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Energy absorption in composite stiffeners
B
UTTE E I N
RWQR E M A
Composites 26 (1995) 291 301 9 1995 Elsevier Science Limited Printed in Great Britain. All rights reserved 0010-4361/95/$10.00
TH N N
Energy absorption in composite stiffeners A.O. Bolukbasi McDonnell Douglas Helicopter Systems, Mesa, AZ 85205-9797, USA and D.H. Laananen* Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ 85287-6106, USA (Received 15 February 1994; revised 11 August 1994) The energy absorption behaviour of composite stiffeners subjected to axial compression has been investigated. A semi-empirical analysis methodology has been developed for prediction of the energy absorption capability of composite stiffeners based on crush tests of flat plate specimens and an understanding of the fundamentals of the energy absorption process. Flat plate, angle and channel specimens were fabricated from T650-35/F584 graphite/epoxy plain-weave fabric using five different lay-ups that consisted of varying percentages of 450 and 0~ plies. The specimens were crush tested under axial compression, and measured levels of sustained crushing stress were compared with model predictions. (Keywords: composite stiffeners; energy absorption; crush initiators)
INTRODUCTION The overall objective of designing an aircraft for crash protection is to minimize the number of injuries and fatalities in survivable crash impacts. The crashworthy design of aircraft involves a systems approach with the fuselage structure, landing gear and seats working together to absorb the aircraft kinetic energy and slow the occupants to rest without injurious loading. An important part of this energy absorption system is the structure below the fuselage floor, which may absorb up to 80% of the aircraft's kinetic energy. Application of composite materials to aircraft fuselage structures offers potentially significant weight and cost reductions relative to metallic structures. However, because composite materials are typically brittle and do not exhibit either plasticity or high elongation prior to failure, special design approaches are required to provide energy absorption capability comparable to that of metal structures. The energy absorption characteristics of various composite structural elements have been experimentally studied by several researchers. Circular tube specimens have been the most extensively studied structural elements I s, but experiments have also been conducted with square tubes 9J~ flat plates 11 and sine-wave beams 12'13. The results obtained with the tube specimens have indicated that the energy absorbed depends on such design parameters as the material system, lay-up and cross-section geometry. The tests have also demonstrated that when controlled stable crushing is produced through selection of appropriate design parameters, the composite tubes can yield a higher specific crushing efficiency than aIuminium tubes. * T o w h o m c o r r e s p o n d e n c e s h o u l d be a d d r e s s e d
In spite of the considerable work done on the energy absorption of composite materials, reliable analytical methods are not yet available to predict the energy absorption capability of practical composite aircraft fuselage structures. The current practice is to conduct expensive and time-consuming design support tests at the element and sub-assembly level prior to fabrication of the fuselage structure. Therefore, additional research is needed to study the energy absorption behaviour of practical composite structural elements and to develop analysis tools to support the design of composite fuselage structures in a timely and cost-effective manner. The objective of this research effort has been to study the energy absorption behaviour of composite stiffeners, specifically angle and channel sections, in order to develop a design technique for such components. Selection of the stiffeners over other structural elements such as sine-wave beams or tubes was based on widespread use of such elements in semi-monocoque fuselage structures. The following section describes experiments that were conducted with flat plate specimens of graphite/epoxy composite that were crushed by uniaxial in-plane loading. Axial crush tests of angle and channel stiffeners fabricated with the same material and lay-ups are then described. Finally, a semi-empirical analysis method, which uses the flat plate crush test data, is described and applied to the angle and channel stiffeners. EXPERIMENTS
Test specimens The crust test specimens were flat plates, angle stiffeners and channel stiffeners, the geometries of which are illustrated in Figure 1. Three different lay-ups were used for most of the specimens: [45]~0, [452/0/452]~ and
COMPOSITES Volume 26 Number 4 1995 291
Energy absorption in stiffeners: A.O. Botukbasi and D.H. Laananen
..%
Machined chamfer crush initiator
19
19
150
I
O0
J'----.... Flat plate
Channel stiffener
Angle stiffener
Dimensions in rnm
All radii = 3 mm
Figure 1 Crush test specimens
