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Vol. 25. NOS 516. pp. 779-791.
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DAMAGE-INDUCED PROPERTY CHANGES IN COMPOSITES SUBJECTED TO CYCLIC THERMAL LOADING CARL T. HERAKOVICH Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, U.S.A. and M. W. HYER Department of Mechanical Engineering, The University of Maryland, College Park, MD 20742, U.S.A. in the form of transverse Crack8 resulting from thermal loading is studied as it relates to the dimensional stability of flat laminates and stiffness changes in cylindrical tubes.
Graphite-epoxy specimens were subjected to cyclic thermal loading in the temperature range -250 to + 250°F. It is shown that transverse cracking is the dominant damage mechanism in both types of structural elements. Fiber splitting is also quite common at the low test temperatures. Experimental results indicate that damage significantly reduces the inplane coefl3cients of thermal expansion of flat laminates and the torsional stiffness of the tubes. Theoretical predictions for coefficients of thermal expansion as a function of crack spacing in flat laminates followed the same trend as experimental
INTRODUCTION COMPOSITE materials
are a prime candidate for use in the space environment because of their high specific stiffness, high specific strength and low coefficient of thermal expansion (CTE). Composites are currently in use in a variety of space applications including telescopes, solar reflectors, antennae, and space craft. There is a strong possibility that resin matrix composites will be the material ofchoice for the tubular components of the space station which is currently in the planning stage. In several of these applications, graphite-epoxy is the chosen material because of requirements on dimensional stability. In other applications, it is the stiffness or strength of composites that is the most important consideration. Resin matrix composites, such as graphite-epoxy, are susceptible to transverse cracking when subjected to the cyclic thermal loading of the space environment. Thus, it is imperative that the resulting degradation in mechanical and expansion properties be determined as a function of the damage state, and that methods be developed to predict the damage state as a function of the combined thermo-mechanical loading of the space environment. It is also intuitively apparent that the influence of transverse cracks on property degradation will be a function of the geometry of the structural component and the type of mechanical loading superimposed on the cyclic thermal loading. This paper is concerned with the development of transverse cracks resulting from cyclic thermal loading corresponding to the extreme conditions of the space environment ( - 250 to + 250”F), and the degradation of CTE in flat laminates and the degradation of axial, bending and torsional stiffnesses in tubes. Only cross-ply configurations are considered. Experimental results are discussed for several different graphite-epoxy material systems. Previous works on thermally induced damage in composites are presented in references [l-13]. THERMALLY
Figure 1 is a schematic of the damage states that can develop in cross-ply laminates and tubes as a result of thermal or mechanical loading. Transverse cracks develop in individual layers when the transverse ply stress c2 exceeds its ultimate value. These cracks form essentially at right angles to cracks in adjacent layers, as depicted in Fig. l(a). For ideally homogeneous materials, cracks in individual layers are equally spaced with the crack spacing a function of the temperature change from 779
C. T. HERAKOVICH and M. W. HYER
ton/90n& Cracking in Inner Loyer
a) Fiat Laminate
b) Tube Fig. 1. Test configurations.
the cure temperature, material properties and laminate configuration. Figure l(b) is a schematic of transverse cracks in the core of tube. Figure 2 shows actual photographs depicting several features of thermally induced damage in flat laminates and tubes. Figure 2(a) shows the uniform spacing of cracks in a cross-ply laminate. Figure 2(b) and (c)gives higher magnification photos showing more detail of individual cracks. Fiber splitting is very evident, as is the aversion the cracks have for resin-rich region. The crack path avoids large resin-rich regions, following a path in regions of high stress concentrations and low strength around fiber-matrix interfaces. In the absence of large resin-rich regions, the cracks grow in a selfsimilar manner including splitting fibers. As will be demonstrated later in the section on tubes, crack density is a function of resin properties. It is also evident from the photographs that the resin-rich region at layer interfaces acts as a crack arrester. FLAT LAMINATES
Crack spacing as a function of temperature Lamination theory. The initial temperature of transverse cracking can be predicted using classical lamination theory with temperature-dependent material properties. A trial-and-error solution must be used since all quantities are temperature-dependent. The equation for temperature-dependent stresses in the kth layer of a laminate has the form
w-)jk = [QV)lk((~o(W+zkIe-)t) -
In ref.  it was determined that the in situ transverse strength of T300/5208 is at least 1.9 times the strength measured in a standard coupon tension test.
