aerospace Engineering, Technion – Israel Institute of Technology, Haifa 32 000, Israel Received 12 July 2004; accepted 27 December 2004 Available online 31 March 2005
Abstract Optic fibers, stripped of their jacket, weakened and embedded in a composite plate structure, cracked due to the occurrence of cracks and delaminations in the composite. At the location of a crack in a fiber, transmitted laser-light energy was converted into thermal energy, causing the temperature in the neighborhood of the crack to rise. The temperature change was detected with the aid of an infrared camera. Dynamic numerical simulations of the heat development in the vicinity of the fiber crack were performed. An analytical solution of the temperature distribution on the surface of the composite plate above a fiber crack was also developed. Both analytical and numerical results showed the feasibility of detecting and monitoring the hot spot on the composite plate caused by optic fiber cracking, by use of infrared emission from the fibers. This was successfully confirmed in experiment. The influence of parameters such as depth of the fiber below the surface of the plate, heat conductivity coefficient and light power, on the temperature distribution was also studied. Ultrasound scan of the damaged plate confirmed the accuracy of the hot-spot method in defining the damaged area. 2005 Elsevier Ltd. All rights reserved. Keywords: Composite materials; Damage detection; Optic fibers; Heat transfer; Infrared photography
1. Introduction Techniques which use embedded optical fibers in composite structures are considered to be very promising for nondestructive detection of damage. In addition to measuring response of a composite structure to external stimuli, embedded fiber optic sensors would make ideal ‘‘nerves’’ for sensing the local integrity of q *
A provisional application for Patent has been filed. Corresponding author. Tel.: +972 4829 2303; fax: +972 4829 3020. E-mail address: [email protected] (P. Pevzner).
1350-6307/$ - see front matter 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.engfailanal.2004.12.019
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861
such structures. Their optical properties and their compatibility with the properties of composite materials (extremely light weight, small diameter, resistance to corrosion and fatigue, mechanical properties similar to those of composites and insensitivity to ambient magnetic fields) have been exploited in many studies [1]. Fiber optic strain sensors have already replaced conventional electrical strain sensors in many cases [2–4], in which the excited frequencies and amplitudes in a structure were formerly measured with the aid of accelerometers or strain gauges. In numerous studies, optic fibers have been applied for health monitoring systems in composite materials [4–9]. Methods for using optic fibers for damage detection include: (1) Use of optic fibers as integral strain sensors and/or integral sensors for vibration measurements, either intensity-based [2] or, more commonly, interferometry-based. The latter includes the Bragg, MachZender, Michelson, Fabry–Perot and Sagnac interferometers and high birefrigence polarization-mode interferometer. (2) Methods employing the fracture of the optic fiber sensor are based on the fact that preliminarily weakened fibers, embedded in a composite structure, crack at points where damage occurs in the structure. These methods use various techniques to determine the location of the crack in the fiber, such as segments of optic fibers connected by Bragg gratings [10], optical fibers disposed orthogonally, measurements of back reflection, backscattering from the crack [1–9]. Using preliminarily weakened optic fibers embedded in a composite structure, the authors of [5,9] identified cracks in the areas at which damage occurred in the structure, by locating cracks in the optic fibers by light leakage from these cracks through translucent composite material. They successfully located both impact and quasi-statically induced damage, and could map the growth of a region of damage with increasing load. In contrast to the light emission methods of [1–9], the present approach identifies cracks in optic fibers by the rise in temperature in the neighborhood of a crack, as part of the light energy transmitted through the cracked optic fiber is transformed into heat energy at the crack location. The study reports on the successful use of infrared photography in an experiment on a graphite–epoxy plate instrumented with optic fibers. Local invisible damage was imposed on the plate by firing a small ball-bearing at it with an air gun. The damaged plate was inspected using laser light and an infrared camera, as well as by ultrasound scanning. The experiment was complemented by development of numerical and analytical methods for calculating the temperature rise and distribution when a cracked optic fiber is exposed to laser light. Both theoretical and experimental studies of the method report that the heat energy emitted by broken fibers embedded in, or bonded to, the composite plate was sufficient to change the local temperature so that it could be accurately identified by an infrared camera. It was shown in experiment that the phenomenon of heating was detectable to a considerable depth of the embedded fiber. One of the advantages of the proposed method is that it can make use of optic fibers which have been embedded into a structure for other purposes, such as strain, temperature and frequency measurements. The method can work together with other methods, such as backscattering from the crack, to pinpoint a remote location where the crack in a fiber has occurred.