[45JOJ45]~. These lay-ups, which are typical of those used with fabric prepregs, were selected to contain 0-40% 0~ plies in order to evaluate their effect on the energy absorbing capability of the laminates. Results of previous studies have indicated that stable crushing can be achieved in tubes consisting entirely of bias plies, and that the addition of some axial pries can increase the specific crush stress for graphite/epoxy laminates2. However, as the percentage of 0 ~ plies is increased, at some point the failure mode may change to a less efficient mode. The 0 e plies tend to split longitudinally without crushing, and the tendency towards delamination increases, with a resulting drop in specific energy absorption capability. Hull 6 reported on the axial crushing of tubes fabricated from glass cloth with various warp to weft ratios that produced a range of ratios of hoop to axial plies. Results indicated that beyond a hoop to axial ratio of 1:1 the initial crash load increased, but the sustained crush stress was reduced. In addition to the 10-ply lay-ups, two channel and two angle specimens were also fabricated using [45]7 and [45]5 lay-ups to evaluate the effect, on the energy absorption capability of the stiffener, of different width to thickness aspect ratios for the stiffener web and flanges. Lay-ups for all specimens are listed in Table 1. All specimens were fabricated using T650-35/F584 Table 1 Test specimens Specimen number F1 F2 F3 A1 A2 A3 A4 A5 C1 C2 C3 C4 C5
292
Specimen type Flat plate Flat plate Flat p]ate Angle Angle Angle Angle Angle Channel Channel Channel Channel Channel
Quantity
graphite/epoxy plain-weave fabric, the mechanical properties of which, based on material supplier data, are listed in Table 2. The cured ply thickness was -0.203 mm. The stiffener specimens were fabricated using a male tool, and all specimens were cured in an autoclave under 690 kPa pressure. A crush initiator in the form of a 2.5 mm long chamfer was machined at one end of all crush test specimens. The unchamfered end of each angle and channel crush test specimen was potted in a 25 mm deep aluminium ring using an epoxy-based potting compound. The flat plate specimens were not potted but were tested in a special test fixture that provided lateral support along the unloaded edges. The dimensions of the flat plate crush test specimens were selected to fit an existing test fixture. The dimensions of the angle and channel stiffener crush specimens were selected based on elastic stability analyses to ensure that these specimens, except the specimens with the [45]5 lay-up, would not undergo local or global buckling during testing. The specimens with the [45]5 lay-up were designed to experience limited local buckling to investigate its effect on the energy absorption capability of the stiffeners. As indicated in Table 1, a total of nine flat plates, five angle stiffener and five channel stiffener specimens of five different lay-ups were fabricated and tested. Flat plate crush tests Flat plate specimens were selected for most of the crush experiments because they are less expensive and easier to fabricate than other types of test specimens such as stiffeners, tubes and sine-wave beams. A simple coupon configuration is also desirable for practical evaluation of material and laminate energy absorption capability. A problem with the fiat plate specimen is, however, the possibility of global buckling of the plate rather than the desired failure mode of sustained crushing. The buckling problem was eliminated by selection of the plate dimensions based on elastic stability analysis and by using a special text fixture that provided lateral support to the specimen during the test. The flat plate specimens were loaded using a special text fixture14, which is shown in Figure 2. The fixture consisted of eight steel rods and upper and lower platens. The four 25 mm diameter steel rods at the corners of the fixture served to guide the movable upper platen. The fixture provided lateral support to the specimen through four 13 mm diameter inner steel rods located at the centre of the platens. The inner support rods were positioned in pairs located 38 mm apart, so that the effective supported plate width was 38 mm. Each pair had a
Lay-up Table 2 Material properties for T650-35/F584 graphite/epoxy plainweave fabric
3 3 3 1 1 1 1 1 1 1 1 1 1
[45]~ [452/0/45z]s [452/02/45]~ [45]10 [45J0/452]s [45j02/45]s [45]7 [45]5 [45]10 [452/0/452]s [452/02/45]s [45]7 [45]5
COMPOSITES Volume 26 Number 4 1995
Material property
Value
Longitudinal Young's modulus, El (GPa) Transverse Young's modulus, E2 (GPa) Out-of-plane Young's modulus, E3 (GPa) Poisson's ratio, v12 In-plane shear modulus, G~2 (GPa) Longitudinal tensile strength, S, (MPa) Transverse tensile strength, S2t (MPa) Longitudinal compressive strength, $1~ (MPa) Transverse compressive strength, $2c (MPa) In-plane shear strength, SI2 (MPa)
70.3 70.3 8.27 0.028 5.65 855 855 848 848 152
Energy absorption in stiffeners: A.O. Bolukbasi and D.H. Laananen
Figure 3 Figure 2
Channel stiffener crush test
Flat plate crush test fixture
separation of 2 mm, the specimen thickness, so that the specimens could slide into the fixture from the side. The load was applied to the specimens and fixture through a 25 mm diameter steel ball which rested in a seat that was machined in the upper platen of the fixture. The displacement-controlled crosshead rate of the testing machine was 1.3 mm min 1. The load and crosshead displacement were digitally recorded during the test. The flat plate specimens were crushed for ~38 mm.
