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Compression bending test for CFRP pipe
Composites Science and Technology 62 (2002) 2075–2081 www.elsevier.com/locate/compscitech
Compression bending test for CFRP pipe Hiroshi Fukuda*, Tetsuya Watanabe1, Masaaki Itabashi, Atsushi Wada Department of Materials Science and Technology, Tokyo University of Science, Yamazaki, Noda, Chiba 278-8510, Japan Received 20 February 2002; received in revised form 20 May 2002; accepted 26 July 2002
Abstract A compression bending test method for CFRP pipes is described in this paper. Although CFRP pipes are widely used in such applications as truss members of architecture, golf clubs and fishing rods, there seem to be no suitable test methods for CFRP pipes. A conventional bending test of three- or four-point bending is not necessarily suitable because a high stress concentration due to a loading device takes place. In the past, we have developed a new bending test method, namely, a compression bending test and it was successfully applied to a flat specimen. In the present paper, we propose to apply this method to a pipe. The results show that the bending modulus was close to that measured by the three-point bending test and that the bending strength was higher than that measured by the three-point bending test. Hence, the proposed test method is well-suited for testing of pipe structures. # 2002 Elsevier Science Ltd. All rights reserved. Keywords: CFRP pipe; B. Mechanical properties; B. Strengh; C. Elastic properties
1. Introduction It is well known that the bending strength of CFRP coupons is strongly affected by the stress concentration due to a hard loading device. The works of Whitney [1] and Cui and Wisnom [2] are some of the examples that dealt with the stress concentration. To reduce this undesirable effect, the Japanese Industrial Standard recommends that a thin film be inserted between the loading nose and the test specimen [3]. This idea came from the work of Hojo et al. [4]. Uemura and his coworkers [5] developed a device for pure bending rather than 3- or 4-point bending. The present authors, on the other hand, took a different approach, that is, we have hitherto proposed and demonstrated a compression bending test method [6–9] which is based on the Euler buckling of a column. By applying the concept of the elastica [10], a methodology to calculate the bending modulus and strength of flat coupons was established. In that method, both the bending strength and the bending modulus can be calculated using the elastica by measuring only the applied * Corresponding author. Tel.: +81-471-241501x4308; fax: +81471-239362. E-mail address: [email protected] (H. Fukuda). 1 Current address: Asahi Glass Matex Co. Ltd.
load and the crosshead movement during the buckling process of a flat column. However, the above review is for flat coupons only and in the case of pipes, undesirable effects by the loading device will be more serious; in most cases the pipe will be crushed by the loading nose rather than the bending failure. Therefore, in the present paper, we tried to apply the compression bending test method to a CFRP pipe. A parametric study of various configurations of CFRP pipes was also conducted with success.
2. Principle of compression bending Since the details of a compression bending test method have already been reported elsewhere [6–9], only a brief summary is presented here. Fig. 1 shows the half length of the present specimen whose experimental methodology is based on the Euler buckling theory. The bending moment at the midspan A is expressed as MA ¼ PA
ð1Þ
where P is the applied load and A is the midspan deflection. The specimen configuration for the present study is shown in Fig. 2. The bending stress (skin stress)
0266-3538/02/$ - see front matter # 2002 Elsevier Science Ltd. All rights reserved. PII: S0266-3538(02)00150-1
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H. Fukuda et al. / Composites Science and Technology 62 (2002) 2075–2081
suring A. In the present paper, this idea is mainly used to calculate the bending modulus of Eq. (3). According to an alternative approach of calculating A and A using the elastica, the following equation is derived [8]: l EðpÞ ¼4 L KðpÞ
ð6Þ
where l is the crosshead movement and E(p) is the perfect elliptic integral of the second kind. From Eqs. (4), (5) and (6), we can calculate A as well as A by measuring l. This point will be discussed in detail later.
3. Specimens and test procedure 3.1. Test specimens All specimens tested in this paper are CFRP pipes where carbon prepregs in the longitudinal direction (thickness: 0.06 mm) and the transverse direction (thickness: 0.015 mm) are wound on a round mandrel of either 3, 5, or 15 mm in diameter. The process of fabrication is schematically shown in Fig. 3. Five kinds of pipes were prepared which are tabulated in Table 1.