2. Effect of local damage in an embedded optic fiber on the temperature on the face of a composite plate Numerical and analytical tools were developed to study the extent of local temperature changes due to local optical fiber damage and evaluate the adequacy of changes to detect the damage. It was concluded from these tools that the change in temperature on the surface of a composite plate is sufficient to point accurately at the position at which the optic fiber is broken. When this conclusion was reached a laboratory
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test was conducted in order to prove the proposed method. Following the presentation of the analytical formulation, specific calculated results will be presented, together with analytically obtained results. 2.1. Numerical formulation A simple numerical simulation of the experiment was performed for an composite plate with a broken optical fiber within. As in the subsequent laboratory experiment, the plate consisted of 16 graphite–epoxy layers 0.135 mm in thickness each. This case is similar to the common heat transfer problem described in [11], with only three features associated with the present numerical formulation: The heat supply function is a Dirac delta function in a three dimensional space, f ðx; y; zÞ ¼ F dx1 ;y 1 ;z1 ðx; y; zÞ;
ð1Þ
where the constant F is the light power that is transmitted through the fiber. This implies that for any function n(x, y, z), continuous throughout a volume X, the following relation holds: Z nðx; y; zÞf ðx; y; zÞdX ¼ F nðx1 ; y 1 ; z1 Þ; ð2Þ X
where the point (x1,y1,z1) 2 X is the point where the optic fiber is broken. The problem being examined is axisymmetric. The treated problem simulates heat distribution in a plate of infinite size. The boundary conditions are taken as: There is no heat flux from the surfaces of the plate, qz ¼ 0 ) u;z ¼ 0 ðNeuman boundary conditionÞ
ð3Þ
where ~ q is the heat flux vector and u is temperature. The temperature at an infinite radius away from the crack is the room temperature ujr¼1 ¼ uroom ðDirichlet boundary condition [11]Þ:
ð4Þ
2.2. Analytical formulation An analytical solution of the temperature distribution in the plate with internal heat source is developed here. In this solution, heat conductivity of the plate material is taken as for homogeneous isotropic material, and the following well-known equation for temperature distribution is used f u;ii ¼ ; k
ð5Þ
where u is the temperature, f defines heat supply per unit volume and k is the coefficient of heat conductivity. Assuming a cylindrical heat source (Fig. 1), the heat supply per the unit volume function f in the last equation can be written in cylindrical coordinates as: F 1 2 f ¼ fH ðz z1 þ r1 Þ H ðz z1 r1 Þg 2 fH ðrÞ H ðr r2 Þg ; ð6Þ 2 p 2r1 r2 whereas in the numerical solution, F is a constant equal to the light power transmitted through the fiber, z1 is the center of the heated cylinder (Fig. 1) and H is a step function. By expanding the function
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Fig. 1. Analytical problem.
{H(z z1 + r1) H(z z1 r1)} of the right side of Eq. (6) in a cosine series and function {H(r) H(r r2)} in a Bessel series, Eq. (5) can be presented as: 1 X 1 X lk2 o2 u ou o2 u k1p þ z J0 þ ¼ ak1 bk2 cos r ; ð7Þ or2 ror oz2 h R1 k ¼0 k ¼1 1
where
8 a0 > > > > > > a > < k1 > > > bk 2 > > > > :
F pkh F 2pkr1
¼ ¼
1 r22
¼
2
pk41 cos k1hp z1 sin k1hp r1 ¼ kk12Fp2 r1 cos k1hp z1 sin k1hp r1
R r 2 lk 2
lk r 2 2
R
0 R1
0
rJ 0
h
r J0
R1
:r dr
lk 2 R1 r
i2 ¼ r22 dr
J1
R1
lk R1 ½J 1 ðlk 2
2
Þ
2
ð8Þ
k 2 ¼ 1; 2; 3 . . .
We seek the solution of the temperature function u in the form 1 X 1 X lk2 k1p u ¼ u0 þ z J0 Ak1 k2 cos r ; h R1 k ¼0 k ¼1 1
k 1 ¼ 1; 2; 3 . . .