Fig. 2. Crack features. resin-rich
(a) Transverse crack spacing (T300/5208). (b) Fiber splitting and deflection region (T300/5208). (c) Fiber splitting in a tube (T3O&P75s/CE339).
Damage-induced property changes in composites Initial
Crack Tronsverse /Crack
Fig. 3. Uniform crack spacing analysis region.
Finite element analysis. Subsequent cracking after the initial crack can be predicted using an analysis which takes into account the presence of the initial crack. The basic problem is depicted in Fig. 3(a). A new crack will form at a distance 2B from an existing crack where eZ first attains its ultimate value. The theoretical results presented in this paper are based upon a two-dimensional finite element “constrained nodal displacement” formulation~9]. The region modeled and appropriate boundary and constraint conditions are depicted in Fig. 3(b) and (c). The CTE, ay, is given in terms of the unknown displacement V* as a,, = I/*/B AT
where the displacement V* is constrained to be uniform above the crack. Individual layers are assumed to be homogeneous, elastic and orthotropic. The problem is treated as a generalized plane problem with the out-of-plane strain determined using classical lamination theory. Four-node isoparametric, quadrilateral elements were used to model the region of interest. The mesh had 272 elements, 306 nodes and 849 unknown degrees of freedom. EXPERIMENTS
Tests were conducted on 2.5in. square [O/90,], and [02/902]S T300/5208 graphite-epoxy laminates. Observation from two perpendicular directions provided results for the two additional laminates [90/O,], and [90Z/02]S. Tests were conducted on six specimens of each type to determine the
C. T. HERAKOVICH
and M. W. HYER
temperature of initial cracking. All specimens were dried and inspected for cracks prior to testing. All were found to be crack-free. The fiber volume fraction of the laminates was 69%. Thermal cracking was monitored through a window of an environmental chamber at 25F increments using a 75 x microscope. (The rate of cooling and heating was maintained at 10-F per min. between observations and the temperature was held constant during inspection.) All specimens were investigated under higher magnification (400 x ) after the specimens were removed from the environmental chamber. The results of the initial thermal cycle were somewhat inconclusive in that only 13 of 36 specimens exhibited cracking. The results for any one specimen configuration varied widely, ranging from no cracking detected under the higher magnification after completion of the test to initial cracking at - 50°F observed under 75 x during the test. These variable results were attributed to the rather short specimen length and the variable transverse strength of the inhomogeneous material; they pointed to the need to study cyclic thermal loading. Crack density as a function of cyclic thermal loading
Two rates of thermal loading were used to obtain results for crack density as a function of cyclic thermal loading for three specimens of each type. All specimens were cut from the same panels of T300/5208 graphite-epoxy discussed previously. They were dried and inspected prior to thermal cycling between + 250 and - 250°F. The rates of thermal loading will be referred to as slow rate and high rate. In the slow rate tests, the specimens were thermally cycled at a rate of approximately 10°F per min. for a total cycle time of lOOmin. This group of specimens was inspected with a 400x microscope at the completion of cycles 2, 3,4, 5, 7, 10, 15 and 20. The second set of specimens was thermally cycled at a much higher rate in order to obtain a significantly higher number of thermal cycles within a reasonable time period. The specimens were placed on a mechanically driven slide tray which alternated between two chambers maintained at the maximum and minimum test temperatures. Each complete thermal cycle took approximately 15 min., more than six times faster than the slow rate tests. These specimens were monitored at the completion of cycles 20, 50, 100, 250 and 500. Results for the average crack density as a function of thermal cycles for the first 20 cycles are presented in Fig. 4, where dashed lines have been hand-fared through the data. It is noted that, even though the total number of cracks in a given specimen is small, the average crack density provides a very consistent trend for each laminate. These slow rate test results indicate that the crack density is a function of layer thickness as well as percentage of 90” plies. Figure 5 shows average crack density curves for four laminates subjected to up to 500 thermal cycles. The first 20 cycles at the slow rate are solid symbols and the high rate tests are indicated by open symbols. It is evident from Fig. 5(b) that the [90,/O& and [0,/90,], laminates exhibit very
l [90/0,1, n co2/90,1, A c90,/0,1, T30015208
Fig. 4. Initial crack density in flat laminates.