Fig. 1. The elastica.
Fig. 2. Specimen configuration.
3.2. Tension, compression and three-point bending test
at point A of Fig. 1 is, under linear elasticity conditions, given as A ¼
M A d2 2I
ð2Þ 3.3. Compression bending test
where I is the moment of inertia for the cross-section and d2 is the outer diameter of the pipe. The bending strength is obtained by substituting the bending moment at failure into MA Eq. (2). The bending modulus is expressed as E¼
MA A I
Tensile tests, compression tests, and three-point bending tests were performed prior to the compression bending test to get necessary data.
ð3Þ
Fig. 4 shows the compression bending test, although details are not shown here. One point worth noting is the detail of the loading device. In the preceding works for flat coupons, we first used a pair of rotation-free devices to realize the end condition of pin support [6–8]. Since such a device was too complicated, we next invented a pair of simplified devices [9] which were adequate for flat coupons. However, this simplified device
where A is the radius of curvature at point A. According to the elastica [10] and succeeding formulation [7], the following equations hold: A 2p ¼ KðpÞ L
ð4Þ
A 1 ¼ 2pKðpÞ L
ð5Þ
where p=sin /2, and K(p) is the perfect elliptic integral of the first kind. Because A and A are mutually related through the parameter p, A can be calculated by mea-
Fig. 3. Schematic view of fabrication.
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H. Fukuda et al. / Composites Science and Technology 62 (2002) 2075–2081 Table 1 Configuration of specimen Specimen type
A
Stacking sequence inner diameter d1 (mm)
B
C
D
(0 /90 )4 (0 /90 )4 (0 /90 )4 (0 /90 )2 5 3 15 5 0 ply : thickness 0.06 mm 90 ply : thickness 0.015 mm ( 45 ) : 0.033 mm(+45 ) + 0.033 mm(45 ) + glass scrim (0.012 mm) Carbon : Toho Rayon HTA, matrix : Epoxy resin
E ( 45 )4 5
plates was attached with screws in accordance with the diameter of pipe. The end of the test pipe was inserted into the hole and this system was sufficient enough to realize a pin-support end. Most of the compression bending tests were performed at the crosshead speed of 2.5 mm/min; for long specimens it was increased to 10 mm/min. By measuring the applied load, the crosshead movement and the midspan deflection, the bending modulus and strength were calculated. Tests were performed with various specimen lengths.
4. Results and discussion 4.1. Buckling load
was not appropriate for pipes and hence, we again designed and machined a new device. Fig. 5 is the schematic view of the present device. We prepared three small plates of 2-mm thickness with a hole of either 3, 5, or 15mm in diameter at the center of the plate. At the bottom of a channel-shape cutout, one of these small
In the following, the test results for the Type A specimens are mainly reported and discussion for other types of specimens are given only when they show some special results. The specimen length suitable for the compression bending test was first determined. Fig. 6 is an example of Pcr (buckling load) vs. the specimen length for the Type A specimens (diameter=5 mm). In this case, if the specimen was shorter than 100 mm, compressive failure (edge crush) took place. Subsequently, a compression bending test was conducted for the specimens whose length was longer than 100 mm but shorter than 400
Fig. 5. Schematic view of loading device.
Fig. 6. Pcr vs. specimen length (Type A).
Fig. 4. Setup of compression bending.
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H. Fukuda et al. / Composites Science and Technology 62 (2002) 2075–2081
Fig. 7. Load, strain vs. crosshead movement (Type A).
