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Determination of J–R curves of thermoplastic starch composites containing crossed quasi-unidirectional flax fiber reinforcement
COMPOSITES SCIENCE AND TECHNOLOGY Composites Science and Technology 66 (2006) 3179–3187 www.elsevier.com/locate/compscitech
Determination of J–R curves of thermoplastic starch composites containing crossed quasi-unidirectional flax fiber reinforcement G. Romha´ny a, T. Cziga´ny a
a,*
, J. Karger-Kocsis
b
Department of Polymer Engineering, Faculty of Mechanical Engineering, Budapest University of Technology and Economics, M}uegyetem rkp. 3., H-1111 Budapest, Hungary b Institut fu¨r Verbundwerkstoffe GmbH (Institute for Composite Materials), Kaiserslautern University of Technology, D-67663 Kaiserslautern, Germany Received 23 September 2004; received in revised form 27 January 2005; accepted 28 January 2005 Available online 24 August 2005
Abstract Thermoplastic starch (MaterBi) composites reinforced with quasi-unidirectional flax fiber in cross-ply (CP) arrangement were produced by film stacking followed by hot pressing. These composites, containing various amount of flax, failed ductilely with pronounced crack growth. Therefore, to determine their fracture mechanical behaviour the J-integral resistance curve concept (J–R) was applied. As the crack growth could not be traced, attempt was made to use the located acoustic emission (AE) events for that purpose. It was established that weighting and smoothing the located cumulative AE amplitudes the crack path can be correctly reconstructed. This was proved by collating the AE results with those derived from infrared thermographic (IT) inspection. Knowing the crack propagation at each point of the force–displacement curves the J–R curves could be determined. Both critical or initiation J-integral and tearing modulus went through a minimum with increase of flax content in the composites. 2005 Elsevier Ltd. All rights reserved. Keywords: Composite; Flax reinforcement; J–R curve; Acoustic emission; Infrared thermography
1. Introduction The application of the linear elastic fracture mechanics is strongly limited for many polymers and composites as their failure occurs via crack propagation. For such systems elastic–plastic (e.g., J-integral) and post-yield fracture mechanics (e.g., essential work of fracture) are used [1–5]. In thermoplastic composites reinforced by textile fabrics (mat, woven, knitted, etc.) the fracture behaviour is even more complicated as therein a large damage zone develops which may even change its shape during crack growth ([6,7] and references therein). In order to characterize the fracture mechanical behaviour of such systems adequately, it is necessary to determine the corresponding resistance curves. Note, that resistance *
Corresponding author. Tel.: +361 463 2003; fax: +361 463 1527. E-mail address: [email protected] (T. Cziga´ny).
0266-3538/$ - see front matter 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.compscitech.2005.01.016
curves reflect the change in a given fracture mechanical parameter as a function of the crack growth (Da). Accordingly, the crack tip and crack growth should be traceable during loading of the specimens, e.g. [8]. However, this is exactly the problem with many composites containing textile reinforcements. The crack growth in the related specimens can hardly be resolved using the usual techniques (visual inspection). Compliance calibration techniques for Da are also less suited as each specimen is unique in respect with the local reinforcing structure. In the past some attempts were made to trace the crack growth during loading of suitable specimens via location of the acoustic emission (AE) and monitoring the heat development using the technique of infrared thermography (IT) [7,9–12]. To construct the resistance curves, however, the apparent fracture toughness (KQ) was used (K–R) [10–12], which is far less suited than that of the J-integral (J–R curves).
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Accordingly, this work was aimed at determining the J-integral resistance curves (J–R) in thermoplastic starch based composites reinforced with aligned flax fiber in crossed lay-up. The reason for our material selection is the effort induced by the strict environmental protection regulation to use biodegradable polymer composites [13]. In order to be able to determine crack propagation, the AE localization method was adopted as an experimental technique. For verification of the results derived from the experiments via mathematical treatise, the IT technique was used.
2. Experimental 2.1. Materials Flax fiber of spinnable quality (average fiber diameter: 68 lm) (Hungaro-Len Ltd., Koma´rom, Hungary) and a thermoplastic starch in the form of film (80 lm; MaterBi LF01U, Novamont, Novara, Italy) were used to produce the composites. The main characteristics of the starch film and flax fiber were published earlier [13]. Composite sheets were prepared by the method of film stacking. Accordingly, the thermoplastic starch film and a layer of flax fibers were placed on one another alternately. The flax fibers were arranged in crossedply (CP) manner. Note that laminates of CP architecture are traditionally used in the composite field in order to assess their mechanical properties. Quasi-unidirectional (UD) lay-up of flax fiber was achieved by combing and fixing their end sections with adhesive tapes, cf. Fig. 1. The flax fiber and the thermoplastic starch film were previously dried at 60 C for 2 h. Pressing was carried out at a pressure of 3 MPa, at 140 C (considering the melting of thermoplastic starch) in a matched tool. The thickness of the sheets prepared by this way ca. 1 mm. The flax content of the composites was 20, 40 and 60 wt%.
Fig. 1. Lay-up of the flax (quasi-unidirectional aligned) and MaterBi layers for hot pressing of CP composites.