Angle and channel stiffener crush tests The angle and channel stiffeners were placed between the platens of the test machine with the stiffeners free standing on the potted ring, as shown for one of the channel stiffeners in Figure 3. The lower surface of each potted ring was precision machined to ensure that the stiffener was vertically aligned between the platens. A smooth steel plate was also placed between the upper end of the specimens containing the failure initiator and the movable platen of the test machine. As in the case of the flat plate specimens, the stiffener specimens were crushed using a displacement-controlled crosshead rate of 1.3 mm rain i. The angle and channel stiffener crush test specimens were crushed for ~38 and 64 ram, respectively. EXPERIMENTAL RESULTS The test results for the flat plate, angle and channel stiffener crush tests consist of force and deflection values, which were analysed to identify loads for initiation of crushing as well as the loads associated with the sustained crushing process for each of the specimens. In addition, photomicrographs of the specimens were prepared to obtain data on the delaminations and material failures associated with the crushing process.
Flat plate crush tests The flat plate specimens, which are shown in Figure 4, crushed between the lateral support rods of the text fixture in what has been called by Hull 6 a 'splaying' mode and by Farley and Jones 8 a 'lamina bending' mode. Each specimen tore against the lateral support rods and exhibited a central crack, which split the plate into a Y-shaped cross-section with multiple lamina bundles in each leg. The crushing force was reacted through bending and compression of the lamina bundles. The load versus crosshead displacement response for specimen F2-1, which is typical of the flat plate specimen data, is shown in Figure 5. The response curves for the flat plate specimens show an initial peak force associated with initiation of the fracture process followed by sustained crushing of the specimen. For crashworthiness applications, it is desirable that the initial peak load should not significantly exceed the average load during steady crushing. The initial peak, maximum and average crushing loads for all flat plate specimens tested are listed in Table 3, where the initial peak load is seen to be less than the maximum crushing load for all specimens and is comparable to the average crushing load. This indicates that the machined chamfer at one end of the specimens was a very effective crush initiator. The experimental data were also repeatable for specimens with identical lay-ups with the exception of specimen F1-2, which experienced a premature delamination. A good indicator of the crushing performance is the specific sustained crushing stress (SSCS), which is a measure of the energy absorption capability of the material: SSCS = r
P
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(1)
293
Energy absorption in stiffeners: A.O. Bolukbasi and D.H. Laananen in which p is the material density and o-~:is the sustained crushing stress given by
P~V
o'~ = ~ A
(2)
where Pa,~is the average crushing load and A is the crosssectional area. Experimental data in Table 3 indicate that the SSCS of the laminates tested increased with increasing percentage of 0~ plies in the laminate. To study the crush regions in more detail, the crushed flat plate specimens were sliced using a diamond saw, and photomicrographs of the plate segment edge surfaces were made. Typical photomicrographs of edge surfaces at the centre of the plate and near one of the lateral supports are shown in Figure 6. The photomicrographs indicate that the principal crack occurred at or close to the centre of the cross-section. The depth of this central crack was about twice the thickness of the plate and tended to be longer in the middle of the plate span away from the lateral supports. The photomicrographs also show interlaminar cracks in the legs of the Y-shaped cross-section, present between all plies. The depths of the interlaminar cracks were less than that of the central crack and extended slightly beyond the lamina surface in contact with the crush surface.
