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Response of thermoplastic and thermosetting composites under compressive loading—An experimental and finite element study
Com~osiles Engmeering, Vol. 4, No. 6. pp. 637.651. 1994 Elsevier Science Ltd Printed in Great Britain
Pergamon
0961-9526(94) E0020-9
RESPONSE OF THERMOPLASTIC AND THERMOSETTING COMPOSITES UNDER COMPRESSIVE LOADING-AN EXPERIMENTAL AND FINITE ELEMENT STUDY Anwarul Haque, Hassan Mahfuz, Cynthia Ingram and Shaik Jeelani Materials Research Laboratory,
Tuskegee University, Tuskegee, AL 36088, U.S.A.
(Received 16 August 1993; final version accepted I March 1994) Abstract-The influence of long-term moisture exposure and temperature on the compressive properties of T-3OO/epoxy (thermosetting) and APC-2 (thermoplastic) composites has been studied. Specimens of quasi-isotropic configuration [45°/90”/-450/O”], were designed on the basis of the Euler buckling criterion, and a temperature range of 23-100°C was considered for both dry as well as wet tests. Specimens for wet tests were soaked in distilled water for a period of 360 days, and the effects of moisture absorption on the compressive properties and geometry of the specimens were investigated. The results of the investigation indicated that the moisture absorption rate of T-3001epoxy was higher than that of APC-2. It was noticed that the geometry of the specimen influenced the moisture absorption rate. The thick plate with a smaller surface area absorbed less moisture than the thin plate with a larger surface area. The compressive strength and modulus of APC-2 were found to be comparatively higher than that of T-3OO/epoxy both in dry and wet conditions. The effect of moisture at 100°C was negligible for both materials. The modes of failure in both materials under compressive load were found to be delamination, interlaminar shear and end brooming. Thick laminates of thermoplastic composites (APC-2) were modeled with isoparametric layered shell elements to predict the responses of the dry laminate at various temperatures under compressive loading. A large-displacement finite element analysis was performed by considering the geometric non-Iinearities in the composite structure. Multiple load steps with linear material behavior were used to model the load-displacement characteristics found in the experimental study. The compressive response with respect of displacements, normal stresses and interlaminar shear stresses under three different temperatures is presented. The laminate response along the length as well as through the thickness is also presented, to analyze and understand the failure mechanisms under such loading. Experimental data were compared with the FEM results to test the accuracy of the finite element analysis (FEA) using the layered shell element under the assumption of first-order shear-deformation theory. A reasonably good correlation between FEA and experimental results was found. 1. INTRODUCTION
Fiber-reinforced plastics have found widespread use in the automotive, aerospace, construction and marine industries due to their excellent specific propeties, improved corrosion resistance, toughness and superior fatigue properties (Khatri and Koczak, 1991). Increased use of fiber-reinforced composites especially in submersible structures makes the compression response of such composites critical (Harris and Morris, 1984; Bogettie et al., 1987). Recent use of high-temperature thermoplastics as the matrix material has opened new horizons for lightweight structural materials with improved toughness, higher impact resistance and better environmental stability (Khatri and Koczak, 1991; Haque and Jeelani, 1992). Characterization of these newly developed thermoplastic composites is well underway and is being reported routinely by the manufacturers and researchers. However, the non-linear compressive response, and the environmental effects on the compressive properties of these composites, are still one of the least-understood topics in composite science. Both thermosetting and thermoplastic resins are used as matrix materials in graphitereinforced composites. Epoxy resins, by far the most widely used thermosetting matrix materials, appear to absorb moisture and lower the matrix glass transition temperature which in turn degrades the high-temperature properties of the resin (Browning et a/., 1977; Tang and Springer, 1988). The environmental resistance of organic matrix composites to temperature and humidity depends on the glass transition temperature and 637
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chemical interactions of the matrix polymer. The physical impact of water is to plasticize the matrix, thereby degrading the mechanical properties. Decomposition of the resin at elevated temperature is also responsible for loss of stiffness and strength. A detailed degradation mechanism for environmental exposures has been studied by Tsai (Tsai, 1967). The effect of moisture on the mechanical properties of graphite/epoxy composites has also been reported by many researchers (Springer, 1984a, b; Haque et al., 1990; Blikstad et al., 1984; Shirrell, 1978). In graphite composites the matrix is the limiting component in the wet environment. Recently, Polyetheretherketon (PEEK)-a thermoplastic resin manufactured by Imperial Chemical Industries Limited (ICI)-has been characterized as a potential matrix material for APC-2, a graphite/PEEK composite. PEEK has a glass transition temperature (T,) of 143°C and melting point of 332°C. It is evident that PEEK possesses useful properties above the glass transition temperature of the resin. However, the primary advantage of the thermoplastic resin over thermosetting is its negligible moisture absorption and reprocessing capabilities. In order to understand the effect of such moisture absorption, as well as to study the stability of APC-2 at elevated temperatures, specimens of both APC-2 and regular graphite/epoxy composites were characterized in this investigation. Wet coupons were soaked in distilled water for a period of 360 days, and were later tested at various temperatures ranging from 23°C to 100°C. Similar tests were conducted with dry coupons of both materials. Test conditions and moisture exposure parameters were kept identical for both APC-2 and graphite/epoxy. The improvement in compressive strength and stiffness is discussed, and possible reasons are identified. Accurate modeling of the non-linear response in composite materials is a theme that pervades modern computational solid mechanics and is likely to intensify in the future (Rice, 1985). The key issue involving both numerical modeling and computational mechanics is the development of a numerical technique that can accurately reflect both geometric and material non-linearities, and that can also predict the onset and development of failures. The compressive failure modes in composites are complex due to transverse tension, fiber kinking, matrix failure and delamination. Aided by the mathematical complexities involved in non-linear mechanics, the task of predicting composite behavior under compression appears to be of profound importance. The finite element method is an attractive tool for performing such rigorous analysis. In the current investigation, an 8-noded isoparametric shell element developed on the basis of first-order shear-deformation theory is used to study the non-linear response of symmetric 40-ply graphite/PEEK (APC-2) composites under compressive loading. In an effort to shed new light on some of the experimental findings observed earlier (Haque and Jeelani, 1992), a large-deflection finite element analysis is performed with maximum stress failure criteria, and is presented in this paper.
2. EXPERIMENTAL
WORK
2.1. Materials A graphite-fiber-reinforced thermoplastic composite, namely APC-2, was procured from Imperial Chemical Company (ICI) Fiberite in the form of 12 in. square consolidated laminates. Each laminate was made of 40 plies in the [+45”/90”/-45”/0”],, quasiisotropic lay-up configuration. The average panel thickness was maintained at 0.20i1-1. with 60% fiber volume. Prepreg tape Cycom 985 manufactured by American Cyanamid was used to fabricate graphite/epoxy laminates. The prepreg was a combination of Thornel 300 graphite fiber and Cycom 985 resin system manufactured by Union Carbide and American Cyanamid, respectively. The laminates were cured in a programmable hot press made by Tetrahedron. Piles were laid up symmetrically in the [ + 45” /90”/ - 45’ 10’1 quasi-isotropic configuration to avoid warpage because of temperature change during curing. Again, the total fiber content was 60% by volume and the average laminate thickness was maintained at 0.2 in.
Response of composites under compressive loading
--u
25.4
T 25.4 A.
Dinensions.
