COMPOSITES SCIENCE AND TECHNOLOGY ELSEVIER Composites Science and Technology 60(2000)219-229 Compressive strengths of single carbon fibres and composite strands M. Shioya*, M. Nakatani Department of Organic and Polymeric Materials, Tokyo Institute of Technology, 2-12-1 O-okayama, Meguro-ku, Tokyo 152-8552, Japan Received 18 September 1998; received in revised form 7 June 1999: accepted 9 August 1999 y. Micro-compression and recoil tests have been carried out on single filaments of pitch- and polyacrylonitrile-based carbon fibres xial compression and bending tests were also carried out on unidirectional composite strands containing these fibres and a reduced compressive strength was calculated by dividing the fracture load of the composite strand by the cross-sectional area of the fibres. The fracture surfaces produced by different test methods were compared and a correlation between the compressive strength values determined by these test methods was investigated. The fracture surfaces of the fibres and composite strands showed different features depending on the type of fibre and matrix resin. The compressive strength of the composite strands increased with increasing matrix modulus. The compressive strengths of the fibres determined by the recoil test and from the axial compression test on the composite strand with a stiff matrix resin were almost in proportion to the strength determined with the micro-compression test. 2000 Elsevier Science Ltd. All rights reserved Keywords: A. Carbon fibres; A Polymer-matrix composites; B Fracture; B Strength; D Scanning electron m 1. Introduction In the loop test, a compressive stress is produced by bending the fibre into a loop. Thus, the compressive The axial compressive strength of carbon fibres is inferior stress is not uniformly distributed in the fibre cross-sec- to the tensile strength and decreases with increasing tensile tion and a tensile stress arises in the convex side of the modulus [1]. Thus, in the structural application of carbon- fibre. With the recoil test, a compressive stress is pro- fibre-reinforced composites, the superior tensile properties duced in the recoil process which takes place after a of the fibres are often not utilized to the maximum possible pretensioned fibre is cut between fixed ends. Lateral extent since the compressive strength of the fibres limits the displacements imposed on the fibre when the recoil loading capacity of the composites process is initiated cause flexural fracture [4], and vis- A considerable effort has been devoted to under- cous damping in the fibre and at the fixed ends of the standing the relationship between the compressive fibre affects the results [3]. In addition, the tested fibre strength and microstructure of the carbon fibres in should be sufficiently stronger in tension than in com- order to improve the compressive strength. To address pression. In a compression test gle-fibre com- these subjects, it is imperative that the compressive posite, residual stresses imposed on the fibre due to strength of the fibres be accurately determined. The matrix shrinkage affect the results. In the axial com small diameter of the carbon fibres, which is usually less pression test of a unidirectional composite, the stress than 10 um, causes difficulty in measuring the axial fields are much more complicated and the precise frac compressive strength. Several techniques have been ture mechanism should be elucidated in order to relate proposed including the loop test [2], the recoil test [3-5, the compressive strength of the composite to that of the the micro-compression test [6-9], compression test of a component fibres. It is possible that even if the compo- single-fibre composite [1, 10] and estimation from the site appears to fracture in compression, the component compressive strength of a unidirectional composite fibres are fractured in flexure microscopically. Thus, in view of applying a true axial compressive stress to a Corresponding author. Tel. +81-3-5734-2434: fax: +81-3-5734- single fibre, the micro-compression test, in which the fibre is directly compressed, is the most suitable. Such a test, however, requires laborious procedures for preparing 0266-3538/00/S. see front matter C 2000 Elsevier Science Ltd. All rights reserved PII:S0266-3538(99)00123-2
Compressive strengths of single carbon ®bres and composite strands M. Shioya*, M. Nakatani Department of Organic and Polymeric Materials, Tokyo Institute of Technology, 2-12-1 O-okayama, Meguro-ku, Tokyo 152-8552, Japan Received 18 September 1998; received in revised form 7 June 1999; accepted 9 August 1999 Abstract Micro-compression and recoil tests have been carried out on single ®laments of pitch- and polyacrylonitrile-based carbon ®bres. Axial compression and bending tests were also carried out on unidirectional composite strands containing these ®bres and a reduced compressive strength was calculated by dividing the fracture load of the composite strand by the cross-sectional area of the ®bres. The fracture surfaces produced by dierent test methods were compared and a correlation between the compressive strength values determined by these test methods was investigated. The fracture surfaces of the ®bres and composite strands showed dierent features depending on the type of ®bre and matrix resin. The compressive strength of the composite strands increased with increasing matrix modulus. The compressive strengths of the ®bres determined by the recoil test and from the axial compression test on the composite strand with a sti matrix resin were almost in proportion to the strength determined with the micro-compression test. # 2000 Elsevier Science Ltd. All rights reserved. Keywords: A. Carbon ®bres; A. Polymer-matrix composites; B. Fracture; B. Strength; D. Scanning electron microscopy 1. Introduction The axial compressive strength of carbon ®bres is inferior to the tensile strength and decreases with increasing tensile modulus [1]. Thus, in the structural application of carbon- ®bre-reinforced composites, the superior tensile properties of the ®bres are often not utilized to the maximum possible extent since the compressive strength of the ®bres limits the loading capacity of the composites. A considerable eort has been devoted to understanding the relationship between the compressive strength and microstructure of the carbon ®bres in order to improve the compressive strength. To address these subjects, it is imperative that the compressive strength of the ®bres be accurately determined. The small diameter of the carbon ®bres, which is usually less than 10 mm, causes diculty in measuring the axial compressive strength. Several techniques have been proposed including the loop test [2], the recoil test [3±5], the micro-compression test [6±9], compression test of a single-®bre composite [1,10] and estimation from the compressive strength of a unidirectional composite. In the loop test, a compressive stress is produced by bending the ®bre into a loop. Thus, the compressive stress is not uniformly distributed in the ®bre cross-section and a tensile stress arises in the convex side of the ®bre. With the recoil test, a compressive stress is produced in the recoil process which takes place after a pretensioned ®bre is cut between ®xed ends. Lateral displacements imposed on the ®bre when the recoil process is initiated cause ¯exural fracture [4], and viscous damping in the ®bre and at the ®xed ends of the ®bre aects the results [3]. In addition, the tested ®bre should be suciently stronger in tension than in compression. In a compression test on a single-®bre composite, residual stresses imposed on the ®bre due to matrix shrinkage aect the results. In the axial compression test of a unidirectional composite, the stress ®elds are much more complicated and the precise fracture mechanism should be elucidated in order to relate the compressive strength of the composite to that of the component ®bres. It is possible that even if the composite appears to fracture in compression, the component ®bres are fractured in ¯exure microscopically. Thus, in view of applying a true axial compressive stress to a single ®bre, the micro-compression test, in which the ®bre is directly compressed, is the most suitable. Such a test, however, requires laborious procedures for preparing 0266-3538/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved. PII: S0266-3538(99)00123-2 Composites Science and Technology 60 (2000) 219±229 * Corresponding author. Tel.: +81-3-5734-2434; fax: +81-3-5734- 2434. E-mail address: mshioya@o.cc.titech.ac.jp (M. Shioya)
