- Email: [email protected]
Evaluation of energy of fatigue damage into GFRC through digital image correlation and thermography
Composites: Part B 47 (2013) 283–289
Contents lists available at SciVerse ScienceDirect
Composites: Part B journal homepage: www.elsevier.com/locate/compositesb
Evaluation of energy of fatigue damage into GFRC through digital image correlation and thermography V. Dattoma, S. Giancane ⇑ Dipartimento di Ingegneria dell’Innovazione, University of Salento, via per Monteroni, 73047 Lecce (LE), Italy
a r t i c l e
i n f o
Article history: Received 30 July 2012 Received in revised form 26 September 2012 Accepted 12 October 2012 Available online 22 November 2012 Keywords: A. Glass fibres B. Fatigue D. Thermal analysis
a b s t r a c t Two different full-field techniques are here used to investigate the heat sources and dissipation sources that compare onto the surface of a composite laminate under fatigue load. The material here studied is a glass fibre reinforced epoxy laminate employed in the field of wind turbine. During fatigue tests, 8-bit (256 grey levels) images and thermal images were acquired and elaborated to relate the hysteresis area and the heat sources, finding the energy of damage in three points of specimens. The data shows a clear intensification of dissipative phenomena just in that region where final failure is then registered. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction The properties of composite materials and their versatility made them attractive to many engineering fields and are gradually replacing their metallic counterparts in various applications. The designer is able to optimise the strength and resistance of a part in a one or more defined directions or regions saving weight and ensuring the requested efficiency; moreover, technology allows the production of even more complex structures in composite with competitive costs and machine times. But these innovative materials present numerous interfaces [1] and the study of deterioration phenomena is quite complex and often it is impossible to elaborate a numerical or analytical model to correctly evaluate the state of deterioration or damage. The necessity to deeply investigate composites rises and often more conventional methods and approaches (extensometry, S–N curves [2,3], FEA, etc.) are not enough to detect defects or to make a prevision of life. In last decades full field techniques are adopted to investigate the presence of flaws, cracks, delaminations into laminates; ultrasound technique, X-ray investigation and thermography are the most used, but other optical techniques are adopted not only in research field but else in industry encouraged by the growing capability of computers and the continuous improvement of electrical devices. Particularly interesting results come from the digital image correlation (DIC) currently used as a powerful and flexible tool for the evaluation of the surface deformation in the field of experimental solid mechanics. The principle is based on the comparison ⇑ Corresponding author. Tel.: +39 832 297786; fax: +39 832 297768. E-mail address: [email protected] (S. Giancane). 1359-8368/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compositesb.2012.10.030
and pattern recognition of digital images of the specimen surface in the undeformed and deformed states respectively, providing a full-field displacement and strain measurements. In this work, digital image correlation (DIC) was used to evaluate the strain field of composite specimens and to calculate an important parameter related to fatigue damage: hysteresis area on a force–strain diagram [4–8]. It represents the amount of energy provided by test machine to the specimen. A part of it is dissipated in heat and the remaining part can be considered as ‘‘stored’’ into the material and contributes to the damage progress according with irreversible thermodynamic processes [9–13] as formulated in one of the next section. The final aim of the paper is to present a methodology for evaluation of various energy contributions and in particular of the damage energy to be used for an identification of the possible critical zones. For this purpose three notched specimens were tested and during every test, temperature maps and strain measurements were collected and opportunely elaborated to obtain the terms of the energy balance. 2. Materials and methods The material here studied is a E-glass/epoxy composite manufactured by vacuum bag moulding technique obtaining a plate (uniform thickness of 4 mm) with a ply sequence of four quadriaxial fabric layers: [0/+45/90/45] 4 (see Table 1 for properties of materials). Notched specimens (Fig. 1) were obtained from a single plate by means of a milling machine; they were provided with opportune tabs according to standard ASTM D3039 [14] allowing an efficient
284
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Table 1 Mechanical properties of E-glass fibres and epoxy resin. E-glass fibres Average value of diameter (lm) Young’s modulus (MPa) Ultimate tensile strength (MPa) Strain to failure (%)
Table 2 Scheme of performed tests.
