2 Materials Major constituents in a fiber-reinforced composite material are the reinforcing fibers and a matrix,which acts as a binder for the fibers.Other constituents that may also be found are coupling agents,coatings,and fillers.Coupling agents and coatings are applied on the fibers to improve their wetting with the matrix as well as to promote bonding across the fiber-matrix interface.Both in turn promote a better load transfer between the fibers and the matrix.Fillers are used with some polymeric matrices primarily to reduce cost and improve their dimensional stability. Manufacturing of a composite structure starts with the incorporation of a large number of fibers into a thin layer of matrix to form a lamina(ply).The thickness of a lamina is usually in the range of 0.1-1 mm (0.004-0.04 in.).If continuous(long)fibers are used in making the lamina,they may be arranged either in a unidirectional orientation (i.e.,all fibers in one direction,Figure 2.1a), in a bidirectional orientation (i.e.,fibers in two directions,usually normal to each other,Figure 2.1b),or in a multidirectional orientation (i.e.,fibers in more than two directions,Figure 2.1c).The bi-or multidirectional orientation of fibers is obtained by weaving or other processes used in the textile industry.The bidirectional orientations in the form of fabrics are shown in Appendix A.1. For a lamina containing unidirectional fibers,the composite material has the highest strength and modulus in the longitudinal direction of the fibers.How- ever,in the transverse direction,its strength and modulus are very low.For a lamina containing bidirectional fibers,the strength and modulus can be varied using different amounts of fibers in the longitudinal and transverse directions. For a balanced lamina,these properties are the same in both directions. A lamina can also be constructed using discontinuous (short)fibers in a matrix.The discontinuous fibers can be arranged either in unidirectional orientation (Figure 2.1c)or in random orientation (Figure 2.1d).Disconti- nuous fiber-reinforced composites have lower strength and modulus than continuous fiber composites.However,with random orientation of fibers (Figure 2.le),it is possible to obtain equal mechanical and physical properties in all directions in the plane of the lamina. The thickness required to support a given load or to maintain a given deflection in a fiber-reinforced composite structure is obtained by stacking several laminas in a specified sequence and then consolidating them to form a laminate.Various laminas in a laminate may contain fibers either all in one 2007 by Taylor&Francis Group.LLC
2 Materials Major constituents in a fiber-reinforced composite material are the reinforcing fibers and a matrix, which acts as a binder for the fibers. Other constituents that may also be found are coupling agents, coatings, and fillers. Coupling agents and coatings are applied on the fibers to improve their wetting with the matrix as well as to promote bonding across the fiber–matrix interface. Both in turn promote a better load transfer between the fibers and the matrix. Fillers are used with some polymeric matrices primarily to reduce cost and improve their dimensional stability. Manufacturing of a composite structure starts with the incorporation of a large number of fibers into a thin layer of matrix to form a lamina (ply). The thickness of a lamina is usually in the range of 0.1–1 mm (0.004–0.04 in.). If continuous (long) fibers are used in making the lamina, they may be arranged either in a unidirectional orientation (i.e., all fibers in one direction, Figure 2.1a), in a bidirectional orientation (i.e., fibers in two directions, usually normal to each other, Figure 2.1b), or in a multidirectional orientation (i.e., fibers in more than two directions, Figure 2.1c). The bi- or multidirectional orientation of fibers is obtained by weaving or other processes used in the textile industry. The