2.2. Tests Static mechanical tests were performed on single edge-notched tensile loaded (SEN-T) specimens. Their dimension allowed the location of the AE via a four sensors array (cf. Fig. 2). Tensile loading of the SEN-T specimens occurred at room temperature at a deformation rate of 1 mm/min on a Zwick 1474 machine. The force vs displacement curves were recorded during the tests. The initially sawed notch (a0) was sharpened by razor blade tapping. The AE activity was recorded in situ by a Defektophone NEZ 220 device (AEKI, Budapest, Hungary). A four sensor quadratic array, as shown in Fig. 2, served to locate the AE events using wide bandwidth (100–600 kHz) microsensors (10 mm diameter,
Fig. 2. Experimental set-up including the dimension of the SEN-T specimen, positioning the AE sensors and view field of the infrared camera.
Micro 30D of Physical Acoustic Co., Princeton, USA). Location occurred by a built-in algorithm of the device in the knowledge of the acoustic wave speed. The latter was determined by the method depicted in Fig. 3. The mean wave speed increased with the flax content. At 20, 40 and 60 wt% flax reinforcement the mean speed was 1700, 2500 and 3100 m/s, respectively. The temperature rise during loading of the SEN-T specimens was detected, also in situ, by an IT camera (Compact Thermo TVS 200, Goratec Technology,
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3. Results and discussions 3.1. Determination of the crack path
Fig. 3. Determination of the mean speed of the acoustic wave in the composites using pencil lead breaking as AE source.
Erding, Germany). IT frames were taken at selected points of the force displacement curves and stored. The related files served for digital processing in order to show the relative heat development in given loading intervals.
As the Defektophone device locates the AE events in best case in 1 mm resolution many hits may be hidden in one single point (x, y-coordinates – cf. Fig. 4) when using a two-dimensional (2D) representation. This problem was early recognized and various weighted mapping were introduced. This covered the number of events [6,7,12], and their energy-related terms [9,10]. In the present case, the following bell-type weighting function was applied for the located field (the latter is seen in Figs. 2 and 4): R sðz; wÞ f ðwÞ dA f ðzÞ ¼ A R ; ð1Þ sðz; wÞ dA A where z = x Æ i + y Æ j, w = u Æ i + v Æ j – represents radius vectors of the located field, f(w) is the cumulative value
Fig. 4. Location of the AE events up to final fracture in a SEN-T specimen cut of the composite sheet containing 60 wt% CP flax.
Fig. 5. Weighted cumulative AE amplitude distribution of a thermoplastic starch composite containing 60 wt% flax fiber in CP arrangement in 2D (a) and 3D (b) contour plots.
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Fig. 6. Weighted cumulative AE amplitude distribution of a thermoplastic starch composite containing 60 wt% flax in CP arrangement in 2D (a) and 3D (b) plots by considering 90% of the located events.
s(z, w) is the weighting function 8 2 2 > < jzwj ; if 0 6 jz wj 6 R; 1 R sðz; wÞ ¼ > : 0; if jz wj > R; ð2Þ
Fig. 7. Sectioning of the cumulative AE amplitude (CA) vs. displacement curve of a thermoplastic starch composite containing 60 wt% flax in CP arrangement to get the same DCA in each section. Note. This figure also contains the correspondent force–displacement curve.
of the parameter of a located AE signal in the point of w coordinate and f(z) is the cumulative value of the parameter of a located AE signal in the point of z coordinate after smoothing
where R is the radius of the weighting function and A is the located area. Considering the fact that the distance between the located points along the expected crack growth in Fig. 4 is 2 mm, R = 3 mm was selected. By this way, a correct smoothing can be achieved. Major argument to choose a bell-type function is that the points closer to the resulting one should be ‘‘overweighted’’. This is due to characteristics of the damage zone and the failure events therein. Note that the AE events related with fiber fracture and fiber pull-out yield events with considerable higher amplitude and energy than those associated with fiber/matrix debonding [14]. Although the function given in Eqs. (1) and (2) can be used for any cumulative AE parameters, in this work the cumulative AE amplitude was selected.
Fig. 8. Change in the weight center points of the damage zone during loading of a SEN-T specimen cut of the composite containing 20 wt% flax fibers in CP arrangement. Note. When DCA is too low (cf. picture a) then no monotonic crack growth occurs.
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Fig. 9. Change in the weight center points of the damage zone during loading of a SEN-T specimen cut of the composite containing 60 wt% flax fibers in CP arrangement. Note. When CA is too high (cf. picture a) then the crack growth is less resolved (only few points are available to ‘‘reconstruct’’ the crack path).
Fig. 10. Calculated crack growth in a SEN-T specimen of thermoplastic starch containing 60 wt% quasi-unidirectional flax fiber in cross-ply arrangement showing also the taking positions of the IT frames.
Fig. 5 compares the 2D and 3D plots on example of a SEN-T specimen containing 60 wt% flax fibers in CP arrangement. One can clearly recognize that the cumulative AE amplitude steeply decreases by leaving the notch-driven, expected crack path. The scenario becomes even clearer when only 90% of the located events is taken into consideration – cf. Fig. 6. The 2D and 3D representations in Fig. 6 prove that the weighting procedure used can trace the damage zone and its change during loading correctly. In order to construct a resistance curve the actual position of the crack tip as a function of loading should be known. In order to trace the crack growth the following procedure was followed. The cumulative amplitude (CA) vs displacement curve was sectioned in equidistance steps, as indicated in Fig. 7. For each section first the smoothed CA distribution has been determined as described above (cf. Eqs. (1) and (2)). After that the weight center points of the corresponding CA distributions were computed. The latter have been assigned to the actual position of the running
Fig. 11. Determination of the crack path using located AE events.
crack tip. By repeating the above tasks the weight center point of the damage zone and its change i.e., the crack path, can well be reconstructed. However, caution is requested when selecting the DCA sections (cf. Fig. 7). If too small DCA intervals are chosen, the geometrical places of weight center points do not increase monotonously, hence the crack seems to move backward in some places.