means of the 3-point bending test is also shown in the figure. The average strength and the coefficient of variance (CV) were 1018 MPa and 13.4%, respectively, for compression bending (a total of 11 specimens) and 528 MPa and 15.7%, respectively, for 3-point bending (a total of 7 specimens). As is clearly shown, the strength by means of the present test is higher than that by the 3point bending test, although there was a wide range of data scattering in the both methods. This clearly demonstrates the superiority of the present method because an undesirable loading device does not act on the gage region. However, the present method inevitably introduces an axial compressive load, P. Fig. 9 shows the ratio of the compressive stress to the bending stress for the Type A specimen. As was expected, when the specimen length increased, this ratio decreased. If this ratio is less than a few percent, it will be of little problem for practical use. For the Type A specimens, the necessary length is 200 mm or longer. The reason why the compression-bending strength for the 100 mm length specimens in Fig. 8 is smaller than those for the longer specimens might be due to the relatively large compressive stress shown in Fig. 9. Fig. 10 summarizes the average bending strengths for 5 types of specimens by means of the 3-point bending (3b) test and the compression bending (cb) test. Axial compressive strengths (comp) are also shown as a reference whereas tensile test data are missing because we could not obtain satisfactory tensile strength data due to the difficulty of the gripping system. The abscissa is arranged in terms of the average radius divided by the thickness, r=t. The superiority of the compression bending has been confirmed for all types of the specimens. Although the Type A–D specimens have essentially the same stacking sequence, the strength decreases with the increase of the r=t ratios. For large r=t ratios, it is speculated that flattening of the cross section from
Fig. 8. Bending strength vs. specimen length (Type A).
Fig. 9. Ratio of compressive stress to bending stress (Type A).
mm. For other types of specimens, a preliminary study similar to the Type A specimens was conducted although it might be possible to determine the length by calculating the Euler buckling load if we know the compressive strength and Young’s modulus of the pipe. 4.2. Data reduction In the experiment, strain gages were also glued at the midspan of each pipe on both the tensile and compressive surfaces. Data of the applied load, the midspan deflection, the crosshead movement, and the strains were saved with a data logging system at an interval of 1 s. Fig. 7 demonstrates typical load–crosshead movement and strain–crosshead movement curves for the Type A specimen. At the very beginning of the test, the specimen suffered from pure compression and afterwards it buckled. 4.3. Bending strength Fig. 8 depicts the bending strength of the Type A pipe with various specimen lengths. The bending strength by
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Fig. 10. Comparison of bending strengths (all types).
circular shape to elliptical shape might have occurred and this might have decreased the strength. It is also noted that the fiber orientation of the Type E specimens is different from that of the other types of specimens. Both the average strengths and the CV values for all types of specimens are listed in Table 2 along with the average bending moduli and their CVs. In the case of flat coupons [6–9], the ratio of the compression bending strength to the 3-point bending strength was relatively small, around 1.2. On the contrary, the ratio was large for the pipe specimens. In the most extreme case of Type C, the ratio was 2.2 (=367/167). This indirectly suggests that the conventional 3-point bending is not adequate for measuring the bending strength of thin pipes with relatively large diameter. Part of the bending moduli in Table 2 will be used later to discuss the bending modulus. 4.4. Bending modulus Fig. 11 shows the bending modulus for the Type A pipes with various specimen lengths. The average bending modulus and its CV value were 70.4 GPa and 7.9%, respectively, for the compression bending specimens (a total of 11 specimens) and 70.8 GPa and 3.9%, respectively, for the 3-point bending specimens (a total of 7