Damage-induced property changes in composites
and [O/30j]s Laminates
300 N (-25OOF
[02/902]s and [902/021s Laminates
Fig. 5. Long-term crack density in fiat laminates. consistent results for high rate tests.’ The results for the [90/O,], laminate indicate a discontinuity between the slow rate and high rate tests between 20 and 100 cycles. (Unfortunately, no results were obtained at 20 and 50 cycles for the high rate tests.) Similar discontinuities in crack density as determined from slow and high rate tests were obtained for other laminates. That is, the slow rate tests often exhibited significantly higher crack densities after 20 cycles than did the high rate tests. It is believed that this behavior may be an indication that the time at temperature is important with creep to failure occurring in those laminates held at low temperatures for longer periods. Additional work is needed to clarify this point. The results in Fig. 5 (and similar results for the orthogonal viewing direction) indicate that none of the laminates has attained a saturation crack density after 500 cycles. Figure 5(b) shows crack density for [0,/90J1 and [9OJO,], laminates compared with the saturation density predicted using the finite element analysis. At 500 cycles the experimental density is approximately 30 % below the predicted limiting value. A least-squares fit of the experimental data for a Weibull distribution of crack density p of the type
p = A(l-elN)
is also shown.
Table 1 presents the values of A and L for these and other tests. From Table 1 it is seen that the data of Fig. 5(b) asymptotically approach a saturation density of 18.5 cracks/in,, reaching 99% of this saturation value at 1350 cycles. The saturation density extrapolated from the experimental data is approximately 17 % below the saturation density predicted by the finite element
Table 1. Least-squares estimates of A and I A (cracks/in.) T300-5208 flat T3W-P75s/934 tube T300-P75s/CE339 tube T300-T300/934 tube tleast-squares
18.5 20.4 18.4 15.7
error high due to lack of data: numbers not reliable.
I (in.-‘) 3.4 x 9.8 x 3.0x 1.9x
10-a IO-’ 1o-3 lo+
C. T. HERAKOVICH and M. W. HYER CRACK
25 50 75 CRACK DENSITY ( CRACKS / IN )
Fig. 6. CTE percent reduction
in flat laminates.
analysis. The finite element results in this figure were based upon an in situ transverse 2.55 Y,. A lower value for the in situ strength would provide better correlation between theory and experiment, A 17 % reduction in predicted saturation density would correspond to an in situ strength of 2.12 r,. CTE as a function of crack spacing
of the displacement L’* (Fig. 3) per unit temperature change for a crack spacing
28 provides the CTE as a function of crack spacing [eq. (2)]. Figure 6 shows predictions for the
decrease in CTE as a function of crack density for three cross-ply laminates. As expected, the largest and sharpest decrease in CTE occurs in the laminates with the largest percentage of 90” layers. The majority of CTE change occurs in the first 20 cracks/in. The percent change in CTE at a crack density of 100 cracks/in. ranges from 55 % for laminates with 25 % 90” layers to 85 % for laminates with 75 % 90’ layers. The curves approach asymptotic values near 100 cracks/in. Two experimental points are also shown in Fig. 6 for a [0,/90,1S laminate. These experimental results for CTE were provided by Bowles[ 143. They show the same trend but somewhat higher values for CTE than the finite element predictions. From the results of Fig. 6 it is obvious that transverse cracks can result in a significant decrease in laminate CTE. TUBES
In the second phase of the study, the issues of microcracking and thermal cycling were also addressed, but in the context of tubular laminates. Previous studies by Cohen and Hyer[15-171 have shown that the thermally induced stresses in cross-ply tubes can be significantly different than the thermally induced stresses in flat laminates, even with the same stacking arrangement. This is particularly true if the laminate is not symmetric with respect to its geometric midplane. The primary reasons for the difference is the constraint of the tubular geometry. A single flat lamina is stress-free (from the macroscopic viewpoint) when cooled from its cure temperature. On the other hand, a single lamina in the form of a tube with its fibers oriented circumferentially experiences considerable residual stress when cooled from the cure temperature. If the fibers are oriented axially, the thermally induced stresses are negligible. For the circumferential fiber case, the stresses result from the difference between the circumferential and radial coefficients of thermal expansion, and the fact that the circumference is constrained to equal 271times the radius. In a tube the circumference constraint and the differences in expansion oppose each other and, as a result, stresses are generated. In a multilayer tube, add to these geometric-based stresses the stresses generated because of the differences in elastic and thermal expansion properties from layer to layer. It is clear that the problem of a tube is different than the problem of a flat laminate. As with the flat laminate portion of the study, this second phase of the study had as one of its objectives the determination of the effect of repeated thermal cycling on the formation of microcracks in tubes. However, knowing the characteristics of microcrack formation was not the sole objective. A