bidirectional orientations in the form of fabrics are shown in Appendix A.1. For a lamina containing unidirectional fibers, the composite material has the highest strength and modulus in the longitudinal direction of the fibers. However, in the transverse direction, its strength and modulus are very low. For a lamina containing bidirectional fibers, the strength and modulus can be varied using different amounts of fibers in the longitudinal and transverse directions. For a balanced lamina, these properties are the same in both directions. A lamina can also be constructed using discontinuous (short) fibers in a matrix. The discontinuous fibers can be arranged either in unidirectional orientation (Figure 2.1c) or in random orientation (Figure 2.1d). Discontinuous fiber-reinforced composites have lower strength and modulus than continuous fiber composites. However, with random orientation of fibers (Figure 2.1e), it is possible to obtain equal mechanical and physical properties in all directions in the plane of the lamina. The thickness required to support a given load or to maintain a given deflection in a fiber-reinforced composite structure is obtained by stacking several laminas in a specified sequence and then consolidating them to form a laminate. Various laminas in a laminate may contain fibers either all in one 2007 by Taylor & Francis Group, LLC
Constituents Fibers matrix+ coupling agent or fiber surface coating fillers and other additives Lamina (thin ply or layer) (a)Unidirectional continuous fibers (b)Bidirectional continuous fibers (c)Multidirectional continuous fibers (d)Unidirectional discontinuous fibers (e)Random discontinuous fibers A Laminate (consolidated stack of many layers) FIGURE 2.1 Basic building blocks in fiber-reinforced composites. direction or in different directions.It is also possible to combine different kinds of fibers to form either an interply or an intraply hybrid laminate.An interply hybrid laminate consists of different kinds of fibers in different laminas, whereas an intraply hybrid laminate consists of two or more different kinds of fibers interspersed in the same lamina.Generally,the same matrix is used throughout the laminate so that a coherent interlaminar bond is formed between the laminas. Fiber-reinforced polymer laminas can also be combined with thin aluminum or other metallic sheets to form metal-composite hybrids, commonly known as fiber metal laminates (FML).Two such commercial metal composite hybrids are ARALL and GLARE.ARALL uses alternate layers of aluminum sheets and unidirectional aramid fiber-epoxy laminates 2007 by Taylor Francis Group,LLC
direction or in different directions. It is also possible to combine different kinds of fibers to form either an interply or an intraply hybrid laminate. An interply hybrid laminate consists of different kinds of fibers in different laminas, whereas an intraply hybrid laminate consists of two or more different kinds of fibers interspersed in the same lamina. Generally, the same matrix is used throughout the laminate so that a coherent interlaminar bond is formed between the laminas. Fiber-reinforced polymer laminas can also be combined with thin aluminum or other metallic sheets to form metal–composite hybrids, commonly known as fiber metal laminates (FML). Two such commercial metal–composite hybrids are ARALL and GLARE. ARALL uses alternate layers of aluminum sheets and unidirectional aramid fiber–epoxy laminates Constituents Fibers + matrix + coupling agent or fiber surface coating + fillers and other additives Lamina (thin ply or layer) (a) Unidirectional continuous fibers (b) Bidirectional continuous fibers (c) Multidirectional continuous fibers (d) Unidirectional discontinuous fibers (e) Random discontinuous fibers Laminate (consolidated stack of many layers) FIGURE 2.1 Basic building blocks in fiber-reinforced composites. 2007 by Taylor & Francis Group, LLC