specimens). Concerning the bending modulus for the Type A specimens, no substantial difference from 3point bending was observed except for the 100mmlength specimen. As is shown in Fig. 9, the specimen length of 100 mm might be too short for the Type A specimen. If we discard one data value for the 100 mmlength specimen, the average and CV become 72.0 GPa and 2.7%, respectively. Fig. 12 summarizes all types of the specimens along with the compressive (comp) and tensile (tens) test data. In general, Young’s moduli by means of the tensile test were larger than those by other methods. For flat coupons, as was described in Refs. [7–9], the bending modulus measured by the compression bending was almost always smaller than that by the 3-point bending test. However, this is not the case with the pipe configuration especially for the Types C and E specimens. The bending moduli for those specimens by means of the compression bending test are higher than those by the 3-point bending test. It is reasonable to infer that for relatively large diameter pipes (Type C) or pipes with a small bending modulus (Type E), a problem of local flattening by the loading device becomes more serious under the 3-point bending test. If we measure the deflection by the crosshead movement, this flattening results in the nominal increase of deflection and hence, the decrease of the bending modulus. This may be a major reason why the Types C and E specimens exhibited a different tendency from other types of the specimens, although we have not confirmed this by measuring the amount of flattening. 4.5. Applicability of elastica So far the data reduction was based on the direct measurement of A rather than using Eq. (4). In the experiment, a special device is required to measure A and from a view-point of experimental convenience, it is desirable to calculate A from Eqs.(4)–(6) by measuring only the crosshead movement, l. Fig. 13 is an example of comparison between the theory and the experiment in terms of the crosshead movement vs. the midspan deflection. Although there exist some discrepancies between the theory and the experiment, this difference is
Table 2 Comparison of test data between 3-point bending and compression bending Type
A B C D E
3-point bending
Compression bending
No. of specimens
Strength/MPa (CV/%)
Modulus/GPa (CV/%)
No. of specimens
Strength/MPa (CV/%)
Modulus/GPa (CV/%)
7 8 4 9 3
528 (15.7) 746 (11.4) 167 (8.9) 357 (14.0) 214 (5.4)
70.8 (3.9) 69.7 (4.4) 62.7 (10.7) 71.0 (8.5) 7.8 (12.8)
11 13 5 16 5
1018 (13.4) 1173 (15.6) 367 (3.7) 574 (7.9) 222 (2.1)
70.4 (7.9) 68.9 (3.4) 72.6 (1.1) 68.3 (5.8) 11.8 (9.1)
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almost negligible if we shift the experimental values to the left by some fixed amount. According to our calculation, this difference is mainly due to the elastic compressive deformation at the beginning of loading. If we modify the compressive strain, the experimental values coincide with those by the theory and hence, it may be concluded that a more sophisticated approach of using Eqs.(4)–(6) is also feasible.
5. Conclusions
Fig. 11. Bending modulus vs. specimen length (Type A).
The applicability of the compression bending test to pipe-shaped specimens was demonstrated. Comparing to the 3-point bending test, the bending strength by means of the compression bending test was much larger which proves the superiority of the present method. This tendency with the pipe-shaped specimens was clearer than that with flat coupons. As for the bending modulus, the measured values were comparable to those by the 3-point bending test except for pipes with large diameters such as the Type C specimens, or pipes with low moduli such as the Type E specimens. In the cases of the Types C and E specimens, the conventional 3-point bending test should not be used. It is concluded that the method proposed in this paper can be used to obtain reliable bending properties for pipe-shaped components.
Acknowledgements We sincerely thank Mr. H. Suzue and Mr. K. Kameda of Daiwa Seiko Co. Ltd. for their supplying test specimens. Thanks are also due to Mr. M. Yamazaki for his assistance in experiments. Fig. 12. Comparison of bending modulus (all types).
References
Fig. 13. Example of midspan deflection vs. crosshead movement.
[1] Whitney JM. Elasticity analysis of orthotropic beams under concentrated loads. Compos Sci Technol 1985;22:167–84. [2] Cui WC, Wisnom MR. Contact finite element analysis of threeand four- point short-beam bending of unidirectional composites. Compos Sci Technol 1992;45:323–54. [3] Bending test method of CFRP. 1988; JIS K 7074–1988. [4] Hojo M, Noguchi Y, Furue H, Matsui J. Bending test methods for advanced composites. In: 28th Annual Meeting on Structural Strength, The Japan Society for Aeronautical and Space Sciences; 1986. p. 370–3 (in Japanese). [5] Iwai H, Uemura M. Development of pure bending test method for advanced composites. In: 34th Annual Meeting on Structural Strength, The Japan Society for Aeronautical and Space Sciences; 1991. p. 70–3 (in Japanese). [6] Fukuda H. A new bending test method of advanced composites. Experimental Mechanics 1989;29:330–5. [7] Fukuda H. Compression bending test method for advanced composites. J Japan Soc Aero Space Sci 1993;41:482–7 (in Japanese).
H. Fukuda et al. / Composites Science and Technology 62 (2002) 2075–2081 [8] Fukuda H, Katoh H, Uesugi H. A modified procedure to measure bending strength and modulus of advanced composites by means of compression bending. J Compos Mater 1995;29:195–207. [9] Fukuda H, Itabashi M. Simplified compression bending test
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method for advanced composites. Composites, Part A 1999;30: 249–56. [10] Timoshenko SP, Gere JM. Theory of elastic stability, 2nd ed. McGraw-Hill; 1961. p. 76–82.
