Pergamon Actamater. Vol. 44, No. 2,pp.573-585, 1996 Elsevier ScienceLtd 0956-7151(95)00184-O Copyright 0 1996 Acta MetallurgicaInc. Printed in Great Britain. All rights reserved 1359-6454196 $15.00 + 0.00 THE EFFECT OF FIBER ARCHITECTURE ON THE MECHANICAL PROPERTIES OF CARBON/CARBON FIBER COMPOSITES J. NEUMEISTER, S. JANSSON and F. LECKIE Department of Mechanical and Environmental Engineering, University of California, Santa Barbara, CA 93106. U.S.A. (Received 25 March 1994; in revised form 4 April 1995) Abstract-The mechanical performance of carbon-fiber matrix composites with different fiber architectures is investigated for various loading modes. All the composites were fabricated from nominally equal constituents and identical consolidation processes, leaving as the only variables, the variations caused by the different fiber weave structures. The fiber architecture drastically affects both composite strength and deformation characteristics. Some systems are almost linear up to a final brittle failure while others exhibit a pronounced non-linearity prior to failure. It is found that the composite tensile strength is dictated by both fiber volume fraction and weave architecture. The weaving can have a beneficial effect in spite of introducing new fiber flaws and stress concentrations, because it causes the composite to be less flaw sensitive. These features are addressed analytically by considering the statistical aspects of the fiber strength and the formation of critical defects. 1. INTRODUCTION Recently, substantial attention has been paid to the mechanical properties and performance of uniaxial continuous fiber reinforced composites with brittle matrices. The application of these unidirectional composites is severely restricted because of their inferior transverse and shear properties. However, because of their simplicity they are attractive for theoretical studies, and the models developed have lead to a deeper understanding of the micromechanics involved. Most structural components are subjected to multiaxial loading and require a substantial multi- axial strength and for this reason three-dimensional reinforcements are attractive as all-purpose structural materials [I]. Specifically the performance in com- pression (resistance to delamination buckling) can be enhanced with through-thickness reinforcements [2]. However, the weave structure adds complexity and cost and many commercially available high tempera- ture composites are two-dimensional, suitable for components of shells, plates and tubes type when the loading is mainly in the plane. It is generally accepted that a gain in material strength is at the cost of ductility and toughness. In composites, however, high strength is combined with a reasonable toughness, because the matrix or the fiber-matrix interface is such that individual fiber breaks do not cause catastrophic failure, and energy is dissipated at failed fibers, groups of fibers or fiber tows sliding relative to the surrounding media. It has been commonly assumed for fiber composites with weak or cracking matrices that the strength scales with the amount of fibers aligned with the load [3], and that fibers are weakened by defects introduced by weaving. Fiber waviness is considered undesirable [4]. The present study investigates how the mechanical performance of carbon/carbon composites are influ- enced by the fiber weave architecture. In the exper- imental program the composites have been subjected to tension, shear and bending. The results provide sufficient data to develop an appreciation of the over- all performance of the composites and to evaluate different strength models. 2. COMPOSITE MATERIALS The composite materials were manufactured by Carbon/Carbon Advanced Technologies in the shape of panels by using the same processing technique (ACC-4) for all panels. The fibers are heat-stabilized Union Carbide T-300 graphite yarns. The ACC4 carbon matrix is deposited by four impregnations with Fiber&e K-650 phenolic, each followed by pyrolysis. Since all the composites consist of the same fiber and matrix only the effects of the fiber weave structure influence the properties. It is expected that the characteristics of the fiber-matrix interface do not vary significantly between the panels. This property is considered to be one of the key parameters controlling the mechanical behavior [5]. The weaving affects the mechanical properties of the composites 573
0956-7151(95)00184-O Copyright 0 1996 Acta Metallurgica Inc.
Printed in Great Britain. All rights reserved 1359-6454196 $15.00 + 0.00
THE EFFECT OF FIBER ARCHITECTURE ON THE MECHANICAL PROPERTIES OF
CARBON/CARBON FIBER COMPOSITES
J. NEUMEISTER, S. JANSSON and F. LECKIE Department of Mechanical and Environmental Engineering, University of California, Santa Barbara,
CA 93106. U.S.A.
(Received 25 March 1994; in revised form 4 April 1995)
Abstract-The mechanical performance of carbon-fiber matrix composites with different fiber architectures is investigated for various loading modes. All the composites were fabricated from nominally equal constituents and identical consolidation processes, leaving as the only variables, the variations caused by the different fiber weave structures. The fiber architecture drastically affects both composite strength and deformation characteristics. Some systems are almost linear up to a final brittle failure while others exhibit a pronounced non-linearity prior to failure. It is found that the composite tensile strength is dictated by both fiber volume fraction and weave architecture. The weaving can have a beneficial effect in spite of introducing new fiber flaws and stress concentrations, because it causes the composite to be less flaw sensitive. These features are addressed analytically by considering the statistical aspects of the fiber strength and the formation of critical defects.