2 Nominal thickness =1.3mm Construction of a 3/2 ARALL Layers 1,3,and 5:Aluminum alloy sheet(each 0.3 mm thick) Layers 2 and 4:Unidirectional aramid fiber/epoxy laminate (each 0.2 mm thick) FIGURE 2.2 Construction of an ARALL laminate. (Figure 2.2).GLARE uses alternate layers of aluminum sheets and either unidirectional or bidirectional S-glass fiber-epoxy laminates.Both metal- composite hybrids have been primarily developed for aircraft structures such as wing panels and fuselage sections. 2.1 FIBERS Fibers are the principal constituents in a fiber-reinforced composite material. They occupy the largest volume fraction in a composite laminate and share the major portion of the load acting on a composite structure.Proper selection of the fiber type,fiber volume fraction,fiber length,and fiber orientation is very important,since it influences the following characteristics of a composite laminate: 1.Density 2.Tensile strength and modulus 3.Compressive strength and modulus 4.Fatigue strength as well as fatigue failure mechanisms 5.Electrical and thermal conductivities 6.Cost A number of commercially available fibers and their properties are listed in Table 2.1.The first point to note in this table is the extremely small filament diameter for the fibers.Since such small sizes are difficult to handle,the useful form of commercial fibers is a bundle,which is produced by gathering a large number of continuous filaments,either in untwisted or twisted form.The untwisted form is called strand or end for glass and Kevlar fibers and tow for carbon fibers (Figure 2.3a).The twisted form is called yarn (Figure 2.3b). Tensile properties listed in Table 2.1 are the average values reported by the fiber manufacturers.One of the test methods used for determining the tensile properties of filaments is the single filament test.In this test method,designated as ASTM D3379,a single filament is mounted along the centerline of a slotted 2007 by Taylor&Francis Group.LLC
(Figure 2.2). GLARE uses alternate layers of aluminum sheets and either unidirectional or bidirectional S-glass fiber–epoxy laminates. Both metal– composite hybrids have been primarily developed for aircraft structures such as wing panels and fuselage sections. 2.1 FIBERS Fibers are the principal constituents in a fiber-reinforced composite material. They occupy the largest volume fraction in a composite laminate and share the major portion of the load acting on a composite structure. Proper selection of the fiber type, fiber volume fraction, fiber length, and fiber orientation is very important, since it influences the following characteristics of a composite laminate: 1. Density 2. Tensile strength and modulus 3. Compressive strength and modulus 4. Fatigue strength as well as fatigue failure mechanisms 5. Electrical and thermal conductivities 6. Cost A number of commercially available fibers and their properties are listed in Table 2.1. The first point to note in this table is the extremely small filament diameter for the fibers. Since such small sizes are difficult to handle, the useful form of commercial fibers is a bundle, which is produced by gathering a large number of continuous filaments, either in untwisted or twisted form. The untwisted form is called strand or end for glass and Kevlar fibers and tow for carbon fibers (Figure 2.3a). The twisted form is called yarn (Figure 2.3b). Tensile properties listed in Table 2.1 are the average values reported by the fiber manufacturers. One of the test methods used for determining the tensile properties of filaments is the single filament test. In this test method, designated as ASTM D3379, a single filament is mounted along the centerline of a slotted Nominal thickness = 1.3 mm 1 3 5 2 4 Construction of a 3/2 ARALL Layers 1, 3, and 5: Aluminum alloy sheet (each 0.3 mm thick) Layers 2 and 4: Unidirectional aramid fiber/epoxy laminate (each 0.2 mm thick) FIGURE 2.2 Construction of an ARALL laminate. 2007 by Taylor & Francis Group, LLC