Compression bending test for CFRP pipe Hiroshi Fukuda*, Tetsuya Watanabe1, Masaaki Itabashi, Atsushi Wada Department of Materials Science and Technology, Tokyo University of Science, Yamazaki, Noda, Chiba 278-8510, Japan Received 20 February 2002; received in revised form 20 May 2002; accepted 26 July 2002
Abstract A compression bending test method for CFRP pipes is described in this paper. Although CFRP pipes are widely used in such applications as truss members of architecture, golf clubs and fishing rods, there seem to be no suitable test methods for CFRP pipes. A conventional bending test of three- or four-point bending is not necessarily suitable because a high stress concentration due to a loading device takes place. In the past, we have developed a new bending test method, namely, a compression bending test and it was successfully applied to a flat specimen. In the present paper, we propose to apply this method to a pipe. The results show that the bending modulus was close to that measured by the three-point bending test and that the bending strength was higher than that measured by the three-point bending test. Hence, the proposed test method is well-suited for testing of pipe structures. # 2002 Elsevier Science Ltd. All rights reserved. Keywords: CFRP pipe; B. Mechanical properties; B. Strengh; C. Elastic properties
1. Introduction It is well known that the bending strength of CFRP coupons is strongly affected by the stress concentration due to a hard loading device. The works of Whitney [1] and Cui and Wisnom [2] are some of the examples that dealt with the stress concentration. To reduce this undesirable effect, the Japanese Industrial Standard recommends that a thin film be inserted between the loading nose and the test specimen [3]. This idea came from the work of Hojo et al. [4]. Uemura and his coworkers [5] developed a device for pure bending rather than 3- or 4-point bending. The present authors, on the other hand, took a different approach, that is, we have hitherto proposed and demonstrated a compression bending test method [6–9] which is based on the Euler buckling of a column. By applying the concept of the elastica [10], a methodology to calculate the bending modulus and strength of flat coupons was established. In that method, both the bending strength and the bending modulus can be calculated using the elastica by measuring only the applied * Corresponding author. Tel.: +81-471-241501x4308; fax: +81471-239362. E-mail address: [email protected] (H. Fukuda). 1 Current address: Asahi Glass Matex Co. Ltd.
load and the crosshead movement during the buckling process of a flat column. However, the above review is for flat coupons only and in the case of pipes, undesirable effects by the loading device will be more serious; in most cases the pipe will be crushed by the loading nose rather than the bending failure. Therefore, in the present paper, we tried to apply the compression bending test method to a CFRP pipe. A parametric study of various configurations of CFRP pipes was also conducted with success.
2. Principle of compression bending Since the details of a compression bending test method have already been reported elsewhere [6–9], only a brief summary is presented here. Fig. 1 shows the half length of the present specimen whose experimental methodology is based on the Euler buckling theory. The bending moment at the midspan A is expressed as MA ¼ PA
ð1Þ
where P is the applied load and A is the midspan deflection. The specimen configuration for the present study is shown in Fig. 2. The bending stress (skin stress)
0266-3538/02/$ - see front matter # 2002 Elsevier Science Ltd. All rights reserved. PII: S0266-3538(02)00150-1
2076
H. Fukuda et al. / Composites Science and Technology 62 (2002) 2075–2081
suring A. In the present paper, this idea is mainly used to calculate the bending modulus of Eq. (3). According to an alternative approach of calculating A and A using the elastica, the following equation is derived [8]: l EðpÞ ¼4 L KðpÞ
ð6Þ
where l is the crosshead movement and E(p) is the perfect elliptic integral of the second kind. From Eqs. (4), (5) and (6), we can calculate A as well as A by measuring l. This point will be discussed in detail later.
3. Specimens and test procedure 3.1. Test specimens All specimens tested in this paper are CFRP pipes where carbon prepregs in the longitudinal direction (thickness: 0.06 mm) and the transverse direction (thickness: 0.015 mm) are wound on a round mandrel of either 3, 5, or 15 mm in diameter. The process of fabrication is schematically shown in Fig. 3. Five kinds of pipes were prepared which are tabulated in Table 1.
Fig. 1. The elastica.
Fig. 2. Specimen configuration.