M. Shioya, M. Nakatani/Composites Science and Technology 60(2000)219-229 specimens with a very small gage length and for adjust- plates prepared by curing these epoxy resins are shown ing the fibre and loading axes. It is beneficial, therefore, in Table 2. These values were determined according to to know the compatibility of various test results so that JIS K7113 [12] using a strain rate of 0.01 min-l.The a relatively simple method can be selected as a supple- tensile modulus was determined in the strain range from mental method, if a large number of fibres are to be 0.001 to 0.02 evaluated The composite strands with a circular cross-section In the present study, axial compressive strengths of vere prepared as follows. A carbon fibre tow was pitch- and polyacrylonitrile(PAN)-based carbon fibres soaked in liquid epoxy resin and passed through a die were determined by means of the micro-compression with an appropriate diameter to adjust the fibre volume and recoil tests on single fibres Axial compression and fraction For X7, X5 and N3 fibres, two fibre tows were axial compression bending tests [ll] were also carried combined before passing through the die. The resin out on unidirectional composite strands. A comparison impregnated carbon fibre tow was wound on a frame was made between the compressive strength values and cured in an air circulating oven. For the epoxy-A determined with these test methods resin, the resin impregnated tow was left for 18 h before curing in order to evaporate methyl ethyl ketone 2. Experimental 2. Materials Pitch- and polyacrylonitrile(PAN)-based carbon fibres with characteristics shown in Table I were used for the experiments. The tensile properties in this table are the values shown by the producers. These pitch-and PAN-based carbon fibres revealed different textures in the cross-section cut with a blade. The X7.X5 and n3 fibres had a pleat-like texture extending radially from the center of the cross-section as shown in Fig. 1 (a) This pleat-like texture was more distinctively developed a 5 um for the X7 and X5 fibres as compared with the N3 fibre which had lower tensile modulus. on the other hand he H4 and T4 fibres had no characteristic cross-section texture as shown in Fig. I(b) As the matrix of the unidirectional composite strand of carbon fibres, three types of epoxy resins named epoxy-A, B and C were used. These were the mixtures of diglycidyl ether of bisphenol A-type epoxy resin(Epi kote 828, Yuka Shell Epoxy), difunctional diluent (YED 205, Yuka Shell Epoxy), methylnadic acid anh dride, benzyldimethylamine and methyl ethyl ketone by the weight ratios of 100: 0: 90: 2.5: 15 for epoxy-A 20:80:100:4.75:0 for epoxy-Band0:100:100:4.75:0for epoxy-C. The cure conditions were 2 h at 110.C and additionally I h at 150C for epoxy-A, and 3 h at 140oC 5 um for epoxy-B and C. The tensile properties of the resin Fig 1. SEM images of cross-section of (a)X5 and (b) T4 fibres Table I Characteristics of carbon fibres Fibre Precursor material Number of filaments per tow Density/g cm Tensile properties Petroleum pitch 9.8 Petroleum pitch 1200 14 PAN 12.000
specimens with a very small gage length and for adjusting the ®bre and loading axes. It is bene®cial, therefore, to know the compatibility of various test results so that a relatively simple method can be selected as a supplemental method, if a large number of ®bres are to be evaluated. In the present study, axial compressive strengths of pitch- and polyacrylonitrile(PAN)-based carbon ®bres were determined by means of the micro-compression and recoil tests on single ®bres. Axial compression and axial compression bending tests [11] were also carried out on unidirectional composite strands. A comparison was made between the compressive strength values determined with these test methods. 2. Experimental 2.1. Materials Pitch- and polyacrylonitrile(PAN)-based carbon ®bres with characteristics shown in Table 1 were used for the experiments. The tensile properties in this table are the values shown by the producers. These pitch- and PAN-based carbon ®bres revealed dierent textures in the cross-section cut with a blade. The X7, X5 and N3 ®bres had a pleat-like texture extending radially from the center of the cross-section as shown in Fig. 1(a). This pleat-like texture was more distinctively developed for the X7 and X5 ®bres as compared with the N3 ®bre which had lower tensile modulus. On the other hand, the H4 and T4 ®bres had no characteristic cross-section texture as shown in Fig. 1(b). As the matrix of the unidirectional composite strands of carbon ®bres, three types of epoxy resins named epoxy-A, B and C were used. These were the mixtures of diglycidyl ether of bisphenol A-type epoxy resin (Epikote 828, Yuka Shell Epoxy), difunctional diluent (YED 205, Yuka Shell Epoxy), methylnadic acid anhydride, benzyldimethylamine and methyl ethyl ketone by the weight ratios of 100:0:90:2.5:15 for epoxy-A, 20:80:100:4.75:0 for epoxy-B and 0:100:100:4.75:0 for epoxy-C. The cure conditions were 2 h at 110C and additionally 1 h at 150C for epoxy-A, and 3 h at 140C for epoxy-B and C. The tensile properties of the resin plates prepared by curing these epoxy resins are shown in Table 2. These values were determined according to JIS K7113 [12] using a strain rate of 0.01 minÿ1 . The tensile modulus was determined in the strain range from 0.001 to 0.02. The composite strands with a circular cross-section were prepared as follows. A carbon ®bre tow was soaked in liquid epoxy resin and passed through a die with an appropriate diameter to adjust the ®bre volume fraction. For X7, X5 and N3 ®bres, two ®bre tows were combined before passing through the die. The resin impregnated carbon ®bre tow was wound on a frame and cured in an air circulating oven. For the epoxy-A resin, the resin impregnated tow was left for 18 h before curing in order to evaporate methyl ethyl ketone. Table 1 Characteristics of carbon ®bres Fibre Precursor material Number of ®laments per tow Diameter/mm Density/g cmÿ3 Tensile properties Modulus/GPa Strength/GPa X7 Petroleum pitch 4,000 9.8 2.16 720 3.6 X5 Petroleum pitch 4,000 10.1 2.14 520 3.6 N3 Coal pitch 3,000 10.3 2.00 296 3.4 H4 PAN 12,000 6.4 1.80 392 4.4 T4 PAN 12,000 6.8 1.80 235 4.9 Fig. 1. SEM images of cross-section of (a) X5 and (b) T4 ®bres. 220 M. Shioya, M. Nakatani / Composites Science and Technology 60 (2000) 219±229
M. Shioya, M. Nakatani/Composites Science and Technology 60(2000)219-229 Table 2 Tensile properties of matrix resins Test fiber Resin Modulus/ Strength/ Strain at Strain at Epoxy resin maximum stress failure EEE Microscope lens Loading piece 2. 2. Measurements of fibre volume fraction and cross- Mechanical stage Load cell section area The volume fractions of the fibres and voids in the Microscope stage composite strand were determined according to JIS K7075 [13] from the densities of the carbon fibre, epoxy (a)Micro-compression test resin and composite strand and the change of the mass of the composite strand when the matrix resin was burned off. The density was measured at 30C by a sink float method using a n-heptane, carbon tetrachloride and ethylene dibromide mixture. The volume fraction of Epoxy resin block the voids in the composite strands estimated in this way was less than 0.015 Composite strand The cross-section area of the fibres in the composit strand was determined from the linear density and the density of the fibres used for the composite strand Metal base 2.3. Micro-compression test Macturk et al. have measured the axial compressive (b)Axial compression test (c) Axial compression bending test strength of single carbon fibres by using a miniature loading apparatus [7]. In their apparatus, the compres- Fig. 2. Schematics illustrations of (a) micro-compression, (b)axial compression and(c) axial compression bending tests. sive load is applied to the fibre through a piezoelectric element while displacement is detected by an optical probe. The compressive load is calculated from the applied voltage and the displacement of the piezoelectric 2. 4. Recoil test element. Thus, the value of the compressive load relies on the accurate correction of the test fixture compliance A single carbon fibre was bonded to a cardboard In the present study, the axial compressive strength of across a rectangular window 25 mm long cut out from single carbon fibres was measured using a miniature the cardboard. To bond the fibre to the cardboard, a loading apparatus where the fibre was compressed by mixture of epoxy resin(Epikote 828, Yuka Shell Epoxy moving a mechanical stage and the compressive load and triethylenetetramin by the weight ratio of 10: I was was directly detected with a load cell as shown in Fig. applied and cured for 120 min at 60C. The diameter of 2(a)[9]. A carbon fibre which was cut perpendicularly to each fibre was determined from the diffraction of He- ne fibre axis and having a flat cross-section was bonded Ne laser beam. The cardboard with the fibre was grip to a carbon tool steel piece so that the gage length ped with the clamps of a mechanical tester and both became from two to three times fibre diameter. The sides of the window were scissored before testing. The diameter of each fibre was determined from the diffrac- fibre was extended to a desired tensile stress level and tion of He-Ne laser beam from the fibre. The steel piece, cut at the center of the gage length with very sharp sur- with the fibre, was mounted on the mechanical stage of gical scissors. Both halves of the fibre were carefully the loading apparatus under observation using an opti- collected from the clamps and observed to ascertain cal microscope. The mechanical stage was moved at a whether or not compressive fracture occurred during the constant velocity of 4.46 mm min- and the fibre was recoil process. Several fibres were tested at each stress axially compressed between the mechanical stage and a level and by changing the stress levels, the fracture loading piece. In the following, quoted values of the probability versus pretensioning stress curve was compressive strength are the averages of at least 6 obtained. For each type of carbon fibre, more than 25 determinations on individual fibres filaments were tested
