TABLE 4.2 Tensile Strengths and First-Ply Failure(FPF)Stresses in High-Strength Carbon-Epoxy Symmetric Laminates Estimated FPF Stress, Tensile Initial Modulus, Tensile UTS,MPa (ksi) MPa (ksi) GPa(Msi) Strain(%a)】 Laminate Resin 1 Resin 2 Resin 1 Resin 2 [O]s 1378(200) 1378(200) 一 一 151.6(22) 0.3 [90s 413(6 82.7(12) 8.96(1.3) 0.5-0.9 [±45s 137.8(20) 89.613) 89.6(13) 89.6(13) 17.2(2.5) 1.5-4.5 [0/90Ls 447.8(65) 757.9110) 413.4(60) 689(100) 82.7(12) 0.5-0.9 [02/±451s 599.4(87) 689(110) 592.5(86) 689(100) 82.7(12) 0.8-0.9 [0/±601s 461.6(67) 551.2(80) 323.8(47) 378.9(55) 62(9) 0.8-0.9 [0/90/±45s 385.8(56) 413.4(60) 275.6(40) 413.4(60) 55.1(8) 0.8-0.9 Source:Adapted from Freeman,W.T.and Kuebeler,G.C.,Composite Materials:Testing and Design (Third Conference),ASTM STP,546,435,1974. Resin 2 is more flexible than resin I and has a higher strain-to-failure. AS carbon-epoxy 8 11.6 [±15s 6 8.7 4 5.8 [仕30ls [±451s 2.9 [±60ls 0 [9o 0 0 12 16 20 Strain (10-3) FIGURE 4.10 Typical tensile stress-strain diagrams for angle-ply laminates.(Adapted from Lagace,P.A.,AIAA J.,23,1583,1985.) 2007 by Taylor&Francis Group.LLC
TABLE 4.2 Tensile Strengths and First-Ply Failure (FPF) Stresses in High-Strength Carbon–Epoxy Symmetric Laminatesa UTS, MPa (ksi) Estimated FPF Stress, MPa (ksi) Tensile Modulus, GPa (Msi) Initial Tensile Strain (%) Laminate Resin 1 Resin 2 Resin 1 Resin 2 [0]S 1378 (200) 1378 (200) — — 151.6 (22) 0.3 [90]S 41.3 (6) 82.7 (12) — — 8.96 (1.3) 0.5–0.9 [±45]S 137.8 (20) 89.6 (13) 89.6 (13) 89.6 (13) 17.2 (2.5) 1.5–4.5 [0=90]S 447.8 (65) 757.9 (110) 413.4 (60) 689 (100) 82.7 (12) 0.5–0.9 [02=±45]S 599.4 (87) 689 (110) 592.5 (86) 689 (100) 82.7 (12) 0.8–0.9 [0=±60]S 461.6 (67) 551.2 (80) 323.8 (47) 378.9 (55) 62 (9) 0.8–0.9 [0=90=±45]S 385.8 (56) 413.4 (60) 275.6 (40) 413.4 (60) 55.1 (8) 0.8–0.9 Source : Adapted from Freeman, W.T. and Kuebeler, G.C., Composite Materials: Testing and Design (Third Conference), ASTM STP, 546, 435, 1974. a Resin 2 is more flexible than resin 1 and has a higher strain-to-failure. AS carbon−epoxy [±15]S [±30]S [±45]S [±60]S Stress (100 MPa) Stress (10,000 psi) [90] 0 0 2 4 6 8 4 8 12 Strain (10−3) 16 20 0 2.9 5.8 8.7 11.6 FIGURE 4.10 Typical tensile stress–strain diagrams for angle-ply laminates. (Adapted from Lagace, P.A., AIAA J., 23, 1583, 1985.) 2007 by Taylor & Francis Group, LLC
is observed so that the modulus increases with increasing load.At larger values of 0,a softening effect is observed so that the modulus decreases with the increasing load [7].The stiffening effect is attributed to the longitudinal tensile stresses in various plies,whereas the softening effect is attributed to the shear stresses.Stiffening laminates do not exhibit residual strain on unloading. Softening laminates,on the other hand,exhibit a residual strain on unloading and a hysteresis loop on reloading.However,the slope of the stress-strain curve during reloading does not change from the slope of the original stress- strain curve. The tensile failure mode and the tensile strength of a multidirectional laminate containing laminas of different fiber orientations depend strongly on the lamina stacking sequence.An example of the stacking sequence effect is observed in the development of cracks in [0/+45/90]s and [0/90/+45]s laminates (Figure 4.11).In both laminates,intralaminar transverse cracks (parallel to fibers)appear in the 90 plies.However,they are arrested at the 0 +45 -45 90 90 -45 +45 0 (a) Delamination Transverse cracks Transverse cracks 10 +45 -45 -45 45 9 0 (b) FIGURE 4.11 Damage development in (a)[0/+45/90]s and (b)[0/90/+45]s laminates subjected to static tension loads in the 0 direction. 2007 by Taylor Francis Group,LLC
is observed so that the modulus increases with increasing load. At larger values of u, a softening effect is observed so that the modulus decreases with the increasing load [7]. The stiffening effect is attributed to the longitudinal tensile stresses in various plies, whereas the softening effect is attributed to the shear stresses. Stiffening laminates do not exhibit residual strain on unloading. Softening laminates, on the other hand, exhibit a residual strain on unloading and a hysteresis loop on reloading. However, the slope of the stress–strain curve during reloading does not change from the slope of the original stress– strain curve. The tensile failure mode and the tensile strength of a multidirectional laminate containing laminas of different fiber orientations depend strongly on the lamina stacking sequence. An example of the stacking sequence effect is observed in the development of cracks in [0=±45=90]S and [0=90=±45]S laminates (Figure 4.11). In both laminates, intralaminar transverse cracks (parallel to fibers) appear in the 908 plies. However, they are arrested at the 0 0 0 +45 −45 90 +45 +45 −45 −45 90 90 90 −45 +45 0 Delamination Transverse cracks Transverse cracks (a) (b) FIGURE 4.11 Damage development in (a) [0=±45=90]S and (b) [0=90=±45]S laminates subjected to static tension loads in the 08 direction. 2007 by Taylor & Francis Group, LLC