14 72,500 GPa 2150 MPa 3.75
Epoxy resin EC 15 + Hardening additive W152 MLR (weight ratio 100:30) (ELANTAS) Density (g/ml) 1.08–1.12 Young’s modulus (MPa) 3100–3500 Ultimate tensile strength (MPa) 68–76 Strain to failure (%) 3.0–8.0
Test ID
Falt (kN)
Fmean (kN)
Cycle to failure
ES-A-3 ES-A-4 ES-A-5
4.63 4.35 4.04
5.66 5.31 4.93
6678 5111 9495
ES-A-1 Static test: Fult = 13.8 kN
load transmission during test and avoiding, at the same time, a damage of specimen caused by the grip system of test machine. 2.1. Experimental setup A preliminary static test and three fatigue tests were carried out with a MTS hydraulic machine with load cells of 10 kN (Table 2). Fatigue tests were performed imposing a sinusoidal load of 21 Hz with a load ratio of 0.1, acquiring the load cell data with a time interval of 0.001 s. During tests infra-red camera (for thermal analysis) and CCD (coupled charged device) camera (for image correlation) were positioned in front of the specimen (see Fig. 2). Thermal maps were acquired with a frame rate of 1 fps, while CCD camera was set to store 8-bit images at 10 fps. The choice of these values allowed a complete reconstruction of displacement (and strain) signal in spite of under-sampling conditions, as reported with an example in Fig. 3. The employed devices were triggered to synchronize the load signal and the acquisition processes. Temperature maps were acquired by means of a FLIR 7500M camera (NETD (noise equivalent thermal sensitivity) = 25 mK, image resolution of 320 256 pixel2, accuracy = ±1%).
Fig. 2. A scheme of parameters calculated through DIC (for the region in yellow square) and thermography (region in red square); the three points (cyan, red and green) where the damage were evaluated. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
2.2. Calibration and resolution of DIC Digital image correlation is based on pattern recognition and on the correspondence between the sub-images associated to the markers of a virtual grid superimposed onto the images [15]. Considering a number of images, the first is taken as reference and a virtual grid is superimposed on it; opportune algorithms [15] allow to find the position of the markers of the grid for every
Fig. 3. An example of sinusoidal displacement at 21 Hz and its relative acquisition at 10 Hz. The choice of those values of frequency allows to retrace one cycle with 10 acquisition points every 21 executed cycles.
image (in terms of pixel) and to calculate the field of superficial displacements at the time, which an image is referred to. The
Fig. 1. Geometry of the specimen.
V. Dattoma, S. Giancane / Composites: Part B 47 (2013) 283–289
images must present a significant contrast to make the process work, so the specimens were previously prepared painting them with white varnish spread on a black background (see Fig. 2). For all tests, images were stored with a spatial resolution of 0.145 mm/pixel by means of a DRS’s Lighting RDT/1 high speed CCD camera. Firstly an evaluation of accuracy of displacement and strain measurements was performed employing an image of a specimen rigidly shifted of 1 pixel in horizontal direction. Correlation of the original and shifted images gave the results exposed in Fig. 4. Strain values were calculated by means of Matlab routines opportunely elaborated at this aim, using an algorithm based on the properties of the wavelet transforms [16]. The adopted procedure allows to calculate the derivative of a signal (in this case displacement data) obtaining an excellent signal-to-noise ratio at the same time. Displacements data is affected by a dispersion of about 0.005 pixel in both direction and we can assert that displacement measurements present an error less than 1 lm; the uncertainty in strain evaluation resulted to be about 160 le. 2.3. Static test A first static test was carried out on the specimen ES-A-1; five images per second were acquired and a speed of actuator of 1 mm/min was imposed. Averaging the values of ey on each row (considering the specimen as mono-dimensional and identifying it with its axis) it is possible to follow the evolution of strain until the final failure occurrence (see Fig. 5) at 13.8 kN. The first layer in
285
front of the camera is a 45° off axis layer and the strain calculated for the area close to the notches shows a strongly not linear behaviour.