Tr
Specimen
-
-) 1
Vedges II
mpl
Fig. 1. Compression test specimen and IITRI fixture.
2.2. Specimen design Both the APC-2 and graphite/epoxy specimens were made from cured panels as shown in Fig. 1. The typical 1 in. gage length was selected considering that the critical buckling length (L,,) would be greater than 1 in. A width of 1 in. appeared to satisfy this criterion and the equation considered for this calculation is as follows: Critical buckling length where
PC1= D,, = W = L =
L,, =
critical buckling load (lbs) bending stiffness (lb.-in.2 in-‘) column width (in.) column length (in.).
A detailed study of specimen design for the IITRI (Illinois Institute of Technology Research Institute) compression test method has been carried out by previous investigators (Gillespie et al., 1988). 2.3. Conditioning Specimens with 360 day moisture exposure and completely dry specimens were used in this investigation. All specimens were pre-conditioned in a vacuum oven at 100°C until a near-equilibrium weight was obtained. This condition of the specimen is referred to as dry. Five pieces of a 1 in. square plate of APC-2 and graphite/epoxy were soaked in distilled water along with other specimens in order to simulate moisture absorption to the gage section of the specimens. This was done because 83% of the specimen surface was covered by tabbing materials which was different than graphite/epoxy and APC-2. Hence the moisture absorption data from the specimens would not accurately represent the absorption rate of APC-2 and graphite/epoxy. The temperature of the distilled water was maintained at 26°C. Square plates of both graphite/epoxy and APC-2 were removed from the container at various time intervals for weight measurements. The weight gain process was continued for a period of 360 days. COE4:6-F
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2.4. Test method The IITRI compression fixture was used in this investigation because it satisfies the positive alignment criterion to minimize the eccentric loading in compression tests (Fig. 1). The IITRI compression fixture was incorporated into ASTM D3410 in the 1987 revision and recommended by many researchers because of its stability. The stability of the test depends on the selection of an adequate gage length. The specimens with 1 in. gage length and width appear to perform well with the IITRI fixture. Specimens were placed in between wedges as shown in Fig. 1. The wedges were clamped using two screws at both ends and placed in the test block of the IITRI fixture mounted to the testing machine. The tests were performed in a 22 Kips MTS machine attached to an environmental chamber. The rate of cross-head motion was maintained at 0.02 in. min-‘. The load was applied to the specimen and load-deflection data were plotted using a recorder. The compressive modulus was calculated from the linear portion of the load-deflection curve. To compare experimental displacement data with those of FEM, strain gages were used only during the room-temperature tests of the dry samples. 3. FINITE ELEMENT
ANALYSIS
A non-linear finite element analysis was performed using the commercially available finite element package ANSYS to study the damage initiation and failure mechanism in APC-2 under compressive loading. Compression-test coupons were modeled with 8-noded isoparametric layered shell elements as shown in Fig. 2. The formulation of the shell element used in the current study is based on Mindlin’s theory that the mid-surface normal after deformation remains straight but not necessarily normal to the mid-surface (Cook, 1981). This allows transverse shear deformation to be taken into consideration. However, this transverse shear deformation has been assumed to remain constant through the thickness of the laminate, limiting the present FEA to what is widely known as the first-order shear-deformation theory. Accordingly, two rotational degrees of freedom were considered at each node. These rotations of the mid-surface normal were considered about the in-plane axes of the laminate. The angular displacement was then translated into linear displacement, and was added to the regular U, u and w displacements by multiplying by the respective directional cosines (Cook, 1981). The discretized model and the boundary conditions for the compression tests are shown in Fig. 3. The laminate was made of 40 plies of [+45”/90”/-45”/0”],, configuration with a total thickness of 0.2 in., and 60% fiber-volume fraction. Three different temperatures, RT 22.78”C (73”F), 80°C (176’F) and 100°C (212”F), similar to the experimental tests, were considered in the finite element analysis to verify the thermal
Fig. 2. Curved shell element.
Response of composites under compressive loading
6 4
7
6
r44
4-
2
3
)67
9
069
641
lo
16
x
Fig. 3. Discretized model and boundary conditions for the compression specimen.
expansion effects at elevated temperatures. The large deflection effect on the geometry was considered to approximate the finite element model to the closest proximity of the experimental tests. Multiple load steps and the up-dating of the stiffness matrix at each load step were considered to account for the geometric non-linearity. The material properties and failure strength used at room temperature were: E, = 17.8 Msi, Ey = 1.53 Msi, VTt’= 0.28, Gv = 0.74 Msi, CY,= 16 x 10m6in. in.-’ (deg. F)-‘, c& = 93.74 Ksi. Maximum shear failure theory was applied to evaluate the failure criteria numbers (Tsai, 1988). 4. RESULTS AND DISCUSSION
4.1. Experimental 4.1.1. Moisture absorption. The absorption of moisture as a function of time is presented in Fig. 4 for both APC-2 and graphite/epoxy. The weight gained as a result of water absorption was computed in terms of per cent fraction of the total weight of the gage section and plotted as a function of the square root of time. It appears from the nature of the curve that the moisture absorption in graphite/epoxy laminates reaches a first peak after 24 days and no significant change was observed within 24 and 90 days. After 90 days the absorption of moisture increased further and continued until the end of a 360 day soaking period. As a result, a well-defined saturation plateau was not observed in the graphite/epoxy laminate. In contrast, APC-2 appears to reach a saturation plateau after 24 days of moisture absorption. The results indicate that APC-2 and graphite/epoxy appear to absorb a maximum moisture content of 0.182% and l%, respectively, in 360 days. It appears from the data that the diffusivity of graphite/epoxy is five times higher than that of APC-2. Previous work on the same graphite/epoxy system shows a higher moisture absorption rate in which a larger surface area of the specimen was exposed to moisture compared to the present work (Haque et al., 1990). This indicates that the moisture absorption rate depends on the geometry of the structure. Thick plates with a smaller surface area absorb less moisture than thinner plates with a larger surface area.
A. Haque ef al.
642 I
^ A 5 ? o T-300/Epoxy APC - 3 3
1.20 1
Square
Root of Time
(Hr)
Fig. 4. Moisture absorption in T-3OO/epoxy and APC-2 composites,
4.1.2. Compressive strength and modulus. Data for the compressive strength and modulus of both graphite/epoxy and APC-2 are presented in Table 1. All the data represent an average value of five specimens tested under the same conditions. A variation of 15% between the maximum and minimum recorded data was observed in some specimens. This discrepancy could be the results of many parameters in specimen fabrication and environmental conditioning that are extremely difficult to maintain exactly similar for all the specimens. A slight geometric variation in specimens cut from a quasi-isotropic configuration laminate could cause significant differences in data for individual samples. Maintaining constant temperature and moisture contents for each sample during testing was also difficult to achieve. Figures 5 and 6 present the effects of moisture content and temperature on the compressive strength and modulus of graphite/epoxy and APC-2. It is evident that both the compressive strength and modulus of APC-2 are comparatively higher than those of Table 1. Moisture and temperature influence on compressive properties: APC-2 vs graphite/epoxy, quasi-isotropic [+45”/90”/-45”/0”],,. Graphite/Epoxy
APC-2 Comp. Ult. Ksi (MPa)
Comp. Mod. Msi @Pa)
Comp. Ult. Ksi (MPa)
Comp. Mod. Msi @Pa)
23°C D M M*
93.74 (637.43) 84.99 (585.92) 80.64 (555.93)
1.26(8.68) 1.27 (8.75) 0.94 (6.48)
92.17 (635.41) 83.58 (576.20) 82.98 (572.06)
l.lO(7.58) 10.5 (7.23) 0.77 (5.30)
80°C D M M*
87.62 (604.05) 83.65 (576.68) 79.54 (548.34)
1.21 (8.34) 1.17(8.06) 0.59 (4.06)
77.27 (532.69) 74.55 (513.94) 74.43 (513.12)
1.08 (7.44) 0.92 (6.34) 0.72 (4.96)
100°C D M M’
77.30 (532.90) 76.68 (528.63) 78.07 (538.21)
1.05 (7.23) 1.11 (7.65) 0.78 (5.37)
76.26 (525.73) 69.39 (478.37) 68.52 (472.37)
0.88 (6.06) 0.86 (5.92) 0.71 (4.89)
Conditioning
D-Dry. M-90 days moisture exposure. M*-360 days moisture exposure.