lamina interfaces and do not immediately propagate into the adjacent plies.The number of transverse cracks in the 90 plies increases until uniformly spaced cracks are formed throughout the specimen length [8];however,these trans- verse cracks are more closely spaced in [0/90/+45]s laminates than [0/+45/90]s laminates.Increasing the tensile load also creates a few intralaminar cracks parallel to the fiber directions in both-45 and +45 plies.Apart from these intralaminar crack patterns,subsequent failure modes in these two apparently similar laminates are distinctly different.In [0/+45/90]s laminates,longitudinal interlaminar cracks grow between the 90 plies,which join together to form continuous edge delaminations with occasional jogging into the 90/-45 inter- faces.With increasing load,the edge delamination extends toward the center of the specimen;however,the specimen fails by the rupture of o fibers before the entire width is delaminated.In contrast to the [0/+45/90]s laminate,there is no edge delamination in the [0/90/+45]s laminate;instead,transverse cracks appear in both +45 and-45 plies before the laminate failure.The difference in edge delamination behavior between the [0/+45/90]s and [0/90/+45]s lamin- ates can be explained in terms of the interlaminar normal stress o=,which is tensile in the former and compressive in the latter. Table 4.3 presents the tensile test data and failure modes observed in several multidirectional carbon fiber-epoxy laminates.If the laminate contains 90 plies,failure begins with transverse microcracks appearing in these plies.With increasing stress level,the number of these transverse microcracks increases until a saturation number,called the characteristic damage state (CDS), is reached.Other types of damages that may follow transverse microcracking are delamination,longitudinal cracking,and fiber failure. 4.1.1.5 Woven Fabric Laminates The principal advantage of using woven fabric laminates is that they provide properties that are more balanced in the 0 and 90 directions than unidirec- tional laminates.Although multilayered laminates can also be designed to produce balanced properties,the fabrication (layup)time for woven fabric laminates is less than that of a multilayered laminate.However,the tensile strength and modulus of a woven fabric laminate are,in general,lower than those of multilayered laminates.The principal reason for their lower tensile properties is the presence of fiber undulation in woven fabrics as the fiber yarns in the fill direction cross over and under the fiber yarns in the warp direction to create an interlocked structure.Under tensile loading,these crimped fibers tend to straighten out,which creates high stresses in the matrix.As a result,micro- cracks are formed in the matrix at relatively low loads.This is also evidenced by the appearance of one or more knees in the stress-strain diagrams of woven fabric laminates(Figure 4.12).Another factor to consider is that the fibers in woven fabrics are subjected to additional mechanical handling during the weaving process,which tends to reduce their tensile strength. 2007 by Taylor Francis Group.LLC
lamina interfaces and do not immediately propagate into the adjacent plies. The number of transverse cracks in the 908 plies increases until uniformly spaced cracks are formed throughout the specimen length [8]; however, these transverse cracks are more closely spaced in [0=90=±45]S laminates than [0=±45=90]S laminates. Increasing the tensile load also creates a few intralaminar cracks parallel to the fiber directions in both 458 and þ458 plies. Apart from these intralaminar crack patterns, subsequent failure modes in these two apparently similar laminates are distinctly different. In [0=±45=90]S laminates, longitudinal interlaminar cracks grow between the 908 plies, which join together to form continuous edge delaminations with occasional jogging into the 90=45 interfaces. With increasing load, the edge delamination extends toward the center of the specimen; however, the specimen fails by the rupture of 08 fibers before the entire width is delaminated. In contrast to the [0=±45=90]S laminate, there is no edge delamination in the [0=90=±45]S laminate; instead, transverse cracks appear in both þ458 and 458 plies before the laminate failure. The difference