3. Thermodynamic frame During a fatigue test a specimen exchanges energy according to a general balance that can be stated as follows [17–21]:
H ¼ ðEtc þ Q dissipated Þ þ Edamage
ð1Þ
where the terms in Eq. (1) are: H: mechanical hysteresis area (calculated from a re diagram) representing the amount of energy supplied by test machine to specimen cycle by cycle; it is calculated considering r = F/Section and obtaining the strain value at each single marker of the grid. The base hypothesis is that the strain measured on the surface directed to camera is valid through the thickness of specimen. Etc: energy associated with thermal capacity and calculated as qcoT/ot (where q is the density (1693 kg/m3), c thermal capacity (1547 J/kg K) and T superficial measured temperature). The time interval for calculation is 1 s (the thermal maps were stored at a rate of 1 fps) and the values of T were obtained averaging the temperatures pertaining to 2 2 mm2 regions (in this paper regions around the points in Fig. 2 were considered). Qdissipated: heat dissipated by convection according to the formula [13,20,21]:
Fig. 4. Image of a notched specimen with a virtual superimposed grid (a); results of displacement (b) and strain (c) calculation between two images shifted of 1 pixel in x-direction.
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V. Dattoma, S. Giancane / Composites: Part B 47 (2013) 283–289
Fig. 5. Static test on ES-A-1 specimen; ey are averaged on every row image per image.
Fig. 6. 2D maps of temperature accumulated heat and dissipated heat for ES-A-3 specimen.
V. Dattoma, S. Giancane / Composites: Part B 47 (2013) 283–289
287
Fig. 7. 2D maps of hysteresis area for ES-A-3 specimen.
Fig. 8. Energy balance and damage energy for the three points of notched section of specimen ES-A-3.
h iA surf Q dissipated ¼ hðT s T a Þ þ ebðT 4s T 4a Þ V
ð2Þ
where Ts is the punctual temperature of the surface of the specimen (K), Ta is the air temperature (293 K), the emissivity e = 0.85, the Stefan–Boltzmann constant b = 5.67 108 W/m2 K4, the coefficient h defined for a flat plate as [19]:
h ¼ 1:42
0:25 Ts Ta L
ð3Þ
and Asurf, V and L respectively are the area, length and volume of the portion of specimen considered for calculation. Edamage: energy absorbed for nucleation of defects, their propagation and general evolution of fatigue damage. In more general terms, Eq. (1) can be intended as composed by a term representing the energy dissipated (due to the dissipated and accumulated heat) a term of energy stored into the composite material that includes all the contributions for the initiation and propagation of material degradation phenomena (matrix cracking, debonding, fibre breakage and delaminations).
4. Experimental results Considering as significant example test ES-A-3, temperature and heat maps are reported in Figs. 6 and 7. Observing the temperature maps, it is evident how the left side of specimen close to notch presents a higher temperature since the very first part of test. Accumulated and dissipated heat also show higher values on the left notch, moreover during the last cycles, Qacc exhibits a 45° tilted line where heat significantly accumulates. A possible interpretation of this phenomenon is due to the presence of 45° and +45° plies as external layers in front of the cameras; the damage starts from the fibre interfaces and then propagates on that direction. At the moment we are not able to settle a univocal correspondence between DIC and temperature maps and only some points, univocally identified, can be considered to calculate the damage energy according to Eq. (1) (the points reported in Fig. 2). Three sets of curves (one for each point) can be traced to evaluate how damage energy and heat sources evolve during fatigue life of specimen in notched section (see Fig. 8).
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Fig. 9. Energy balance and damage energy for the three points of notched section of specimen ES-A-4.
Fig. 10. Energy balance and damage energy for the three points of notched section of specimen ES-A-5.