Response of composites under compressive loading
643
o 0 o Dry T300/E ory 0 0 0 Wet90 Daya, P T300/Epoxy ts A A Wet I 380 Days).TJOO/Epory
Fig. 5. Moisture and temperature effect on compressive strength of APC-2 and T-3OO/epoxy.
graphite/epoxy. The data for graphite/epoxy and APC-2 show a reduction of 17.26% and 17.53% in compressive strength at 100°C compared with the corresponding values at 23°C. The addition of moisture in graphite/epoxy due to 360 days moisture exposure further reduces the strength by 25.7%. The sensitivity of moisture in the compressive strength of APC-2 is negligible at 100°C. It appears that APC-2 is a better candidate for moisture resistance to sustain its compressive strength as compared to the graphite/epoxy composite. Figure 7 indicates that significant compressive strength reduction does not take place in between long-term (360 days) and short-term (90 days) moisture exposure. In contrast, Fig. 8 shows that the compressive modulus reduces significantly for both APC-2 and graphite/epoxy during the period of short-term (90 days) and long-term (360 days) moisture exposure. The compressive modulus of graphite/epoxy and APC-2 decreased by 20% and 16.44%, respectively, at lOO”C, and a similar trend was observed at room temperature. The absorption of moisture for a period of 360 days further reduced the compressive modulus of graphite/epoxy and APC-2 by 35.45% and 39.09%, respectively. It appears that the influence of moisture is comparatively higher in the temperature range of 50-80°C. The effect of moisture at 100°C is negligible for both materials. Micrographs of Figs 9 and 10 present the optical examination of the fractured specimens of APC-2 and graphite/epoxy. Specimens were not completely separated after Dry, T300/E oxy Wet{90 Days! T300/E ory We1360
Day&
TBOO/!!poxy
1.50 =: $4 z 1.25
-
2 2g
1.00
-
w g 0.75
-
2 g 0.50
-
r-
b
8
0.25 +-r-n-7 0
g--y--l-TEhH'ldT"RE("~~
0.25 100
+ 0
25 =15rg
TEhiPERATURE(‘C) Fig. 6. Moisture and temperature effect on compressive modulus
of
APC-2 and T-300/epoxy.
100
A. Haque et al.
644
1
0
100
200
11
II
300
"
MOISTURE EXPOSURE DAYS
T300/Epoxy
11
400
400 100 200 300 MOISTURE EXPOSURE DAYS
0
Fig. 7. Compressive strength of APC-2 and T-300/epoxy as a function of moisture exposure days and temperature.
failure, rather the ends of the specimens appeared to be interlocked in between plies. Compression failure in the form of delamination and interlaminar shear with end brooming can be observed in these micrographs. 4.2. Finite element analysis Distribution of maximum a, with temperature at the failure load is shown in Fig. 11. Values shown in this figure were obtained from the last iteration. Five iterative steps with a Newton-Raphson scheme were used to implement the geometric non-linearities of the elements. Stiffness matrices were updated at each load step on the basis of the displacement undergone in each iteration. The failure load and stiffness were determined from the experimental data. In fact the stiffness data used in the FEM program were obtained from the uniaxial tests. Correlation of crX with the experimental data is shown in Fig. 11. Gradual reduction in strength with increase in temperature is observed. It is also noticed that the compressive stresses are largest at the clamped end, significantly reduced between nodes 1 and 3, and remain more-or-less uniform throughout the rest of the gage section. At elevated temperatures, the correlation between the experimental results and FEM prediction diverges. The reason for this is believed to be the cross-sectional area
APC -2
0
100
200 300 400 MOISTURE EXPOSURE DAYS
I I ” 0
T300/Epoxy
1’
I ’ ” 100
’ I ““I””
I
200 300 400 MOISTURE EXPOSURE TIME
Fig. 8. Compressive modulus of APC-2 and T-3OO/epoxy as a function of moisture exposure days and temperature.
Response of composites under compressive loading
Fig. 9. Optical examination of fracture specimen of APC-2.
Fig. 10. Optical examination of fracture specimen of T-3OO/epoxy.
645
Response of composites under compressive loading
647
k-4 -75 2 g -100 g 73’F FEM o 176OF FEM A 212’F FEM
Y tj -125 z E E -150 8 -175
m73”F Exp. 9 i76”F Exp. A 212°F Exp.
-200 1
3
Fig. 11. Distribution
5 7 9 NODES ALONG THE LENGTH
11
of a, along the length of the laminate for layer no. 1.
considered during the experiment. Experimental calculation did not take into account the increase in area due to thermal expansion and the transverse tensile strain undergone during the test. FEM prediction, which is based on piece-wise continuous displacement, and updated with the thermal expansion coefficient CY,seems to be a better representation of strength at higher temperature. The experimental value of the maximum displacement at room temperature is compared with the FEM prediction in Fig. 12. The experimental displacement value was determined from the strain gage used during the roomtemperature tests of the dry specimens. The correlation between the two is excellent. Figure 12 also shows that the distribution of u, along the length of the specimen is almost linear. A decrease in the absolute values of displacements with temperatures is observed. The phenomenon is believed to be the resultant effect between the thermal expansion and the degradation of the stiffness of the composite. The interlaminar shear stress (ILSUM) distribution along the length is shown in Fig. 13. The variation of ILSUM with temperature is observed only near the clamped end, elsewhere it is negligible. This may not be the true representation at elevated temperatures. It is to be noted that the FEM analysis assumes perfect bonding between layers throughout the temperature range, which
0.000 -0.001
F = & g e 2 2 cI
0 73°F FEM 4 176°F
-0.002 -0.003 -0.004 -0.005 -0.006 -0.007 -0.008 -0.009 -0.010 -0.011 -0.012 -0.013 -0.014 -0.015
FEM
~212°F FEM
1
3
5 7 9 NODES ALONG THE LENGTH
11
Fig. 12. Maximum displacement (UX) of the top layer along the length at Y = 0.