in edge delamination behavior between the [0=±45=90]S and [0=90=±45]S laminates can be explained in terms of the interlaminar normal stress szz, which is tensile in the former and compressive in the latter. Table 4.3 presents the tensile test data and failure modes observed in several multidirectional carbon fiber–epoxy laminates. If the laminate contains 908 plies, failure begins with transverse microcracks appearing in these plies. With increasing stress level, the number of these transverse microcracks increases until a saturation number, called the characteristic damage state (CDS), is reached. Other types of damages that may follow transverse microcracking are delamination, longitudinal cracking, and fiber failure. 4.1.1.5 Woven Fabric Laminates The principal advantage of using woven fabric laminates is that they provide properties that are more balanced in the 08 and 908 directions than unidirectional laminates. Although multilayered laminates can also be designed to produce balanced properties, the fabrication (layup) time for woven fabric laminates is less than that of a multilayered laminate. However, the tensile strength and modulus of a woven fabric laminate are, in general, lower than those of multilayered laminates. The principal reason for their lower tensile properties is the presence of fiber undulation in woven fabrics as the fiber yarns in the fill direction cross over and under the fiber yarns in the warp direction to create an interlocked structure. Under tensile loading, these crimped fibers tend to straighten out, which creates high stresses in the matrix. As a result, microcracks are formed in the matrix at relatively low loads. This is also evidenced by the appearance of one or more knees in the stress–strain diagrams of woven fabric laminates (Figure 4.12). Another factor to consider is that the fibers in woven fabrics are subjected to additional mechanical handling during the weaving process, which tends to reduce their tensile strength. 2007 by Taylor & Francis Group, LLC.
2007 by Taykr&Francis Group. TABLE 4.3 Tensile Test Data and Failure Modes of Several Symmetric Carbon Fiber-Reinforced Epoxy Laminates Secant Modulus Transverse at Low Failure Stress, Failure Ply Strain Laminate Type Strain,GPa MPa Strain Cracking Failure Modes (in Sequence) [04/90Ls 122 1620 0.0116 0.0065 Small transverse ply cracks in 90 plies,transverse cracks growing [04/902s 109 1340 0.011 0.004 in number as well as in length up to 0 plies,delamination at 0/90 04/90小s 1230 0.0114 0.0035 interfaces,0 ply failure 104/90sls 2 930 0.0115 0.003 [±45s 17.3 126 0.017 Edge crack formation,edge cracks growing across the width parallel [+452/-452小s 19 135 0.0117 to fiber direction,delamination at the +45/-45 interfaces,single [+453/-45s 14 89 0.01 or multiple ply failure [+45/-452/4s 18.2 152 0.016 [(+45/-452s 17 125 0.014 [±45/902/02ls 64.2 690 0.014 0.0028 Transverse microcracks in 90 plies,longitudinal or angled cracks [±45/02/902ks 61.2 630 0.014 0.0022 in 90 plies in the first three laminates,a few edge cracks in 45 plies. 02/±45/902s 56.4 640 0.012 0.0016 delamination(45/90,0/90,+45,and 45/0 interfaces in ascending 02/902/士±45s 59.1 670 0.012 0.0035 order of threshold strain),longitudinal ply failure Source:Adapted from Harrison,R.P.and Bader,M.G.,Fibre Sci.Technol.,18.163,1983
TABLE 4.3 Tensile Test Data and Failure Modes of Several Symmetric Carbon Fiber-Reinforced Epoxy Laminates Laminate Type Secant Modulus at Low Strain, GPa Failure Stress, MPa Failure Strain Transverse Ply Strain Cracking Failure Modes (in Sequence) [04=90]S [04=902]S [04=904]S [04=908]S 122 109 93 72 1620 1340 1230 930 0.0116 0.011 0.0114 0.0115 0.0065 0.004 0.0035 0.003 Small transverse ply cracks in 908 plies, transverse cracks growing in number as well as in length up to 08 plies, delamination at 0=90 interfaces, 08 ply failure [±45]S [þ452=452]S [þ453=453]S [þ45=452=45]S [(þ45=45)2]S 17.3 19 14 18.2 17 126 135 89 152 125 0.017 0.0117 0.01 0.016 0.014 — — — — — Edge crack formation, edge cracks growing across the width parallel to fiber direction, delamination at the þ45=45 interfaces, single or multiple ply failure [±45=902=02]S [±45=02=902]S [02=±45=902]S [02=902=±45]S 64.2 61.2 56.4 59.1 690 630 640 670 0.014 0.014 0.012 0.012 0.0028 0.0022 0.0016 0.0035 Transverse microcracks in 908 plies, longitudinal or angled cracks in 908 plies in the first three laminates, a few edge cracks in 458 plies, delamination (45=90, 0=90, ±45, and 45=0 interfaces in ascending order of threshold strain), longitudinal ply failure Source: Adapted from Harrison, R.P. and Bader, M.G., Fibre Sci. Technol., 18, 163, 1983. 2007 by Taylor & Francis Group, LLC.