Stiffener crush tests Examples of crushed angle and channel stiffener specimens are shown in Figures 7 and 8, respectively. Except for specimens A5 and C5, the stiffener specimens exhibited a crushing behaviour similar to the flat plate specimens. They tore at the corners, and each segment of the cross-section exhibited a central crack, which split the segment into a Y-shaped cross-section with multiple lamina bundles on each leg. Specimens A5 and C5 were [45]5 laminates. Due to the greater width to thickness ratio of the flanges, these specimens experienced limited local buckling, and their crushing behaviour was very different from that of the other stiffeners. The A5 and C5 specimens tore at the corners and did not exhibit a central crack. The crushing force was reacted through bending and compression of the torn flanges as a whole. As the crushing force increased, the flanges started to tear at the corners, and interlaminar cracks formed within the flanges. After the flanges were torn at the corners, the crush load decreased slightly and the flange lamina bundles slid laterally on
Figure 4 Crushed flat plate specimens: (a) side view of all specimens; (b) top view of specimen F2-1
Figure 5
Crush test results for specimen F2-1
Table 3
Summary of flat plate crush test results
Specimen
Initial peak load (kN)
Average load (kN)
Maximum load (kN)
Sustained crush stress (MPa)
Specific sustained crush stress (kJ kg 1)
FI-1 F1-2 Ft-3 F2-1 F2-2 F2-3 F3-1 F3-2 F3-3
15.3 16.4 16.4 15.1 16.1 15.1 13.8 15.3 15.5
14.9 10.5 14.3 15.4 15.1 15.4 16.0 15.4 15.8
19.8 16.5 22.2 20.9 20.9 20,7 20,5 20.4 20.3
144 102 138 150 147 149 155 149 153
91,1 64.6 87.3 94.9 93.0 94.3 98.1 94.3 96.8
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Energy absorption in stiffeners: A.O. Bolukbasi and D.H. Laananen
Figure7 Crushedanglestiffenerspecimens:(a) specimenA2; (b) specimen A5
Figure 6 Photomicrographsof flat plate specimenF2-1: (a) centre of plate; (b) near lateral support the crush surface. As the stiffeners were crushed further, the crush loads once again increased, and the flanges tore further, repeating the crushing process. The load versus crosshead displacement for the stiffener specimens A2 and C2, which are typical for their stiffener types, are shown in Figures 9 and 10. As noted previously for the flat plate specimens, the response curves show an initial peak force associated with initiation of the crushing process, followed by sustained crushing of the specimen. The initial peak, maximum and average crushing loads, and S S C S for all angle and channel specimens tested are listed in Tables 4 and 5, respectively. The experimental data in Tables 4 and 5 show that the initial peak load was less than the maximum crush load and is comparable to the average crushing load, indicating that the crush initiator was effective. The only exception was specimen A l, where the initiation load was about 5% higher than the maximum crushing load. The S S C S values for all specimens except A5 and C5 (the [4515 lay-ups) are comparable but somewhat less than those for the flat plate specimens. This is due to differences in boundary conditions between the flat plate
test fixture and the stiffener specimens. The flat plate specimens were supported at both edges, where they tore as they crushed. The stiffener specimens, however, had flanges with free edges and tore only on the corners. The S S C S tor both the angle and channel stiffener specimens shows an increase with increasing percentage of 0 ~ plies. The S S C S values for specimens A5 and C5 are much less than those of the other stiffener specimens. This indicates that energy absorbed with flange bending as a whole without the formation of a central crack is less efficient than energy absorption in the presence of a central crack. The formation and growth of the central crack significantly contributes to the crushing force and, consequently, to the energy absorbed during the crushing process. To study the crush regions in more detail, the crushed stiffener specimens were sliced using a diamond saw, and photomicrographs of the edge surfaces were made. The photomicrographs of all the stiffener specimens except specimens A5 and C5 showed failures similar to those of the flat plates. Photomicrographs of specimens A1 and C3, which are typical of these stiffeners, are shown in Figures I1 and 12. The photomicrographs indicate that the central crack occurred at or close to the middle of the cross-section. For the channel stiffener specimens, the depth of the central crack was about twice the thickness of the stiffener and tended to be longer at the free edge of the flange and at the centre of the web than near the corners of the stiffener where the web and flanges intersected. The photomicrographs also show inter/intralaminar cracks in the legs of the Y-shaped cross-section. The
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Energy absorption in stiffeners: A.O. Bolukbasi and D.H. Laananen 30 25
/,
2O
z 10
0
0
10
20
30 40 50 Displacement (mm)
60
70
Figure 10 Crush test result for channel stiffener specimen C2