2.2. Measurements of ®bre volume fraction and crosssection area The volume fractions of the ®bres and voids in the composite strand were determined according to JIS K7075 [13] from the densities of the carbon ®bre, epoxy resin and composite strand and the change of the mass of the composite strand when the matrix resin was burned o. The density was measured at 30C by a sink- ¯oat method using a n-heptane, carbon tetrachloride and ethylene dibromide mixture. The volume fraction of the voids in the composite strands estimated in this way was less than 0.015. The cross-section area of the ®bres in the composite strand was determined from the linear density and the density of the ®bres used for the composite strand. 2.3. Micro-compression test Macturk et al. have measured the axial compressive strength of single carbon ®bres by using a miniature loading apparatus [7]. In their apparatus, the compressive load is applied to the ®bre through a piezoelectric element while displacement is detected by an optical probe. The compressive load is calculated from the applied voltage and the displacement of the piezoelectric element. Thus, the value of the compressive load relies on the accurate correction of the test ®xture compliance. In the present study, the axial compressive strength of single carbon ®bres was measured using a miniature loading apparatus where the ®bre was compressed by moving a mechanical stage and the compressive load was directly detected with a load cell as shown in Fig. 2(a) [9]. A carbon ®bre which was cut perpendicularly to the ®bre axis and having a ¯at cross-section was bonded to a carbon tool steel piece so that the gage length became from two to three times ®bre diameter. The diameter of each ®bre was determined from the diraction of He±Ne laser beam from the ®bre. The steel piece, with the ®bre, was mounted on the mechanical stage of the loading apparatus under observation using an optical microscope. The mechanical stage was moved at a constant velocity of 4.46 mm minÿ1 and the ®bre was axially compressed between the mechanical stage and a loading piece. In the following, quoted values of the compressive strength are the averages of at least 6 determinations on individual ®bres. 2.4. Recoil test A single carbon ®bre was bonded to a cardboard across a rectangular window 25 mm long cut out from the cardboard. To bond the ®bre to the cardboard, a mixture of epoxy resin (Epikote 828, Yuka Shell Epoxy) and triethylenetetramin by the weight ratio of 10:1 was applied and cured for 120 min at 60C. The diameter of each ®bre was determined from the diraction of He± Ne laser beam. The cardboard with the ®bre was gripped with the clamps of a mechanical tester and both sides of the window were scissored before testing. The ®bre was extended to a desired tensile stress level and cut at the center of the gage length with very sharp surgical scissors. Both halves of the ®bre were carefully collected from the clamps and observed to ascertain whether or not compressive fracture occurred during the recoil process. Several ®bres were tested at each stress level and by changing the stress levels, the fracture probability versus pretensioning stress curve was obtained. For each type of carbon ®bre, more than 25 ®laments were tested. Table 2 Tensile properties of matrix resins Resin Modulus/ GPa Strength/ GPa Strain at maximum stress Strain at failure Epoxy-A 3.0 75 0.027 0.027 Epoxy-B 2.7 64 0.035 0.088 Epoxy-C 2.4 51 0.028 0.15< Fig. 2. Schematics illustrations of (a) micro-compression, (b) axial compression and (c) axial compression bending tests. M. Shioya, M. Nakatani / Composites Science and Technology 60 (2000) 219±229 221
M. Shioya, M. Nakatani/Composites Science and Technology 60(2000)219-229 2.5. Axial compression test of composite strand 3. Results and discussion Determination of the axial compressive strength of 3. Fracture surface ne fibres from the axial compressive strength of uni- directional composites has been reviewed by Kozey et Fracture surfaces of the carbon fibres and composite aL. [14]. In the present study, the axial compression test strands produced by various compression tests revealed of the composite strands was carried out by supporting different features depending on the types of fibres and, both ends of the specimen with resin blocks as shown in in the case of composite strands, the matrix resins Fig. 2(b)in order to prevent local fracture at the loading During the micro-compression tests of single fibres points. A circular hole was drilled through rectangula two types of fracture surfaces were produced. One is a epoxy resin blocks with cross-section sizes of 20 mm by fracture surface inclined with an angle of about 450 20 mm and with a thickness of 10 mm, in the thickness against the fibre axis as shown in Fig 3(a )and the other direction. Both ends of the specimen were put into the is a fracture surface which runs almost transversely to holes of the resin blocks and bonded with an epoxy the fibre axis. The formation of transverse fracture sur- resin so that the gage length of the specimen between face was only observed by the optical microscopy during two resin blocks became 5 mm. This gage length assured the micro-compression test because fractured specimens compressive fracture of the specimen before buckling. suitable for SEM observation could not be collected The specimen with resin blocks was compressed by successfully. The inclined fracture surface was produced using a mechanical tester with a crosshead speed of 0.5 for X7 and X5 pitch-based carbon fibres In the cases of mm min-l Reduced compressive strength of the com- N3 pitch-based carbon fibre, and H4 and T4 PAN ponent fibres was calculated by dividing the fracture based carbon fibres, both the inclined fracture surface load of the composite strand with the cross-section area and a transverse fracture surface were produced. of the fibres The compressive fracture by the recoil tests took place almost invariably in the zone close to the fixed ends of 2.6. Axial compression bending test of composite strand the fibre. During the recoil tests of single fibres, two types of fracture surfaces were produced. One is a frac- used techniques while these tests are insufficient for the fibre axis as shown in Fig. 3(b)and the other l p The three- and the four-point bending tests are widely ture surface inclined with an angle of about 45 agains advanced composite materials because local fracture fracture surface suggesting flexural fracture as shown in tends to occur at the loading points owing to stress Fig 3(c). In Fig 3(c), two regions with different features concentration [15]. Fukuda has proposed a method and which can be attributed to the tensile and compression a loading zig for the axial compression bending tests to sides of the fibre, appeared in a fibre cross-section. The overcome the disadvantages of the three- and the four- inclined fracture surface was produced for X7, X5 and point bending tests [16] N3 fibres. The fracture surface suggesting flexural fracture In the present study, the axial compression bending was produced for H4 and T4 fibres tests were carried out on the composite strands without The difference between the pitch- and PAN-based using any special loading zig as shown in Fig. 2(c)[11]. carbon fibres in the appearance of the fracture surface The composite strand was axially compressed between produced by the micro-compression and recoil tests is metal bases attached to the mechanical tester. without considered to be related to the fibre cross-section texture applying a bending moment at both ends of the speci- It seems that the inclined fracture surface is produced for men. The metal bases had a dimple in order to prevent the fibres with the pleat-like cross-section texture recoiling of the specimen, and both ends of the speci During the axial compression tests of composite men were ground into a hemispherical shape with strands, two types of fracture surfaces of the composite abrasive. By increasing the axial compressive load, the strands were produced. One is a fracture surface specimen was buckled, bent into an increasing curva- inclined with an angle of about 45 against the fibre axis ture and eventually fractured at either the convex or as shown in Fig 4a)and the other is a fracture surface the concave side of the specimen due to the tensile or which runs almost transversely to the fibre axis as the compressive stress whichever was critical. The axial shown in Fig. 4(b). The inclined fracture surface was displacement was calculated from the loading time and produced for the X7, X5 and N3 fibre composite the crosshead speed. The gage length was 50 mm and strands. The transverse fracture surface was produced the crosshead speed was 0.5 mm min-. Reduced for the H4 fibre composite strands. In the case of the strength of the component fibres was calculated by T4 /epoxy-A and T4/epoxy-B composite strands, both of dividing the bending strength of the composite strand these two types of fracture surfaces were produced with the fibre volume fraction. The axial compression Near the transverse fracture surface, segmented fibre bending test will be simply called a bending test hen- bundles which were inclined from the longitudinal direction ceforth of the composite strand, suggesting microbuckling of the