648
A. Haque et al.
ELEMENTS Fig. 13. Interlaminar
shear stress distribution (between layers 1 and 2) along the length of the laminate.
may not be physically true at higher temperatures. The distribution of ILSUM along the length shows a gradual increase up to element 2, and then a sharp rise towards the clamped end. This indicates initiation of delamination somewhere between element 1 and 2. The interlaminar shear stresses are not uniform through the thickness of the laminate, as shown in Fig. 14. Layers at the point of symmetry have significantly low interlaminar shear stress, indicating that layers laid up with same fiber orientation are most stable during delamination. Figure 14 also shows that peaks are also occurring in a sequence different from the lay-up sequences. The reasons are attributed to the variations of a,, a,, and rxy . Interlaminar shear stresses were computed by the integration of the equations of equilibrium in a finite difference form which includes a,, o,, and Q,, at eight integration points. Therefore, ILSUM is a direct consequence of these stresses. The variation of a, through the thickness of the laminate is shown in Fig. 15, which reveals some of the interesting features of the compressive responses. It is noticed that the 0” layers experience maximum stresses (a,) from compression and are likely to fail first. The second level of stresses is observed in the +45” layers, followed by the -45” layers. Except at the point
0
1 2 3 4 5 6 7 6 9 10 11 12 13 14 15 16 17 18 19 20 LAYER NUMBER
Fig. 14. Interlaminar shear stress distribution
across the thickness of the laminate.
Response of composites under compressive loading
649
-30 c2 D E & y =E = % 0 v
-50 -70 -90 -110 -130 -150 -170 -190
1
-210 -2307 -2501,
, , , , ,
, , , , , , , , ,
, ,
,
,
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 16 19 20 LAYER NUbIRER Fig. 15. Compressive stress distribution
across the thickness.
of symmetry, the adjacent layers experience transverse stresses that differ in sign. This contributes to higher interlaminar stresses between these layers. Progressive failure of the specimen is studied by determining the failure criteria numbers at each iteration. These as shown in Fig. 16 are the ratios of the actual layer stresses in the layer coordinates to the strength of the laminate. It is observed that the failure of the specimen is linearly proportional to the increments of loads. This linearity is due to the constancy of E conidered in the analysis. The progressive failure rates at different temperatures, as shown in Fig. 16, vary slightly with temperatures and remain consistent throughout the iterations. Distributions of longitudinal and transverse strains at room temperatures along the length are shown in Fig. 17. It is noted that both E, and E,, are almost linear along the length beyond node 3, and both strains are compressive. These compressive transverse strains in the top and bottom surfaces of the laminate are likely to inhibit premature microbuckling failure. The in-plane distribution of the longitudinal stress, a,, at room temperature is shown in Fig. 18. Maximum stress occurs in the vicinity of node 1, indicating that the matrix crack will initiate at the edge of the specimen in the neighborhood of this node. At elevated temperatures the a, distribution was also found to be similar to that of Fig. 18.
g ii 2 d ii2 w g
2.40 i 2.20 2.00 1.80 1.80 1.40 1.20
E l-O0 2 OAO 2 0.60 0.40 0.00
, 1
I 2
I 3 ITERATIONS
I 4
Fig. 16. Progressive failure criteria vs load steps.
I 5
A. Haque et al.
650
-0.002 -0.004 -0.006 -0.006 2 z -0.010 it -0.012 -0.014 -0.016 -0.018 -0.020
1
Fig. 17. Distribution
I 3
I I I 7 9 5 NODES ALONG TEE LENGTH
I 11
of ex and .zyof the top layer along the length of the laminate.
POST1 SERp’51 = %P
STRESS CAUGB
hELoB*L=@. 813364 SMN =-I33387 SMX z-43597 jr D '3':::;
Fig. 18. In-plane distribution
of CT,at room temperature (top layer).
Response of composites under compressive loading
651
5. CLOSURE
The following conclusions are drawn from the above study: (1) It appears that the moisture absorption rate of graphite/epoxy reaches a first plateau after 24 days and continue to increase further after 90 days until the end of a 360 day moisture exposure time. The diffusivity of graphite/epoxy was found to be five times higher than that of APC-2. The geometry of the structure considerably influences the moisture absorption rate. A thick plate with a smaller surface area absorbs Iess moisture than a thin plate with a larger surface area. (2) It is evident that both the compressive strength and modulus of APC-2 are comparatively higher than those of graphite/epoxy. APC-2 sustains higher compressive stress in presence of moisture as compared to graphite/epoxy. (3) The compressive strength and modulus decrease with increasing temperature in the range between 23 and 100°C. The addition of moisture further degrades the compressive strength. The influence of moisture on the compressive modulus is comparatively higher in the temperature range 50-75°C. (4) The compression failure was in the form of delamination, interlaminar shear and end brooming. (5) It is shown that thick laminates of thermoplastic composites can be modeled using isoparametric layered shell elements with reasonable accuracy. (6) Good correlation between the experimental results and the finite element analysis with respect to the global maximum displacement, u+, and the maximum compressive stress, or, is observed. (7) Non-linear distributions of transverse stresses and strains are observed along the length. (8) Both normal and interlaminar shear stresses were found to be varying nonlinearly through the thickness of the laminate. Acknowledgement-The authors acknowledge with appreciation Marshall Flight Center through grant NAG% I3 1.
the support for this work from NASA-
REFERENCES Blikstad, M., Sjoblem, P. W. and Johannesson, T. R. (1984). Long-term moisture absorption in graphite/epoxy angle-ply laminates. J. Compos. Mater. 18, OO-OO. Bogetti, T. A., Gillespie, J. W. and Pipes, R. B. (1987). Report #87-55, Center for Composite Materials, University of Delaware. Browning, C. E., Husman, G. E. and Whitney, J. M. (1977). Moisture effects in epoxy matrix composites. In Composites Materials: Testing and Design, ASTM STP 617, pp. 481-496. ASTM, Philadelphia, PA. Cook, R. D. (1981). Concepts and Applications of Finite Element Analysis, 2nd edn. John Wiley, New York. Gillespie, J. W., Jr, Bogetti, T. A. and Pipes, R. B. (1988). Evaluation of the IITRI compression test method for stiffness and strength. Compos. Sci. Technol. 32 (l), 57-76. Haque, A. and Jeelani, S. (1992). Environmental effects on the compressive properties: thermosetting vs thermoplastic composites. J. Rein. Plastics Compos. 11(2), 146-157. Haque, A., Copeland, C. W., Zadoo, D. P., and Jeelani S. (1990). Hygrothermal influence on the flexural properties of Kevlar-graphite/epoxy hybrid composites. J. Reinf. Plastics Compos. 9, 602-613. Harris, C. E. and Morris, D. H. (1990). CompositeMaterials: Testing and Design (7th Conf.), ASTM STP 893. ASTM, Philadelphia, PA. Khatri, S. C. and Koczak, M. J. (1991). Enhanced compressive response of unidirectional thick section thermoplastic composites by fiber hybridization. Int. Conf. on Composite Materials (ZCCM/VIZI), Honolulu, pp. 35-A-I to 35-A-10. Rice J. R. (Ed.) (1985). Solid mechanics: research trends and opportunities. Appl. Mech. Rev. 38, 1247-1308.11. Shirrell, C. D. (1978). Diffusion of Water Vapor in Graphite/Epoxy Composites, ASTM STP 658, pp. 21-42. ASTM, Philadelphia, PA. Springer, G. S. (1984a). Environmental Effects on Composite Materials, Vol. 1. Technomic, Lancaster, PA. Springer, G. S. (1984b). Environmental Effects on Composite Materials, Vol. 2. Technomic, Lancaster, PA. Tang, J. and Springer, G. S. (1988). Effects of cure and moisture on the properties of Fiberite 976 resin. J. Compos. Muter. 22, OO-OO. Tsai, S. W. (1967). Environmental factors in the design of composite materials. 5th Symp. on Nova1 Sfructural Mechanics. Pergamon, New York. Tsai, S. W. (1988). Composire Design, 4th edn. Think Composires, Dayton, OH.