ð9Þ
2
where u0 is the initial temperature (taken here as uroom) and Ak1 k2 are yet unknown coefficients. It should be l noted that functions u0, cosðk1hpzÞ and J 0 ð Rk12 rÞ comply with the boundary conditions (4) and (3). Thus, all terms of the sum on the right side of Eq. (9) fulfil the boundary conditions for any value of the coefficients Ak 1 k 2 . Finally, the equation for temperature distribution becomes l r
8 9 k2 2 = 1 < R J X 1 1 lk 2 R1 F 2 u ¼u0 þ r 2 J 0 3 : ; pkh r R1 2 ðl Þ J 1 l k 2 ¼1 k2 k2
9 8 lk r 2 2 > > J 1 R1 > > k p k p > > 4F sin 1 r cos 1 z > > 1 1 2r 2 = < 1 1 h h kk p XX 1 1 r2 lk R1 ½J 1 ðlk Þ k p lk 1 2 2 2 : ð10Þ þ z J cos r
0 k p2 lk 2 > > h R1 1 2 > k 1 ¼1 k 2 ¼1 > > > þ > > R1 h ; :
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2.3. Analytical and numerical results All numerical and analytical calculations were performed for an infinite length composite plate containing a broken optic fiber. As in the subsequent experimental study the plate consisted of 16 layers, 0.135 mm in thickness each. Both the analytical and numerical investigations were performed for a fiber embedded a few layers below one of the plate surfaces (Fig. 2). Ten milliwatts of light power was transmitted by the optical fiber and was converted into heat energy at the crack location. The range of heat conductivity k for epoxy resin is 0.2–0.4 W/m C. Both 0.2 and 0.4 W/m C were investigated. Room temperature u0 was taken to be 23 C. Eq. (10) indicates that the temperature u on the surface above the crack location is directly proportional to the light power F and inversely proportional to the heat conductivity coefficient k.
Fig. 2. Composite plate model.
Fig. 3. Analytical and numerical results of temperature distribution through the thickness of a composite plate.
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Also, the closer the fiber is to the surface, the higher is the temperature on the surface. The temperature distribution along the axis of symmetry, for both the numerical and analytical investigations, for different cases of heat sources, is depicted in Fig. 3. The temperature distribution on the surface of a composite plate as function of radius due to a crack in the optic fiber, conductivity coefficient k, light power source F and depth of the optic fiber beneath the plate surface, is shown in Fig. 4. The temperature on the surface at the point above the fiber crack as a function of time is shown at Fig. 5. A temperature rise of at least 6 C was
Fig. 4. Analytically calculated temperature distribution on the surface of the composite plate.
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Fig. 5. Time dependence of temperaute on the surface of a composite plate at point above the crack in the fiber optic u0 = 23 C, F = 10 mW, k = 0.4 W/mC, depth = 0.5 mm.
obtained from these theoretical results. This change in temperature on the surface is distinct enough to accurately point out the position at which the optic fiber is broken.
3. Experimental study In order to check the main ideas of the study in practice and evaluate the new approach to damage detection a rectangular composite plate was instrumented with optic fibers. Local damage was introduced in the plate. The optic fibers were then energized with laser light, and the resulting temperature rise was recorded by infrared camera. The experimental method was also compared with an ultrasound scanning study of the damaged plate. Details of the investigation are given in this section. 3.1. Test specimen A 16-ply (0; 90)4s layup AS4/3502 graphite–epoxy composite plate (243 mm · 145 mm · 2.16 mm) was employed as the test specimen. Eight optic fibers of 125 lm diameter were stripped of their jackets and glued to the face of the plate 20 mm apart, parallel to each other (Fig. 6). An epoxy ply and black paint ply were applied on the fibers and plate. This operation was repeated twice in order to cover the optic fibers with up to 0.5 mm of opaque material. The rear surface of the plate was affixed to a cardboard base in which a square hole 70 mm · 70 mm had been cut. Two strips of aluminum foil were glued on the specimen to provide a basis for measurements. This aluminum foil was visible on infrared pictures, and thus afforded a geometric reference. 3.2. Infliction of local damage A calibrated air gun was used to impact the specimen with a given energy using a steel ball-bearing, 13 mm in diameter, shot at the plate through the hole in the cardboard base. For this purpose, the specimen
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Fig. 6. Test specimen.
was clamped along its shorter edges (Fig. 7). The ball impacted the composite plate with an incident speed of 40 m/s, inducing damage in the plate. The damaged area was not discernible from the impact side to the naked eye, but could be defined with the aid of ultrasonic scanning.
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Fig. 7. Set-up for inducing local damage.
3.3. Detection of damage with laser light A helium–neon laser with maximum power of 8 W was used to introduce light into the optic fibers. The power of the laser beam used in this experiment was in the range of 300–700 mW. The experiment was performed at the Fiber Optic Laboratory, Faculty of Electrical Engineering, Technion. Initially, infrared pictures were taken of the surface for which the optic fibers were located less than 0.5 mm beneath the surface. The laser light was introduced into the optic fiber at one end and an infrared photograph was taken. The light was then introduced from the other end of the fiber and a photograph was again taken. Dark spots indicating crack points were clearly observed (Fig. 8). The power of laser light used in this case was in the range of 300–400 mW. The difference of the temperatures between the crack point and the background was 10–16 C, sufficient to eliminate any temperature disturbances on the infrared pictures. The temperature disturbance introduced by reflection from the aluminum reference foil (Fig. 8) could be eliminated by artificially increasing the minimum temperature seen by the camera (Fig. 9). All the heat spots engendered are presented simultaneously in Fig. 10. It can be seen on this figure that in two cases optical fibers were broken at the edge of the plate, in places where fibers were handled as they were embedded in the plate. All other points appear in the region inside the plate where damage apparently occurred. In this way, the damaged area was defined and bounded. After the successful detection of the fiber crack location at 0.5 mm below the plate surface, attempts were made to find cracks which were located further below the surface. Infrared photos were taken of the opposite surface of the plate, where the optic fibers were 2.16 mm deep. Fig. 11 shows that in this case the cracks in the optic fiber were discerned equally as well. Again, all pictures of hot spots from this surface can be simultaneously used to define the extent of the damage area (Fig. 12). In Fig. 13 pictures of a hot spot due to crack in an optic fiber exposed to different laser light powers are shown. The laser light power was in the range of 300–700 mW. As expected, improved results were obtained with higher laser light power.