2.5. Axial compression test of composite strand Determination of the axial compressive strength of the ®bres from the axial compressive strength of unidirectional composites has been reviewed by Kozey et al. [14]. In the present study, the axial compression test of the composite strands was carried out by supporting both ends of the specimen with resin blocks as shown in Fig. 2(b) in order to prevent local fracture at the loading points. A circular hole was drilled through rectangular epoxy resin blocks with cross-section sizes of 20 mm by 20 mm and with a thickness of 10 mm, in the thickness direction. Both ends of the specimen were put into the holes of the resin blocks and bonded with an epoxy resin so that the gage length of the specimen between two resin blocks became 5 mm. This gage length assured compressive fracture of the specimen before buckling. The specimen with resin blocks was compressed by using a mechanical tester with a crosshead speed of 0.5 mm minÿ1 . Reduced compressive strength of the component ®bres was calculated by dividing the fracture load of the composite strand with the cross-section area of the ®bres. 2.6. Axial compression bending test of composite strand The three- and the four-point bending tests are widely used techniques while these tests are insucient for advanced composite materials because local fracture tends to occur at the loading points owing to stress concentration [15]. Fukuda has proposed a method and a loading zig for the axial compression bending tests to overcome the disadvantages of the three- and the fourpoint bending tests [16]. In the present study, the axial compression bending tests were carried out on the composite strands without using any special loading zig as shown in Fig. 2(c) [11]. The composite strand was axially compressed between metal bases attached to the mechanical tester, without applying a bending moment at both ends of the specimen. The metal bases had a dimple in order to prevent recoiling of the specimen, and both ends of the specimen were ground into a hemispherical shape with abrasive. By increasing the axial compressive load, the specimen was buckled, bent into an increasing curvature and eventually fractured at either the convex or the concave side of the specimen due to the tensile or the compressive stress whichever was critical. The axial displacement was calculated from the loading time and the crosshead speed. The gage length was 50 mm and the crosshead speed was 0.5 mm min-1. Reduced strength of the component ®bres was calculated by dividing the bending strength of the composite strand with the ®bre volume fraction. The axial compression bending test will be simply called a bending test henceforth. 3. Results and discussion 3.1. Fracture surface Fracture surfaces of the carbon ®bres and composite strands produced by various compression tests revealed dierent features depending on the types of ®bres and, in the case of composite strands, the matrix resins. During the micro-compression tests of single ®bres, two types of fracture surfaces were produced. One is a fracture surface inclined with an angle of about 45 against the ®bre axis as shown in Fig. 3(a) and the other is a fracture surface which runs almost transversely to the ®bre axis. The formation of transverse fracture surface was only observed by the optical microscopy during the micro-compression test because fractured specimens suitable for SEM observation could not be collected successfully. The inclined fracture surface was produced for X7 and X5 pitch-based carbon ®bres. In the cases of N3 pitch-based carbon ®bre, and H4 and T4 PANbased carbon ®bres, both the inclined fracture surface and a transverse fracture surface were produced. The compressive fracture by the recoil tests took place almost invariably in the zone close to the ®xed ends of the ®bre. During the recoil tests of single ®bres, two types of fracture surfaces were produced. One is a fracture surface inclined with an angle of about 45o against the ®bre axis as shown in Fig. 3(b) and the other is a fracture surface suggesting ¯exural fracture as shown in Fig. 3(c). In Fig. 3(c), two regions with dierent features, which can be attributed to the tensile and compression sides of the ®bre, appeared in a ®bre cross-section. The inclined fracture surface was produced for X7, X5 and N3 ®bres. The fracture surface suggesting ¯exural fracture was produced for H4 and T4 ®bres. The dierence between the pitch- and PAN-based carbon ®bres in the appearance of the fracture surface produced by the micro-compression and recoil tests is considered to be related to the ®bre cross-section texture. It seems that the inclined fracture surface is produced for the ®bres with the pleat-like cross-section texture. During the axial compression tests of composite strands, two types of fracture surfaces of the composite strands were produced. One is a fracture surface inclined with an angle of about 45o against the ®bre axis as shown in Fig. 4(a) and the other is a fracture surface which runs almost transversely to the ®bre axis as shown in Fig. 4(b). The inclined fracture surface was produced for the X7, X5 and N3 ®bre composite strands. The transverse fracture surface was produced for the H4 ®bre composite strands. In the case of the T4/epoxy-A and T4/epoxy-B composite strands, both of these two types of fracture surfaces were produced. Near the transverse fracture surface, segmented ®bre bundles which were inclined from the longitudinal direction of the composite strand, suggesting microbuckling of the 222 M. Shioya, M. Nakatani / Composites Science and Technology 60 (2000) 219±229
M. Shioya, M. Nakatani/Composites Science and logy60(2000)219229 The SEM images of the X5, T4 and H4 fibre comp site strands using epoxy-A matrix after bending tests are shown in Fig. 5. Final fracture of the X5/epoxy-A composite strand seemed to initiate from the tensile side of the specimen although definite determination of the fracture mode of this specimen from the observation of the fracture process was difficult. Final fracture of the T4/epoxy-A composite strand was observed to initiate from the tensile side of the specimen. On the other hand, final fracture of the H4/epoxy-A composite strand was observed to initiate from the compressive side of the specimen 10m In the compression side of the X5/epoxy-A composite strand, an inclined fracture surface was produced. In the compression side of the T4 epoxy-A composite strand tep wise surfaces transverse to the fibre axis were pro duced. Therefore, the fracture surfaces produced by the bending test, in the compi side of the resemble those of the axial compression It should be noted that the fracture surface is pro duced after the fracture criterion is reached and does not necessarily manifest the fracture criterion 3. 2. Compressive strength determined with the mIcro-compression fest 10 um The tensile and compressive strengths of various carbon fibres are plotted against the tensile modulus in Fig. 6. In this figure, tensile properties referred to Table I and the compressive strength was determined with the micro- compression test. The compressive strength of carbon fibres is lower than the tensile strength and decreases with increasing tensile modulus. It has been reported in a previous paper [9] that the length dependence and distribution of the compressive strength of the carbon fibre are significantly smaller as compared with those of the tensile strength Dobb et al. have discussed that improved compressive strength requires disordered regions in the carbon fibre 10 um homogeneously distributed throughout the fibre and crystallites should have dimensions below about 5 nm in all directions [5]. The present authors have proposed Fig3. SEM images of fracture surfaces of (a) x5 fibre after micro- that the compressive strength is limited by the buckling compression test and(b)N3 and(c)T4 fibres after recoil test. stress of individual carbon layers in the transversely unsupported regions of the crystallites, the length of the fibres, were produced as shown in Fig 4(c). In the trans- unsupported regions being determined by the axial verse fracture surface, fibre cross-sections characteristic to length of the microvoids [9]. By transferring the critical posite strand was deformed into a way shape over a osTE gth or carbe obtained for the axile flexural fracture, and debonding of the fibre-matrix inter- stress to cause buckling of a bar to the faces were also revealed as shown in Fig 4(d) following expression ha In the case of the T4/epoxy-C composite strand, frac- compressive str ture of the fibres and matrix resin did not take place poa S3 When the compression load was removed, the wavy where Eo is the longitudinal modulus of the carbon shape disappeared within a few tens of minutes layer stacks parallel to the layer plane(1020 GPa)[171