1. INTRODUCTION
Recently, substantial attention has been paid to the mechanical properties and performance of uniaxial continuous fiber reinforced composites with brittle matrices. The application of these unidirectional composites is severely restricted because of their inferior transverse and shear properties. However, because of their simplicity they are attractive for theoretical studies, and the models developed have lead to a deeper understanding of the micromechanics involved. Most structural components are subjected to multiaxial loading and require a substantial multi- axial strength and for this reason three-dimensional reinforcements are attractive as all-purpose structural materials [I]. Specifically the performance in com- pression (resistance to delamination buckling) can be enhanced with through-thickness reinforcements [2]. However, the weave structure adds complexity and cost and many commercially available high tempera- ture composites are two-dimensional, suitable for components of shells, plates and tubes type when the loading is mainly in the plane.
It is generally accepted that a gain in material strength is at the cost of ductility and toughness. In composites, however, high strength is combined with a reasonable toughness, because the matrix or the fiber-matrix interface is such that individual fiber breaks do not cause catastrophic failure, and energy is dissipated at failed fibers, groups of fibers or fiber tows sliding relative to the surrounding media.
It has been commonly assumed for fiber composites with weak or cracking matrices that the strength scales with the amount of fibers aligned with the load [3], and that fibers are weakened by defects introduced by weaving. Fiber waviness is considered undesirable [4]. The present study investigates how the mechanical performance of carbon/carbon composites are influ- enced by the fiber weave architecture. In the exper- imental program the composites have been subjected to tension, shear and bending. The results provide sufficient data to develop an appreciation of the over- all performance of the composites and to evaluate different strength models.
2. COMPOSITE MATERIALS
The composite materials were manufactured by Carbon/Carbon Advanced Technologies in the shape of panels by using the same processing technique (ACC-4) for all panels. The fibers are heat-stabilized Union Carbide T-300 graphite yarns. The ACC4 carbon matrix is deposited by four impregnations with Fiber&e K-650 phenolic, each followed by pyrolysis. Since all the composites consist of the same fiber and matrix only the effects of the fiber weave structure influence the properties. It is expected that the characteristics of the fiber-matrix interface do not vary significantly between the panels. This property is considered to be one of the key parameters controlling the mechanical behavior [5]. The weaving affects the mechanical properties of the composites
573
NEUMEISTER et al.: MECHANICAL PROPERTIES OF COMPOSITES
8.5 mm I- J !slSrnrn
Fig. 1. The internal structure of the weaves: (a) 8HSW and (b) PW.
by introducing additional fiber flaws and gives rise to different matrix porosity and cracking. The consolidation process also affects the fiber strength significantly.
In this study six different fiber architectures have been tested. Their main characteristics are summar- ized in Table 1, and the weave structures depicted in Fig. 1. Five of the composites have a nominal fiber volume fraction of 55-60%. The unidirectional material was also available with a lower fiber volume fraction of 35-40%. The two unidirectional com- posites are manufactured from tapes in 0” lay-ups. The one with the lower fiber volume fraction is de- noted (1 D-al. 1) and that with higher volume fraction by (lD-a1.2). The biaxial unwoven composite (ID-O’/ 90”) is made of tapes in 0’/90” lay-ups. Two com- posites have balanced weaves; one being an 8-harness satin weave (BHSW) with 3000 fiber tows and the other a plain weave (PW) with 6000 fiber tows. The quasi-isotropic composite (Q-iso) consists of 16 layers
of 8-harness satin weave with equal portions in 0’/90”/ f 45” directions.
As indicated in Table 1 the thickness varies throughout each individual panel. The variation is most pronounced for the unwoven materials. In the woven material the fibers are held in place sideways by the weave resulting in a more uniform thickness. Depending on the composite architecture, two differ- ent methods were used to measure the fiber volume fraction. For the three unwoven architectures, the fiber fractions were determined by measurements on SEM micrographs of transversely sectioned polished samples. For the woven materials, the fiber content was calculated from tow spacing, tow size, number of layers, layer thickness and fiber diameter, see Table 1. In only one case did the fiber content differ from the manufacturer’s data. The fiber cross sections are elliptical or kidney shaped, cf. Fig. 2. The average diameter corresponding to the measured fiber area is 6.2 pm. For the woven structures, the fiber volume
Table 1. Composite materials and main macroscopic characteristics
Material
lD-al.1
ID-al.2
ID 0”/90 8HSW
Material type
1D tapes aligned (lower fiber content) 1D tapes aligned (higher fiber content) 1D tapes in V/90” lay-ups 8-harness satin weave Plain weave Quasi isotropic: 8HSW in 0”/90”/+45” lay-ups
Fiber Panel content Number thickness Weave wave-length
NEUMEISTER et al.: MECHANICAL PROPERTIES OF COMPOSITES 515
Fig. 2. SEM micrograph of a polished sample (ID-a1.2) taken with topographical backscatter. Note the non-circular cross section of the fibers. the scatter in fiber packing and the presence of voids.
fraction varies noticeably throughout the composites. Locally, the fiber volume fraction can be as high as 70% in a tow while the average volume fraction is less than 60%.