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Fig. 8. Hot spot photographs obtained by infrared camera for broken fibers in a number of hot spots. fiber depth: 0.5 mm laser beam power range used: 300–400 mW. Temperature rise at crack tip: 10–16 C.
3.4. Detection of damage by ultrasound scanning For evaluation and verification of the results yielded by the proposed method a comparison with the results obtained by ultrasound scanning of the plate was performed. The results of the ultrasound scan were compared in Fig. 14 with results of the infrared method depicted in Fig. 10. Except for the two points where fibers were broken at the edge of the plate all other hot spots undoubtedly point to the damage region. It is clear from this figure that the proposed method can define and enclose the damage region satisfactorily.
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Fig. 9. Disturbance elimination by artificially raising u0.
Fig. 10. Damaged area demarcated in heat spots (front surface).
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Fig. 11. Infrared photographs taken from of the rear surface of the plate. Fiber depth: 2.16 mm
Fig. 12. Damaged area demarcated by heat spots (rear surface). Fiber depth: 2.16 mm
4. Conclusions and recommendations for future studies A new approach to damage detection in composites has been demonstrated. The approach is based on the phenomenon that light energy transmitted through fiber-optics is converted into heat energy at the location of broken fibers leading to a local increase in temperature, indicating the presence of a crack in the composite plate. Complementary analytical and numerical tools for evaluating the temperature rise in the neighborhood of broken fibers were developed and presented. Results of the analyses performed with these tools indicated that the temperature generated at the breaks in the fibers can be sufficient to permit satisfactory detection in tests. Tests with impact-damaged graphite–epoxy plates showed that the heat energy emitted by broken fibers was adequate to change the local temperature so that it could quite easily be detected by an infrared camera. Comparison of the damage signatures obtained by the new approach compared favorably with signatures obtained by ultrasonic methods.
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Fig. 13. Heat spot temperature for varying laser power. u0 20 C
The effects of various laser powers transmitted through the fiber on the damage signatures were studied. As anticipated, the higher the laser power the more distinctive was the observed signature. The influence of fiber-optic depth below the monitored composite surface, and of heat conductivity, on results were also been examined theoretically and/or experimentally. One of the advantages of the proposed method is that it can make use of optic fibers which have already been embedded into a structure for other purposes, such as strain, temperature and frequency measurements. The proposed method can be used in existing structures. In some cases, fibers can be glued to the rear surface of pressure vessels. In this case not only will they find damage easily, but when damaged can also be conveniently replaced. A provisional application for Patent has been filed.
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Fig. 14. Agreement between results obtained by infrared photography and by ultrasound scanning.
References [1] Valis T. Localized and distributed fiber-optic sensors embedded in composite materials. UTIAS Report 346, Institute for Aerospace Studies, University of Toronto, Sept. 1992. CN ISSN 0082-5255. [2] Buckley LJ, Neumeister GC. Fiber optic strain measurements using an optically-active polymer. Smart Mater Struct 1992;1(1):1–4. [3] Masalkar PJ, Malhotra SK, Sirohi RS, Asundi A. Use of optical fiber strain sensor for damage detection in composite structures. In: Smart Structures and Materials 1995 Smart Structures and Integrated Systems, vol. 2443. San Diego, California: SPIE – The International Society for Optical Engineering; February–March 1995. p. 230–5. [4] Andrews JP, Zisk EJ. Use of optical fiber strain sensor for damage detection in composite structures. In: Smart Structures and Materials 1995 Smart Structures and Integrated Systems, vol. 2443. San Diego, California: SPIE – The International Society for Optical Engineering; February–March 1995. p. 308–12. [5] Measures RM. Progress in the development of fiber-optic smart structures. CASI Meeting, May 1990. [6] Glossop NDW. An embedded fibre optic sensor for impact damage detection in composite materials. PhD thesis, University of Toronto, Institute for Aerospace Studies, 1988. [7] LeBlanc M, Dubois S, McEwen K, Hogg D, Park B, Tsaw W et al.. Development of a fibre optic damage assessment system for an aircraft leading edge. Fiber optic smart structures and skins, spie, vol. 1170. p. 196–204. [8] LeBlanc M. A prototype fibre optic damage assessment system for an aircraft composite leading edge. MasterÕs thesis, UTIAS, 1990.