Pergamon
0961-9526(94) E0020-9
RESPONSE OF THERMOPLASTIC AND THERMOSETTING COMPOSITES UNDER COMPRESSIVE LOADING-AN EXPERIMENTAL AND FINITE ELEMENT STUDY Anwarul Haque, Hassan Mahfuz, Cynthia Ingram and Shaik Jeelani Materials Research Laboratory,
Tuskegee University, Tuskegee, AL 36088, U.S.A.
(Received 16 August 1993; final version accepted I March 1994) Abstract-The influence of long-term moisture exposure and temperature on the compressive properties of T-3OO/epoxy (thermosetting) and APC-2 (thermoplastic) composites has been studied. Specimens of quasi-isotropic configuration [45°/90”/-450/O”], were designed on the basis of the Euler buckling criterion, and a temperature range of 23-100°C was considered for both dry as well as wet tests. Specimens for wet tests were soaked in distilled water for a period of 360 days, and the effects of moisture absorption on the compressive properties and geometry of the specimens were investigated. The results of the investigation indicated that the moisture absorption rate of T-3001epoxy was higher than that of APC-2. It was noticed that the geometry of the specimen influenced the moisture absorption rate. The thick plate with a smaller surface area absorbed less moisture than the thin plate with a larger surface area. The compressive strength and modulus of APC-2 were found to be comparatively higher than that of T-3OO/epoxy both in dry and wet conditions. The effect of moisture at 100°C was negligible for both materials. The modes of failure in both materials under compressive load were found to be delamination, interlaminar shear and end brooming. Thick laminates of thermoplastic composites (APC-2) were modeled with isoparametric layered shell elements to predict the responses of the dry laminate at various temperatures under compressive loading. A large-displacement finite element analysis was performed by considering the geometric non-Iinearities in the composite structure. Multiple load steps with linear material behavior were used to model the load-displacement characteristics found in the experimental study. The compressive response with respect of displacements, normal stresses and interlaminar shear stresses under three different temperatures is presented. The laminate response along the length as well as through the thickness is also presented, to analyze and understand the failure mechanisms under such loading. Experimental data were compared with the FEM results to test the accuracy of the finite element analysis (FEA) using the layered shell element under the assumption of first-order shear-deformation theory. A reasonably good correlation between FEA and experimental results was found. 1. INTRODUCTION
Fiber-reinforced plastics have found widespread use in the automotive, aerospace, construction and marine industries due to their excellent specific propeties, improved corrosion resistance, toughness and superior fatigue properties (Khatri and Koczak, 1991). Increased use of fiber-reinforced composites especially in submersible structures makes the compression response of such composites critical (Harris and Morris, 1984; Bogettie et al., 1987). Recent use of high-temperature thermoplastics as the matrix material has opened new horizons for lightweight structural materials with improved toughness, higher impact resistance and better environmental stability (Khatri and Koczak, 1991; Haque and Jeelani, 1992). Characterization of these newly developed thermoplastic composites is well underway and is being reported routinely by the manufacturers and researchers. However, the non-linear compressive response, and the environmental effects on the compressive properties of these composites, are still one of the least-understood topics in composite science. Both thermosetting and thermoplastic resins are used as matrix materials in graphitereinforced composites. Epoxy resins, by far the most widely used thermosetting matrix materials, appear to absorb moisture and lower the matrix glass transition temperature which in turn degrades the high-temperature properties of the resin (Browning et a/., 1977; Tang and Springer, 1988). The environmental resistance of organic matrix composites to temperature and humidity depends on the glass transition temperature and 637
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chemical interactions of the matrix polymer. The physical impact of water is to plasticize the matrix, thereby degrading the mechanical properties. Decomposition of the resin at elevated temperature is also responsible for loss of stiffness and strength. A detailed degradation mechanism for environmental exposures has been studied by Tsai (Tsai, 1967). The effect of moisture on the mechanical properties of graphite/epoxy composites has also been reported by many researchers (Springer, 1984a, b; Haque et al., 1990; Blikstad et al., 1984; Shirrell, 1978). In graphite composites the matrix is the limiting component in the wet environment. Recently, Polyetheretherketon (PEEK)-a thermoplastic resin manufactured by Imperial Chemical Industries Limited (ICI)-has been characterized as a potential matrix material for APC-2, a graphite/PEEK composite. PEEK has a glass transition temperature (T,) of 143°C and melting point of 332°C. It is evident that PEEK possesses useful properties above the glass transition temperature of the resin. However, the primary advantage of the thermoplastic resin over thermosetting is its negligible moisture absorption and reprocessing capabilities. In order to understand the effect of such moisture absorption, as well as to study the stability of APC-2 at elevated temperatures, specimens of both APC-2 and regular graphite/epoxy composites were characterized in this investigation. Wet coupons were soaked in distilled water for a period of 360 days, and were later tested at various temperatures ranging from 23°C to 100°C. Similar tests were conducted with dry coupons of both materials. Test conditions and moisture exposure parameters were kept identical for both APC-2 and graphite/epoxy. The improvement in compressive strength and stiffness is discussed, and possible reasons are identified. Accurate modeling of the non-linear response in composite materials is a theme that pervades modern computational solid mechanics and is likely to intensify in the future (Rice, 1985). The key issue involving both numerical modeling and computational mechanics is the development of a numerical technique that can accurately reflect both geometric and material non-linearities, and that can also predict the onset and development of failures. The compressive failure modes in composites are complex due to transverse tension, fiber kinking, matrix failure and delamination. Aided by the mathematical complexities involved in non-linear mechanics, the task of predicting composite behavior under compression appears to be of profound importance. The finite element method is an attractive tool for performing such rigorous analysis. In the current investigation, an 8-noded isoparametric shell element developed on the basis of first-order shear-deformation theory is used to study the non-linear response of symmetric 40-ply graphite/PEEK (APC-2) composites under compressive loading. In an effort to shed new light on some of the experimental findings observed earlier (Haque and Jeelani, 1992), a large-deflection finite element analysis is performed with maximum stress failure criteria, and is presented in this paper.
2. EXPERIMENTAL
WORK
2.1. Materials A graphite-fiber-reinforced thermoplastic composite, namely APC-2, was procured from Imperial Chemical Company (ICI) Fiberite in the form of 12 in. square consolidated laminates. Each laminate was made of 40 plies in the [+45”/90”/-45”/0”],, quasiisotropic lay-up configuration. The average panel thickness was maintained at 0.20i1-1. with 60% fiber volume. Prepreg tape Cycom 985 manufactured by American Cyanamid was used to fabricate graphite/epoxy laminates. The prepreg was a combination of Thornel 300 graphite fiber and Cycom 985 resin system manufactured by Union Carbide and American Cyanamid, respectively. The laminates were cured in a programmable hot press made by Tetrahedron. Piles were laid up symmetrically in the [ + 45” /90”/ - 45’ 10’1 quasi-isotropic configuration to avoid warpage because of temperature change during curing. Again, the total fiber content was 60% by volume and the average laminate thickness was maintained at 0.2 in.
Response of composites under compressive loading
--u
25.4
T 25.4 A.
Dinensions.
Tr
Specimen
-
-) 1
Vedges II
mpl
Fig. 1. Compression test specimen and IITRI fixture.