The central point shows a lower damage energy while the right one and in particular the left one are interested by a constant increasing of damage energy and in the final part of life (at about at 90% of life) damage energy has a strong rise as a mark of catastrophic damage process happening. The measures here reported demonstrate that the proposed approach can effectively identify the heterogeneities where damage evolves and the energy of damage can be considered as an important index to monitor the status of material. With regard to test ESA-4 and ESA-5, the curves traced for the three points highlight that the energy of damage is higher where
final rupture takes place. Watching the energetic exchanges and their temporal evolution, also in these cases the central points result less interested by dissipative phenomena respect to right and left ones, confirming the conclusions made before. One last consideration has to be done on the value of frequency of load: 21 Hz. This value is quite high for a composite material and this avoid or reduce thermal dispersion making negligible or less significant the dissipation terms if compared with hysteresis energies and accumulated heat allowing to highlight the damage energy released during lifetime. This appears as clear in the diagrams in Figs. 8–10.
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5. Conclusions Fatigue damage on GFRC was evaluated staring from a theoretical frame of energy balance during a typical fatigue test. The amount of external energy that test machine passes on the specimen is transformed into heat (accumulated into the bulk material and dissipated through the exposed surfaces) and into energy of damage. This last parameter was considered crucial for the identification of regions or points where damage is more relevant. Two different and complementary techniques were used to estimate the terms of the energy balance: thermography and digital image correlation. The adopted specimens present two severe symmetrical notches that confine the fatigue degradation allowing damage energy evaluations on three points for each specimen during all lifetime. The results highlight how the proposed procedure can correctly evaluate the damage accumulation allowing an identification of critical points before the definitive rupture of the specimen. References [1] Reifsnider KL. Damage and damage mechanics. In: Reifsnider KL, editor. Fatigue of composite materials; 1990. p. 1–77. [2] Sutherland Herbert J, Mandell John F. Updated Goodman diagrams for fiberglass composite materials using the DOE/MSU fatigue database. Albuquerque (NM): Sandia National Laboratories; 1998. [3] Mu Peng Gang, Wan Xiao Peng, Zhao Mei Yang. A new S–N curve model of fiber reinforced plastic composite. Key Eng Mater 2011;462,463:484–8. [4] Dharan CKH, Tan TF. A hysteresis-based damage parameter for notched composite laminates subjected to cycle loading. J Mater Sci 2007;42:2204–7. [5] Giancane S, Panella FW, Dattoma V. Characterization of fatigue damage in long fiber epoxy composite laminates. Int J Fatigue 2010;32:46–53. [6] Giancane S, Panella FW, Nobile R, Dattoma V. Fatigue damage evolution of fiber reinforced composites with digital image correlation analysis. Procedia Eng 2 – Sci Direct 2010:1307–15.
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[7] Giancane S, Panella FW, Nobile R, Dattoma V. Damage evolution of composite laminates with digital image correlation. Key Eng Mater 2011;452,453:377–80. [8] Iannucci L, Ankersen J. An energy based damage model for thin laminated composites. Compos Sci Technol 2006;66:934–51. [9] Naderi M, Khonsari MM. Thermodynamic analysis of fatigue failure in a composite laminate. Mech Mater 2012;46:113–22. [10] Naderi M, Kahirdeh A, Khonsari MM. Dissipated thermal energy and damage evolution of glass/epoxy using infrared thermography and acoustic emission. J Compos Part B 2012;43:1613–20. [11] Meneghetti G, Quaresimin M. Fatigue strength assessment of a short fiber composite based on the specific heat dissipation. J Compos Part B 2011;42:217–25. [12] Giancane S, Chrysochoos A, Dattoma V, Wattrisse B. Deformation and dissipated energies for high cycle fatigue of 2024-T3 aluminium alloy. Theor Appl Fract Mech 2009;52:117–21. [13] Redon O. Fatigue damage development and failure in unidirectional and angleply glass fibre/carbon fibre hybrid laminates, Thesis. Risø National