3. EXPERIMENTAL PROGRAM 1 75 I125 mm tabs
3.1. Introduction /
In order to determine mechanical properties of the composite three different tests were performed. These were
0 tensile tests ?? Iosipescu shear tests ??short three point bending tests.
Because of size limitations of the as-received composite panels and because of the low shear and transverse strength in relation to the tensile strength, special consideration had to be given to the design of the specimens whose dimensions are shown in Fig. 3. Some of the specimens required aluminum end tabs. All the tests were performed in a screw driven 50 kip universal test system under displacement control. Nominal strain rates were in approx. 1 x 10m61/s. The strain was measured with strain gages, and because the strain gage readings are invalid when localization or debond occurs RAM displacements were also recorded.
F 2.5-3.0 mm
C) #
/ 1 l/fj I
Fig. 3. The specimen geometries for: (a) the tensile test; (b) the Iosipescu (in plane) shear; and (c) the 3-point bending (interlaminar) shear test. The thickness t of the original panel indicates the way the specimens were cut from those. Tabs as shown were used for the Iosipescu specimens
on unidirectional materials (lD-al.1 and lD-a1.2).
It - 2.5 mm I
N /
\ J/ -
516 NEUMEISTER et al.: MECHANICAL PROPERTIES OF COMPOSITES
Table 2. Tensile properties of the materials
Initial Tensile strength Initial Poisson’s Strain to
-range modulus ratio’ failure2 Material (MPa) @Pa) (-) (%)
‘Poisson’s ratios reflect through panel thickness deformation. ZFailure strain is calculated from displacement at grips.
3.2. Tensile tests
The minimum gripping length L, is related to the specimen thickness h by L, = &i/(2r,), where c and z, are the tensile and interlaminar shear strengths respectively. This implies for the strongest materials, with an acceptable minimum thickness of h = 2.5 mm, that a specimen length of three times the gage length was required to avoid a premature shear failure in the grips. Strain gages with a length longer than the repeating element of the composite were used. Because of the restrictions in specimen geometry contraction only is measured in one direction, cf. Fig. 3. The bending stresses introduced by clamping were found to be lower than 5 MPa.
The tensile strengths, failure strains and (initial) elastic moduli are presented in Table 2. The moduli are based on strain gage readings while the failure strains are estimated from the RAM displacement by matching the RAM readings to the strain gage readings at the initial response. At the peak stress (or close to it) localization of deformation occurs, and strain is not a relevant measure thereafter. The failure strain was defined as the value at the peak stress.
Stress-displacement and stress-strain curves for all the composites are shown in Figs 4 and 5. The failure modes of the composites can been grouped in the following categories.
5oc
4oc
2
g 300
D
z a 200
100
9
08880 1D al.1 - 1D al.2 ~;;,~/"o"
*mr PW
- 1
Displacement A (mm)
Fig. 4. Tensile stress-displacement curves for the materials.
d,,,/..,,L,,,~, 11,,,,,,,,,,1,,,1
0.20 0.40 0.60 0.60 1.00
StKiiIl E (%)
01.i
400
- Q-is0
300
Fig. 5. Tensile stress-strain curves for the materials.
(1) Catastrophic. The specimen loses its load carrying capacity (> 95%) instantly after the peak stress. The unwoven material (ID-0’/90”) failed in this manner. (2) Semi-catastrophic. The specimen loses its load carrying capacity quickly, but not instantly. Closely after the peak stress there is evolution of damage, accompanied by a modest decrease in stress. This behavior was observed for the two uniaxial composites (1 D-al. 1) and (l D-a1.2) and the plain weave (PW). (3) Gradual. In this case damage evolves more progressively. After reaching its peak value the stress decreases gradually, sometimes discontinu- ously, over a large deformation. This behavior was observed for the &harness satin weaves. The quasi-isotropic (Q-iso) maintains a higher stress after the load maximum than the (8HSW). This is caused by friction that develops in the f 45” layers as they are pulled apart.
3.3. Iosipescu shear tests
Specimens of Iosipescu type were used to measure the in-plane shear response. The gage portion of the specimen has a -50% reduction, a notch angle of 110” and a notch root radius of -0.5 mm, see Fig. 3. Strain gages were mounted in the +45” and in the -45” directions on opposite sides of the specimens. The shear stress is assumed to be the average value and shear strain is evaluated from the relation y = c+~>” - t_450. The gage section of the specimen is narrow and calls for small strain gages. On the other hand, a representative portion of the material has to contain at least one full weave repetition (cf. Table 1 and Fig. 1) which calls for larger gages. As a compromise a strain gage length of 1.6 mm was selected.