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[9] Glossop DW, Dubios S, Tsaw W, LeBlanc M, Lymer J, Measures RM et al.. Optical fibre damage detection for an aircraft composite leading edge. Composites 1990;21(1):71–80. [10] Gu Xianglin, Chen Zhongyu, Ansari Fadhad. Method and theory for a multi-gauge distributed fiber optic crack sensor. J Intel Mat Syst Struct 1999;10(2). [11] Hughes Thomas JR. The finite element method linear static and dynamic finite element analysis. Prentice-Hall International Inc.; 1987.
Use of heat emitted by broken optic fibers: A new approach for damage detection in composites q Pavel Pevzner *, Tanchum Weller, Avraham Berkovits Faculty of Aerospace Engineering, Technion – Israel Institute of Technology, Haifa 32 000, Israel Received 12 July 2004; accepted 27 December 2004 Available online 31 March 2005
Abstract Optic fibers, stripped of their jacket, weakened and embedded in a composite plate structure, cracked due to the occurrence of cracks and delaminations in the composite. At the location of a crack in a fiber, transmitted laser-light energy was converted into thermal energy, causing the temperature in the neighborhood of the crack to rise. The temperature change was detected with the aid of an infrared camera. Dynamic numerical simulations of the heat development in the vicinity of the fiber crack were performed. An analytical solution of the temperature distribution on the surface of the composite plate above a fiber crack was also developed. Both analytical and numerical results showed the feasibility of detecting and monitoring the hot spot on the composite plate caused by optic fiber cracking, by use of infrared emission from the fibers. This was successfully confirmed in experiment. The influence of parameters such as depth of the fiber below the surface of the plate, heat conductivity coefficient and light power, on the temperature distribution was also studied. Ultrasound scan of the damaged plate confirmed the accuracy of the hot-spot method in defining the damaged area. 2005 Elsevier Ltd. All rights reserved. Keywords: Composite materials; Damage detection; Optic fibers; Heat transfer; Infrared photography
1. Introduction Techniques which use embedded optical fibers in composite structures are considered to be very promising for nondestructive detection of damage. In addition to measuring response of a composite structure to external stimuli, embedded fiber optic sensors would make ideal ‘‘nerves’’ for sensing the local integrity of q *
A provisional application for Patent has been filed. Corresponding author. Tel.: +972 4829 2303; fax: +972 4829 3020. E-mail address: [email protected] (P. Pevzner).
1350-6307/$ - see front matter 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.engfailanal.2004.12.019
P. Pevzner et al. / Engineering Failure Analysis 12 (2005) 860–874
861
such structures. Their optical properties and their compatibility with the properties of composite materials (extremely light weight, small diameter, resistance to corrosion and fatigue, mechanical properties similar to those of composites and insensitivity to ambient magnetic fields) have been exploited in many studies [1]. Fiber optic strain sensors have already replaced conventional electrical strain sensors in many cases [2–4], in which the excited frequencies and amplitudes in a structure were formerly measured with the aid of accelerometers or strain gauges. In numerous studies, optic fibers have been applied for health monitoring systems in composite materials [4–9]. Methods for using optic fibers for damage detection include: (1) Use of optic fibers as integral strain sensors and/or integral sensors for vibration measurements, either intensity-based [2] or, more commonly, interferometry-based. The latter includes the Bragg, MachZender, Michelson, Fabry–Perot and Sagnac interferometers and high birefrigence polarization-mode interferometer. (2) Methods employing the fracture of the optic fiber sensor are based on the fact that preliminarily weakened fibers, embedded in a composite structure, crack at points where damage occurs in the structure. These methods use various techniques to determine the location of the crack in the fiber, such as segments of optic fibers connected by Bragg gratings [10], optical fibers disposed orthogonally, measurements of back reflection, backscattering from the crack [1–9]. Using preliminarily weakened optic fibers embedded in a composite structure, the authors of [5,9] identified cracks in the areas at which damage occurred in the structure, by locating cracks in the optic fibers by light leakage from these cracks through translucent composite material. They successfully located both impact and quasi-statically induced damage, and could map the growth of a region of damage with increasing load. In contrast to the light emission methods of [1–9], the present approach identifies cracks in optic fibers by the rise in temperature in the neighborhood of a crack, as part of the light energy transmitted through the cracked optic fiber is transformed into heat energy at the crack location. The study reports on the successful use of infrared photography in an experiment on a graphite–epoxy plate instrumented with optic fibers. Local invisible damage was imposed on the plate by firing a small ball-bearing at it with an air gun. The damaged plate was inspected using laser light and an infrared camera, as well as by ultrasound scanning. The experiment was complemented by development of numerical and analytical methods for calculating the temperature rise and distribution when a cracked optic fiber is exposed to laser light. Both theoretical and experimental studies of the method report that the heat energy emitted by broken fibers embedded in, or bonded to, the composite plate was sufficient to change the local temperature so that it could be accurately identified by an infrared camera. It was shown in experiment that the phenomenon of heating was detectable to a considerable depth of the embedded fiber. One of the advantages of the proposed method is that it can make use of optic fibers which have been embedded into a structure for other purposes, such as strain, temperature and frequency measurements. The method can work together with other methods, such as backscattering from the crack, to pinpoint a remote location where the crack in a fiber has occurred.