Laboratory, Roskilde, Denmark, January; 2000. [14] ASTM – standard test method for tensile properties of polymer matrix composite materials – designation: D 3039/D 3039M-00;2000 (Reapproved 2006). [15] Deuflhard P. Newton methods for nonlinear problems. Affine invariance and adaptive algorithms. Springer series in computational mathematics, vol. 35. Berlin: Springer; 2004. [16] Luo Jianwen, Bai Jing, Shao Jinhua. Application of the wavelet transforms on axial calculation in ultrasound elastography. Progr Nat Sci 2009;16(9):942–7. [17] Giancane S, Panella FW, Dattoma V. Fatigue damage in notched GFR composites with thermal and digital image measurements. In: Proceedings of ECCM-15 conference, Venice (Italy), June 24–28. [18] Gamestedt EK, Redon O, Brøndsted P. Fatigue dissipation and failure in unidirectional and angle-ply glass fibre/carbon fibre hybrid laminates. Key Eng Mater 2002;221:35–48. [19] Holman JP. Heat transfer. 7th ed. McGraw-Hill; 1992. p. 354. [20] Naderi M, Khonsari MM. On the role of damage energy in the fatigue degradation characterization of a composite laminate. J Compos Part B 2012;45(1):528–37. [21] Song Bo, Chen Weinong, Yanagita Tamaki, Frew Danny J. Temperature effects on dynamic compressive behavior of an epoxy syntactic foam. Compos Struct 2005;67:289–98.
Contents lists available at SciVerse ScienceDirect
Composites: Part B journal homepage: www.elsevier.com/locate/compositesb
Evaluation of energy of fatigue damage into GFRC through digital image correlation and thermography V. Dattoma, S. Giancane ⇑ Dipartimento di Ingegneria dell’Innovazione, University of Salento, via per Monteroni, 73047 Lecce (LE), Italy
a r t i c l e
i n f o
Article history: Received 30 July 2012 Received in revised form 26 September 2012 Accepted 12 October 2012 Available online 22 November 2012 Keywords: A. Glass fibres B. Fatigue D. Thermal analysis
a b s t r a c t Two different full-field techniques are here used to investigate the heat sources and dissipation sources that compare onto the surface of a composite laminate under fatigue load. The material here studied is a glass fibre reinforced epoxy laminate employed in the field of wind turbine. During fatigue tests, 8-bit (256 grey levels) images and thermal images were acquired and elaborated to relate the hysteresis area and the heat sources, finding the energy of damage in three points of specimens. The data shows a clear intensification of dissipative phenomena just in that region where final failure is then registered. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction The properties of composite materials and their versatility made them attractive to many engineering fields and are gradually replacing their metallic counterparts in various applications. The designer is able to optimise the strength and resistance of a part in a one or more defined directions or regions saving weight and ensuring the requested efficiency; moreover, technology allows the production of even more complex structures in composite with competitive costs and machine times. But these innovative materials present numerous interfaces [1] and the study of deterioration phenomena is quite complex and often it is impossible to elaborate a numerical or analytical model to correctly evaluate the state of deterioration or damage. The necessity to deeply investigate composites rises and often more conventional methods and approaches (extensometry, S–N curves [2,3], FEA, etc.) are not enough to detect defects or to make a prevision of life. In last decades full field techniques are adopted to investigate the presence of flaws, cracks, delaminations into laminates; ultrasound technique, X-ray investigation and thermography are the most used, but other optical techniques are adopted not only in research field but else in industry encouraged by the growing capability of computers and the continuous improvement of electrical devices. Particularly interesting results come from the digital image correlation (DIC) currently used as a powerful and flexible tool for the evaluation of the surface deformation in the field of experimental solid mechanics. The principle is based on the comparison ⇑ Corresponding author. Tel.: +39 832 297786; fax: +39 832 297768. E-mail address: [email protected] (S. Giancane). 1359-8368/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compositesb.2012.10.030