The initial moduli for the different composites are given in Table 3. The modulus measured for all composites with 0”/90” reinforcement showed little variation. For the present loading the shear deform- ation in the composites is matrix dominated since large
NEUMEISTER et al.: MECHANICAL PROPERTIES OF COMPOSITES 517
shear strains can be accommodated in the matrix without significantly straining the fibers. This would suggest that the shear moduli are close for all the systems. The (Q-iso) composite is stiffer, however, because it has reinforcements in the f45” directions which coincide with the principal stress directions of the loading.
Failure strains in shear are not reported. After the initial linear response a band forms between the notches with localized shear deformation and matrix damage. The band is bridged by intact fibers. Over
80.00 , I oeeea 1D al.1 ~rte%eo 1D 01.2
2 60.00 - Q-is0
zi kJ
; 40.00
R
3 G 20.00
0.00 0.0 0.4 0.6 1.2
Displacement A (mm)
Fig. 6. Shear stress~isplacement curves for the materials.
80 L I
: m 1D al.1 maeem 1D al.2
E 60 : - PW
E - - Q-is0
I+
0 0.0 2.0 4.0 6.0
Shear Strain y (%)
Fig. 7. Shear stress-strain curves for the materials.
such a band the shear strain y becomes ambiguous and cannot be measured by strain gages. The graphs of shear stress and strain, Fig. 6, and shear stress and displacement, Fig. 7, exhibit similar tails. However, it is clearly seen in the stress displacement graph that failure of the layered material (lD-0’/90”) is much more abrupt than it is for the more ductile failure of the two unidirectional composites (lD-al.1 and lD-a1.2). The failure strains are specimen dependent and would be much lower for the uniaxial materials with the fibers orientated in the direction of the two notches. No specimens with this fiber orientation were available. An appreciation for the later type of loading can be gained from the short 3-point bending tests reported as follows.
3.4. Short beam 3-point bending tests
The interlaminar shear strength was measured by loading short beams in 3-point bending. The shear stress in the central layer is given by elementary beam theory as
3F r=-
4wt (1)
where F is the load at the center of the beam. In 3-point bending tests the span has to be shorter
than the length L, (given in Section 3.2) to ensure a shear failure in the central layer of the beam occurs prior to tensile failure. The beams satisfy this criterion so failure is by central shear.
The resulting shear strengths are shown in Table 3. As expected, all materials failed at approximately the same shear stress of lo-12 MPa. The unwoven materials failed through the entire half of the beam and exhibited multiple shear cracks, similar behavior to those observed in [6] for a Nicalon/LAS composite. This behavior was inhibited in the woven composites where the deformations localized in a band of shear cracks through the specimen thickness. The width of each crack being related directly to the weave wave length 1, cf. Table 1.
In unidirectional material the intra- and inter- laminar shear strengths are equivalent. The present results indicate that the intralaminar shear strength is insensitive to the weave architecture. This implies that the measured intralaminar shear strength can be used as a good estimate of the interlaminar shear strength. It is also found, Table 3, that the inplane shear strength is substantially higher that the interlaminar shear strength. Similar features have also been observed in [7] for a different C/C composite and test method.
4. CHARACTERIZATION
4.1. Fracture morphologies
To understand the failure mechanisms in tension it is helpful to examine the fracture morphology, the growth of the failure regions and the length over which the gradually evolving damage regions interact
578 NEUMEISTER et al.: MECHANICAL PROPERTIES OF COMPOSITES
1 D-al.1
Fig. 8. Fracture morphologies for the tensile tests. The specimen widths are ~4.5 mm. (a) lD-al.2 and lD-a1.2; (b) lD-0”/90”; (c) 8HSW; (d) PW; and (e) Q-iso.
Figure 8 (c), (d) and (e) opposite
NEUMEISTER et al.: MECHANICAL PROPERTIES OF COMPOSITES 519
580 NEUMEISTER et al.: MECHANICAL PROPERTIES OF COMPOSITES
Table 4. The region of the fracture process zone for the materials
Percentage of Length of failure specimen Failure length/
Material region-range gage length wave-length test direction (mm) (“/) (-)
into a global failure. In Fig. 8 representative (repeat- able) pictures of morphologies are shown for the different composites. The different composites have distinctly different fracture morphologies.
The two unidirectional composites (lD-al.1 and ID-a1.2), Fig. 8(a), exhibited a very jagged fracture surface with delamination cracks running along the entire specimen and even into the tab-section. The shear cracks appear to have a sharper angle in the system with the higher fiber volume fraction.
In the layered 1 D material (1 D-0’/90”) each layer failed almost perpendicular to the loading direction. Sometimes all the individual layers failed at roughly the same plane, whereas in other cases the failed layers clustered in several places, as shown in Fig. 8(b). However, the amount of pullout of both individual fibers and bundles of fibers with matrix between them was observably lower here than in any of the other composites.
In both the balanced weaves (8HSW and PW), the general fracture planes were inclined to the direction of tension, Fig. 8(cd). Individual tows protruded from this plane with the length being longer in the (8HSW) than in the (PW) composite. The tows of the plain weave pulled out over several wavelengths. This was less evident in other materials.