2. Effect of local damage in an embedded optic fiber on the temperature on the face of a composite plate Numerical and analytical tools were developed to study the extent of local temperature changes due to local optical fiber damage and evaluate the adequacy of changes to detect the damage. It was concluded from these tools that the change in temperature on the surface of a composite plate is sufficient to point accurately at the position at which the optic fiber is broken. When this conclusion was reached a laboratory
862
P. Pevzner et al. / Engineering Failure Analysis 12 (2005) 860–874
test was conducted in order to prove the proposed method. Following the presentation of the analytical formulation, specific calculated results will be presented, together with analytically obtained results. 2.1. Numerical formulation A simple numerical simulation of the experiment was performed for an composite plate with a broken optical fiber within. As in the subsequent laboratory experiment, the plate consisted of 16 graphite–epoxy layers 0.135 mm in thickness each. This case is similar to the common heat transfer problem described in [11], with only three features associated with the present numerical formulation: The heat supply function is a Dirac delta function in a three dimensional space, f ðx; y; zÞ ¼ F dx1 ;y 1 ;z1 ðx; y; zÞ;
ð1Þ
where the constant F is the light power that is transmitted through the fiber. This implies that for any function n(x, y, z), continuous throughout a volume X, the following relation holds: Z nðx; y; zÞf ðx; y; zÞdX ¼ F nðx1 ; y 1 ; z1 Þ; ð2Þ X
where the point (x1,y1,z1) 2 X is the point where the optic fiber is broken. The problem being examined is axisymmetric. The treated problem simulates heat distribution in a plate of infinite size. The boundary conditions are taken as: There is no heat flux from the surfaces of the plate, qz ¼ 0 ) u;z ¼ 0 ðNeuman boundary conditionÞ
ð3Þ
where ~ q is the heat flux vector and u is temperature. The temperature at an infinite radius away from the crack is the room temperature ujr¼1 ¼ uroom ðDirichlet boundary condition [11]Þ:
ð4Þ
2.2. Analytical formulation An analytical solution of the temperature distribution in the plate with internal heat source is developed here. In this solution, heat conductivity of the plate material is taken as for homogeneous isotropic material, and the following well-known equation for temperature distribution is used f u;ii ¼ ; k
ð5Þ
where u is the temperature, f defines heat supply per unit volume and k is the coefficient of heat conductivity. Assuming a cylindrical heat source (Fig. 1), the heat supply per the unit volume function f in the last equation can be written in cylindrical coordinates as: F 1 2 f ¼ fH ðz z1 þ r1 Þ H ðz z1 r1 Þg 2 fH ðrÞ H ðr r2 Þg ; ð6Þ 2 p 2r1 r2 whereas in the numerical solution, F is a constant equal to the light power transmitted through the fiber, z1 is the center of the heated cylinder (Fig. 1) and H is a step function. By expanding the function
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Fig. 1. Analytical problem.
{H(z z1 + r1) H(z z1 r1)} of the right side of Eq. (6) in a cosine series and function {H(r) H(r r2)} in a Bessel series, Eq. (5) can be presented as: 1 X 1 X lk2 o2 u ou o2 u k1p þ z J0 þ ¼ ak1 bk2 cos r ; ð7Þ or2 ror oz2 h R1 k ¼0 k ¼1 1
where
8 a0 > > > > > > a > < k1 > > > bk 2 > > > > :
F pkh F 2pkr1
¼ ¼
1 r22
¼
2
pk41 cos k1hp z1 sin k1hp r1 ¼ kk12Fp2 r1 cos k1hp z1 sin k1hp r1
R r 2 lk 2
lk r 2 2
R
0 R1
0
rJ 0
h
r J0
R1
:r dr
lk 2 R1 r
i2 ¼ r22 dr
J1
R1
lk R1 ½J 1 ðlk 2
2
Þ
2
ð8Þ
k 2 ¼ 1; 2; 3 . . .