interlaminar cracks were present between all plies. The depths of the interlaminar cracks were less than that of the central crack and extended slightly beyond the lamina surface in contact with the crush surface. Photomicrographs of specimens A5 and C5 are shown in Figures 13 and 14. These photomicrographs indicate that, as the flange was torn at the stiffener corner and then was bent, interlaminar cracks were formed in the flange between all plies, as observed in other stiffener specimens. The section of the flange undergoing bending and cracking was about three times the thickness of the specimen. ANALYSIS
Figure 8 Crushed channel stiffener specimens: (a) specimen C1; (b) specimen C5
Figure 9 Crush test results for angle stiffener specimen A2
Table 4
A semi-empirical analysis methodology, which has been developed for use in design of energy-absorbing composite structures, is based on observations of the energy absorption process during the experimental studies, on phenomenological failure criteria and on fiat plate crush test data. The concept behind this analysis method is to be able to predict the energy absorption capability of composite structural elements such as stiffeners based on crush tests of fiat plate specimens. The fiat plate specimens are relatively easy to fabricate and test using a specialized text fixture. Therefore, the fiat plate specimens potentially can be used to reduce or eliminate costly fabrication and testing of actual structural elements. The energy absorption capability of composite structures is strongly dependent on the crushing mode 8. Therefore, a fundamental requirement of the semiempirical analysis is that the crushing behaviour of the structural elements being analysed should be identical to that of the fiat plate specimens tested. The experimental studies that were described in the previous section have indicated that most of the angle and channel stiffeners crushed in a lamina bending crushing mode much like the fiat plate specimens. The only exceptions were the angle and channel stiffeners of [45]5
Summary of angle stiffener crush test results
Specimen
Initial peak load (kN)
Average load (kY)
Maximum load (kN)
Sustained crush stress (MPa)
Specific sustained crush stress (kJ kg-~)
A1 A2 A3 A4 A5
8.90 8.10 8.63 4.80 2.31
6.23 7.43 7.74 3.91 1.19
8.90 9.92 10.90 5.20 3.87
84.9 101.4 105.6 83.7 50.7
53.7 64.2 66.8 53.0 32.1
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COMPOSITES Volume 26 Number 4 1995
Energy absorption in stiffeners: A.O. Bolukbasi and D.H. Laananen Table 5
Specimen
Summary of channel stiffcncr crush test results Initial peak load (kN)
Average load (kN)
Maximum load (kN)
Sustained crush stress (MPa)
Specific sustained crush stress (kJ kg ~) 67.7
C1
20,(1
18,5
24.2
lt)7
C2
22.7
22,1
27.4
128
81.0
C3
18.7
22.8
27,8
132
83.5
C4
14.9
10.6
14,9
C5
7.83
5.56
lqgure 11 I'hotomicrographs of angle stiffener specimen A l: (a) near free edge; (b) near corner
lay-up, which experienced local buckling and demonstrated much lower SSCS values than other specimens. Therefore, to ensure that the stiffeners crush in the same mode as the fiat plate specimens, it is necessary to develop a composite design criterion that will avoid local buckling of the stiffener cross-section. The design Of metal stiffeners is performed using a crippling analysis, which predicts compression failure due to the stress distribution associated with local buckling. This type of analysis tbr isotropic materials has traditionally been carried out using empirically derived design curves of the form shown in Figure 15. A similar approach has been developed for crippling of composite
8.14
96.9
61.3
63.0
39.9
Figure 12 Photomicrographs of channel stiflkner specimen C3 (flange): (a) near free edge; (b) near corner
plates 15and applied to postbuckling and crippling behaviour of composite stiffeners 16'17. To utilize the empirical crippling curves, the stiffener cross-section is divided into a number of rectangular plate segments of width b and thickness t with either oneedge free or no-edge free boundary conditions. Definitions of element dimensions and the distinctions between one-edge and no-edge free elements for angle and channel stiffeners are illustrated in Figure 16. Materials properties used are the elastic modulus E and the compressive yield strength ~roy. The parameter r is the crippling compressive stress. If all the parameters except crcc arc known, then the curves shown in Figure 15 can be used to calculate a crippling stress value for each element of a cross-section. The total cross-
COMPOSITES Volume 26 Number 4 1995
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Energy absorption in stiffeners: A.O. Bolukbasi and D.H. Laananen
Figure 14 Photomicrographs of channel stiffener specimen C5: (a) flange near free edge; (b) web near corner Figure 13 Photomicrographs of angle stiffener specimen AS: (a) near free edge; (b) near corner
section crippling strength can then be found by a weighted average of the contributions of the individual elements as follows: n
Z (cr~c)iAiE; a,~ = i=1
(3)
Y. AiEI i=1