In the (Q-iso) composite the +45” layers (which are loaded in shear) first developed cracks along the tows and fibers. A noticeable amount of interlaminar failures also occurred because of the different lateral contractions of the weave for loadings in the 0”/90” and the f45” directions. This allows the different layers to behave rather independently. Finally, upon failure of the 0” fibers the laminate fails and the f45” layers separate along the tows through the specimen width, Fig. 8(e).
A crude measure of the size of the failure region can be obtained by adding the lengths of the two separated halves of the specimen and subtracting the original length. The pictures in Fig. 8 show that fracture morphology is complex with compact regions, individual fibers, bundles of fibers, tows and to some extent even layers being pulled out of the bulk material. Two stages of the failure process can be deduced from the mechanical response: an initial stable accumulation of distributed damage and a second with an interaction and localization of dam- age that causes an unstable dynamic global failure. The first stage is of importance for strength pre-
dictions. However, it is not possible to distinguish how those two stages contribute to the fracture morphologies. This implies that taking the difference in lengths of the specimens before and after the test might overestimate the length of the zone where fracture was initiated.
Table 4 shows the length of the failure region together with length in relation to gage length and weave repetition, 1. The woven materials exhibit the most consistent behavior. For both the unidirectional materials (ID-al.1 and lD-al.2) the failure region exceeds the length of the gage section. In the grip section the composite is loaded in shear at stresses lower, but of the same order, as the interlaminar shear strength. This implies that shear cracks, once initiated in the gage section, could propagate into the grip region.
Another expected observation is that there is a correlation between failure region and the length of the weave repetition 1. In the unidirectional materials with 1 = co, the failure region is only limited by the specimen length. The 1-D V/90” composite exhibits both long and short failure regions because it has 1 = cc in the 0” layers and 0 in the 90” layers. The two 8-harness satin materials (8HSW and Q-iso) exhibit similar failure regions, while the plain weave shows a longer failure region in relation to its weave repetition. The plain weave has the most wavy fibers and it is the only architecture which shows consider- able nonlinearities prior to peak stress level, see Fig. 4. It is also the material with the highest strain to failure, cf. Table 2, which indicates that the fibers “straighten out” during loading. The straightening of the fibers gives rise to out of plane stresses that cause interlaminar cracking.
4.2. Fiber and interface characteristics
Many parameters influence the performance of composite materials, but the most dominant are the fiber content, strength and orientation. The fiber strength is an ambiguous quantity, since it is dictated by a defect population. It has to be given in statistical terms and related to a gage length. Most commonly used is the two-parameter Weibull distribution which encompasses a characteristic strength at a given gage length and a variability index, the Weibull exponent m. A high value of m implies a more uniform fiber strength. It is very difficult to extract fibers from a carbon/carbon composite to measure the in situ fiber statistics. For other fibers for which the Weibull modulus m can be obtained, it often lies in the range of 2-7. Tests on carbon fibers exposed to a thermal history similar to the one used in the composite fabrication indicate a modulus m = 3-5 [8]. Fortun- ately, available theories for composite strengths depend only weakly on m in this range. This holds for both asymptotic [3] as well as statistical theories [6,9-l 11.
The role of the fiber-matrix interface [5] is also important. The simplest description of a constant
NEUMEISTER et al.: MECHANICAL PROPERTIES OF COMPOSITES 581
interfacial sliding stress ri will be employed here. This property provides an indication of the stress recovery from a fiber break. This interface strength is also difficult to estimate. Two approximate methods to determine zi are described below:
(1) A failed fiber exerts shear stresses on the surrounding matrix. The shear stresses arising from several adjacent failed fibers may over- come the shear strength of the composite, so that whole clusters of fibers are pulled out, see Fig. 9. With the composite (interlaminar) shear strength known, the interface strength can be calculated from the size of these clusters [6] according to the relation
&=d”’ vfZi
where vf is the fiber volume fraction, d is the fiber diameter and 7, is the interlaminar shear strength, see Table 3.
(2) The fracture surfaces are examined and the longest individual fiber pullout is measured. This length cannot exceed the load transfer length L, ,
which is related to the sliding strength through the relation
where or is the stress in the fiber. Assuming that all fibers break at the same stress gives or=
curs /vf. A simple model for the tensile strength [3] that considers already broken fibers and stress recovery adjacent to the fiber breaks gives
where m is the Weibull exponent. Combining equations (3) and (4) gives an expression for the interfacial strength as
The fiber bundles observed in the fracture surface of the failed specimens were almost exclusively in the range D, = loo-160 pm in diameter. (A few larger bundles were observed, with up to 200pm). These values are of the same order of magnitude as the tow thickness. However, the bundles have the same dimen- sions in both the thickness and width directions, while the tows are deformed, and are therefore considered as representative.