2007 by Taykr&Francis Group. TABLE 2.1 Properties of Selected Commercial Reinforcing Fibers Coefficient of Typical Tensile Tensile Thermal Diameter Density Modulus Strength Strain-to-Failure Expansion Poisson's Fiber (μm)2 (g/cm) GPa (Msi) GPa(ksi) (%) (10-6/C) Ratio Glass E-glass 10(round) 2.54 72.4(10.5) 3.45(500) 4.8 5 0.2 S-glass 10 (round) 2.49 86.9(12.6 4.30(625) 5.0 2.9 0.22 PAN carbon T-300° 7(round) 1.76 231(33.5) 3.65(530) 1.4 -0.6 (longitudinal) 0.2 7-12 (radial) AS-1d 8(round) 1.80 228(33) 3.10(450) 1.32 AS-44 7 (round) 1.80 248(36) 4.07(590) 1.65 T.40f 5.1 (round) 1.81 290(42) 5.65(820) 1.8 -0.75 (longitudinal) IM-7d 5(round) 1.78 301(43.6) 5.31(770) 1.81 HMS-44 8 (round) 1.80 345(50) 2.48(360) 0.7 GY-70 8.4 (bilobal) 1.96 483(70) 1.52(220) 0.38 Pitch carbon P.55 1 2.0 380(55) 1.90(275) 0.5 -1.3 (longitudinal) P.100 10 2.15 758(110) 2.41(350) 0.32 -1.45 (longitudinal) Aramid Kevlar 49 11.9 (round) 1.45 131(19) 3.62(525) 2.8 -2 (longitudinal) 0.35 59 (radial) Kevlar 149 1.47 179(26) 3.45(500) 1.9 Technoras 139 70(10.1) 3.0(435) 4.6 -6 (longitudinal)
TABLE 2.1 Properties of Selected Commercial Reinforcing Fibers Fiber Typical Diameter (mm)a Density (g=cm3) Tensile Modulus GPa (Msi) Tensile Strength GPa (ksi) Strain-to-Failure (%) Coefficient of Thermal Expansion (106=8C)b Poisson’s Ratio Glass E-glass 10 (round) 2.54 72.4 (10.5) 3.45 (500) 4.8 5 0.2 S-glass 10 (round) 2.49 86.9 (12.6) 4.30 (625) 5.0 2.9 0.22 PAN carbon T-300c 7 (round) 1.76 231 (33.5) 3.65 (530) 1.4 0.6 (longitudinal) 0.2 7–12 (radial) AS-1d 8 (round) 1.80 228 (33) 3.10 (450) 1.32 AS-4d 7 (round) 1.80 248 (36) 4.07 (590) 1.65 T-40c 5.1 (round) 1.81 290 (42) 5.65 (820) 1.8 0.75 (longitudinal) IM-7d 5 (round) 1.78 301 (43.6) 5.31 (770) 1.81 HMS-4d 8 (round) 1.80 345 (50) 2.48 (360) 0.7 GY-70e 8.4 (bilobal) 1.96 483 (70) 1.52 (220) 0.38 Pitch carbon P-55c 10 2.0 380 (55) 1.90 (275) 0.5 1.3 (longitudinal) P-100c 10 2.15 758 (110) 2.41 (350) 0.32 1.45 (longitudinal) Aramid Kevlar 49f 11.9 (round) 1.45 131 (19) 3.62 (525) 2.8 2 (longitudinal) 0.35 59 (radial) Kevlar 149f 1.47 179 (26) 3.45 (500) 1.9 Technorag 1.39 70 (10.1) 3.0 (435) 4.6 6 (longitudinal) 2007 by Taylor & Francis Group, LLC
Extended chain polyethylene Spectra 900h 38 0.97 117(17) 2.59(375) 3.5 Spectra 1000h 27 0.97 172(25) 3.0(435) 2.7 Boron 140 (round) 2.7 393(57) 3.1(450) 0.79 5 0.2 Taykr&Francis Group.LLC. SiC Monofilament 140(round) 3.08 400(58) 3.44(499) 0.86 1.5 Nicalon'(multifilament) 14.5 (round) 2.55 196(28.4) 2.75(399) 1.4 A03 Nextel 610 10-12 (round) 3.9 380(55) 3.1(450) 8 Nextel 720 10-12 3.4 260(38) 2.1(300) 6 A1203-Si03 Fiberfrax(discontinuous) 2-12 2.73 103(15) 1.03-1.72 (150-250) 41μm=0.0000393in. bm/m per C =0.556 in./in.per F. e Amoco. d Hercules. e BASF. f DuPont. 8 Teijin. h Honeywell. i Nippon carbon. j3-M
Extended chain polyethylene Spectra 900h 38 0.97 117 (17) 2.59 (375) 3.5 Spectra 1000h 27 0.97 172 (25) 3.0 (435) 2.7 Boron 140 (round) 2.7 393 (57) 3.1 (450) 0.79 5 0.2 SiC Monofilament 140 (round) 3.08 400 (58) 3.44 (499) 0.86 1.5 Nicaloni (multifilament) 14.5 (round) 2.55 196 (28.4) 2.75 (399) 1.4 Al2O3 Nextel 610j 10–12 (round) 3.9 380 (55) 3.1 (450) 8 Nextel 720j 10–12 3.4 260 (38) 2.1 (300) 6 Al2O3–SiO2 Fiberfrax (discontinuous) 2–12 2.73 103 (15) 1.03–1.72 (150–250) a 1 mm ¼ 0.0000393 in. b m=m per 8C ¼ 0.556 in.=in. per 8F. c Amoco. d Hercules. e BASF. f DuPont. g Teijin. h Honeywell. i Nippon carbon. j 3-M. 2007 by Taylor & Francis Group, LLC
(a) (b) FIGURE 2.3 (a)Untwisted and(b)twisted fiber bundle. tab by means of a suitable adhesive(Figure 2.4).After clamping the tab in the grips of a tensile testing machine,its midsection is either cut or burned away. The tension test is carried out at a constant loading rate until the filament Cut or burned out Cement or sealing wax Single filament specimen Tab slot 10-15mm Grip Grip area 4-20-30mm area 60-90mm FIGURE 2.4 Mounting tab for tensile testing of single filament. 2007 by Taylor Francis Group.LLC