and pattern recognition of digital images of the specimen surface in the undeformed and deformed states respectively, providing a full-field displacement and strain measurements. In this work, digital image correlation (DIC) was used to evaluate the strain field of composite specimens and to calculate an important parameter related to fatigue damage: hysteresis area on a force–strain diagram [4–8]. It represents the amount of energy provided by test machine to the specimen. A part of it is dissipated in heat and the remaining part can be considered as ‘‘stored’’ into the material and contributes to the damage progress according with irreversible thermodynamic processes [9–13] as formulated in one of the next section. The final aim of the paper is to present a methodology for evaluation of various energy contributions and in particular of the damage energy to be used for an identification of the possible critical zones. For this purpose three notched specimens were tested and during every test, temperature maps and strain measurements were collected and opportunely elaborated to obtain the terms of the energy balance. 2. Materials and methods The material here studied is a E-glass/epoxy composite manufactured by vacuum bag moulding technique obtaining a plate (uniform thickness of 4 mm) with a ply sequence of four quadriaxial fabric layers: [0/+45/90/45] 4 (see Table 1 for properties of materials). Notched specimens (Fig. 1) were obtained from a single plate by means of a milling machine; they were provided with opportune tabs according to standard ASTM D3039 [14] allowing an efficient
284
V. Dattoma, S. Giancane / Composites: Part B 47 (2013) 283–289
Table 1 Mechanical properties of E-glass fibres and epoxy resin. E-glass fibres Average value of diameter (lm) Young’s modulus (MPa) Ultimate tensile strength (MPa) Strain to failure (%)
Table 2 Scheme of performed tests.
14 72,500 GPa 2150 MPa 3.75
Epoxy resin EC 15 + Hardening additive W152 MLR (weight ratio 100:30) (ELANTAS) Density (g/ml) 1.08–1.12 Young’s modulus (MPa) 3100–3500 Ultimate tensile strength (MPa) 68–76 Strain to failure (%) 3.0–8.0
Test ID
Falt (kN)
Fmean (kN)
Cycle to failure
ES-A-3 ES-A-4 ES-A-5
4.63 4.35 4.04
5.66 5.31 4.93
6678 5111 9495
ES-A-1 Static test: Fult = 13.8 kN
load transmission during test and avoiding, at the same time, a damage of specimen caused by the grip system of test machine. 2.1. Experimental setup A preliminary static test and three fatigue tests were carried out with a MTS hydraulic machine with load cells of 10 kN (Table 2). Fatigue tests were performed imposing a sinusoidal load of 21 Hz with a load ratio of 0.1, acquiring the load cell data with a time interval of 0.001 s. During tests infra-red camera (for thermal analysis) and CCD (coupled charged device) camera (for image correlation) were positioned in front of the specimen (see Fig. 2). Thermal maps were acquired with a frame rate of 1 fps, while CCD camera was set to store 8-bit images at 10 fps. The choice of these values allowed a complete reconstruction of displacement (and strain) signal in spite of under-sampling conditions, as reported with an example in Fig. 3. The employed devices were triggered to synchronize the load signal and the acquisition processes. Temperature maps were acquired by means of a FLIR 7500M camera (NETD (noise equivalent thermal sensitivity) = 25 mK, image resolution of 320 256 pixel2, accuracy = ±1%).
Fig. 2. A scheme of parameters calculated through DIC (for the region in yellow square) and thermography (region in red square); the three points (cyan, red and green) where the damage were evaluated. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
2.2. Calibration and resolution of DIC Digital image correlation is based on pattern recognition and on the correspondence between the sub-images associated to the markers of a virtual grid superimposed onto the images [15]. Considering a number of images, the first is taken as reference and a virtual grid is superimposed on it; opportune algorithms [15] allow to find the position of the markers of the grid for every
Fig. 3. An example of sinusoidal displacement at 21 Hz and its relative acquisition at 10 Hz. The choice of those values of frequency allows to retrace one cycle with 10 acquisition points every 21 executed cycles.
image (in terms of pixel) and to calculate the field of superficial displacements at the time, which an image is referred to. The
Fig. 1. Geometry of the specimen.