We seek the solution of the temperature function u in the form 1 X 1 X lk2 k1p u ¼ u0 þ z J0 Ak1 k2 cos r ; h R1 k ¼0 k ¼1 1
k 1 ¼ 1; 2; 3 . . .
ð9Þ
2
where u0 is the initial temperature (taken here as uroom) and Ak1 k2 are yet unknown coefficients. It should be l noted that functions u0, cosðk1hpzÞ and J 0 ð Rk12 rÞ comply with the boundary conditions (4) and (3). Thus, all terms of the sum on the right side of Eq. (9) fulfil the boundary conditions for any value of the coefficients Ak 1 k 2 . Finally, the equation for temperature distribution becomes l r
8 9 k2 2 = 1 < R J X 1 1 lk 2 R1 F 2 u ¼u0 þ r 2 J 0 3 : ; pkh r R1 2 ðl Þ J 1 l k 2 ¼1 k2 k2
9 8 lk r 2 2 > > J 1 R1 > > k p k p > > 4F sin 1 r cos 1 z > > 1 1 2r 2 = < 1 1 h h kk p XX 1 1 r2 lk R1 ½J 1 ðlk Þ k p lk 1 2 2 2 : ð10Þ þ z J cos r
0 k p2 lk 2 > > h R1 1 2 > k 1 ¼1 k 2 ¼1 > > > þ > > R1 h ; :
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2.3. Analytical and numerical results All numerical and analytical calculations were performed for an infinite length composite plate containing a broken optic fiber. As in the subsequent experimental study the plate consisted of 16 layers, 0.135 mm in thickness each. Both the analytical and numerical investigations were performed for a fiber embedded a few layers below one of the plate surfaces (Fig. 2). Ten milliwatts of light power was transmitted by the optical fiber and was converted into heat energy at the crack location. The range of heat conductivity k for epoxy resin is 0.2–0.4 W/m C. Both 0.2 and 0.4 W/m C were investigated. Room temperature u0 was taken to be 23 C. Eq. (10) indicates that the temperature u on the surface above the crack location is directly proportional to the light power F and inversely proportional to the heat conductivity coefficient k.
Fig. 2. Composite plate model.
Fig. 3. Analytical and numerical results of temperature distribution through the thickness of a composite plate.
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Also, the closer the fiber is to the surface, the higher is the temperature on the surface. The temperature distribution along the axis of symmetry, for both the numerical and analytical investigations, for different cases of heat sources, is depicted in Fig. 3. The temperature distribution on the surface of a composite plate as function of radius due to a crack in the optic fiber, conductivity coefficient k, light power source F and depth of the optic fiber beneath the plate surface, is shown in Fig. 4. The temperature on the surface at the point above the fiber crack as a function of time is shown at Fig. 5. A temperature rise of at least 6 C was
Fig. 4. Analytically calculated temperature distribution on the surface of the composite plate.
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Fig. 5. Time dependence of temperaute on the surface of a composite plate at point above the crack in the fiber optic u0 = 23 C, F = 10 mW, k = 0.4 W/mC, depth = 0.5 mm.
obtained from these theoretical results. This change in temperature on the surface is distinct enough to accurately point out the position at which the optic fiber is broken.
3. Experimental study In order to check the main ideas of the study in practice and evaluate the new approach to damage detection a rectangular composite plate was instrumented with optic fibers. Local damage was introduced in the plate. The optic fibers were then energized with laser light, and the resulting temperature rise was recorded by infrared camera. The experimental method was also compared with an ultrasound scanning study of the damaged plate. Details of the investigation are given in this section. 3.1. Test specimen A 16-ply (0; 90)4s layup AS4/3502 graphite–epoxy composite plate (243 mm · 145 mm · 2.16 mm) was employed as the test specimen. Eight optic fibers of 125 lm diameter were stripped of their jackets and glued to the face of the plate 20 mm apart, parallel to each other (Fig. 6). An epoxy ply and black paint ply were applied on the fibers and plate. This operation was repeated twice in order to cover the optic fibers with up to 0.5 mm of opaque material. The rear surface of the plate was affixed to a cardboard base in which a square hole 70 mm · 70 mm had been cut. Two strips of aluminum foil were glued on the specimen to provide a basis for measurements. This aluminum foil was visible on infrared pictures, and thus afforded a geometric reference. 3.2. Infliction of local damage A calibrated air gun was used to impact the specimen with a given energy using a steel ball-bearing, 13 mm in diameter, shot at the plate through the hole in the cardboard base. For this purpose, the specimen
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Fig. 6. Test specimen.
was clamped along its shorter edges (Fig. 7). The ball impacted the composite plate with an incident speed of 40 m/s, inducing damage in the plate. The damaged area was not discernible from the impact side to the naked eye, but could be defined with the aid of ultrasonic scanning.