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The upper limit of DCA is obviously given by the cumulative AE amplitude related to final fracture. As the crack propagates steadily during loading of the SEN-T specimens the optimum CA has to be chosen iteratively considering that the weight center of the damage zone should propagate monotonously. So, some deviations in the crack growth can be recognized when using not proper DCA intervals (cf. Figs. 8 and 9). Note that the crack position before final fracture is never correct. In both Figs. 8 and 9 some of the ending points (marked by A) suggest an apparent crack closure. This is due to side (edge) effects. Near to the specimen edge (70 mm not all events are captured by the sensors), so their location is impossible. In addition, the weight center point can never reach the edge of the SEN-T specimen. As a consequence, the points marked by ‘‘A’’ in Figs. 8 and 9 were neglected. For the remaining weight center points of the damage zone (representing the crack growth) a Weibull-type function (four parameters sigmoid type) was fitted C
fB ðxÞ ¼ A ðA a0 Þ eðBxÞ ;
ð3Þ
where a0, A, B, C are parameters, a0 equals with the initial notch length (cf. Fig. 2). During parameter fitting the least square method has been adopted. Thus, the ‘‘actual’’ crack length corresponding to a given load of the SEN-T specimen can be determined by this curve fitting (cf. Fig. 10). The steps performed to deduce the crack propagation curve along the ligament are summarized in a block diagram in Fig. 11. 3.2. Validation of the crack propagation via IT Fig. 10 indicates also the taking position of the IT frames on the force–displacement curve of the composite containing 60 wt% CP flax. Based on the fact that the background was set cooler than the specimen, the notch and edges of the specimens are well resolved in the IT frames (cf. Fig. 12). This allows us to locate the x, y coordinates in the IT field (note, that the overall width of IT view filed corresponds to 256 pixels). Frame 3 in Fig. 12 was taken 11 s later than frame 2. So, the former one contains some superposition in the thermal field. However, by subtracting frame 2
Fig. 12. Comparison of the damage zone derived from IT and AE measurements respectively on a SEN-T specimen of the starch composite containing 60 wt% flax in CP arrangement.
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Fig. 14. Determination of Up and Ue schematically.
3.3. Determination of the J–R curves The force–displacement curves presented (cf. Figs. 7– 10 and 13) already indicated that the thermoplastic starch composites studied failed always ductility with pronounced crack growth. Therefore it is appropriate to determine the J–R curves. For the purpose the Paris-Rice approach was followed: J ¼ J e þ J p; ge U e Je ¼ ; B ðW aÞ gp U p Jp ¼ ; B ðW aÞ
Fig. 13. Position of the damage zone (i.e., actual crack length) derived from IT and AE measurements, respectively, for the composites containing 20, 40 and 60 wt% flax fiber in CP arrangement.
from frame 3 we can get the heat development that occurred in this time interval (i.e., 11 s). The weight centre point of the relative temperature distribution can be considered as the actual crack tip at 150 s of the specimen loading. Needless to say that this approach assumes adiabatic heating in the specimen. If we compare the 2D plots of the damage zones derived from IT and AE (by using the above approach considering the cumulative AE amplitude), respectively, a very good agreement can be found (cf. Fig. 12). Fig. 13 collates the positions of the damage zone derived from IT and AE techniques as a function of loading for the composites containing various amount of flax. One can recognize the good agreement between the related crack propagation data. So, via IT we succeeded to show that our AE results in respect of the crack propagation are reliable. As a consequence, the actual crack position is known and thus the J–R curves can be constructed.
ð4Þ ð5Þ ð6Þ
where Je and Jp are, respectively, the elastic and plastic components of the total J value, Ue and Up are, respectively, the elastic and plastic components of the external work, ge and gp are elastic and plastic work factors dependent upon the specimen geometry, W is the width of the SEN-T specimen, B is the thickness of the SEN-T specimen, a is the actual crack length (cf. Fig. 2). The elastic and plastic work factors for the SEN-T geometry were calculated using [15]
Fig. 15. J–R curves of the thermoplastic starch and its flax fiber reinforced CP arranged composites at various flax content. Note. the crack growth of the matrix was followed visually. The J–R curves indicate the onset of stable crack growth (s) and the points related to the maximum load (h), as well.
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Fig. 16. J0 (a) and DJ/Da (b) as a function of CP flax content.