Damage-induced property changes in composites
second objective was to determine the effect of the microcracking on the torsional, extensional, and bending stiffnesses of the tube. These stiffnesses, as well as the thermal expansion characteristics, are key indicators of tube performance. Finally, a third objective of this phase of the study was to determine the effect of microcracking, and subsequent stiffness loss, as a function of material system. Three material systems were considered, one involving a toughened resin. The first objective was addressed by thermally cycling tube specimens and counting microcracks after cycling. The second objective was addressed by measuring the bending, extensional and torsional stiffnesses with specially constructed fixtures. The third objective of comparing material systems was implicit. The microcracking characteristics and stiffness losses could be examined as a function of the material system. Tube geometry and construction. Figure l(b) illustrates the tubes considered in the study. The inner diameter of the tubes was 0.50 in. and the laminating sequence was [90/0,/90], 0 being the axial direction. The inner and outer circumferential layers are referred to here as skins and they served to keep the six axial layers, or core, together. The wall thicknesses were nominally 0.040 in. and so the tubes would be classified as thick-walled tubes. The fibers used in the tubes were T300 and P75s. The resin systems used were 934 and CE339. The T300 fiber is well known while the P75s fiber is a newer high-modulus pitch-based fiber with a modulus of 75 Msi. The 934 resin is a standard resin that cures at 350°F while the CE339 is a resin that is toughened by an elastomer additive and cures at 250°F. These materials were arranged in three specific combinations. The combinations, and the designation used to identify them, are shown in Table 2. The high modulus fiber is not as easy to work with as the T300 fiber and so only T300 was used in the skin. When the P75s fiber was used it was used in the core. The T3O&P75s/934 and the T300-P75s/CE339 were the tubes of primary interest, the T300-T300/ 934 tube served as a baseline. Experimental procedure Microscopic examination. Using a 100 x and a 400 x microscope, an examination
of the tube cross-sections was conducted before any thermal cycling began. This was done to determine if there were any microcracks or other forms of damage present in the tubes, perhaps from cutting or from fabrication. There were no microcracks detected but the examination revealed a number of anomalies in the tube construction, the most noticeable being resin-rich regions and overlapping of the prepreg tapes used in the skins. There was no doubt that the overlap regions would influence cracking when cycling began and would lead to a lack of polar symmetry in the tube’s stiffness characteristics, even with no thermal cycling. During the microscopic examination, the volume fractions of fibers in the tube cores were estimated. For the tubes with the P75s core, the volume fraction of fibers was estimated to be 44 %, while for the tubes with the T300 core the volume fraction was 50 %. Both of these values represent a low volume fraction of fibers as compared with the laminates studied. Subsequent to thermal cycling the specimen ends were inspected for damage using the microscope. The number of transverse cracks in the core and their circumferential positions were recorded. Following the microscopic examination, an edge replica of each specimen end was made. To evaluate whether or not the core cracks propagated along the entire length of the specimen, and to study the damage characteristics of the skins, X-rays were employed. Following the microscopic examination, the specimens were fitted with cylindrical grips. The grips were bonded to both the inner and outer walls of the tubes and they were designed in such a way that bending, tensile and torsional loads could be transmitted to the tube specimens with the same grips. Thermal cycle treatment. The tubes were thermally cycled between -250 and +200”F. Five thermal cycle levels were considered, in addition to the control case of no thermal cycles. The five
Table 2. Tube material systems Skin fiber
T300 T300 T300
T300 P75s P75s
934 934 CE339
T300-T300/934 T300-P75sJ934 [email protected]
C. T. HERAKOVICH
and M. W. HYER