The fiber pullout length was taken as the distance from the fiber break to the location where the bundle becomes a unit with intact matrix between the fibers. The tip of this bundle is one place where it can be assumed with certainty that the individual protruding fibers have been pulled out. In other parts of the fracture surface this condition may not be satisfied, see Fig. 9. The longest single protruding fibers were in the range L, = 0.8-1.5 mm. Since the flaws
Fig. 9. SEM micrograph of characteristic fracture surface features: clustered fiber failures with individual pullout at the bundle tip.
582 NEUMEISTER et al.: MECHANICAL PROPERTIES OF COMPOSITES
Table 5. Strength and stiffness efficiency of 0” fibers and efficiency for the materials. For the quasi-isotropic material also the reduced values (without the contribution of
causing the fiber breaking are evenly distributed, only the longest pullout length should be limited by the interfacial shear strength. Hence, more attention should be paid to the longer pullout lengths. All material had some fibers protruding at least 1.3 mm. The bundle diameters and fiber pullout lengths were similar for all the composites with no systematic variation, although both fewer bundles and individually pulled out fibers were observed in the layered material (ID-0’/90”). Equations (2) and (3) indicate that these lengths (D, and L,) depend on the volume fraction vr and the maximum stress. Possibly such trends could be discerned among the observed values.
Using the averages values for r, = lo-12 MPa (cf. Table 3), D, = loo-160 pm, ur= 46659% and d = 6.2 pm in equation (2) gives an interface strength of r, = 1.0 MPa. Using the endpoints of these intervals suggests that the value of r, is in the range 0.66- 1.6 MPa. Equation (5) is derived for unidirectional composite. For woven or layered architectures, ur should be taken as the amount of fibers in the loading direction. This correction has been employed in Table 5 and the “effective” failure stress is in the range 660-860 MPa. Using a Weibull exponent m = 3-5, [8] and L, = 1.3-1.5 mm in equation (5) gives the range ri = 0.80-1.3 MPa.
The two methods are approximate and give indications of the magnitude, rather than absolute values of the interfacial strength. [Equation (2) gives the minimum bundle size and equation (5) assumes that the fiber break occurs at the UTS]. However, both methods give numbers of the same order. More- over, strength models [3,6,9-111 depend weakly on z, in this range and it is sufficient to note that ri is in the range l-2 MPa.
5. INTERPRETATION OF COMPOSITE STRENGTH
A simple measure of how efficiently the fibers are used in each material, is the ultimate stress divided by the fiber volume fraction in the 0” dire&ion. This is the average stress carried by the longitudinal fibers, if these alone carry the load at failure. Table 5 shows the resulting values as well as the initial stiffness per
fiber content in the loading direction. For a com- posite with a weak matrix, these numbers should be of the same order for all materials with reinforce- ments in the 0 and 90” directions.
Comparing the three materials containing 1D tapes, it appears that in spite of the fact that the same fibers (tapes) have been used and that they have undergone the same history-the fewer fibers there are in the loading direction, the more efficiently they are utilized. The range of fiber efficiency correlates well to the range in failure strains obtained for these materials, cf. Table 2.
The difference in strength efficiency between the two unidirectional materials can be explained with the “bundle pullout” failure mechanism [6], both qualitatively and quantitatively. A brief description and the main equations are provided in the Appendix. The jagged fracture surface, clearly indicates that failure is caused by some critical defect which initiates shear crack propagation. The slightly lower inter- laminar shear strength of the composite with the higher fiber volume fraction (lD-a1.2) in conjunction with the denser fiber packing enables shear crack growth for a smaller defect size, i.e. less failed fibers in a small region, cf. equation (2). For similar reasons, the layered material (1 D-0’/90”) should be even more efficient since the layers are only slightly thicker than the minimum bundle to be pulled out. Hence, defects large enough to cause crack propagation can only exist in the central part of the layer. This is a type of volume effect, since part of the material is discrimin- ated from participating in the failure process. More- over, the propagation of shear cracks is constrained to one layer. Thus initiation by this mechanism does not need to lead to specimen failure, and although the fracture surface shows clustered fiber failures, it does not exhibit the same degree of longitudinal splitting as in the unidirectional materials. Instead it seems that cracks in the 90”-layers cause the O”-reinforce- ments to fail in quite a planar manner, see Fig. 8(b). Recent tests on other systems (Sic/glasses), compar- ing uniaxially reinforced and 0”/90” layered structures show a similar increase in fiber efficiency for the layered materials [12-141. The higher efficiency of 0”/90” layered materials also shows in the fact that failure, when it happens, is more catastrophic, cf. Section 3.2.
NEUMEISTER et al.: MECHANICAL PROPERTIES OF COMPOSITES 583
Proceeding as outlined in the Appendix and using the average value z, = 1.5 MPa the bundle pullout model predicts the (lD-a1.2) composite to be 17% stronger than the (lD-al.1) composite. The exper- iments indicate a difference of 14%. (Using ~~ = 1.7 MPa gives a perfect fit. These relative differences are insensitive to m.) If the fiber fraction alone deter- mines the strength, as is assumed in several existing theories, the difference would be 26%.