V. Dattoma, S. Giancane / Composites: Part B 47 (2013) 283–289
images must present a significant contrast to make the process work, so the specimens were previously prepared painting them with white varnish spread on a black background (see Fig. 2). For all tests, images were stored with a spatial resolution of 0.145 mm/pixel by means of a DRS’s Lighting RDT/1 high speed CCD camera. Firstly an evaluation of accuracy of displacement and strain measurements was performed employing an image of a specimen rigidly shifted of 1 pixel in horizontal direction. Correlation of the original and shifted images gave the results exposed in Fig. 4. Strain values were calculated by means of Matlab routines opportunely elaborated at this aim, using an algorithm based on the properties of the wavelet transforms [16]. The adopted procedure allows to calculate the derivative of a signal (in this case displacement data) obtaining an excellent signal-to-noise ratio at the same time. Displacements data is affected by a dispersion of about 0.005 pixel in both direction and we can assert that displacement measurements present an error less than 1 lm; the uncertainty in strain evaluation resulted to be about 160 le. 2.3. Static test A first static test was carried out on the specimen ES-A-1; five images per second were acquired and a speed of actuator of 1 mm/min was imposed. Averaging the values of ey on each row (considering the specimen as mono-dimensional and identifying it with its axis) it is possible to follow the evolution of strain until the final failure occurrence (see Fig. 5) at 13.8 kN. The first layer in
285
front of the camera is a 45° off axis layer and the strain calculated for the area close to the notches shows a strongly not linear behaviour.
3. Thermodynamic frame During a fatigue test a specimen exchanges energy according to a general balance that can be stated as follows [17–21]:
H ¼ ðEtc þ Q dissipated Þ þ Edamage
ð1Þ
where the terms in Eq. (1) are: H: mechanical hysteresis area (calculated from a re diagram) representing the amount of energy supplied by test machine to specimen cycle by cycle; it is calculated considering r = F/Section and obtaining the strain value at each single marker of the grid. The base hypothesis is that the strain measured on the surface directed to camera is valid through the thickness of specimen. Etc: energy associated with thermal capacity and calculated as qcoT/ot (where q is the density (1693 kg/m3), c thermal capacity (1547 J/kg K) and T superficial measured temperature). The time interval for calculation is 1 s (the thermal maps were stored at a rate of 1 fps) and the values of T were obtained averaging the temperatures pertaining to 2 2 mm2 regions (in this paper regions around the points in Fig. 2 were considered). Qdissipated: heat dissipated by convection according to the formula [13,20,21]:
Fig. 4. Image of a notched specimen with a virtual superimposed grid (a); results of displacement (b) and strain (c) calculation between two images shifted of 1 pixel in x-direction.
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V. Dattoma, S. Giancane / Composites: Part B 47 (2013) 283–289
Fig. 5. Static test on ES-A-1 specimen; ey are averaged on every row image per image.
Fig. 6. 2D maps of temperature accumulated heat and dissipated heat for ES-A-3 specimen.
V. Dattoma, S. Giancane / Composites: Part B 47 (2013) 283–289
287
Fig. 7. 2D maps of hysteresis area for ES-A-3 specimen.
Fig. 8. Energy balance and damage energy for the three points of notched section of specimen ES-A-3.
h iA surf Q dissipated ¼ hðT s T a Þ þ ebðT 4s T 4a Þ V
ð2Þ
where Ts is the punctual temperature of the surface of the specimen (K), Ta is the air temperature (293 K), the emissivity e = 0.85, the Stefan–Boltzmann constant b = 5.67 108 W/m2 K4, the coefficient h defined for a flat plate as [19]:
h ¼ 1:42
0:25 Ts Ta L
ð3Þ
and Asurf, V and L respectively are the area, length and volume of the portion of specimen considered for calculation. Edamage: energy absorbed for nucleation of defects, their propagation and general evolution of fatigue damage. In more general terms, Eq. (1) can be intended as composed by a term representing the energy dissipated (due to the dissipated and accumulated heat) a term of energy stored into the composite material that includes all the contributions for the initiation and propagation of material degradation phenomena (matrix cracking, debonding, fibre breakage and delaminations).