were: 10. 50, 100, 300 and 500 cycles. Each thermal cycle treatment included three replicate specimens from each material system. Due to the thinness of the tube walls, as far as heat transfer characteristics were concerned, relatively short cycle times could be used. Specifically, the specimens were cycled from -250 to +200’F and back to -250°F in the sliding tray mechanism mentioned earlier. Each specimen was 6 in. in length, this length being sufficient to grip the specimens after thermal treatment to measure the stiffnesses. To eliminate the possibility of an interaction between thermal cycling and material moisture content, all cycled tubes were dried under vacuum prior to cycling. [email protected]
tests. The extensional and bending tests were conducted using special fixtures in conjunction with a standard screw-driven load frame. The torsional tests were conducted in a separate fixture. The torsion fixture was constructed knowing that only low torque levels were needed because of the cross-ply nature of the tubes. In fact, all tests were conducted with the constraint that the strain levels generated by the applied loads should be kept low enough that no additional microcracking would be introduced by the stiffness testing itself. This was important because each tube specimen was tested in bending, extension and torsion. If high load levels were used in the bending tests, for example, the tests could introduce microcracking beyond the level introduced by thermal cycling. The torsion tests would then not accurately reflect the effects of thermal cycling alone. (Due to the grip design, it was not possible to recount the number of microcracks between stiffness tests to determine whether or not new cracks had been introduced.) The stiffnesses were measured by recording a displacement-related tube response and the applied load. Since the strain levels were to be kept low, bending deflections in the bending tests would be very small and subject to experimental error. Therefore, cross-section rotations (in the sense of Bernoulli beam theory) at two known locations along the length of the tube were measured. The difference between these rotations was a direct measure of curvature. This technique proved to be very sensitive and is now felt to be a much better way to measure bending response than to measure deflections. For the extension tests, a 1.0 in, long extensometer was used. It was felt that strain gages measure too localized a response (unless long-gage-length gages are used) and measurements from them would not properly reflect a change of properties. For the torsion test, cross-section rotations (in the sense of St. Venant torsion theory) at two known locations along the length of the tube were measured. The difference between these rotations was a direct measure of twist. These measurements were also quite sensitive and provided an accurate measure of tube response. Because of the aforementioned anomalies in the tube cross-sections. possible misalignments of the specimens in the loading fixtures, and possible misalignments in the fixtures themselves. each tube was tested in bending in four orthogonal planes and the results averaged. For extensional testing. each tube was also tested in four orientations, the tube being rotated 90’ about its axis between tests. The anomalies in tube construction would not influence the torsion tests but each tube was also tested in torsion four times and the results averaged. Experimental results Microcracking characteristics. Figure 7 shows the relationship between the core crack density accumulation and the number of thermal cycles for the three material systems. A crack was counted if it propagated entirely through the radial thickness of the core. There were very few cracks that did not meet this criteria. Skin cracks were not counted. The core crack density was computed by dividing the number of cracks observed in the core by the mean circumference. Generally the spacing of cracks was uniform and so the crack density calculation is meaningful. Several points of interest can be noted in Fig. 7. First, it is clear that all three material systems cracked with thermal cycling, the T300-T300/934 showing the least amount of damage and the T3O&P75s/934 showing the most. That these two material systems represent extremes is not surprising. Both the T300 and the P75s fibers show very low (perhaps even negative) thermal expansion characteristics. However, the P75s fiber is 2.5 times stiffer than the T300 fiber and so the mismatch in elastic properties between resin and fiber characteristics is much worse for the P75s case. As a result, in the same resin (934 in this case) the residual stress state with P75s fibers would be much more conducive to cracking than with T300 fibers. Since the resin is somewhat brittle, cracking did occur in the more highly stressed case. Also, as can be noted in Fig. 7, the T300-P75s/CE339 system showed less damage than the T300-P75s/934 system. The difference can be attributed to two factors. The CE339 resin cures at a lower temperature, and it is toughened. Since the lower cure temperature
Damage-induced property changes in composites
n T300(skin)-T300(core]1934 AT300(skin)-P75S(COrd/S34 0 T300(skin)-P75S(core)/CE339
Fig, 7, Core crack density in tubes.