3.2. Tension, compression and three-point bending test
at point A of Fig. 1 is, under linear elasticity conditions, given as A ¼
M A d2 2I
ð2Þ 3.3. Compression bending test
where I is the moment of inertia for the cross-section and d2 is the outer diameter of the pipe. The bending strength is obtained by substituting the bending moment at failure into MA Eq. (2). The bending modulus is expressed as E¼
MA A I
Tensile tests, compression tests, and three-point bending tests were performed prior to the compression bending test to get necessary data.
ð3Þ
Fig. 4 shows the compression bending test, although details are not shown here. One point worth noting is the detail of the loading device. In the preceding works for flat coupons, we first used a pair of rotation-free devices to realize the end condition of pin support [6–8]. Since such a device was too complicated, we next invented a pair of simplified devices [9] which were adequate for flat coupons. However, this simplified device
where A is the radius of curvature at point A. According to the elastica [10] and succeeding formulation [7], the following equations hold: A 2p ¼ KðpÞ L
ð4Þ
A 1 ¼ 2pKðpÞ L
ð5Þ
where p=sin /2, and K(p) is the perfect elliptic integral of the first kind. Because A and A are mutually related through the parameter p, A can be calculated by mea-
Fig. 3. Schematic view of fabrication.
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H. Fukuda et al. / Composites Science and Technology 62 (2002) 2075–2081 Table 1 Configuration of specimen Specimen type
A
Stacking sequence inner diameter d1 (mm)
B
C
D
(0 /90 )4 (0 /90 )4 (0 /90 )4 (0 /90 )2 5 3 15 5 0 ply : thickness 0.06 mm 90 ply : thickness 0.015 mm ( 45 ) : 0.033 mm(+45 ) + 0.033 mm(45 ) + glass scrim (0.012 mm) Carbon : Toho Rayon HTA, matrix : Epoxy resin
E ( 45 )4 5
plates was attached with screws in accordance with the diameter of pipe. The end of the test pipe was inserted into the hole and this system was sufficient enough to realize a pin-support end. Most of the compression bending tests were performed at the crosshead speed of 2.5 mm/min; for long specimens it was increased to 10 mm/min. By measuring the applied load, the crosshead movement and the midspan deflection, the bending modulus and strength were calculated. Tests were performed with various specimen lengths.
4. Results and discussion 4.1. Buckling load
was not appropriate for pipes and hence, we again designed and machined a new device. Fig. 5 is the schematic view of the present device. We prepared three small plates of 2-mm thickness with a hole of either 3, 5, or 15mm in diameter at the center of the plate. At the bottom of a channel-shape cutout, one of these small
In the following, the test results for the Type A specimens are mainly reported and discussion for other types of specimens are given only when they show some special results. The specimen length suitable for the compression bending test was first determined. Fig. 6 is an example of Pcr (buckling load) vs. the specimen length for the Type A specimens (diameter=5 mm). In this case, if the specimen was shorter than 100 mm, compressive failure (edge crush) took place. Subsequently, a compression bending test was conducted for the specimens whose length was longer than 100 mm but shorter than 400
Fig. 5. Schematic view of loading device.
Fig. 6. Pcr vs. specimen length (Type A).
Fig. 4. Setup of compression bending.
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H. Fukuda et al. / Composites Science and Technology 62 (2002) 2075–2081
Fig. 7. Load, strain vs. crosshead movement (Type A).