2.2. Specimen design Both the APC-2 and graphite/epoxy specimens were made from cured panels as shown in Fig. 1. The typical 1 in. gage length was selected considering that the critical buckling length (L,,) would be greater than 1 in. A width of 1 in. appeared to satisfy this criterion and the equation considered for this calculation is as follows: Critical buckling length where
PC1= D,, = W = L =
L,, =
critical buckling load (lbs) bending stiffness (lb.-in.2 in-‘) column width (in.) column length (in.).
A detailed study of specimen design for the IITRI (Illinois Institute of Technology Research Institute) compression test method has been carried out by previous investigators (Gillespie et al., 1988). 2.3. Conditioning Specimens with 360 day moisture exposure and completely dry specimens were used in this investigation. All specimens were pre-conditioned in a vacuum oven at 100°C until a near-equilibrium weight was obtained. This condition of the specimen is referred to as dry. Five pieces of a 1 in. square plate of APC-2 and graphite/epoxy were soaked in distilled water along with other specimens in order to simulate moisture absorption to the gage section of the specimens. This was done because 83% of the specimen surface was covered by tabbing materials which was different than graphite/epoxy and APC-2. Hence the moisture absorption data from the specimens would not accurately represent the absorption rate of APC-2 and graphite/epoxy. The temperature of the distilled water was maintained at 26°C. Square plates of both graphite/epoxy and APC-2 were removed from the container at various time intervals for weight measurements. The weight gain process was continued for a period of 360 days. COE4:6-F
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2.4. Test method The IITRI compression fixture was used in this investigation because it satisfies the positive alignment criterion to minimize the eccentric loading in compression tests (Fig. 1). The IITRI compression fixture was incorporated into ASTM D3410 in the 1987 revision and recommended by many researchers because of its stability. The stability of the test depends on the selection of an adequate gage length. The specimens with 1 in. gage length and width appear to perform well with the IITRI fixture. Specimens were placed in between wedges as shown in Fig. 1. The wedges were clamped using two screws at both ends and placed in the test block of the IITRI fixture mounted to the testing machine. The tests were performed in a 22 Kips MTS machine attached to an environmental chamber. The rate of cross-head motion was maintained at 0.02 in. min-‘. The load was applied to the specimen and load-deflection data were plotted using a recorder. The compressive modulus was calculated from the linear portion of the load-deflection curve. To compare experimental displacement data with those of FEM, strain gages were used only during the room-temperature tests of the dry samples. 3. FINITE ELEMENT
ANALYSIS
A non-linear finite element analysis was performed using the commercially available finite element package ANSYS to study the damage initiation and failure mechanism in APC-2 under compressive loading. Compression-test coupons were modeled with 8-noded isoparametric layered shell elements as shown in Fig. 2. The formulation of the shell element used in the current study is based on Mindlin’s theory that the mid-surface normal after deformation remains straight but not necessarily normal to the mid-surface (Cook, 1981). This allows transverse shear deformation to be taken into consideration. However, this transverse shear deformation has been assumed to remain constant through the thickness of the laminate, limiting the present FEA to what is widely known as the first-order shear-deformation theory. Accordingly, two rotational degrees of freedom were considered at each node. These rotations of the mid-surface normal were considered about the in-plane axes of the laminate. The angular displacement was then translated into linear displacement, and was added to the regular U, u and w displacements by multiplying by the respective directional cosines (Cook, 1981). The discretized model and the boundary conditions for the compression tests are shown in Fig. 3. The laminate was made of 40 plies of [+45”/90”/-45”/0”],, configuration with a total thickness of 0.2 in., and 60% fiber-volume fraction. Three different temperatures, RT 22.78”C (73”F), 80°C (176’F) and 100°C (212”F), similar to the experimental tests, were considered in the finite element analysis to verify the thermal
Fig. 2. Curved shell element.
Response of composites under compressive loading
6 4
7
6
r44
4-
2
3
)67
9
069
641
lo
16
x
Fig. 3. Discretized model and boundary conditions for the compression specimen.
expansion effects at elevated temperatures. The large deflection effect on the geometry was considered to approximate the finite element model to the closest proximity of the experimental tests. Multiple load steps and the up-dating of the stiffness matrix at each load step were considered to account for the geometric non-linearity. The material properties and failure strength used at room temperature were: E, = 17.8 Msi, Ey = 1.53 Msi, VTt’= 0.28, Gv = 0.74 Msi, CY,= 16 x 10m6in. in.-’ (deg. F)-‘, c& = 93.74 Ksi. Maximum shear failure theory was applied to evaluate the failure criteria numbers (Tsai, 1988). 4. RESULTS AND DISCUSSION
4.1. Experimental 4.1.1. Moisture absorption. The absorption of moisture as a function of time is presented in Fig. 4 for both APC-2 and graphite/epoxy. The weight gained as a result of water absorption was computed in terms of per cent fraction of the total weight of the gage section and plotted as a function of the square root of time. It appears from the nature of the curve that the moisture absorption in graphite/epoxy laminates reaches a first peak after 24 days and no significant change was observed within 24 and 90 days. After 90 days the absorption of moisture increased further and continued until the end of a 360 day soaking period. As a result, a well-defined saturation plateau was not observed in the graphite/epoxy laminate. In contrast, APC-2 appears to reach a saturation plateau after 24 days of moisture absorption. The results indicate that APC-2 and graphite/epoxy appear to absorb a maximum moisture content of 0.182% and l%, respectively, in 360 days. It appears from the data that the diffusivity of graphite/epoxy is five times higher than that of APC-2. Previous work on the same graphite/epoxy system shows a higher moisture absorption rate in which a larger surface area of the specimen was exposed to moisture compared to the present work (Haque et al., 1990). This indicates that the moisture absorption rate depends on the geometry of the structure. Thick plates with a smaller surface area absorb less moisture than thinner plates with a larger surface area.
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^ A 5 ? o T-300/Epoxy APC - 3 3
1.20 1
Square
Root of Time
(Hr)
Fig. 4. Moisture absorption in T-3OO/epoxy and APC-2 composites,
4.1.2. Compressive strength and modulus. Data for the compressive strength and modulus of both graphite/epoxy and APC-2 are presented in Table 1. All the data represent an average value of five specimens tested under the same conditions. A variation of 15% between the maximum and minimum recorded data was observed in some specimens. This discrepancy could be the results of many parameters in specimen fabrication and environmental conditioning that are extremely difficult to maintain exactly similar for all the specimens. A slight geometric variation in specimens cut from a quasi-isotropic configuration laminate could cause significant differences in data for individual samples. Maintaining constant temperature and moisture contents for each sample during testing was also difficult to achieve. Figures 5 and 6 present the effects of moisture content and temperature on the compressive strength and modulus of graphite/epoxy and APC-2. It is evident that both the compressive strength and modulus of APC-2 are comparatively higher than those of Table 1. Moisture and temperature influence on compressive properties: APC-2 vs graphite/epoxy, quasi-isotropic [+45”/90”/-45”/0”],,. Graphite/Epoxy
APC-2 Comp. Ult. Ksi (MPa)
Comp. Mod. Msi @Pa)
Comp. Ult. Ksi (MPa)
Comp. Mod. Msi @Pa)
23°C D M M*
93.74 (637.43) 84.99 (585.92) 80.64 (555.93)
1.26(8.68) 1.27 (8.75) 0.94 (6.48)
92.17 (635.41) 83.58 (576.20) 82.98 (572.06)
l.lO(7.58) 10.5 (7.23) 0.77 (5.30)
80°C D M M*
87.62 (604.05) 83.65 (576.68) 79.54 (548.34)
1.21 (8.34) 1.17(8.06) 0.59 (4.06)
77.27 (532.69) 74.55 (513.94) 74.43 (513.12)
1.08 (7.44) 0.92 (6.34) 0.72 (4.96)
100°C D M M’
77.30 (532.90) 76.68 (528.63) 78.07 (538.21)
1.05 (7.23) 1.11 (7.65) 0.78 (5.37)
76.26 (525.73) 69.39 (478.37) 68.52 (472.37)
0.88 (6.06) 0.86 (5.92) 0.71 (4.89)
Conditioning
D-Dry. M-90 days moisture exposure. M*-360 days moisture exposure.