where o'cc is the critical compressive stress for the total cross-section, and A~ and Ei are the cross-sectional area and elastic modulus associated with each individual noedge or one-edge free element, for which the crippling stress is (o-=)i. The empirical crippling curves shown in Figure 15 indicate that, for relatively thick sections which lie on the horizontal line to the left of the empirical crippling curve, the cross-section will experience no local buckling and the element will fail due to a reduction in material stiffness after yielding. For thinner cross-sections, which lie on the sloped line to the right of the empirical crippling curve, the section will experience local buckling prior to reaching the yield strength under compressive load. It is possible to draw an analogy between metal and composite stiffeners. The sustained crushing stress o'so which was defined in equation (2) can be considered
298
COMPOSITES Volume 26 Number 4 1995
analogous to ~rcyfor metal stiffeners. Therefore, to avoid local buckling effects which may change the crushing mode, it is necessary to select the stiffener element dimensions so that the crippling stress lies on the horizontal part of the empirical curve. Beyond this analogy, however, the empirically derived crippling curves for isotropic materials are not directly applicable for laminated composite materials for several reasons. The traditional crippling curve has taken advantage of the fact that, for an isotropic material, the stiffness can be represented in terms of a single elastic modulus. This simplicity is not possible for laminated composite materials. For isotropic materials, there is also a direct proportionality relationship between bending and extensional stiffness given by the expression
T 0.8 Gc~ 0.6
Gcy 0.4
~
~ _ _ N o
Edge Free
b O~r
10
0,2
0.1 0.1
1
TVT Figure 15 Empirical crippling curves for isotropic materials
Energy absorption in stiffeners: A.O. Bolukbasi and D.H. Laananen ,,~jb
t
One end of the angle and channel specimens was potted and the other end was restrained by friction on the crosshead; the end conditions were assumed to be those of a column with one end fixed and the other end pinned. The effective length was then -0.7L (ref. 18), and c was set to a value of 2.04. Given that equation (5) is applicable, consider a noedge free stiffener cross-section for which crushing occurs at a load equal to or less than the load for which local elastic buckling of the cross-section as a whole occurs. This case can be represented mathematically as
"
b
L One-Edge Free Element
No-Edge Free Eleroeot
Figure 16 Definition of one-edge and no-edge frec elements acr 2> 1 G~frp.
El 3
D 12(1
(4)
vz )
where D is the isotropic bending stiffness; E is the elastic modulus; t is the thickness; and v is Poisson's ratio. The relationship between the bending and extensional stiffnesses for a composite laminate is not as straightforward, and the bending stiffness is defined by a 3 • 3 flexural stiffness matrix D. The approach taken in formulating the semi-empirical analysis model is, therefore, to develop expressions for local buckling of the elements of the stiffener crosssection with one-edge free and no-edge frcc boundary conditions using the coefficients of the D matrix.
fp, where o-~ is the sustained crushing stress of the flat plate specimen of identical material and lay-up, and ~re~is the critical buckling stress for the one-edge free stiffener element. Substituting for ~r~ from equation (5) into equation (7), the design criterion to ensure that the no-edge free stiffener element crushes in the same mode as the flat plate specimen, without local buckling of the cross section as a whole, can be written as
bZt \IDI1022+(D]2
+2D66)
(8)
One-edge free element
No-edge fi'ee element A no-edge free element with a length of at least twice the width b may be modelled as a rectangular plate simply supported on all four edges 18. An example of such an element is the web of the channel stiffeners tested. The critical buckling stress for a simply supported orthotropic plate can then be calculated by 19
Gcr
(7)
2rc2[-'D 11/9,
-2
+(/912+2/966)
]
Stability analysis of the one-edge free element is similar to that for the no-edge free element, except that one of the edges parallel to the loading direction is free rather than simply supported 18, Examples of one-edge free elements are the flanges of the angle and channel stiffeners tested. The critical buckling stress for a rectangular, orthotropic plate with one free, unloaded edge is given by 2~
(5) a~
where o-0~is the critical buckling stress; b is the width of the element; and Dll, D12, D22 and D06 are coefficients of the laminate flexural stiffness. This equation is strictly true only for specially orthotropic laminates. However, any balanced symmetric angle-ply laminate considered for structural applications will be approximately orthotropic, so that equation (5) will be applicable. The critical buckling stress given by equation (5) also does not take into account the stiffener length, other than assuming that the length is at least twice the width of the individual stiffener elements, but not long enough for the stiffener to fail in global column buckling. In general, a segment with a slenderness ratio (L'/p) less than 20 will not be subject to column buckling, and all of the stiffener specimens were designed to have a slenderness ratio below this limit. The effective length L' in the slenderness ratio is defined as
L ' = L/,,,;cc
(6)
where L is the actual length and c is the fixity coefficient, which takes into account the end support conditions.