09 100 690 Style 143 80 552 Style 181 60 414 0 p90 40 276 -045 20 138 0909 45° 0 0 0 0.01 0.02 0.03 0.040.05 Strain FIGURE 4.12 Stress-strain diagrams of woven glass fabric-epoxy laminates with fabric style 143(crowfoot weave with 49 x 30 ends)and fabric style 181(8-harness satin weave with57×54ends). Tensile properties of woven fabric laminates can be controlled by varying the yarn characteristics and the fabric style (see Appendix A.1).The yarn charac- teristics include the number of fiber ends,amount of twist in the yarn,and relative number of yarns in the warp and fill directions.The effect of fiber ends can be seen in Table 4.4 when the differences in the 0and 90 tensile properties of the parallel laminates with 181 fabric style and 143 fabric style are compared. The difference in the tensile properties of each of these laminates in the0and 90 directions reflects the difference in the number of fiber ends in the warp and fill TABLE 4.4 Tensile Properties of Glass Fabric Laminates Tensile Strength,MPa Tensile Modulus,GPa Direction of Testing Direction of Testing Fabric Style o°(Warp) 90°(Fill) 45 o°(Warp) 90°(Fill) 45 181 Parallel lamination 310.4 287.7 182.8 21.4 20.34 15.5 143 Parallel lamination 293.1 34.5 31.0 16.5 6.9 5.5 143 Cross lamination 327.6 327.6 110.3 23.4 23.4 12.2 Source:Adapted from Broutman,L.J.,in Modern Composite Materials,L.J.Broutman and R.H.Krock,eds.,Addison-Wesley,Reading.MA,1967. Style 181:8-harness satin weave,57(warp)x 54(fill)ends,Style 143:Crowfoot weave,49(warp) ×30(fill)ends 2007 by Taylor&Franeis Group.LLC
Tensile properties of woven fabric laminates can be controlled by varying the yarn characteristics and the fabric style (see Appendix A.1). The yarn characteristics include the number of fiber ends, amount of twist in the yarn, and relative number of yarns in the warp and fill directions. The effect of fiber ends can be seen in Table 4.4 when the differences in the 08 and 908 tensile properties of the parallel laminates with 181 fabric style and 143 fabric style are compared. The difference in the tensile properties of each of these laminates in the 08 and 908 directions reflects the difference in the number of fiber ends in the warp and fill 100 80 60 Stress (ksi) Stress (MPa) Style 143 Style 181 40 20 0 0 0.01 0.02 0.03 Strain 0.04 0.05 690 552 414 276 138 0 0 0 90 90 45 45 FIGURE 4.12 Stress–strain diagrams of woven glass fabric-epoxy laminates with fabric style 143 (crowfoot weave with 49 3 30 ends) and fabric style 181 (8-harness satin weave with 57 3 54 ends). TABLE 4.4 Tensile Properties of Glass Fabric Laminates Tensile Strength, MPa Direction of Testing Tensile Modulus, GPa Direction of Testing Fabric Stylea 08 (Warp) 908 (Fill) 458 08 (Warp) 908 (Fill) 458 181 Parallel lamination 310.4 287.7 182.8 21.4 20.34 15.5 143 Parallel lamination 293.1 34.5 31.0 16.5 6.9 5.5 143 Cross lamination 327.6 327.6 110.3 23.4 23.4 12.2 Source: Adapted from Broutman, L.J., in Modern Composite Materials, L.J. Broutman and R.H. Krock, eds., Addison-Wesley, Reading, MA, 1967. a Style 181: 8-harness satin weave, 57 (warp) 3 54 (fill) ends, Style 143: Crowfoot weave, 49 (warp) 3 30 (fill) ends. 2007 by Taylor & Francis Group, LLC.