tab by means of a suitable adhesive (Figure 2.4). After clamping the tab in the grips of a tensile testing machine, its midsection is either cut or burned away. The tension test is carried out at a constant loading rate until the filament (a) (b) FIGURE 2.3 (a) Untwisted and (b) twisted fiber bundle. Cement or sealing wax Cut or burned out Single filament specimen Tab slot 20−30 mm 60−90 mm 10−15 mm Grip area Grip area FIGURE 2.4 Mounting tab for tensile testing of single filament. 2007 by Taylor & Francis Group, LLC
fractures.From the load-time record of the test,the following tensile properties are determined: Tensile strength ofu= Fu (2.1) A and Tensile modulus Ef= (2.2) CA where Fu=force at failure Ae average filament cross-sectional area,measured by a planimeter from the photomicrographs of filament ends Lr gage length C =true compliance,determined from the chart speed,loading rate,and the system compliance Tensile stress-strain diagrams obtained from single filament test of reinforcing fibers in use are almost linear up to the point of failure,as shown in Figure 2.5. They also exhibit very low strain-to-failure and a brittle failure mode.Although the absence of yielding does not reduce the load-carrying capacity of the fibers, it does make them prone to damage during handling as well as during contact with other surfaces.In continuous manufacturing operations,such as filament winding,frequent fiber breakage resulting from such damages may slow the rate of production. The high tensile strengths of the reinforcing fibers are generally attributed to their filamentary form in which there are statistically fewer surface flaws than in the bulk form.However,as in other brittle materials,their tensile strength data exhibit a large amount of scatter.An example is shown in Figure 2.6. The experimental strength variation of brittle filaments is modeled using the following Weibull distribution function [1]: fc)=ao。" 2-(2))门 (2.3) where f(ofu)=probability of filament failure at a stress level equal to ofu oru filament strength filament length Lo reference length shape parameter 0。 scale parameter (the filament strength atL=Lo) 2007 by Taylor Francis Group.LLC
fractures. From the load-time record of the test, the following tensile properties are determined: Tensile strength sfu ¼ Fu Af (2:1) and Tensile modulus Ef ¼ Lf CAf , (2:2) where Fu ¼ force at failure Af ¼ average filament cross-sectional area, measured by a planimeter from the photomicrographs of filament ends Lf ¼ gage length C ¼ true compliance, determined from the chart speed, loading rate, and the system compliance Tensile stress–strain diagrams obtained from single filament test of reinforcing fibers in use are almost linear up to the point of failure, as shown in Figure 2.5. They also exhibit very low strain-to-failure and a brittle failure mode. Although the absence of yielding does not reduce the load-carrying capacity of the fibers, it does make them prone to damage during handling as well as during contact with other surfaces. In continuous manufacturing operations, such as filament winding, frequent fiber breakage resulting from such damages may slow the rate of production. The high tensile strengths of the reinforcing fibers are generally attributed to their filamentary form in which there are statistically fewer surface flaws than in the bulk form. However, as in other brittle materials, their tensile strength data exhibit a large amount of scatter. An example is shown in Figure 2.6. The experimental strength variation of brittle filaments is modeled using the following Weibull distribution function [1]: f (sfu) ¼ asa o sa1 fu Lf Lo exp Lf Lo sfu so a , (2:3) where f(sfu) ¼ probability of filament failure at a stress level equal to sfu sfu ¼ filament strength Lf ¼ filament length Lo ¼ reference length a ¼ shape parameter so ¼ scale parameter (the filament strength at Lf ¼ Lo) 2007 by Taylor & Francis Group, LLC.