-
12D66
- -
b2t
+
tc2Dll - -
L'2t
(9)
where L' is the effective length given by equation (6). Therefore, the design criterion that the one-edge free stiffener element should crush in the same mode as the flat plate specimen, without local buckling of the crosssection as a whole, can be written as a~r~ p _ 12/966 4 - Jv2Du -b2t L'2t
(10)
When the stiffener is designed to meet both these criteria for the one-edge and no-edge free elements, the experimental data indicate that the crushing modes of the stiffeners will be identical to those for the flat plates. However, the experimental data also indicate that the ~r~, values for one-edge free elements are less than those for the flat plate specimens. The no-edge free elements such as the webs of the channel specimen, on the other hand, have o-~ very close to that of the flat plate specimens. Therefore, taking into account the free edge effect,
COMPOSITES Volume 26 Number 4 1995
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Energy absorption in stiffeners: A.O. Bolukbasi and D.H. Laananen the sustained crushing stress O'~cfor a stiffener designed to comply with the local buckling criteria of equations (8) and (10) is given by the following empirical relationship: nweb nflange A web + ~ Y~ A flange O~ ~ --i O-sc = O-sfP i:l i=1
(11)
A where A web and A/flange a r e the areas for the stiffener web and flange elements; nweb and nflange indicate the numbers of each element in the cross-section; A is the total stiffener cross-sectional area; and a and/3 are experimentally determined constants. ANALYSIS RESULTS An analysis of the energy absorption capability of the angle and channel stiffeners was performed using the semi-empirical analysis method described above. The critical buckling stresses for the web and flange elements of the stiffeners tested were calculated using equations (5) and (9). These critical stresses and the measured Crsc of the corresponding fiat plate specimens with the same lay-up are compared in Table 6. The flanges of the angle and channel stiffeners have different critical buckling stresses due to the fact that the angle and channel stiffener lengths were different, 100 and 150 mm, respectively. The data in Table 6 indicate that, for all stiffener elements except those with the [45]5 lay-up, the critical buckling stress O'er is greater than the fiat plate fp sustained crushing stress o-s~. Therefore, the semiempirical analysis predicts that these stiffener specimens will crush in the same crushing mode as the fiat plate specimens. On the other hand, for the stiffener elements with the [45]5 lay-up, Crcris less than O'SfPC, and the analysis predicts that they will suffer local buckling of the entire cross-section and will not crush in the same mode as the flat plate specimens. These predictions are consistent with the experimental observations where all the specimens crushed in the same mode as the flat plate
specimens except those with the [45]5 lay-up, which buckled locally. The energy absorption capability of the stiffeners that have crushed in the same mode as the fiat plate specimens can be calculated using equation (11), provided that the coefficients o~and/3 have been determined. Using the values of a -- 0.978 and /3 -- 0.680 determined by multiple linear regression of experimental data 22 and equation (11), the ~sc for the angle and channel stiffeners were calculated and are shown in Table 7. To evaluate the accuracy of the semi-empirical method to predict the energy absorption capability of the stiffeners using equation (11), a statistical error analysis of the data presented in Table 7 was performed. The average spread of the experimentally measured sustained crushing stress from that predicted by the multiple linear regression analysis of the semi-empirical method is 2.52 MPa, which represents less than 3% variation between test and analysis data. A coefficient of determination of 0.988 indicates that 98.8% of the original uncertainty in the data has been explained by the semi-empirical model using a multiple linear regression analysis. These results support the conclusion that the semi-empirical analysis method provides an accurate means of predicting the energy absorption capability of composite stiffeners. CONCLUSIONS The angle and channel stiffeners fabricated using T65035/F584 plain-weave graphite/epoxy fabric material with Table 7 Sustained crushing stress for angle and channel stiffeners Sustained crushing stress, cr~c(MPa) Specimen no.