®bres, were produced as shown in Fig. 4(c). In the transverse fracture surface, ®bre cross-sections characteristic to ¯exural fracture, and debonding of the ®bre±matrix interfaces were also revealed as shown in Fig. 4(d). In the case of the T4/epoxy-C composite strand, fracture of the ®bres and matrix resin did not take place even at the maximum compression load but the composite strand was deformed into a wavy shape over a whole length owing to microbuckling of the ®bres. When the compression load was removed, the wavy shape disappeared within a few tens of minutes. The SEM images of the X5, T4 and H4 ®bre composite strands using epoxy-A matrix after bending tests are shown in Fig. 5. Final fracture of the X5/epoxy-A composite strand seemed to initiate from the tensile side of the specimen although de®nite determination of the fracture mode of this specimen from the observation of the fracture process was dicult. Final fracture of the T4/epoxy-A composite strand was observed to initiate from the tensile side of the specimen. On the other hand, ®nal fracture of the H4/epoxy-A composite strand was observed to initiate from the compressive side of the specimen. In the compression side of the X5/epoxy-A composite strand, an inclined fracture surface was produced. In the compression side of the T4/epoxy-A composite strand, step wise surfaces transverse to the ®bre axis were produced. Therefore, the fracture surfaces produced by the bending test, in the compression side of the specimen, resemble those of the axial compression test. It should be noted that the fracture surface is produced after the fracture criterion is reached and does not necessarily manifest the fracture criterion. 3.2. Compressive strength determined with the micro-compression test The tensile and compressive strengths of various carbon ®bres are plotted against the tensile modulus in Fig. 6. In this ®gure, tensile properties referred to Table 1 and the compressive strength was determined with the microcompression test. The compressive strength of carbon ®bres is lower than the tensile strength and decreases with increasing tensile modulus. It has been reported in a previous paper [9] that the length dependence and distribution of the compressive strength of the carbon ®bre are signi®cantly smaller as compared with those of the tensile strength. Dobb et al. have discussed that improved compressive strength requires disordered regions in the carbon ®bre homogeneously distributed throughout the ®bre and crystallites should have dimensions below about 5 nm in all directions [5]. The present authors have proposed that the compressive strength is limited by the buckling stress of individual carbon layers in the transversely unsupported regions of the crystallites, the length of the unsupported regions being determined by the axial length of the microvoids [9]. By transferring the critical stress to cause buckling of a bar to the micro scale, the following expression has been obtained for the axial compressive strength of carbon ®bres,c. c 3Eofd2 002 48o 2S3 1 where Eo is the longitudinal modulus of the carbon layer stacks parallel to the layer plane (1020 GPa) [17], Fig. 3. SEM images of fracture surfaces of (a) X5 ®bre after microcompression test and (b) N3 and (c) T4 ®bres after recoil test. M. Shioya, M. Nakatani / Composites Science and Technology 60 (2000) 219±229 223
M. Shioya, M. Nakatani/ Composites Science and Technology 60(2000)219-229 a 10 um (d) O um Fig. 4. SEM images of fracture surfaces of (a)X7epoxy.A and(b) H4/epoxy.A composite strands after axial compression test and magnified images of fibres near fracture surface of (c)T4/epoxy-B and(d) H4/epoxy.A composite strands Po the density of graphite(2.26 g cm-3), pr the density of the compressive strength of the fibre can be obtained by fibre, doo2 the interlayer spacing of carbon layer stacks, finding the pretensioning stress at which compressive S3 the average area of microvoid cross-section per fracture takes place during the recoil process ular to the fibre axis and a the ratio of the axial length In the actual test, the compressive fracture occurs against the transverse diameter of the microvoids. The stocastically, so that the probability of the compressive relation between the compressive strength determined with fracture, F, is obtained as a function of the pretensioning the micro-compression test and the average area of micro- stress, o. The fracture probability versus pretensioning void cross-section determined with small-angle X-ray stress curves obtained for two types of carbon fibres are scattering is shown in Fig. 7 together with the compressive shown in Fig 8. The fracture probability can be repre- strength predicted by Eq (1)for a= 3.2 sented by a logistic distribution function [4] 3.3. Compressive strength determined with the recoil test fla)- exp(o+ Bio) +exp(o+Bio) The development of compressive stress during the recoil process of a fibre has been described by Allen [3]. where Bo and BI are the constants. In Fig. 8, the best fit When the pretensioned fibre is cut between fixed ends, a of the above equation to the observed fracture prob- zero stress front moves toward the fixed end of the fibre ability is shown by solid lines. From the logistic dis- as the initial tensile strain energy is converted to kinetic tribution function, the compressive strength was energy. After the zero stress front reaches at the fixed determined as the pretensioning stress at the fracture end of the fibre, the kinetic energy is transformed back probability of 0.5 into strain energy and a compressive stress begins to compressive strength determined with the recoil propagate back toward the free end of the fibre. If test is almost in proportion to the value determined with energy dissipation due to damping in the fibre and at the the micro-compression test as shown in Fig 9. The ratio fixed end of the fibre is neglected, the compressive stress of the compressive strength determined with the recoil is equal in magnitude to the pretensioning stress. Thus, test against those of the micro-compression test is 0.74
o the density of graphite (2.26 g cmÿ3 ), f the density of ®bre, d002 the interlayer spacing of carbon layer stacks, S3 the average area of microvoid cross-section perpendicular to the ®bre axis and the ratio of the axial length against the transverse diameter of the microvoids. The relation between the compressive strength determined with the micro-compression test and the average area of microvoid cross-section determined with small-angle X-ray scattering is shown in Fig. 7 together with the compressive strength predicted by Eq. (1) for 3:2. 3.3. Compressive strength determined with the recoil test The development of compressive stress during the recoil process of a ®bre has been described by Allen [3]. When the pretensioned ®bre is cut between ®xed ends, a zero stress front moves toward the ®xed end of the ®bre as the initial tensile strain energy is converted to kinetic energy. After the zero stress front reaches at the ®xed end of the ®bre, the kinetic energy is transformed back into strain energy and a compressive stress begins to propagate back toward the free end of the ®bre. If energy dissipation due to damping in the ®bre and at the ®xed end of the ®bre is neglected, the compressive stress is equal in magnitude to the pretensioning stress. Thus, the compressive strength of the ®bre can be obtained by ®nding the pretensioning stress at which compressive fracture takes place during the recoil process. In the actual test, the compressive fracture occurs stocastically, so that the probability of the compressive fracture, F, is obtained as a function of the pretensioning stress, . The fracture probability versus pretensioning stress curves obtained for two types of carbon ®bres are shown in Fig. 8. The fracture probability can be represented by a logistic distribution function [4], F exp 0 1 1 exp 0 1 2 where 0 and 1 are the constants. In Fig. 8, the best ®t of the above equation to the observed fracture probability is shown by solid lines. From the logistic distribution function, the compressive strength was determined as the pretensioning stress at the fracture probability of 0.5. The compressive strength determined with the recoil test is almost in proportion to the value determined with the micro-compression test as shown in Fig. 9. The ratio of the compressive strength determined with the recoil test against those of the micro-compression test is 0.74. Fig. 4. SEM images of fracture surfaces of (a) X7/epoxy-A and (b) H4/epoxy-A composite strands after axial compression test and magni®ed images of ®bres near fracture surface of (c) T4/epoxy-B and (d) H4/epoxy-A composite strands. 224 M. Shioya, M. Nakatani / Composites Science and Technology 60 (2000) 219±229