ðW a0 Þ Y 2 ða0 Þ a0 ge ¼ R a0 2 ; Y ðaÞ a da þ ZW 0 2 ðW a0 Þ gp ¼ h i1 ; a0 W aða0 Þ W ½aðaW0 Þða þ 1 0 =W Þ
ð7Þ ð8Þ
where 2 1=2
a ¼ ½1 2ða0 =W Þ þ 2ða0 =W Þ ; a a 2 Y ¼ 1:99 0:41 þ 18:7 W W a 3 a 4 38:48 þ 53:84 : W W
ð9Þ
ð10Þ
During loading of the SEN-T specimen the external work done is partly stored elastically (Ue) and partly dissipated by plastic deformation (Up) (damage zone development and propagation). To compute the J-integral in a point of the loading curve (Fi) the overall area under the curve was determined (Up + Ue). The approximation that the actual stiffness agrees with that of the initial one was used hence Ue can be determined separately – cf. Fig. 14. In order to construct the J–R curves the actual crack length (ai) should be known. ai was computed via the Weibull-fit described above. The J–R curves received are depicted in Fig. 15. From the J–R curves usually two parameters are read: the critical J-integral and the tearing modulus. There are different methods to determine the critical J-integral whether or not the crack tip blunting process is considered. In this work, the intersection of the linear part of the J–R curve with the Y-axis (J0 at Da = 0) has been considered as critical value. Accordingly, the following linear relationship holds: J ¼ J0 þ
DJ Da; Da
where DJ/Da is the slope or tearing modulus.
Note that the higher the value of J0 and DJ/Da the higher the resistance of the notch to crack growth and crack propagation, respectively. Plotting J0 and DJ/Da as a function of flax content both curves go through a minimum (Fig. 16). The reinforcement usually increases the initiation value (J0) and decreases the resistance to crack growth (DJ/Da) at the same time when compared to the matrix. Note that this is the case when the flax content surpasses 40 wt%. Incorporation of flax at 20 wt% results in a ‘‘weak’’ composite. This often the scenario with thermoplastic composites containing a very ductile polymer matrix [16,17].
4. Conclusion Based on this work devoted to determine the J–R curves of thermoplastic starch reinforced by quasi-unidirectional flax fibers arranged in cross-ply (CP) form, the following conclusions can be drawn: • Location of the acoustic emission (AE) is a straightforward technique to estimate the damage development and growth during loading of notched specimens of suitable size. • Considering the weight center of the smoothed distribution of the cumulative AE amplitude the actual position of the running crack can be reliably determined and even mathematically described. This was proved by infrared thermographic (IT) results. • In the knowledge of the crack growth function and corresponding force–displacement curves the J–R curves could be determined.
Acknowledgements ð11Þ The authors are indebted to Prof. J.G. Williams (Imperial College, London) to solve some problems with
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the J determination on SEN-T specimens. This work was supported by the Hungarian Ministry of Education (NKFP 3A/0036/2002).
References [1] Friedrich K. Application of fracture mechanics to composite materials. Amsterdam: Elsevier; 1989. [2] Joyce JA. Elastic–plastic fracture test method: the users experience, vol. 2. American Society for Testing and Materials, ASTM STP 1114, ASTM PCN 04-011140-30. [3] Grellmann W, Seidler S. Deformation and fracture behaviour of polymers. Berlin: Springer; 2001. [4] Williams JG, Pavan A. Fracture of polymers, composites and adhesives. Oxford: Elsevier; 2000. [5] Moore DR. The application of fracture mechanics to polymers, adhesives and composites. Oxford: Elsevier; 2004. [6] Czigany T, Karger-Kocsis J. Determination of the damage zone size in textile fabric reinforced polypropylene composites by locating the acoustic emission. Polym Polym Compos 1993;1:329. [7] Karger-Kocsis J. Microstructural aspects of fracture in polypropylene and in its filled chopped fiber and fiber mat reinforced composites. Polypropylene: structure, blends and composites. London: Chapman & Hall; 1995. [8] Cayard MS, Bradley WL. A comparison of several analytical techniques for calculating J–R curves from load–displacement data and their relation to specimen geometry. Eng Frac Mech 1989;33:121.
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[9] Karger-Kocsis J, Fejes-Kozma Zs. Failure mode and damage zone development in a GM-TPP by acoustic emission and thermography. J Reinf Plast Compos 1994;13:768. [10] Karger-Kocsis J, Benevolenski O. Fracture and failure behaviour of partially consolidated discontinuous glass fiber mat-reinforced polypropylene composites (Azdel Superlite). Macromol Symp 2001;170:165. [11] Karger-Kocsis J, Benevolenski O. Comparative study of the fracture behaviour of flow-molded GMT-PP with random and chopped-fiber mats. Compos Sci Technol 2001;61:2413. [12] Benevolenski O, Karger-Kocsis J, Cziga´ny T, Romha´ny G. Mode I fracture resistance of glass fiber mat-reinforced polypropylene composites at various degree of consolidation. Compos Part A 2003;34:267. [13] Romha´ny G, Karger-Kocsis J, Cziga´ny T. Tensile fracture and failure behavior of thermoplastic starch with unidirectional and cross-ply flax fiber reinforcements. Macrom Mater Eng 2003; 288:699. [14] Karger-Kocsis J, Harmia T, Cziga´ny T. Comparison of the fracture and failure behavior of polypropylene composites reinforced by long glass fibers and by glass mats. Compos Sci Technol 1995;54:287. [15] Arkhireyeva A, Hashemi S. Determination of fracture toughness of poly (ethylene terephthalate) film by essential work of fracture and J integral measurements. Plast Rubber Compos 2001;30:337. [16] Friedrich K. Microstructural efficiency and fracture toughness of short fiber/thermoplastic matrix composites. Compos Sci Technol 1985;22:43. [17] Friedrich K, Karger-Kocsis J. Fracture and fatigue of unfilled and reinforced polyamides and polyesters. In: Schultz JM, Fakirov S, editors. Solid state behavior of linear polyesters and polyamides. Englewood Cliffs, NJ: Prentice Hall; 1990.