means of the 3-point bending test is also shown in the figure. The average strength and the coefficient of variance (CV) were 1018 MPa and 13.4%, respectively, for compression bending (a total of 11 specimens) and 528 MPa and 15.7%, respectively, for 3-point bending (a total of 7 specimens). As is clearly shown, the strength by means of the present test is higher than that by the 3point bending test, although there was a wide range of data scattering in the both methods. This clearly demonstrates the superiority of the present method because an undesirable loading device does not act on the gage region. However, the present method inevitably introduces an axial compressive load, P. Fig. 9 shows the ratio of the compressive stress to the bending stress for the Type A specimen. As was expected, when the specimen length increased, this ratio decreased. If this ratio is less than a few percent, it will be of little problem for practical use. For the Type A specimens, the necessary length is 200 mm or longer. The reason why the compression-bending strength for the 100 mm length specimens in Fig. 8 is smaller than those for the longer specimens might be due to the relatively large compressive stress shown in Fig. 9. Fig. 10 summarizes the average bending strengths for 5 types of specimens by means of the 3-point bending (3b) test and the compression bending (cb) test. Axial compressive strengths (comp) are also shown as a reference whereas tensile test data are missing because we could not obtain satisfactory tensile strength data due to the difficulty of the gripping system. The abscissa is arranged in terms of the average radius divided by the thickness, r=t. The superiority of the compression bending has been confirmed for all types of the specimens. Although the Type A–D specimens have essentially the same stacking sequence, the strength decreases with the increase of the r=t ratios. For large r=t ratios, it is speculated that flattening of the cross section from
Fig. 8. Bending strength vs. specimen length (Type A).
Fig. 9. Ratio of compressive stress to bending stress (Type A).
mm. For other types of specimens, a preliminary study similar to the Type A specimens was conducted although it might be possible to determine the length by calculating the Euler buckling load if we know the compressive strength and Young’s modulus of the pipe. 4.2. Data reduction In the experiment, strain gages were also glued at the midspan of each pipe on both the tensile and compressive surfaces. Data of the applied load, the midspan deflection, the crosshead movement, and the strains were saved with a data logging system at an interval of 1 s. Fig. 7 demonstrates typical load–crosshead movement and strain–crosshead movement curves for the Type A specimen. At the very beginning of the test, the specimen suffered from pure compression and afterwards it buckled. 4.3. Bending strength Fig. 8 depicts the bending strength of the Type A pipe with various specimen lengths. The bending strength by
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H. Fukuda et al. / Composites Science and Technology 62 (2002) 2075–2081
Fig. 10. Comparison of bending strengths (all types).
circular shape to elliptical shape might have occurred and this might have decreased the strength. It is also noted that the fiber orientation of the Type E specimens is different from that of the other types of specimens. Both the average strengths and the CV values for all types of specimens are listed in Table 2 along with the average bending moduli and their CVs. In the case of flat coupons [6–9], the ratio of the compression bending strength to the 3-point bending strength was relatively small, around 1.2. On the contrary, the ratio was large for the pipe specimens. In the most extreme case of Type C, the ratio was 2.2 (=367/167). This indirectly suggests that the conventional 3-point bending is not adequate for measuring the bending strength of thin pipes with relatively large diameter. Part of the bending moduli in Table 2 will be used later to discuss the bending modulus. 4.4. Bending modulus Fig. 11 shows the bending modulus for the Type A pipes with various specimen lengths. The average bending modulus and its CV value were 70.4 GPa and 7.9%, respectively, for the compression bending specimens (a total of 11 specimens) and 70.8 GPa and 3.9%, respectively, for the 3-point bending specimens (a total of 7