M. Shioya, M. Nakatani/Composites Science and Technology 60(2000)219-229 3 后2 0.5mm 0 0 200 400600 800 Tensile modulus /GPa Fg.6.(口,■) Tensile and(O.●) compressive strength versus tensile modulus for(口,O) pitch- and(■,●) PAN-based carbon fibres Compressive strength was determined with micro-compression test. 2.5 22a0 0.5mm 20 1.5 ① 1.0 0.5 0DD 25 20 00 0.5mm Cross-section area/nm Fig. 5. SEM images of (a)X5/epoxy.A, (b)T4/epoxy.A and(c)H4 pressive strength determined with epoxy.A composite strands after axial compression bending test. versus average area of microvoid cross-section perpendicular to fibre axis, S,, for(O)pitch- and(O)PAN-based carbon fibres. Solid line shows relation of Eq (1)for a=3.2. If there is an energy dissipation during the recoil pro- cess due to damping in the fibre and at the fixed end of back into strain energy uniformly over the entire cross- the fibre, the compressive stress applied to the fibre section. In this case, the recoil test underestimates the becomes lower than the pretensioning stress. Thus, the compressive strength of the fibre. The obtained ratio of recoil test overestimates the compressive strength of the 0. 74 indicates the occurrence of flexural fracture fibre. If. on the other hand. flexural deformation takes place during the recoil process, the compressive stress is 3.4. Compressive strength determined with the axial not distributed uniformly in the cross-section. That is, compression test of the composite stran the compressive stress at the concave side of the fibre becomes larger as compared with the compressive stress The reduced compressive strength of the carbon fibres which will arise when the kinetic energy is transformed was determined by the compression tests of the composite
If there is an energy dissipation during the recoil process due to damping in the ®bre and at the ®xed end of the ®bre, the compressive stress applied to the ®bre becomes lower than the pretensioning stress. Thus, the recoil test overestimates the compressive strength of the ®bre. If, on the other hand, ¯exural deformation takes place during the recoil process, the compressive stress is not distributed uniformly in the cross-section. That is, the compressive stress at the concave side of the ®bre becomes larger as compared with the compressive stress which will arise when the kinetic energy is transformed back into strain energy uniformly over the entire crosssection. In this case, the recoil test underestimates the compressive strength of the ®bre. The obtained ratio of 0.74 indicates the occurrence of ¯exural fracture. 3.4. Compressive strength determined with the axial compression test of the composite strand The reduced compressive strength of the carbon ®bres was determined by the compression tests of the composite Fig. 5. SEM images of (a) X5/epoxy-A, (b) T4/epoxy-A and (c) H4/ epoxy-A composite strands after axial compression bending test. Fig. 6. (&,&) Tensile and (*, *) compressive strength versus tensile modulus for (&, *) pitch- and (&, *) PAN-based carbon ®bres. Compressive strength was determined with micro-compression test. Fig. 7. Compressive strength determined with micro-compression test versus average area of microvoid cross-section perpendicular to ®bre axis, S3, for (*) pitch- and (*) PAN-based carbon ®bres. Solid line shows relation of Eq. (1) for 3:2. M. Shioya, M. Nakatani / Composites Science and Technology 60 (2000) 219±229 225
M. Shioya, M. Nakatani/ Composites Science and Technology 60(2000)219-229 1.0 2.5 8 看20 感06 2∽ 1.5 0.4 方1.0 0.2 E8g 00.51.01.52.02.5 0051.01.5202.5 Tensile stress /GPa Compressive strength from Fig. 8. Probability, F, that compressive fracture occurs at stress level, micro-compression test / GPa o, for(O)X5 and(o)T4 fibres. Solid lines show relations of Eq (2) pression test of carbon fibre/ th determined with axial com- Fig. 10. Reduced co pressive strength determined with micro-compression test for (O) 2.5 pitch-and(o) PAN-based carbon fibres 2.0 It is considered that the larger reduced compressive trength than the compressive strength of bare fibres, is obtained owing to the ability of the surrounding matrix 方方15 to prevent lateral displacements of the fibres at the fracture points. In the case of bare fibres, the fibres split into pieces after the carbon layers in the fibres are 1.0 buckled at the critical load, accompanying lateral dis- placements. On the other hand, in the case of the com- the alignment of the fibres can be 0.5 maintained even though the carbon layers in the fibres are buckled. Thus, the compressive load can be trans mitted through the damaged region, beyond the fracture 00.51.01.52.02.5 load of the bare fibres It is considered that the selection of the matrix resin Compressive strength from has an important influence on the reduced compressive micro-compression test /GPa strength. The variation of the axial compressive strength nal composites with the properties etermined with micro-compression test for(O) pitch-and(O)PAN. the matrix can be predicted by Rosen's model [18]. In directional composites is limited by the buckling stress of the component fibres supported elastically by the strands using the matrix resin with a tensile modulus of matrix, where buckling of the fibres occurs in either the 3.0 GPa. The reduced compressive strength is almost in shear or the extension mode. In the shear mode, the proportion to the compressive strength determined with fibres buckle into sinusoidal wave forms with coincident the micro-compression test as shown in Fig. 10. The phases so that the buckled fibres can be superimposed ratio of the reduced compressive strength against the with each other by translation in the transverse direc compressive strength determined with the micro-com- tion of the composite. In this case, the matrix between pression test is 1. 15. Therefore, if a stiff resin was used the fibres is deformed in shear In the extension mode, for the matrix, the compressive strength of the fibres are the phases of adjacent waves differ by I so that the sufficiently utilized in the compressive strength of uni- tensile and compressive deformations of the matrix, in directional composites. the transverse direction of the composite, take place
strands using the matrix resin with a tensile modulus of 3.0 GPa. The reduced compressive strength is almost in proportion to the compressive strength determined with the micro-compression test as shown in Fig. 10. The ratio of the reduced compressive strength against the compressive strength determined with the micro-compression test is 1.15. Therefore, if a sti resin was used for the matrix, the compressive strength of the ®bres are suciently utilized in the compressive strength of unidirectional composites. It is considered that the larger reduced compressive strength than the compressive strength of bare ®bres, is obtained owing to the ability of the surrounding matrix to prevent lateral displacements of the ®bres at the fracture points. In the case of bare ®bres, the ®bres split into pieces after the carbon layers in the ®bres are buckled at the critical load, accompanying lateral displacements. On the other hand, in the case of the composite strand, the alignment of the ®bres can be maintained even though the carbon layers in the ®bres are buckled. Thus, the compressive load can be transmitted through the damaged region, beyond the fracture load of the bare ®bres. It is considered that the selection of the matrix resin has an important in¯uence on the reduced compressive strength. The variation of the axial compressive strength of the unidirectional composites with the properties of the matrix can be predicted by Rosen's model [18]. In his model, the axial compressive strength of the unidirectional composites is limited by the buckling stress of the component ®bres supported elastically by the matrix, where buckling of the ®bres occurs in either the shear or the extension mode. In the shear mode, the ®bres buckle into sinusoidal wave forms with coincident phases so that the buckled ®bres can be superimposed with each other by translation in the transverse direction of the composite. In this case, the matrix between the ®bres is deformed in shear. In the extension mode, the phases of adjacent waves dier by so that the tensile and compressive deformations of the matrix, in the transverse direction of the composite, take place Fig. 9. Compressive strength determined with recoil test versus that determined with micro-compression test for (*) pitch- and (*) PANbased carbon ®bres. Fig. 10. Reduced compressive strength determined with axial compression test of carbon ®bre/epoxy-A composite strands versus compressive strength determined with micro-compression test for (*) pitch- and (*) PAN-based carbon ®bres. Fig. 8. Probability, F, that compressive fracture occurs at stress level, , for (*) X5 and (*) T4 ®bres. Solid lines show relations of Eq. (2). 226 M. Shioya, M. Nakatani / Composites Science and Technology 60 (2000) 219±229