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Fig. 7. Set-up for inducing local damage.
3.3. Detection of damage with laser light A helium–neon laser with maximum power of 8 W was used to introduce light into the optic fibers. The power of the laser beam used in this experiment was in the range of 300–700 mW. The experiment was performed at the Fiber Optic Laboratory, Faculty of Electrical Engineering, Technion. Initially, infrared pictures were taken of the surface for which the optic fibers were located less than 0.5 mm beneath the surface. The laser light was introduced into the optic fiber at one end and an infrared photograph was taken. The light was then introduced from the other end of the fiber and a photograph was again taken. Dark spots indicating crack points were clearly observed (Fig. 8). The power of laser light used in this case was in the range of 300–400 mW. The difference of the temperatures between the crack point and the background was 10–16 C, sufficient to eliminate any temperature disturbances on the infrared pictures. The temperature disturbance introduced by reflection from the aluminum reference foil (Fig. 8) could be eliminated by artificially increasing the minimum temperature seen by the camera (Fig. 9). All the heat spots engendered are presented simultaneously in Fig. 10. It can be seen on this figure that in two cases optical fibers were broken at the edge of the plate, in places where fibers were handled as they were embedded in the plate. All other points appear in the region inside the plate where damage apparently occurred. In this way, the damaged area was defined and bounded. After the successful detection of the fiber crack location at 0.5 mm below the plate surface, attempts were made to find cracks which were located further below the surface. Infrared photos were taken of the opposite surface of the plate, where the optic fibers were 2.16 mm deep. Fig. 11 shows that in this case the cracks in the optic fiber were discerned equally as well. Again, all pictures of hot spots from this surface can be simultaneously used to define the extent of the damage area (Fig. 12). In Fig. 13 pictures of a hot spot due to crack in an optic fiber exposed to different laser light powers are shown. The laser light power was in the range of 300–700 mW. As expected, improved results were obtained with higher laser light power.
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Fig. 8. Hot spot photographs obtained by infrared camera for broken fibers in a number of hot spots. fiber depth: 0.5 mm laser beam power range used: 300–400 mW. Temperature rise at crack tip: 10–16 C.
3.4. Detection of damage by ultrasound scanning For evaluation and verification of the results yielded by the proposed method a comparison with the results obtained by ultrasound scanning of the plate was performed. The results of the ultrasound scan were compared in Fig. 14 with results of the infrared method depicted in Fig. 10. Except for the two points where fibers were broken at the edge of the plate all other hot spots undoubtedly point to the damage region. It is clear from this figure that the proposed method can define and enclose the damage region satisfactorily.
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Fig. 9. Disturbance elimination by artificially raising u0.
Fig. 10. Damaged area demarcated in heat spots (front surface).
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Fig. 11. Infrared photographs taken from of the rear surface of the plate. Fiber depth: 2.16 mm
Fig. 12. Damaged area demarcated by heat spots (rear surface). Fiber depth: 2.16 mm
4. Conclusions and recommendations for future studies A new approach to damage detection in composites has been demonstrated. The approach is based on the phenomenon that light energy transmitted through fiber-optics is converted into heat energy at the location of broken fibers leading to a local increase in temperature, indicating the presence of a crack in the composite plate. Complementary analytical and numerical tools for evaluating the temperature rise in the neighborhood of broken fibers were developed and presented. Results of the analyses performed with these tools indicated that the temperature generated at the breaks in the fibers can be sufficient to permit satisfactory detection in tests. Tests with impact-damaged graphite–epoxy plates showed that the heat energy emitted by broken fibers was adequate to change the local temperature so that it could quite easily be detected by an infrared camera. Comparison of the damage signatures obtained by the new approach compared favorably with signatures obtained by ultrasonic methods.
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Fig. 13. Heat spot temperature for varying laser power. u0 20 C
The effects of various laser powers transmitted through the fiber on the damage signatures were studied. As anticipated, the higher the laser power the more distinctive was the observed signature. The influence of fiber-optic depth below the monitored composite surface, and of heat conductivity, on results were also been examined theoretically and/or experimentally. One of the advantages of the proposed method is that it can make use of optic fibers which have already been embedded into a structure for other purposes, such as strain, temperature and frequency measurements. The proposed method can be used in existing structures. In some cases, fibers can be glued to the rear surface of pressure vessels. In this case not only will they find damage easily, but when damaged can also be conveniently replaced. A provisional application for Patent has been filed.
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Fig. 14. Agreement between results obtained by infrared photography and by ultrasound scanning.
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