results in a smaller temperature change from the stress-free state, the residual stresses are lower, decreasing the tendency to crack. With the toughened resin, there is a resistance to cracking. The solid lines in Fig. 7 are least-squares Weibull estimates computed from the data. Table 1 presents values of the Weibull parameters. The microscopic examination revealed other interesting info~ation regarding the material systems. First, compared with the T300-P75s/CE339 system, the T300-P75s/934 system showed more extensive damage. The additional damage was in the form of skin/core interlaminar circumferential cracks bridging the radial core cracks. Second, the core cracks in the 934 system often propagated to the fiber, disbonded the fibers from the matrix with a semicircular separation of the fiber and matrix, and continued on to the next fiber, where the semicircular separation repeated. In the CE339 system, the cracks generally propagated to the fiber and then continued across the diameter of the fiber, splitting the fiber. As mentioned previously, liber splitting was evident in the fiat laminates of T300/5208. Difference in crack propagation behavior may indicate the interfacial bond in the CE339 system was stronger than in the 934 system. The T300-T300/934 system showed characteristics similar to the T300-P75s/934 system. The X-rays used to examine the inner and outer skins after the stiffness tests were conducted also revealed interesting differences between the P75s/934 and P75s/CE339 systems. In the skins, the circumferential cracks in the T300-T300/934 and T300-P75s/934 systems propagated entirely around the tube. In the T300-P75s/CE339 system the skin cracks did not propagate around the full circumference. Not only does this reflect the toughness of the CE339 resin, but it also suggests that in the toughened system the length of the cracks grew gradually, cycle by cycle. In the more brittle system, the increase in crack length was more sudden. tests Figure 8 shows the torsional stiffnesses in the tubes as a function of core crack density. Data from the three material systems are shown. The stiffnesses of the three material systems have been normalized by the three stiffness measured for the no-thermal-cycle case. Also shown on the figure is a second-order least-squares lit to the data. A single second-order relation was used as opposed to one for each material system because it seems logical that the normalized torsional stiffness loss should not depend on material properties. It should depend solely on the crack density. The clustering of the data from the three material systems seems to confirm this hypothesis. By using Figs 7 and 8 it is possible to determine the torsional stiffness loss as a function of the number of thermal cycles. For example, for the T300-T300/934 system, a torsional stiffness loss of 35% was measured after 500 thermal cycles. Before closing the discussion of torsional stiffness losses, a point should be mentioned. It is realized that skin cracks affect the torsional stiffness. However, as mentioned earlier, it was difficult to obtain an accurate counting of these cracks, pa~icularly in the inner skin. Since the core accounted for 75% of the torsional stiffness of the tube, it is felt the conclusion drawn from Fig. 8 regarding
C. T. HERAKOVICH and M. W. HYER
q T300(sk1n) -T300(coreV934 a T300(skin)-P75S(core)/934’
07qr 0 72 t
0 T300(skin)-P75Sicore)/339 REGRESSION
0,601 ’ 0 2
Fig. 8. Torsional stiffness vs crack density.