M. Shioya, M. Nakatani/Composites Science and Technology 60(2000)219-229 alternately along the longitudinal direction of the com posite. By using a two-dimensional composite model, the axial compressive strength of the composite, oe, has been derived 1.0 Em v2(1+v)(1-v 0.8 for the shear mode and b06 yeE Oc 80.4 for the extension mode. In the above equations, Em, Gr and Vm are the tensile modulus, shear modulus and 0.2 Poisson ratio of the matrix and Er and v the tensile modulus and volume fraction of the fibres For the carbon fibre/epoxy resin systems used in this study, the critical stress which causes fracture in the Tensile modulus/GPa extension mode is higher than that in the shear mode Thus, the compressive strength of the composite strands Fig. Il. Compressive strength of composite strand versus tensile used in this study is given by Eq- (3). The dotted line in modulus of matrix for (O)XS and (o) Ta foe, relation of Eq(3) Fig. II shows the compressive strength of the composite using epoxy. A B and C matrices. Dotted line show strand predicted by Eq(3)for v=0.42, Vm=0.33 and strength of X5 and T4 fibre composite strands using b=tnF various values of Emm. In this figure, the compressive (5) different matrix resins are also shown. The experimental values are extremely lower than the predicted values. As where I is the moment of inertia of area, t the thickness qualitatively predicted by Rosen's model, however, the of the specimen measured in the bending direction, Fb compressive strength increases with increasing matrix the compression load at fracture and 8, the deflection at modulus for the T4 fibre composite strands. The matrix fracture. The deflection can be calculated from the axial modulus dependence of the compressive strength of the displacement, &a, using the equations, X5 fibre composite strands is much smaller than that of the T4 fibre composite strands δa E(P) This is because the compressive strength of the X5 ()」 fibre composite strand is almost limited by the fibre trength. That is, the reduced compressive strength of 8r p the X5 fibre at the lowest matrix modulus of 2. 4 GPa is L K(p) 0.49 GPa, which is close to the compressive strength of this fibre determined with the micro-compression test, where K(p) and E(p) are the complete elliptic integrals 0.51 GPa. Thus, the compressive strength of this com- of the first and the second kinds and L is the specimen posite strand cannot be increased even if the matrix length. If the composite strand shows a falling load modulus is increased above 2. 4 GPa. On the other hand, compression curve or the accurate determination of the the reduced compressive strength of the T4 fibre at the cross-section size is difficult, the bending strength can be matrix modulus of 2.4 GPa is only 0.59 GPa, which is practically estimated by using an effective cross-section lower than the compressive strength of this fibre deter- size of the composite strand at fracture, which can be mined with the micro-compression test, 2.0 GPa. Thus, obtained with the knowledge of the elastic modulus of the compressive strength of this composite strand can be the composite strand [ll increased by increasing the matrix modulus until the The bending strength of the composite strands using fibre strength is reached the matrix with a tensile modulus of 3.0 GPa and the reduced strength of the component fibres are shown in 3.5. Compressive strength determined with the axial Table 3. Among the composite strands shown in Table compression bending test of composite strand 3, only the H4 fibre composite strand finally fractured from compression. It is found that the reduced strength With the axial compression bending test of the com- is larger than the tensile or compressive strength of the posite strand, the bending strength, Ob, is obtained by fibre corresponding to the fracture mode of the comp he equation
alternately along the longitudinal direction of the composite. By using a two-dimensional composite model, the axial compressive strength of the composite, c, has been derived as c Gm 1 ÿ vf Em 2 1 m 1 ÿ vf ÿ 3 for the shear mode and c 4v3 fEfEm 3 1 ÿ vf ÿ " #1=2 4 for the extension mode. In the above equations, Em; Gm and m are the tensile modulus, shear modulus and Poisson ratio of the matrix and Ef and vf the tensile modulus and volume fraction of the ®bres. For the carbon ®bre/epoxy resin systems used in this study, the critical stress which causes fracture in the extension mode is higher than that in the shear mode. Thus, the compressive strength of the composite strands used in this study is given by Eq.(3). The dotted line in Fig. 11 shows the compressive strength of the composite strand predicted by Eq. (3) for vf 0:42, m 0:33 and various values of Em. In this ®gure, the compressive strength of X5 and T4 ®bre composite strands using dierent matrix resins are also shown. The experimental values are extremely lower than the predicted values. As qualitatively predicted by Rosen's model, however, the compressive strength increases with increasing matrix modulus for the T4 ®bre composite strands. The matrix modulus dependence of the compressive strength of the X5 ®bre composite strands is much smaller than that of the T4 ®bre composite strands. This is because the compressive strength of the X5 ®bre composite strand is almost limited by the ®bre strength. That is, the reduced compressive strength of the X5 ®bre at the lowest matrix modulus of 2.4 GPa is 0.49 GPa, which is close to the compressive strength of this ®bre determined with the micro-compression test, 0.51 GPa. Thus, the compressive strength of this composite strand cannot be increased even if the matrix modulus is increased above 2.4 GPa. On the other hand, the reduced compressive strength of the T4 ®bre at the matrix modulus of 2.4 GPa is only 0.59 GPa, which is lower than the compressive strength of this ®bre determined with the micro-compression test, 2.0 GPa. Thus, the compressive strength of this composite strand can be increased by increasing the matrix modulus until the ®bre strength is reached. 3.5. Compressive strength determined with the axial compression bending test of composite strand With the axial compression bending test of the composite strand, the bending strength, b, is obtained by the equation, b ttFb 2I 5 where I is the moment of inertia of area, t the thickness of the specimen measured in the bending direction, Fb the compression load at fracture and t the de¯ection at fracture. The de¯ection can be calculated from the axial displacement, a, using the equations, a L 2 1 ÿ E p K p 6 t L p K p 7 where K p and E p are the complete elliptic integrals of the ®rst and the second kinds and L is the specimen length. If the composite strand shows a falling load compression curve or the accurate determination of the cross-section size is dicult, the bending strength can be practically estimated by using an eective cross-section size of the composite strand at fracture, which can be obtained with the knowledge of the elastic modulus of the composite strand [11]. The bending strength of the composite strands using the matrix with a tensile modulus of 3.0 GPa and the reduced strength of the component ®bres are shown in Table 3. Among the composite strands shown in Table 3, only the H4 ®bre composite strand ®nally fractured from compression. It is found that the reduced strength is larger than the tensile or compressive strength of the ®bre corresponding to the fracture mode of the composite strand. Fig. 11. Compressive strength of composite strand versus tensile modulus of matrix for (*) X5 and (*) T4 ®bre composite strands using epoxy-A, B and C matrices. Dotted line shows relation of Eq. (3) for vf 0:42 and m 0:33. M. Shioya, M. Nakatani / Composites Science and Technology 60 (2000) 219±229 227