Determination of J–R curves of thermoplastic starch composites containing crossed quasi-unidirectional flax fiber reinforcement G. Romha´ny a, T. Cziga´ny a
a,*
, J. Karger-Kocsis
b
Department of Polymer Engineering, Faculty of Mechanical Engineering, Budapest University of Technology and Economics, M}uegyetem rkp. 3., H-1111 Budapest, Hungary b Institut fu¨r Verbundwerkstoffe GmbH (Institute for Composite Materials), Kaiserslautern University of Technology, D-67663 Kaiserslautern, Germany Received 23 September 2004; received in revised form 27 January 2005; accepted 28 January 2005 Available online 24 August 2005
Abstract Thermoplastic starch (MaterBi) composites reinforced with quasi-unidirectional flax fiber in cross-ply (CP) arrangement were produced by film stacking followed by hot pressing. These composites, containing various amount of flax, failed ductilely with pronounced crack growth. Therefore, to determine their fracture mechanical behaviour the J-integral resistance curve concept (J–R) was applied. As the crack growth could not be traced, attempt was made to use the located acoustic emission (AE) events for that purpose. It was established that weighting and smoothing the located cumulative AE amplitudes the crack path can be correctly reconstructed. This was proved by collating the AE results with those derived from infrared thermographic (IT) inspection. Knowing the crack propagation at each point of the force–displacement curves the J–R curves could be determined. Both critical or initiation J-integral and tearing modulus went through a minimum with increase of flax content in the composites. 2005 Elsevier Ltd. All rights reserved. Keywords: Composite; Flax reinforcement; J–R curve; Acoustic emission; Infrared thermography
1. Introduction The application of the linear elastic fracture mechanics is strongly limited for many polymers and composites as their failure occurs via crack propagation. For such systems elastic–plastic (e.g., J-integral) and post-yield fracture mechanics (e.g., essential work of fracture) are used [1–5]. In thermoplastic composites reinforced by textile fabrics (mat, woven, knitted, etc.) the fracture behaviour is even more complicated as therein a large damage zone develops which may even change its shape during crack growth ([6,7] and references therein). In order to characterize the fracture mechanical behaviour of such systems adequately, it is necessary to determine the corresponding resistance curves. Note, that resistance *
Corresponding author. Tel.: +361 463 2003; fax: +361 463 1527. E-mail address: [email protected] (T. Cziga´ny).
0266-3538/$ - see front matter 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.compscitech.2005.01.016
curves reflect the change in a given fracture mechanical parameter as a function of the crack growth (Da). Accordingly, the crack tip and crack growth should be traceable during loading of the specimens, e.g. [8]. However, this is exactly the problem with many composites containing textile reinforcements. The crack growth in the related specimens can hardly be resolved using the usual techniques (visual inspection). Compliance calibration techniques for Da are also less suited as each specimen is unique in respect with the local reinforcing structure. In the past some attempts were made to trace the crack growth during loading of suitable specimens via location of the acoustic emission (AE) and monitoring the heat development using the technique of infrared thermography (IT) [7,9–12]. To construct the resistance curves, however, the apparent fracture toughness (KQ) was used (K–R) [10–12], which is far less suited than that of the J-integral (J–R curves).
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Accordingly, this work was aimed at determining the J-integral resistance curves (J–R) in thermoplastic starch based composites reinforced with aligned flax fiber in crossed lay-up. The reason for our material selection is the effort induced by the strict environmental protection regulation to use biodegradable polymer composites [13]. In order to be able to determine crack propagation, the AE localization method was adopted as an experimental technique. For verification of the results derived from the experiments via mathematical treatise, the IT technique was used.
2. Experimental 2.1. Materials Flax fiber of spinnable quality (average fiber diameter: 68 lm) (Hungaro-Len Ltd., Koma´rom, Hungary) and a thermoplastic starch in the form of film (80 lm; MaterBi LF01U, Novamont, Novara, Italy) were used to produce the composites. The main characteristics of the starch film and flax fiber were published earlier [13]. Composite sheets were prepared by the method of film stacking. Accordingly, the thermoplastic starch film and a layer of flax fibers were placed on one another alternately. The flax fibers were arranged in crossedply (CP) manner. Note that laminates of CP architecture are traditionally used in the composite field in order to assess their mechanical properties. Quasi-unidirectional (UD) lay-up of flax fiber was achieved by combing and fixing their end sections with adhesive tapes, cf. Fig. 1. The flax fiber and the thermoplastic starch film were previously dried at 60 C for 2 h. Pressing was carried out at a pressure of 3 MPa, at 140 C (considering the melting of thermoplastic starch) in a matched tool. The thickness of the sheets prepared by this way ca. 1 mm. The flax content of the composites was 20, 40 and 60 wt%.
Fig. 1. Lay-up of the flax (quasi-unidirectional aligned) and MaterBi layers for hot pressing of CP composites.