specimens). Concerning the bending modulus for the Type A specimens, no substantial difference from 3point bending was observed except for the 100mmlength specimen. As is shown in Fig. 9, the specimen length of 100 mm might be too short for the Type A specimen. If we discard one data value for the 100 mmlength specimen, the average and CV become 72.0 GPa and 2.7%, respectively. Fig. 12 summarizes all types of the specimens along with the compressive (comp) and tensile (tens) test data. In general, Young’s moduli by means of the tensile test were larger than those by other methods. For flat coupons, as was described in Refs. [7–9], the bending modulus measured by the compression bending was almost always smaller than that by the 3-point bending test. However, this is not the case with the pipe configuration especially for the Types C and E specimens. The bending moduli for those specimens by means of the compression bending test are higher than those by the 3-point bending test. It is reasonable to infer that for relatively large diameter pipes (Type C) or pipes with a small bending modulus (Type E), a problem of local flattening by the loading device becomes more serious under the 3-point bending test. If we measure the deflection by the crosshead movement, this flattening results in the nominal increase of deflection and hence, the decrease of the bending modulus. This may be a major reason why the Types C and E specimens exhibited a different tendency from other types of the specimens, although we have not confirmed this by measuring the amount of flattening. 4.5. Applicability of elastica So far the data reduction was based on the direct measurement of A rather than using Eq. (4). In the experiment, a special device is required to measure A and from a view-point of experimental convenience, it is desirable to calculate A from Eqs.(4)–(6) by measuring only the crosshead movement, l. Fig. 13 is an example of comparison between the theory and the experiment in terms of the crosshead movement vs. the midspan deflection. Although there exist some discrepancies between the theory and the experiment, this difference is
Table 2 Comparison of test data between 3-point bending and compression bending Type
A B C D E
3-point bending
Compression bending
No. of specimens
Strength/MPa (CV/%)
Modulus/GPa (CV/%)
No. of specimens
Strength/MPa (CV/%)
Modulus/GPa (CV/%)
7 8 4 9 3
528 (15.7) 746 (11.4) 167 (8.9) 357 (14.0) 214 (5.4)
70.8 (3.9) 69.7 (4.4) 62.7 (10.7) 71.0 (8.5) 7.8 (12.8)
11 13 5 16 5
1018 (13.4) 1173 (15.6) 367 (3.7) 574 (7.9) 222 (2.1)
70.4 (7.9) 68.9 (3.4) 72.6 (1.1) 68.3 (5.8) 11.8 (9.1)
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almost negligible if we shift the experimental values to the left by some fixed amount. According to our calculation, this difference is mainly due to the elastic compressive deformation at the beginning of loading. If we modify the compressive strain, the experimental values coincide with those by the theory and hence, it may be concluded that a more sophisticated approach of using Eqs.(4)–(6) is also feasible.
5. Conclusions
Fig. 11. Bending modulus vs. specimen length (Type A).
The applicability of the compression bending test to pipe-shaped specimens was demonstrated. Comparing to the 3-point bending test, the bending strength by means of the compression bending test was much larger which proves the superiority of the present method. This tendency with the pipe-shaped specimens was clearer than that with flat coupons. As for the bending modulus, the measured values were comparable to those by the 3-point bending test except for pipes with large diameters such as the Type C specimens, or pipes with low moduli such as the Type E specimens. In the cases of the Types C and E specimens, the conventional 3-point bending test should not be used. It is concluded that the method proposed in this paper can be used to obtain reliable bending properties for pipe-shaped components.
Acknowledgements We sincerely thank Mr. H. Suzue and Mr. K. Kameda of Daiwa Seiko Co. Ltd. for their supplying test specimens. Thanks are also due to Mr. M. Yamazaki for his assistance in experiments. Fig. 12. Comparison of bending modulus (all types).
References
Fig. 13. Example of midspan deflection vs. crosshead movement.
[1] Whitney JM. Elasticity analysis of orthotropic beams under concentrated loads. Compos Sci Technol 1985;22:167–84. [2] Cui WC, Wisnom MR. Contact finite element analysis of threeand four- point short-beam bending of unidirectional composites. Compos Sci Technol 1992;45:323–54. [3] Bending test method of CFRP. 1988; JIS K 7074–1988. [4] Hojo M, Noguchi Y, Furue H, Matsui J. Bending test methods for advanced composites. In: 28th Annual Meeting on Structural Strength, The Japan Society for Aeronautical and Space Sciences; 1986. p. 370–3 (in Japanese). [5] Iwai H, Uemura M. Development of pure bending test method for advanced composites. In: 34th Annual Meeting on Structural Strength, The Japan Society for Aeronautical and Space Sciences; 1991. p. 70–3 (in Japanese). [6] Fukuda H. A new bending test method of advanced composites. Experimental Mechanics 1989;29:330–5. [7] Fukuda H. Compression bending test method for advanced composites. J Japan Soc Aero Space Sci 1993;41:482–7 (in Japanese).
H. Fukuda et al. / Composites Science and Technology 62 (2002) 2075–2081 [8] Fukuda H, Katoh H, Uesugi H. A modified procedure to measure bending strength and modulus of advanced composites by means of compression bending. J Compos Mater 1995;29:195–207. [9] Fukuda H, Itabashi M. Simplified compression bending test
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method for advanced composites. Composites, Part A 1999;30: 249–56. [10] Timoshenko SP, Gere JM. Theory of elastic stability, 2nd ed. McGraw-Hill; 1961. p. 76–82.