Response of composites under compressive loading
643
o 0 o Dry T300/E ory 0 0 0 Wet90 Daya, P T300/Epoxy ts A A Wet I 380 Days).TJOO/Epory
Fig. 5. Moisture and temperature effect on compressive strength of APC-2 and T-3OO/epoxy.
graphite/epoxy. The data for graphite/epoxy and APC-2 show a reduction of 17.26% and 17.53% in compressive strength at 100°C compared with the corresponding values at 23°C. The addition of moisture in graphite/epoxy due to 360 days moisture exposure further reduces the strength by 25.7%. The sensitivity of moisture in the compressive strength of APC-2 is negligible at 100°C. It appears that APC-2 is a better candidate for moisture resistance to sustain its compressive strength as compared to the graphite/epoxy composite. Figure 7 indicates that significant compressive strength reduction does not take place in between long-term (360 days) and short-term (90 days) moisture exposure. In contrast, Fig. 8 shows that the compressive modulus reduces significantly for both APC-2 and graphite/epoxy during the period of short-term (90 days) and long-term (360 days) moisture exposure. The compressive modulus of graphite/epoxy and APC-2 decreased by 20% and 16.44%, respectively, at lOO”C, and a similar trend was observed at room temperature. The absorption of moisture for a period of 360 days further reduced the compressive modulus of graphite/epoxy and APC-2 by 35.45% and 39.09%, respectively. It appears that the influence of moisture is comparatively higher in the temperature range of 50-80°C. The effect of moisture at 100°C is negligible for both materials. Micrographs of Figs 9 and 10 present the optical examination of the fractured specimens of APC-2 and graphite/epoxy. Specimens were not completely separated after Dry, T300/E oxy Wet{90 Days! T300/E ory We1360
Day&
TBOO/!!poxy
1.50 =: $4 z 1.25
-
2 2g
1.00
-
w g 0.75
-
2 g 0.50
-
r-
b
8
0.25 +-r-n-7 0
g--y--l-TEhH'ldT"RE("~~
0.25 100
+ 0
25 =15rg
TEhiPERATURE(‘C) Fig. 6. Moisture and temperature effect on compressive modulus
of
APC-2 and T-300/epoxy.
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1
0
100
200
11
II
300
"
MOISTURE EXPOSURE DAYS
T300/Epoxy
11
400
400 100 200 300 MOISTURE EXPOSURE DAYS
0
Fig. 7. Compressive strength of APC-2 and T-300/epoxy as a function of moisture exposure days and temperature.
failure, rather the ends of the specimens appeared to be interlocked in between plies. Compression failure in the form of delamination and interlaminar shear with end brooming can be observed in these micrographs. 4.2. Finite element analysis Distribution of maximum a, with temperature at the failure load is shown in Fig. 11. Values shown in this figure were obtained from the last iteration. Five iterative steps with a Newton-Raphson scheme were used to implement the geometric non-linearities of the elements. Stiffness matrices were updated at each load step on the basis of the displacement undergone in each iteration. The failure load and stiffness were determined from the experimental data. In fact the stiffness data used in the FEM program were obtained from the uniaxial tests. Correlation of crX with the experimental data is shown in Fig. 11. Gradual reduction in strength with increase in temperature is observed. It is also noticed that the compressive stresses are largest at the clamped end, significantly reduced between nodes 1 and 3, and remain more-or-less uniform throughout the rest of the gage section. At elevated temperatures, the correlation between the experimental results and FEM prediction diverges. The reason for this is believed to be the cross-sectional area
APC -2
0
100
200 300 400 MOISTURE EXPOSURE DAYS
I I ” 0
T300/Epoxy
1’
I ’ ” 100
’ I ““I””
I
200 300 400 MOISTURE EXPOSURE TIME
Fig. 8. Compressive modulus of APC-2 and T-3OO/epoxy as a function of moisture exposure days and temperature.
Response of composites under compressive loading
Fig. 9. Optical examination of fracture specimen of APC-2.
Fig. 10. Optical examination of fracture specimen of T-3OO/epoxy.
645
Response of composites under compressive loading
647
k-4 -75 2 g -100 g 73’F FEM o 176OF FEM A 212’F FEM
Y tj -125 z E E -150 8 -175
m73”F Exp. 9 i76”F Exp. A 212°F Exp.
-200 1
3
Fig. 11. Distribution
5 7 9 NODES ALONG THE LENGTH
11
of a, along the length of the laminate for layer no. 1.
considered during the experiment. Experimental calculation did not take into account the increase in area due to thermal expansion and the transverse tensile strain undergone during the test. FEM prediction, which is based on piece-wise continuous displacement, and updated with the thermal expansion coefficient CY,seems to be a better representation of strength at higher temperature. The experimental value of the maximum displacement at room temperature is compared with the FEM prediction in Fig. 12. The experimental displacement value was determined from the strain gage used during the roomtemperature tests of the dry specimens. The correlation between the two is excellent. Figure 12 also shows that the distribution of u, along the length of the specimen is almost linear. A decrease in the absolute values of displacements with temperatures is observed. The phenomenon is believed to be the resultant effect between the thermal expansion and the degradation of the stiffness of the composite. The interlaminar shear stress (ILSUM) distribution along the length is shown in Fig. 13. The variation of ILSUM with temperature is observed only near the clamped end, elsewhere it is negligible. This may not be the true representation at elevated temperatures. It is to be noted that the FEM analysis assumes perfect bonding between layers throughout the temperature range, which
0.000 -0.001
F = & g e 2 2 cI
0 73°F FEM 4 176°F
-0.002 -0.003 -0.004 -0.005 -0.006 -0.007 -0.008 -0.009 -0.010 -0.011 -0.012 -0.013 -0.014 -0.015
FEM
~212°F FEM
1
3
5 7 9 NODES ALONG THE LENGTH
11
Fig. 12. Maximum displacement (UX) of the top layer along the length at Y = 0.