2.2. Tests Static mechanical tests were performed on single edge-notched tensile loaded (SEN-T) specimens. Their dimension allowed the location of the AE via a four sensors array (cf. Fig. 2). Tensile loading of the SEN-T specimens occurred at room temperature at a deformation rate of 1 mm/min on a Zwick 1474 machine. The force vs displacement curves were recorded during the tests. The initially sawed notch (a0) was sharpened by razor blade tapping. The AE activity was recorded in situ by a Defektophone NEZ 220 device (AEKI, Budapest, Hungary). A four sensor quadratic array, as shown in Fig. 2, served to locate the AE events using wide bandwidth (100–600 kHz) microsensors (10 mm diameter,
Fig. 2. Experimental set-up including the dimension of the SEN-T specimen, positioning the AE sensors and view field of the infrared camera.
Micro 30D of Physical Acoustic Co., Princeton, USA). Location occurred by a built-in algorithm of the device in the knowledge of the acoustic wave speed. The latter was determined by the method depicted in Fig. 3. The mean wave speed increased with the flax content. At 20, 40 and 60 wt% flax reinforcement the mean speed was 1700, 2500 and 3100 m/s, respectively. The temperature rise during loading of the SEN-T specimens was detected, also in situ, by an IT camera (Compact Thermo TVS 200, Goratec Technology,
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3. Results and discussions 3.1. Determination of the crack path
Fig. 3. Determination of the mean speed of the acoustic wave in the composites using pencil lead breaking as AE source.
Erding, Germany). IT frames were taken at selected points of the force displacement curves and stored. The related files served for digital processing in order to show the relative heat development in given loading intervals.
As the Defektophone device locates the AE events in best case in 1 mm resolution many hits may be hidden in one single point (x, y-coordinates – cf. Fig. 4) when using a two-dimensional (2D) representation. This problem was early recognized and various weighted mapping were introduced. This covered the number of events [6,7,12], and their energy-related terms [9,10]. In the present case, the following bell-type weighting function was applied for the located field (the latter is seen in Figs. 2 and 4): R sðz; wÞ f ðwÞ dA f ðzÞ ¼ A R ; ð1Þ sðz; wÞ dA A where z = x Æ i + y Æ j, w = u Æ i + v Æ j – represents radius vectors of the located field, f(w) is the cumulative value
Fig. 4. Location of the AE events up to final fracture in a SEN-T specimen cut of the composite sheet containing 60 wt% CP flax.
Fig. 5. Weighted cumulative AE amplitude distribution of a thermoplastic starch composite containing 60 wt% flax fiber in CP arrangement in 2D (a) and 3D (b) contour plots.
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Fig. 6. Weighted cumulative AE amplitude distribution of a thermoplastic starch composite containing 60 wt% flax in CP arrangement in 2D (a) and 3D (b) plots by considering 90% of the located events.
s(z, w) is the weighting function 8 2 2 > < jzwj ; if 0 6 jz wj 6 R; 1 R sðz; wÞ ¼ > : 0; if jz wj > R; ð2Þ
Fig. 7. Sectioning of the cumulative AE amplitude (CA) vs. displacement curve of a thermoplastic starch composite containing 60 wt% flax in CP arrangement to get the same DCA in each section. Note. This figure also contains the correspondent force–displacement curve.
of the parameter of a located AE signal in the point of w coordinate and f(z) is the cumulative value of the parameter of a located AE signal in the point of z coordinate after smoothing
where R is the radius of the weighting function and A is the located area. Considering the fact that the distance between the located points along the expected crack growth in Fig. 4 is 2 mm, R = 3 mm was selected. By this way, a correct smoothing can be achieved. Major argument to choose a bell-type function is that the points closer to the resulting one should be ‘‘overweighted’’. This is due to characteristics of the damage zone and the failure events therein. Note that the AE events related with fiber fracture and fiber pull-out yield events with considerable higher amplitude and energy than those associated with fiber/matrix debonding [14]. Although the function given in Eqs. (1) and (2) can be used for any cumulative AE parameters, in this work the cumulative AE amplitude was selected.
Fig. 8. Change in the weight center points of the damage zone during loading of a SEN-T specimen cut of the composite containing 20 wt% flax fibers in CP arrangement. Note. When DCA is too low (cf. picture a) then no monotonic crack growth occurs.
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Fig. 9. Change in the weight center points of the damage zone during loading of a SEN-T specimen cut of the composite containing 60 wt% flax fibers in CP arrangement. Note. When CA is too high (cf. picture a) then the crack growth is less resolved (only few points are available to ‘‘reconstruct’’ the crack path).
Fig. 10. Calculated crack growth in a SEN-T specimen of thermoplastic starch containing 60 wt% quasi-unidirectional flax fiber in cross-ply arrangement showing also the taking positions of the IT frames.
Fig. 5 compares the 2D and 3D plots on example of a SEN-T specimen containing 60 wt% flax fibers in CP arrangement. One can clearly recognize that the cumulative AE amplitude steeply decreases by leaving the notch-driven, expected crack path. The scenario becomes even clearer when only 90% of the located events is taken into consideration – cf. Fig. 6. The 2D and 3D representations in Fig. 6 prove that the weighting procedure used can trace the damage zone and its change during loading correctly. In order to construct a resistance curve the actual position of the crack tip as a function of loading should be known. In order to trace the crack growth the following procedure was followed. The cumulative amplitude (CA) vs displacement curve was sectioned in equidistance steps, as indicated in Fig. 7. For each section first the smoothed CA distribution has been determined as described above (cf. Eqs. (1) and (2)). After that the weight center points of the corresponding CA distributions were computed. The latter have been assigned to the actual position of the running
Fig. 11. Determination of the crack path using located AE events.
crack tip. By repeating the above tasks the weight center point of the damage zone and its change i.e., the crack path, can well be reconstructed. However, caution is requested when selecting the DCA sections (cf. Fig. 7). If too small DCA intervals are chosen, the geometrical places of weight center points do not increase monotonously, hence the crack seems to move backward in some places.