The behavior of the quasi-isotropic composite (Q-iso) can be well understood using Classical Laminate Theory [ 151. The laminate consists of layers of 8-harness satin weave. Using the measured prop- erties for the (8HSW) composite and CLT to predict the properties for the O”/90”/ +45” laminate gives a tensile modulus of 69 GPa and a shear modulus of 22.5 GPa (for in-plane Poisson’s ratio between 0.2 and 0.4). These values are close, but approx. 10% lower than the measured properties for the (Q-iso) composite. Reasons for these differences are edge effects (each lamina is not fully effective at the edge) and somewhat lower fiber content in the Q-iso specimens. Based on a CLT calculation the f45” layers contribute 47% to the composite stress, and 41% to the stiffness.
Failure is controlled by the O”-fibers because these are the first to reach the critical strain and the f 45”-layers cannot support the additional load. The efficiency for the (Q-iso) composite with and without the stress and stiffness contributions from the f45”- layers (based on CLT) is shown in Table 5. When the contribution from f45”-layers is included the fiber efficiency is close to the results for the (8HSW) material. A check indicates that the shear stress in the f45”-layers (22 MPa at failure) does not exceed the corresponding strength of the (8HSW) lamina, cf. Table 3. It seems that the quasi-isotropic material is isotropic (in its plane) with regard to strength and follows the Tresca maximum shear stress criterion in tension, 5 g 22. Other failure mechanisms are expected in compression.
The fiber efficiencies for the woven structures sort in the same order as the failure strains. To understand the difference between the two materials with balanced weaves (8HSW and PW), requires knowledge about the statistical properties at two different levels. From the pictures of fractured specimens, it is evident that failure of one tow can occur independently from the surrounding tows. However, the actual failure plane still seems to be in a well contained region. A rudimentary model of the composite is the “chain of bundles” originally introduced by Giicer and Gurland [16], Fig. 10. In this context, the “bundles” consist of the individual tows or groups of fibers, rather than the fibers themselves, and the length of every “chain-link” is the wave length 1. The parallel elements (e.g. fibers tows) in the bundles are described with a statistical strength. For illustration purposes the Weibull distribution will be utilized for the tows as well.
h PW
> Link separators 1 (crack barriers)
F 1
Fig. 10. The chain of bundles model of a woven composite with a repetition feature.
Thus, consider a bundle consisting of a large num- ber of parallel elements, each with a characteristic strength of c,, (at gage length L,) and a variability given by the Weibull modulus M (to be distinguished from m for the individual fibers). The strength of a bundle of length 1 containing many such elements is given by
Lll - 0 I/M
g=oo z e-IIM
For details, see e.g. Appendix 1 in Ref. [6]. Obviously, if 1 is lowered, the bundle strength increases. With 1 ,nSW/lPW = 3.95 the measured difference of 19% is achieved for a Weibull modulus M = 6.2, indicating that 15% (1 - exp[ - l/M]) of the elements in one layer (chain link) have failed at the load maximum. The apparent Weibull modulus, M = 6.2, is slightly higher than the corresponding value for the individual fibers. The fracture morphologies clearly show that the fiber failures occur in clusters and the Weibull modulus for a cluster of fibers is higher than for the individual fibers, cf. [6]. The low Weibull modulus indicates that the failure mechanism involved is sub- ject to substantial statistical scatter as well. However, this is only a crude model, and the real picture is far more complicated with more effects which increase and decrease the difference in strength.
If the defects were introduced by the weaving only, and in proportion to how many times the tow winds around the fill fibers, the same defects are introduced in the two weaves but over different lengths. Then, the gage lengths Lo in equation (6) would be different for the two systems and scale linearly with 1. This implies that the asymptotic bundle strength, equation (6) would be the same for the two systems.
If the significant defects are introduced by the processing rather than by the weaving, trends given by equation (6) should be discernible. The strength given by equation (6) is based on the
584 NEUMEISTER et al.: MECHANICAL PROPERTIES OF COMPOSITES
assumption of an infinite number of elements in every layer. With a finite number of members, the links, bundles of tows/fiber groups, themselves will have a distributed strength, and a chain with more links as (PW) will be weaker in relation to the asymptotic strength, equation (6) than the (8HSW).
The loss of load due to element failure accom- panied with shear splitting may depend on the length over which splitting can occur. Hence, a material with shorter wave-lengths can be less flaw sensitive.
Clearly the picture is too complicated to be summed up in one or two simple equations. For instance, results by other authors indicated that the &harness satin weave is more efficient than the plain weave [17], and tests on other C/C systems have found significant loss of fiber efficiency in Quasi-isotropic lay-ups of plain-weave laminae [ 181.
6. SUMMARY/CONCLUSIONS
The experimental results from the six carbon/ carbon composites with different fiber architecture and fiber volume fractions clearly contradict two hitherto common assumptions regarding continuous fiber com- posites with weak matrices. Instead it is found that
?? the tensile strength of these composites does not scale solely with the fiber volume fraction under otherwise equivalent conditions
?? the weaving can enhance the longitudinal strength and fiber efficiency in spite of intro- ducing new fiber defects and fiber waviness that results in higher fiber stresses.