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ELEMENTS Fig. 13. Interlaminar
shear stress distribution (between layers 1 and 2) along the length of the laminate.
may not be physically true at higher temperatures. The distribution of ILSUM along the length shows a gradual increase up to element 2, and then a sharp rise towards the clamped end. This indicates initiation of delamination somewhere between element 1 and 2. The interlaminar shear stresses are not uniform through the thickness of the laminate, as shown in Fig. 14. Layers at the point of symmetry have significantly low interlaminar shear stress, indicating that layers laid up with same fiber orientation are most stable during delamination. Figure 14 also shows that peaks are also occurring in a sequence different from the lay-up sequences. The reasons are attributed to the variations of a,, a,, and rxy . Interlaminar shear stresses were computed by the integration of the equations of equilibrium in a finite difference form which includes a,, o,, and Q,, at eight integration points. Therefore, ILSUM is a direct consequence of these stresses. The variation of a, through the thickness of the laminate is shown in Fig. 15, which reveals some of the interesting features of the compressive responses. It is noticed that the 0” layers experience maximum stresses (a,) from compression and are likely to fail first. The second level of stresses is observed in the +45” layers, followed by the -45” layers. Except at the point
0
1 2 3 4 5 6 7 6 9 10 11 12 13 14 15 16 17 18 19 20 LAYER NUMBER
Fig. 14. Interlaminar shear stress distribution
across the thickness of the laminate.
Response of composites under compressive loading
649
-30 c2 D E & y =E = % 0 v
-50 -70 -90 -110 -130 -150 -170 -190
1
-210 -2307 -2501,
, , , , ,
, , , , , , , , ,
, ,
,
,
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 16 19 20 LAYER NUbIRER Fig. 15. Compressive stress distribution
across the thickness.
of symmetry, the adjacent layers experience transverse stresses that differ in sign. This contributes to higher interlaminar stresses between these layers. Progressive failure of the specimen is studied by determining the failure criteria numbers at each iteration. These as shown in Fig. 16 are the ratios of the actual layer stresses in the layer coordinates to the strength of the laminate. It is observed that the failure of the specimen is linearly proportional to the increments of loads. This linearity is due to the constancy of E conidered in the analysis. The progressive failure rates at different temperatures, as shown in Fig. 16, vary slightly with temperatures and remain consistent throughout the iterations. Distributions of longitudinal and transverse strains at room temperatures along the length are shown in Fig. 17. It is noted that both E, and E,, are almost linear along the length beyond node 3, and both strains are compressive. These compressive transverse strains in the top and bottom surfaces of the laminate are likely to inhibit premature microbuckling failure. The in-plane distribution of the longitudinal stress, a,, at room temperature is shown in Fig. 18. Maximum stress occurs in the vicinity of node 1, indicating that the matrix crack will initiate at the edge of the specimen in the neighborhood of this node. At elevated temperatures the a, distribution was also found to be similar to that of Fig. 18.
g ii 2 d ii2 w g
2.40 i 2.20 2.00 1.80 1.80 1.40 1.20
E l-O0 2 OAO 2 0.60 0.40 0.00
, 1
I 2
I 3 ITERATIONS
I 4
Fig. 16. Progressive failure criteria vs load steps.
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-0.002 -0.004 -0.006 -0.006 2 z -0.010 it -0.012 -0.014 -0.016 -0.018 -0.020
1
Fig. 17. Distribution
I 3
I I I 7 9 5 NODES ALONG TEE LENGTH
I 11
of ex and .zyof the top layer along the length of the laminate.
POST1 SERp’51 = %P
STRESS CAUGB
hELoB*L=@. 813364 SMN =-I33387 SMX z-43597 jr D '3':::;
Fig. 18. In-plane distribution
of CT,at room temperature (top layer).
Response of composites under compressive loading
651
5. CLOSURE
The following conclusions are drawn from the above study: (1) It appears that the moisture absorption rate of graphite/epoxy reaches a first plateau after 24 days and continue to increase further after 90 days until the end of a 360 day moisture exposure time. The diffusivity of graphite/epoxy was found to be five times higher than that of APC-2. The geometry of the structure considerably influences the moisture absorption rate. A thick plate with a smaller surface area absorbs Iess moisture than a thin plate with a larger surface area. (2) It is evident that both the compressive strength and modulus of APC-2 are comparatively higher than those of graphite/epoxy. APC-2 sustains higher compressive stress in presence of moisture as compared to graphite/epoxy. (3) The compressive strength and modulus decrease with increasing temperature in the range between 23 and 100°C. The addition of moisture further degrades the compressive strength. The influence of moisture on the compressive modulus is comparatively higher in the temperature range 50-75°C. (4) The compression failure was in the form of delamination, interlaminar shear and end brooming. (5) It is shown that thick laminates of thermoplastic composites can be modeled using isoparametric layered shell elements with reasonable accuracy. (6) Good correlation between the experimental results and the finite element analysis with respect to the global maximum displacement, u+, and the maximum compressive stress, or, is observed. (7) Non-linear distributions of transverse stresses and strains are observed along the length. (8) Both normal and interlaminar shear stresses were found to be varying nonlinearly through the thickness of the laminate. Acknowledgement-The authors acknowledge with appreciation Marshall Flight Center through grant NAG% I3 1.
the support for this work from NASA-
REFERENCES Blikstad, M., Sjoblem, P. W. and Johannesson, T. R. (1984). Long-term moisture absorption in graphite/epoxy angle-ply laminates. J. Compos. Mater. 18, OO-OO. Bogetti, T. A., Gillespie, J. W. and Pipes, R. B. (1987). Report #87-55, Center for Composite Materials, University of Delaware. Browning, C. E., Husman, G. E. and Whitney, J. M. (1977). Moisture effects in epoxy matrix composites. In Composites Materials: Testing and Design, ASTM STP 617, pp. 481-496. ASTM, Philadelphia, PA. Cook, R. D. (1981). Concepts and Applications of Finite Element Analysis, 2nd edn. John Wiley, New York. Gillespie, J. W., Jr, Bogetti, T. A. and Pipes, R. B. (1988). Evaluation of the IITRI compression test method for stiffness and strength. Compos. Sci. Technol. 32 (l), 57-76. Haque, A. and Jeelani, S. (1992). Environmental effects on the compressive properties: thermosetting vs thermoplastic composites. J. Rein. Plastics Compos. 11(2), 146-157. Haque, A., Copeland, C. W., Zadoo, D. P., and Jeelani S. (1990). Hygrothermal influence on the flexural properties of Kevlar-graphite/epoxy hybrid composites. J. Reinf. Plastics Compos. 9, 602-613. Harris, C. E. and Morris, D. H. (1990). CompositeMaterials: Testing and Design (7th Conf.), ASTM STP 893. ASTM, Philadelphia, PA. Khatri, S. C. and Koczak, M. J. (1991). Enhanced compressive response of unidirectional thick section thermoplastic composites by fiber hybridization. Int. Conf. on Composite Materials (ZCCM/VIZI), Honolulu, pp. 35-A-I to 35-A-10. Rice J. R. (Ed.) (1985). Solid mechanics: research trends and opportunities. Appl. Mech. Rev. 38, 1247-1308.11. Shirrell, C. D. (1978). Diffusion of Water Vapor in Graphite/Epoxy Composites, ASTM STP 658, pp. 21-42. ASTM, Philadelphia, PA. Springer, G. S. (1984a). Environmental Effects on Composite Materials, Vol. 1. Technomic, Lancaster, PA. Springer, G. S. (1984b). Environmental Effects on Composite Materials, Vol. 2. Technomic, Lancaster, PA. Tang, J. and Springer, G. S. (1988). Effects of cure and moisture on the properties of Fiberite 976 resin. J. Compos. Muter. 22, OO-OO. Tsai, S. W. (1967). Environmental factors in the design of composite materials. 5th Symp. on Nova1 Sfructural Mechanics. Pergamon, New York. Tsai, S. W. (1988). Composire Design, 4th edn. Think Composires, Dayton, OH.