700 4830 600 4140 S-glass 500 3450 夏 High-strength Kevlar 49 carbon 400 2760 High- E-glass modulus SSells carbon 300 2070 200 1380 100 690 0 0 1.0 2.0 3.0 4.0 5.0 Tensile strain (% FIGURE 2.5 Tensile stress-strain diagrams for various reinforcing fibers. The cumulative distribution of strength is given by the following equation: F()=1-exp -())门 (2.4) where F(ofu)represents the probability of filament failure at a stress level lower than or equal to ofu.The parameters a and oo in Equations 2.3 and 2.4 are called the Weibull parameters,and are determined using the experimental data.a can be regarded as an inverse measure of the coefficient of variation.The higher the value of a,the narrower is the distribution of filament strength.The scale parameter oo may be regarded as a reference stress level. 2007 by Taylor Francis Group,LLC
The cumulative distribution of strength is given by the following equation: F(sfu) ¼ 1 exp Lf Lo sfu so a , (2:4) where F(sfu) represents the probability of filament failure at a stress level lower than or equal to sfu. The parameters a and so in Equations 2.3 and 2.4 are called the Weibull parameters, and are determined using the experimental data. a can be regarded as an inverse measure of the coefficient of variation. The higher the value of a, the narrower is the distribution of filament strength. The scale parameter so may be regarded as a reference stress level. 700 4830 4140 3450 2760 2070 Tensile stress (MPa) Tensile stress (103 psi) 1380 690 0 600 500 High-strength carbon Highmodulus carbon 400 300 200 100 0 0 1.0 2.0 Tensile strain (%) S-glass E-glass Kevlar 49 3.0 4.0 5.0 FIGURE 2.5 Tensile stress–strain diagrams for various reinforcing fibers. 2007 by Taylor & Francis Group, LLC.
20 MODMOR I Carbon fiber 10 (a) 20 GY-70 Carbon fiber 10 T 100 200 300 400 500 ksi 690 1380 2070 2760 3450 MPa () Tensile strength FIGURE 2.6 Histograms of tensile strengths for (a)Modmor I carbon fibers and (b) GY-70 carbon fibers.(After McMahon,P.E.,Analysis of the Test Methods for High Modulus Fibers and Composites,ASTM STP,521,367,1973.) The mean filament strength ofu is given by a + (2.5) where I represents a gamma function.Equation 2.5 clearly shows that the mean strength of a brittle filament decreases with increasing length.This is also demonstrated in Figure 2.7. Tensile properties of fibers can also be determined using fiber bundles.It has been observed that even though the tensile strength distribution of individual filaments follows the Weibull distribution,the tensile strength distribution of fiber bundles containing a large number of parallel filaments follows a normal distribution [1].The maximum strength,ofm,that the filaments in the bundle will exhibit and the mean bundle strength,ob,can be expressed in terms of the Weibull parameters determined for individual filaments.They are given as follows: m=[2)丹 e-ila (2.6 2007 by Taylor Francis Group.LLC
The mean filament strength fu is given by sfu ¼ so Lf Lo 1=a G 1 þ 1 a , (2:5) where G represents a gamma function. Equation 2.5 clearly shows that the mean strength of a brittle filament decreases with increasing length. This is also demonstrated in Figure 2.7. Tensile properties of fibers can also be determined using fiber bundles. It has been observed that even though the tensile strength distribution of individual filaments follows the Weibull distribution, the tensile strength distribution of fiber bundles containing a large number of parallel filaments follows a normal distribution [1]. The maximum strength, sfm, that the filaments in the bundle will exhibit and the mean bundle strength, b, can be expressed in terms of the Weibull parameters determined for individual filaments. They are given as follows: sfm ¼ so Lf Lo a 1=a , sb ¼ so Lf Lo a 1=a e1=a: (2:6) 20 (a) MODMOR I Carbon fiber (b) GY-70 Carbon fiber Frequency Frequency 10 0 20 10 0 100 200 300 400 500 ksi 690 1380 2070 MPa Tensile strength 2760 3450 FIGURE 2.6 Histograms of tensile strengths for (a) Modmor I carbon fibers and (b) GY-70 carbon fibers. (After McMahon, P.E., Analysis of the Test Methods for High Modulus Fibers and Composites, ASTM STP, 521, 367, 1973.) 2007 by Taylor & Francis Group, LLC.