Table 3. Effective stiffnesses before thermal cycling
Tube T3OGT300/934 T300-P75s/934 T300-P75s/CE339
Torsional (lb-in. x 103)
Bending (lb-in.’ x 103)
3.08 2.67 2.18
36.1 62.7 69.9
Extensional (lb x 103) 828 1568 1710
material-independence of the stiffness loss with crack density is accurate. The second-order relation may be changed by adding skin cracks to the count but the conclusion will not change. Regarding the extensional and bending stiffnesses, to within the resolution of the measurements, there was no detectable change in these stiffnesses for any material system. The scatter among the three replicates far outweighed the apparent changes and, in fact, stiffness increases were actually measured. For completeness, Table 3 indicates the torsional, bending, and extensional stiffnesses of the three material systems at the no-thermal-cycle condition. CONCLUSIONS Several important conclusions can be drawn from the work on flat laminates and tubes: (1) thermal cycling in the temperature range of the space environment results in transverse cracking in cross-ply configurations, (2) the transverse crack density increases with thermal cycling, in most cases approaching a limiting value at a cycle count in excess of 500, (3) significant reduction in laminate CTE and torsional stiffness results from the presence of transverse cracks, (4) fiber splitting is a common occurrence for graphite composites thermally loaded to -250”F, (5) transverse crack density is lower with a toughened resin system. Acknowledgement-This work was supported by the NASA Virginia Tech. Composites Program through NASA Grant NAG l-343 and NASA Cooperative Agreement NCC I- 15. The authors are grateful for this support. The authors would also like to acknowledge the work of D. Adams, D. Bowles and D. Cohen in acquiring most of the results presented in this paper. Professor Hyer was a faculty member at Virginia Tech. during the majority of this work.
REFERENCES [I] D. R. Donner and R. C. Novak, Structural behavior of laminated graphite filament composites. Proc. 24th Annuul SAMPE Technical Cor$ ( 1969).  R. C. Novak and M. A. DeCresente, Fabrication stresses in graphite-resin composites. J. Engng Pwr 377-380 (1970).
Damage-induced property changes in composites
 R. G. Spain, Thermal microcracking of carbon fiber/resin composites. Composites 2, 33-37 (1971).  C. C. Chamis, Lamination residual stresses in cross-plied fiber composites. Proc. 26th Annual SAMPE Technical Conf. (1971).  A. Molcho and 0. Ishai, Thermal cracking of C.F.R.P. laminates. SAMPE 10 (1978).  S. A. Eselum, H. D. Neubert and E. G. Wolff, Microcracking effects on dimensional stability. 24th Nat. SAMPE Symp. 24, Book 1 (1979).  C. T. Herakovich, J. G. Davis, Jr. and J. S. Mills, Thermal microcracking in Celion 6OOO/PMR-15graphite/polyimide, in Thermal Stresses in Severe Environments (Edited by D. P. H. Hasselman and R. A. Heller), pp. 649664. Plenum Press (1980).  D. S. Adams, D. E. Bowles and C. T. Herakovich, Characteristics of thermally-induced transverse cracks in graphiteepoxy composite laminates. VPI-E-83-23, Virginia Polytechnic Institute (June 1983).  D. S. Adams and C. T. Herakovich, Influence of damage on the thermal response of graphite-epoxy laminates. J. Thermal Stresses 7, 9 l-103 (1984). [lo] D. E. Bowles, Effect of microcracks on the thermal expansion of composite laminates. J. compos. Muter. 17, 173-187 (1984). [1 l] D. Cohen, M. W. Hyer and S. S. Tompkins, The effect of thermal cycling on matrix cracking and stiffness changes in cross-ply graphite-epoxy tubes. VPI-E-84-29 and CCMS-84- 12, Virginia Polytechnique Institute (1984). 112) D. Cohen, M. W. Hyer and S. Tompkins, The effects of thermal cycling on matrix cracking and stiffness changes in composite tubes. 16th SAMPE Technical Co& 577-588 (1984).  D. S. Adams, D. E. Bowles and C. T. Herakovich, Thermally induced transverse cracking in graphite-epoxy cross-ply laminates. J. Reinforced Plastics and Composites 5, 152-169, 1986. [ 141 D. E. Bowles, Private communication; data to be published.  D. Cohen and M. W. Hyer, Residual stresses in cross-ply composite tubes. VP1 & SU Center for Composite Materials and Structures Report CCMS-84-02 (1984). [ 163 D. Cohen and M. W. Hyer, Residual thermal stresses in cross-ply graphite epoxy tubes, in Advances in Aerospace Sciences and Engineering (Edited by U. Yuceoglu and R. Hesser), pp. 87-93. ASME Publication AD-08 (1984).  M. W. Hyer, D. E. Cooper and D. Cohen, Stresses and deformations in cross-ply tubes subjected to a uniform temperature change. J. Thermal Stress 9, 97-l 17, 1986.