M. Shioya, M. Nakatani/Composites Science and Technology 60(2000)219-229 Results of axial bending test of composite strands and properties of fibres Fibre Composite strand Properties of fibre Diameter Fibre volume bending Reduced be fraction GPa strength/GPa strength/GPa strength"/GPa 19±0.10 0.42 18±0.0 Compressive T4 Estimated with micro-compression test of single fibres [9 During the bending test of the composite strand of the has a circular cross-section. Thus, the volume of the fibres having a compressive strength lower than the specimen where the stress at this level can be applied is tensile strength, fracture initiates from the compressive roughly calculated to be 0.20.007x 1/2=0.07% of the side of the composite strand. The composite strand, entire specimen volume. This value is the maximum however, does not split into pieces immediately because estimate and the effective specimen volume decreases the tensile side of the composite strand is not fractured with increasing total specimen length and with decreas- yet, and the compressive load can be transmitted ing specimen diameter [11]. Therefore, an extremely through the damaged region of the compressive side of smaller volume of the material is involved in the axial the composite strand. This is presumably responsible for compression bending test as compared with the simple the result of the observation that the final fracture of axial compression test even though longer specimens are some composite strands initiated from the tensile side of used in the former test. The difference in the volume of the composite strand. It is considered that the compressive the tested material together with the size dependence of racture or microbuckling of the fibres inside the com- the strength of the material cause inconsistency of the posite strand commences earlier than the final fracture strength values determined with different test method of the composite strand. Therefore, in order to estimate The difference between the effective specimen volum the accurate strength of the component fibres from the and the entire specimen volume should also be take bending test of the composite strand, it is necessary to into account in the compression tests of single fibres. It detect the initial fracture of the fibres inside the composite has been pointed out that in the micro-compression test strand by using some method such as the acoustic of single fibres, the uniform stress distribution along the emission technique fibre length is provided in the region apart from the In discussing inconsistency of the strength values clamps by a certain fibre length [6, 7, 14]. In the recoil determined with different test methods, difference of the test of single fibres, bending-induced stress causes frac- volume of the tested material should be addressed ture near the fixed end of the fibre and in such a case oppressive stresses reach maximum, respectively, at the the limited volume of the fibre resents the strength of convex and concave sides of the specimen in the central crOSs-section. and decrease with increasing distance from these points in both longitudinal and transverse 4. Conclusions directions. The detailed calculation of the size of the effectively stressed region of the specimen during the The fracture surfaces of the carbon fibres and com- axial compression bending test has been given in a pre- posite strands produced by various compression tests vious paper [11]. By calculating similarly, it can be showed different features depending on the types of obtained that the tensile and compressive stresses aris- fibres and matrix resins. An inclined fracture surface ing at the convex and concave sides of the cross-section was typically produced for the pitch-based carbon fibres lecay less than 95% of the maximum value if the cross- by the micro-compression and recoil tests and for their section is apart from the central cross-section more than composite strands by the axial compression and bend 10% of the entire specimen length. Thus, the effective ing tests. A fracture surface characteristic to the flexural specimen length is 20% of the entire specimen length. fracture was produced by the recoil test of the PAN On the other hand, the tensile and compressive stresses based carbon fibres. A transverse fracture surface, in in the cross-section change linearly with the distance addition to the inclined fracture surface, was produced from the neutral plane of the cross-section. In the cen- for the PAN-based carbon fibres by the micro-com- tral cross-section, the tensile and compressive stresses pression test and for their composite strands by the no less than 95% of the maximum value can be applied axial compression and bending tests. Since segmented only to 0.7% of the cross-section area if the specimen fibre bundles inclined from the longitudinal direction
During the bending test of the composite strand of the ®bres having a compressive strength lower than the tensile strength, fracture initiates from the compressive side of the composite strand. The composite strand, however, does not split into pieces immediately because the tensile side of the composite strand is not fractured yet, and the compressive load can be transmitted through the damaged region of the compressive side of the composite strand. This is presumably responsible for the result of the observation that the ®nal fracture of some composite strands initiated from the tensile side of the composite strand. It is considered that the compressive fracture or microbuckling of the ®bres inside the composite strand commences earlier than the ®nal fracture of the composite strand. Therefore, in order to estimate the accurate strength of the component ®bres from the bending test of the composite strand, it is necessary to detect the initial fracture of the ®bres inside the composite strand by using some method such as the acoustic emission technique. In discussing inconsistency of the strength values determined with dierent test methods, dierence of the volume of the tested material should be addressed. During the axial bending test, the axial tensile and compressive stresses reach maximum, respectively, at the convex and concave sides of the specimen in the central cross-section, and decrease with increasing distance from these points in both longitudinal and transverse directions. The detailed calculation of the size of the eectively stressed region of the specimen during the axial compression bending test has been given in a previous paper [11]. By calculating similarly, it can be obtained that the tensile and compressive stresses arising at the convex and concave sides of the cross-section decay less than 95% of the maximum value if the crosssection is apart from the central cross-section more than 10% of the entire specimen length. Thus, the eective specimen length is 20% of the entire specimen length. On the other hand, the tensile and compressive stresses in the cross-section change linearly with the distance from the neutral plane of the cross-section. In the central cross-section, the tensile and compressive stresses no less than 95% of the maximum value can be applied only to 0.7% of the cross-section area if the specimen has a circular cross-section. Thus, the volume of the specimen where the stress at this level can be applied is roughly calculated to be 0.20.0071/2=0.07% of the entire specimen volume. This value is the maximum estimate and the eective specimen volume decreases with increasing total specimen length and with decreasing specimen diameter [11]. Therefore, an extremely smaller volume of the material is involved in the axial compression bending test as compared with the simple axial compression test even though longer specimens are used in the former test. The dierence in the volume of the tested material together with the size dependence of the strength of the material cause inconsistency of the strength values determined with dierent test methods. The dierence between the eective specimen volume and the entire specimen volume should also be taken into account in the compression tests of single ®bres. It has been pointed out that in the micro-compression test of single ®bres, the uniform stress distribution along the ®bre length is provided in the region apart from the clamps by a certain ®bre length [6,7,14]. In the recoil test of single ®bres, bending-induced stress causes fracture near the ®xed end of the ®bre and in such a case, the obtained strength value represents the strength of the limited volume of the ®bre near the ®xed end [4]. 4. Conclusions The fracture surfaces of the carbon ®bres and composite strands produced by various compression tests showed dierent features depending on the types of ®bres and matrix resins. An inclined fracture surface was typically produced for the pitch-based carbon ®bres by the micro-compression and recoil tests and for their composite strands by the axial compression and bending tests. A fracture surface characteristic to the ¯exural fracture was produced by the recoil test of the PANbased carbon ®bres. A transverse fracture surface, in addition to the inclined fracture surface, was produced for the PAN-based carbon ®bres by the micro-compression test and for their composite strands by the axial compression and bending tests. Since segmented ®bre bundles inclined from the longitudinal direction Table 3 Results of axial bending test of composite strands and properties of ®bres Fibre Composite strand Properties of ®bre Diameter/ mm Fibre volume fraction Bending strength/GPa Reduced bending strength/GPa Fracture mode Tensile strength/GPa Compressive strengtha /GPa X5 1.2 0.50 1.90.10 3.7 Tensile 3.6 0.51 H4 1.0 0.42 1.80.05 4.2 Compressive 4.4 1.6 T4 1.2 0.42 2.40.13 5.7 Tensile 4.9 2.0 a Estimated with micro-compression test of single ®bres [9]. 228 M. Shioya, M. Nakatani / Composites Science and Technology 60 (2000) 219±229