4. Experimental results Considering as significant example test ES-A-3, temperature and heat maps are reported in Figs. 6 and 7. Observing the temperature maps, it is evident how the left side of specimen close to notch presents a higher temperature since the very first part of test. Accumulated and dissipated heat also show higher values on the left notch, moreover during the last cycles, Qacc exhibits a 45° tilted line where heat significantly accumulates. A possible interpretation of this phenomenon is due to the presence of 45° and +45° plies as external layers in front of the cameras; the damage starts from the fibre interfaces and then propagates on that direction. At the moment we are not able to settle a univocal correspondence between DIC and temperature maps and only some points, univocally identified, can be considered to calculate the damage energy according to Eq. (1) (the points reported in Fig. 2). Three sets of curves (one for each point) can be traced to evaluate how damage energy and heat sources evolve during fatigue life of specimen in notched section (see Fig. 8).
288
V. Dattoma, S. Giancane / Composites: Part B 47 (2013) 283–289
Fig. 9. Energy balance and damage energy for the three points of notched section of specimen ES-A-4.
Fig. 10. Energy balance and damage energy for the three points of notched section of specimen ES-A-5.
The central point shows a lower damage energy while the right one and in particular the left one are interested by a constant increasing of damage energy and in the final part of life (at about at 90% of life) damage energy has a strong rise as a mark of catastrophic damage process happening. The measures here reported demonstrate that the proposed approach can effectively identify the heterogeneities where damage evolves and the energy of damage can be considered as an important index to monitor the status of material. With regard to test ESA-4 and ESA-5, the curves traced for the three points highlight that the energy of damage is higher where
final rupture takes place. Watching the energetic exchanges and their temporal evolution, also in these cases the central points result less interested by dissipative phenomena respect to right and left ones, confirming the conclusions made before. One last consideration has to be done on the value of frequency of load: 21 Hz. This value is quite high for a composite material and this avoid or reduce thermal dispersion making negligible or less significant the dissipation terms if compared with hysteresis energies and accumulated heat allowing to highlight the damage energy released during lifetime. This appears as clear in the diagrams in Figs. 8–10.
V. Dattoma, S. Giancane / Composites: Part B 47 (2013) 283–289
5. Conclusions Fatigue damage on GFRC was evaluated staring from a theoretical frame of energy balance during a typical fatigue test. The amount of external energy that test machine passes on the specimen is transformed into heat (accumulated into the bulk material and dissipated through the exposed surfaces) and into energy of damage. This last parameter was considered crucial for the identification of regions or points where damage is more relevant. Two different and complementary techniques were used to estimate the terms of the energy balance: thermography and digital image correlation. The adopted specimens present two severe symmetrical notches that confine the fatigue degradation allowing damage energy evaluations on three points for each specimen during all lifetime. The results highlight how the proposed procedure can correctly evaluate the damage accumulation allowing an identification of critical points before the definitive rupture of the specimen. References [1] Reifsnider KL. Damage and damage mechanics. In: Reifsnider KL, editor. Fatigue of composite materials; 1990. p. 1–77. [2] Sutherland Herbert J, Mandell John F. Updated Goodman diagrams for fiberglass composite materials using the DOE/MSU fatigue database. Albuquerque (NM): Sandia National Laboratories; 1998. [3] Mu Peng Gang, Wan Xiao Peng, Zhao Mei Yang. A new S–N curve model of fiber reinforced plastic composite. Key Eng Mater 2011;462,463:484–8. [4] Dharan CKH, Tan TF. A hysteresis-based damage parameter for notched composite laminates subjected to cycle loading. J Mater Sci 2007;42:2204–7. [5] Giancane S, Panella FW, Dattoma V. Characterization of fatigue damage in long fiber epoxy composite laminates. Int J Fatigue 2010;32:46–53. [6] Giancane S, Panella FW, Nobile R, Dattoma V. Fatigue damage evolution of fiber reinforced composites with digital image correlation analysis. Procedia Eng 2 – Sci Direct 2010:1307–15.
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