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The upper limit of DCA is obviously given by the cumulative AE amplitude related to final fracture. As the crack propagates steadily during loading of the SEN-T specimens the optimum CA has to be chosen iteratively considering that the weight center of the damage zone should propagate monotonously. So, some deviations in the crack growth can be recognized when using not proper DCA intervals (cf. Figs. 8 and 9). Note that the crack position before final fracture is never correct. In both Figs. 8 and 9 some of the ending points (marked by A) suggest an apparent crack closure. This is due to side (edge) effects. Near to the specimen edge (70 mm not all events are captured by the sensors), so their location is impossible. In addition, the weight center point can never reach the edge of the SEN-T specimen. As a consequence, the points marked by ‘‘A’’ in Figs. 8 and 9 were neglected. For the remaining weight center points of the damage zone (representing the crack growth) a Weibull-type function (four parameters sigmoid type) was fitted C
fB ðxÞ ¼ A ðA a0 Þ eðBxÞ ;
ð3Þ
where a0, A, B, C are parameters, a0 equals with the initial notch length (cf. Fig. 2). During parameter fitting the least square method has been adopted. Thus, the ‘‘actual’’ crack length corresponding to a given load of the SEN-T specimen can be determined by this curve fitting (cf. Fig. 10). The steps performed to deduce the crack propagation curve along the ligament are summarized in a block diagram in Fig. 11. 3.2. Validation of the crack propagation via IT Fig. 10 indicates also the taking position of the IT frames on the force–displacement curve of the composite containing 60 wt% CP flax. Based on the fact that the background was set cooler than the specimen, the notch and edges of the specimens are well resolved in the IT frames (cf. Fig. 12). This allows us to locate the x, y coordinates in the IT field (note, that the overall width of IT view filed corresponds to 256 pixels). Frame 3 in Fig. 12 was taken 11 s later than frame 2. So, the former one contains some superposition in the thermal field. However, by subtracting frame 2
Fig. 12. Comparison of the damage zone derived from IT and AE measurements respectively on a SEN-T specimen of the starch composite containing 60 wt% flax in CP arrangement.
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Fig. 14. Determination of Up and Ue schematically.
3.3. Determination of the J–R curves The force–displacement curves presented (cf. Figs. 7– 10 and 13) already indicated that the thermoplastic starch composites studied failed always ductility with pronounced crack growth. Therefore it is appropriate to determine the J–R curves. For the purpose the Paris-Rice approach was followed: J ¼ J e þ J p; ge U e Je ¼ ; B ðW aÞ gp U p Jp ¼ ; B ðW aÞ
Fig. 13. Position of the damage zone (i.e., actual crack length) derived from IT and AE measurements, respectively, for the composites containing 20, 40 and 60 wt% flax fiber in CP arrangement.
from frame 3 we can get the heat development that occurred in this time interval (i.e., 11 s). The weight centre point of the relative temperature distribution can be considered as the actual crack tip at 150 s of the specimen loading. Needless to say that this approach assumes adiabatic heating in the specimen. If we compare the 2D plots of the damage zones derived from IT and AE (by using the above approach considering the cumulative AE amplitude), respectively, a very good agreement can be found (cf. Fig. 12). Fig. 13 collates the positions of the damage zone derived from IT and AE techniques as a function of loading for the composites containing various amount of flax. One can recognize the good agreement between the related crack propagation data. So, via IT we succeeded to show that our AE results in respect of the crack propagation are reliable. As a consequence, the actual crack position is known and thus the J–R curves can be constructed.
ð4Þ ð5Þ ð6Þ
where Je and Jp are, respectively, the elastic and plastic components of the total J value, Ue and Up are, respectively, the elastic and plastic components of the external work, ge and gp are elastic and plastic work factors dependent upon the specimen geometry, W is the width of the SEN-T specimen, B is the thickness of the SEN-T specimen, a is the actual crack length (cf. Fig. 2). The elastic and plastic work factors for the SEN-T geometry were calculated using [15]
Fig. 15. J–R curves of the thermoplastic starch and its flax fiber reinforced CP arranged composites at various flax content. Note. the crack growth of the matrix was followed visually. The J–R curves indicate the onset of stable crack growth (s) and the points related to the maximum load (h), as well.
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Fig. 16. J0 (a) and DJ/Da (b) as a function of CP flax content.