Both findings can be explained by the statistical nature of fiber failures and the formation of a global failure. The composite strength is limited by a critical flaw size or aggregation of flaws, which depend on and evolve with the loading.
Two important conclusions based on these observations are
?? the fiber strength is important because global failure is initiated from clusters of individual failed fiber
??due to the very inferior transverse properties of the composites with aligned fibers, failure is typically associated with shear splitting originat- ing from weak regions, flaws or defects. This phenomenon limits the tensile strength since it occurs over a large length scale and enables separated weak regions to link up and interact
?? the composite strength substantially relies on the capacity of the structure to arrest and restrict growth of the shear cracks that link the weak regions, as in woven architectures.
These observations of trends are qualitative and the available information is insufficient to make
quantitative predictions about fiber efficiency in different architectures. A major variables which are missing are the in situ fiber strength statistics for every system and the local variations of shear strengths, due to e.g. porosity and fiber packing, have to be considered. One anticipated observation, however, is
?? the woven composites behave more consistently than the unwoven composites. They are geo- metrically more uniform and all the measured properties show less variation than those for the 1D materials.
Acknowledgements-This work was supported financially by DARPA through the URI at UC Santa Barbara (ONR N442-2429-23100) and NCEL contract (N47408/93R7308). The authors are grateful to Allied Signal Aerospace Com- pany, Garret Engine Division for providing the composite materials and to Dr F. Heredia at Materials Department, UCSB. for valuable discussions.
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S. Chou, H-C. Chen and H-E. Chen, Comp. Sci. Tech. 45, 23 (1992). B. N. Cox, M. S. Dadkhah, R. V. Inman, W. L. Morris and J. Zupon, Acta metall. mater. 40, 3285 (1992). W. A. Curtin, J. Am. Ceram. Sot. 74, 2837 (1991). J. Jortner, Carbon 30, 153 (1990). H. C. Cao, E. Bischoff, 0. Sbaizero, M. Riihle, A. G. Evans, D. B. Marshall and J. J. Brennan, 1. Am. Ceram. sot. 73, 1933 (1990). S. Jansson and F. A. Leckie. Acta metall. mater. 40. 2967 (1992). K. Anand, V. Ciupta and D. Dartford, Acta metall. mater. 42, 797 (1994). F. E. Heredia, private communication. J. M. Neumeister, J. Mech. Phys. Sol& 41, 1405 (1993). S. L. Phoenix, Comp. Sci. Tech. 48, 65 (1993). W. A. Curtin, J. Mech. Phys. Solids 41, 217 (1993). F. W. Zok and J. McNulty, Report Materials Dept, UCSB (1993). D. S. Beyerle, S. M. Spearing, F. W. Zok and A. G. Evans, J. Am. Ceram. Sot. 75,2719 (1992); ibid. 76,560 (1993). D. S. Beyerle, S. M. Spearing and A. G. Evans, J. Am. Ceram. ioc. 75, 3321.(1992). R. M. Jones. Mechanics of Comoosite Materials. McGraw-Hill, New York (1975). _ D. E. Giicer and J. Gurland, J. Mech. Phys. Solidr, 10, 365 (1962). L. M. Manocha and 0. P. Bahl, Carbon 26, 13 (1988). G. Popp, H. Bidder and U. Gruber, Z. Werkstofftech. 16, 252 (1985).
APPENDIX
Failure by uninhibited shear crack propagation (especially in unidirectional composites), caused by the bundle pullout mechanism [6] is anticipated when element, diameter Da and length L, [equations (2) and (3)] fails. Element failure is predicted when a critical fiber break density is reached with it [3,6,9]. Here, an element becomes unstable when
n*=keJ[l--exp(-i)] (Al)
NEUMEISTER et al.: MECHANICAL PROPERTIES OF COMPOSITES 585
fiber breaks within it (m is the Weibull modulus). The element volume Vs is
(0
which depends on the strain c, and where E, is the fiber modulus. Using weakest link statistics, the probability of survival of a tensile specimen is given by
where w is related to the strain c as
In equation (A5) crO is the characteristic fiber strength at gage length L,. A simple description gives stress in a strained composite as [3,9]
V P, = exp lo1 ( 1 -yP’
B (A3)
where pf is the probability of failure of one element, i.e. the probability of finding n* failed fibers within the element. This probability is found from Weibull and Poisson statistics. It depends on the global strain and is accurately approximated by [9]
e’log[(w + l)(zm+5)/4] n* (w + l)Pn+5M
> (A4)
\ L/ where the second term accounts for the softening, the deviation from the linear response due to individual fiber breaks. The strain that gives P, = 50% [equation (A3)] is taken as a representative value and insertion of this strain in equation (A6) gives the median strength. Equations (A3))(A6) can be used to compare specimens of different volumes or volume fractions, without knowing the exact in situ fiber strength (provided the fibers are the same).