600 ◇ 4140 Kevlar 49 500 0 Boron 400 High-strength carbon S-glass 2760 (10820 300 E-glass 200 1380 (x)Corresponds to 1 in.(25.4 mm)gage length 100 690 0 100 200 50010002000 5000 Gage length/filament diameter ratio(10) FIGURE 2.7 Filament strength variation as a function of gage length-to-diameter ratio. (After Kevlar 49 Data Manual,E.I.duPont de Nemours Co.,1975.) The fiber bundle test method is similar to the single filament test method.The fiber bundle can be tested either in dry or resin-impregnated condition.Gener- ally,the average tensile strength and modulus of fiber bundles are lower than those measured on single filaments.Figure 2.8 shows the stress-strain diagram of a dry glass fiber bundle containing 3000 filaments.Even though a single glass filament shows a linear tensile stress-strain diagram until failure,the glass fiber strand shows not only a nonlinear stress-strain diagram before reaching the maximum stress,but also a progressive failure after reaching the maximum stress.Both nonlinearity and progressive failure occur due to the statistical distribution of the strength of glass filaments.The weaker filaments in the bundle fail at low stresses,and the surviving filaments continue to carry the tensile load;however,the stress in each surviving filament becomes higher. Some of them fail as the load is increased.After the maximum stress is reached, the remaining surviving filaments continue to carry even higher stresses and start to fail,but not all at one time,thus giving the progressive failure mode as seen in Figure 2.8.Similar tensile stress-strain diagrams are observed with carbon and other fibers in fiber bundle tests. In addition to tensile properties,compressive properties of fibers are also of interest in many applications.Unlike the tensile properties,the compressive properties cannot be determined directly by simple compression tests on fila- ments or strands.Various indirect methods have been used to determine the compressive strength of fibers [2].One such method is the loop test in which a filament is bent into the form of a loop until it fails.The compressive strength 2007 by Taylor Francis Group,LLC
The fiber bundle test method is similar to the single filament test method. The fiber bundle can be tested either in dry or resin-impregnated condition. Generally, the average tensile strength and modulus of fiber bundles are lower than those measured on single filaments. Figure 2.8 shows the stress–strain diagram of a dry glass fiber bundle containing 3000 filaments. Even though a single glass filament shows a linear tensile stress–strain diagram until failure, the glass fiber strand shows not only a nonlinear stress–strain diagram before reaching the maximum stress, but also a progressive failure after reaching the maximum stress. Both nonlinearity and progressive failure occur due to the statistical distribution of the strength of glass filaments. The weaker filaments in the bundle fail at low stresses, and the surviving filaments continue to carry the tensile load; however, the stress in each surviving filament becomes higher. Some of them fail as the load is increased. After the maximum stress is reached, the remaining surviving filaments continue to carry even higher stresses and start to fail, but not all at one time, thus giving the progressive failure mode as seen in Figure 2.8. Similar tensile stress–strain diagrams are observed with carbon and other fibers in fiber bundle tests. In addition to tensile properties, compressive properties of fibers are also of interest in many applications. Unlike the tensile properties, the compressive properties cannot be determined directly by simple compression tests on filaments or strands. Various indirect methods have been used to determine the compressive strength of fibers [2]. One such method is the loop test in which a filament is bent into the form of a loop until it fails. The compressive strength 600 4140 2760 1380 690 500 400 300 Filament tensile strength (103 psi) Filament tensile strength (MPa) 200 100 50 100 200 (x) Corresponds to 1 in. (25.4 mm) gage length 500 Gage length/filament diameter ratio (10−4 ) 1000 2000 Boron High-strength carbon Kevlar 49 S-glass E-glass 5000 FIGURE 2.7 Filament strength variation as a function of gage length-to-diameter ratio. (After Kevlar 49 Data Manual, E. I. duPont de Nemours & Co., 1975.) 2007 by Taylor & Francis Group, LLC