ðW a0 Þ Y 2 ða0 Þ a0 ge ¼ R a0 2 ; Y ðaÞ a da þ ZW 0 2 ðW a0 Þ gp ¼ h i1 ; a0 W aða0 Þ W ½aðaW0 Þða þ 1 0 =W Þ
ð7Þ ð8Þ
where 2 1=2
a ¼ ½1 2ða0 =W Þ þ 2ða0 =W Þ ; a a 2 Y ¼ 1:99 0:41 þ 18:7 W W a 3 a 4 38:48 þ 53:84 : W W
ð9Þ
ð10Þ
During loading of the SEN-T specimen the external work done is partly stored elastically (Ue) and partly dissipated by plastic deformation (Up) (damage zone development and propagation). To compute the J-integral in a point of the loading curve (Fi) the overall area under the curve was determined (Up + Ue). The approximation that the actual stiffness agrees with that of the initial one was used hence Ue can be determined separately – cf. Fig. 14. In order to construct the J–R curves the actual crack length (ai) should be known. ai was computed via the Weibull-fit described above. The J–R curves received are depicted in Fig. 15. From the J–R curves usually two parameters are read: the critical J-integral and the tearing modulus. There are different methods to determine the critical J-integral whether or not the crack tip blunting process is considered. In this work, the intersection of the linear part of the J–R curve with the Y-axis (J0 at Da = 0) has been considered as critical value. Accordingly, the following linear relationship holds: J ¼ J0 þ
DJ Da; Da
where DJ/Da is the slope or tearing modulus.
Note that the higher the value of J0 and DJ/Da the higher the resistance of the notch to crack growth and crack propagation, respectively. Plotting J0 and DJ/Da as a function of flax content both curves go through a minimum (Fig. 16). The reinforcement usually increases the initiation value (J0) and decreases the resistance to crack growth (DJ/Da) at the same time when compared to the matrix. Note that this is the case when the flax content surpasses 40 wt%. Incorporation of flax at 20 wt% results in a ‘‘weak’’ composite. This often the scenario with thermoplastic composites containing a very ductile polymer matrix [16,17].
4. Conclusion Based on this work devoted to determine the J–R curves of thermoplastic starch reinforced by quasi-unidirectional flax fibers arranged in cross-ply (CP) form, the following conclusions can be drawn: • Location of the acoustic emission (AE) is a straightforward technique to estimate the damage development and growth during loading of notched specimens of suitable size. • Considering the weight center of the smoothed distribution of the cumulative AE amplitude the actual position of the running crack can be reliably determined and even mathematically described. This was proved by infrared thermographic (IT) results. • In the knowledge of the crack growth function and corresponding force–displacement curves the J–R curves could be determined.
Acknowledgements ð11Þ The authors are indebted to Prof. J.G. Williams (Imperial College, London) to solve some problems with
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the J determination on SEN-T specimens. This work was supported by the Hungarian Ministry of Education (NKFP 3A/0036/2002).
References [1] Friedrich K. Application of fracture mechanics to composite materials. Amsterdam: Elsevier; 1989. [2] Joyce JA. Elastic–plastic fracture test method: the users experience, vol. 2. American Society for Testing and Materials, ASTM STP 1114, ASTM PCN 04-011140-30. [3] Grellmann W, Seidler S. Deformation and fracture behaviour of polymers. Berlin: Springer; 2001. [4] Williams JG, Pavan A. Fracture of polymers, composites and adhesives. Oxford: Elsevier; 2000. [5] Moore DR. The application of fracture mechanics to polymers, adhesives and composites. Oxford: Elsevier; 2004. [6] Czigany T, Karger-Kocsis J. Determination of the damage zone size in textile fabric reinforced polypropylene composites by locating the acoustic emission. Polym Polym Compos 1993;1:329. [7] Karger-Kocsis J. Microstructural aspects of fracture in polypropylene and in its filled chopped fiber and fiber mat reinforced composites. Polypropylene: structure, blends and composites. London: Chapman & Hall; 1995. [8] Cayard MS, Bradley WL. A comparison of several analytical techniques for calculating J–R curves from load–displacement data and their relation to specimen geometry. Eng Frac Mech 1989;33:121.
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[9] Karger-Kocsis J, Fejes-Kozma Zs. Failure mode and damage zone development in a GM-TPP by acoustic emission and thermography. J Reinf Plast Compos 1994;13:768. [10] Karger-Kocsis J, Benevolenski O. Fracture and failure behaviour of partially consolidated discontinuous glass fiber mat-reinforced polypropylene composites (Azdel Superlite). Macromol Symp 2001;170:165. [11] Karger-Kocsis J, Benevolenski O. Comparative study of the fracture behaviour of flow-molded GMT-PP with random and chopped-fiber mats. Compos Sci Technol 2001;61:2413. [12] Benevolenski O, Karger-Kocsis J, Cziga´ny T, Romha´ny G. Mode I fracture resistance of glass fiber mat-reinforced polypropylene composites at various degree of consolidation. Compos Part A 2003;34:267. [13] Romha´ny G, Karger-Kocsis J, Cziga´ny T. Tensile fracture and failure behavior of thermoplastic starch with unidirectional and cross-ply flax fiber reinforcements. Macrom Mater Eng 2003; 288:699. [14] Karger-Kocsis J, Harmia T, Cziga´ny T. Comparison of the fracture and failure behavior of polypropylene composites reinforced by long glass fibers and by glass mats. Compos Sci Technol 1995;54:287. [15] Arkhireyeva A, Hashemi S. Determination of fracture toughness of poly (ethylene terephthalate) film by essential work of fracture and J integral measurements. Plast Rubber Compos 2001;30:337. [16] Friedrich K. Microstructural efficiency and fracture toughness of short fiber/thermoplastic matrix composites. Compos Sci Technol 1985;22:43. [17] Friedrich K, Karger-Kocsis J. Fracture and fatigue of unfilled and reinforced polyamides and polyesters. In: Schultz JM, Fakirov S, editors. Solid state behavior of linear polyesters and polyamides. Englewood Cliffs, NJ: Prentice Hall; 1990.