Test
A1
84.9 101 106 107 128 132
A2 A3 C1 C2 C3
Analysis 87.2 101 104 110 127 131
Table 6 Critical buckling stress for stiffener web and flange elements Stiffener element Web Flange Flange Web Flange Flange Web Flange Flange Web Flange Flange Web Flange Flange
300
(angle) (channel) (angle) (channel) (angle) (channel) (angle) (channel) (angle) (channel)
Lay-up
Element critical buckling stress, o'er (MPa)
[45]10 [45h0 [45]10 [45d0/452]s [452/0/452]s [452/0/452]s [452/0J45]s [45d0d45]s [45d0d45]s [45]7 [45]7 [45]7 [45]5 [45]5 [45]5
370 438 406 348 395 360 339 379 360 182 215 199 92.7 110 102
COMPOSITES Volume 26 Number 4 1995
Flat plate sustained crushing stress, o~ (MPa) 128 128 128 148 148 148 152 152 152 128 128 128 128 128 128
Energy absorption in stiffeners: A.O. Bolukbasi and D.H. Laananen
[45110, [45]7, [452/0/452]s and [45J02/45]s lay-ups all crushed in a lamina bending mode similar to the flat plate specimens of the same lay-ups. The stiffeners with the [45]5 lay-up and fabricated using the same material crushed in a local buckling mode and demonstrated an SSCS much lower than the other stiffeners. The SSCS values of the flat angle and channel specimens tested showed an increase with increasing number of 0 ~ plies in the laminate. However, the SSCS values for all stiffeners were lower than those of the flat plate specimens with identical lay-ups. The failure initiator, in the form of a 2.5 mm long chamfer machined at one of all crush specimens, was very effective. The initial peak crush loads for most specimens were at or below the maximum crush loads recorded during the sustained crushing phase of the specimens. Using the criterion that the sustained crushing stress ~rsc for the web and flange elements of the stiffener be less than a critical buckling stress ~rcr,the semi-empirical model successfully predicted that all stiffeners except the stiffeners with [45]5 would crush in a lamina bending mode similar to the flat plate specimens. These predictions were consistent with the experimental observations. The semi-empirical analysis method was also used to predict the energy absorption capability of the stiffeners based on data from flat plate crush tests of identical layups and multiple regression analysis. The multiple regression analysis successfully accounted for the free edge effects associated with stiffeners, and the predicted energy absorption capability was within 3% of the stiffener crush test results. The flat plate specimens are relatively easy to fabricate and test using a special test fixture. Therefore, the semi-empirical analysis method along with flat plate crush test data can potentially be used to eliminate or reduce costly fabrication and crush testing of actual composite structural elements.
State University, in whose laboratory the fiat plate crush tests were conducted.
REFERENCES
4
Thornton, P.H.J. Compos. Mater. 1979, 13, 247 Farley, G.L.J. Compos. Mater. 1983, 17, 267 Hull, D. in 'Structural Crashworthiness' (Eds N. Jones and T. Wierzbicki), Butterworths, London, 1983, pp. 118-135 Kindervater, C. in 'Proc. National Specialists Meeting on
5
Composite Structures', American Helicopter Society, Alexandria, VA, 1983 Schmueser, D.W. and Wickliffe, L.E.J. Eng. Mater. Technol.
1 2 3
6 7 8 9 10 11 12 13 14
National Aeronautics and Space Administration, Washington, 15
16 17
18 19 20 21
ACKNOWLEDGEMENT The authors wish to acknowledge the assistance of Professor J. Morton of Virginia Polytechnic Institute and
1987, 109, 72 Hull, D. Compos. Sci. Technol. 1991, 40, 377 Sigalas, I., Kumosa, M. and Hull, D. Compos. Sci. Technol. 1991, 40, 265 Farley, G.L. and Jones, R.M.J. Compos. Mater. 1992, 26, 59 Thornton, P.H. and Edwards, P.J.J. Compos. Mater. 1982, 16, 521 Czaplicki, M.J., Robertson, R.E. and Thornton, P.H. Compos. Sei. Technol. 1991, 40, 31 Jackson, K., Morton, J., Lavoie, J.A. and Boitnott, R. J. Am. Helicopter Soc. 1994, 39, 17 Kindervater, C.M. in 'Proc 30th National SAMPE Symposium, SAMPE, Covina, CA, 1985, pp. 1191-1201 Hanagud, S., Craig, J.I., Sriram, P. and Zhou, W. Z Compos. Mater. 1989, 23, 448 Lavoie, J.A. and Morton, J. NASA Contractor Report 4526,
22
DC, 1993 Spier, E.E. and Klouman, F.L. in 'Composite Materials: Testing and Design (Fourth Conference), A S T M STP 617, American Society for Testing and Materials, Philadelphia, PA, 1977, pp. 255-271 Renieri, M.P. and Garrett, R.A. Report MDC A7091, McDonnell Aircraft Company, St Louis, MO, 1981 Reddy, A.D. and Rehfield, L.W. AIAA Paper No. 85~9672, 26th AIAA/ASME/SAE SDM Conference, American Institute of Aeronautics and Astronautics, Washington, DC, 1985 Timoshenko, S. 'Theory of Elastic Stability', McGraw-Hill Book Company, Inc., New York, 1961 Whitney, J.M. 'Structural Analysis of Laminated Anisotropic Plates,' Technomic Publishing Company, Inc., Lancaster, PA, 1987 Fogarty, J.H.J. Compos. Mater. 1992, 26, 991 US Air Force Flight Dynamics Laboratory, 'DOD/NASA Advanced Composites Design Guide', DTIC Accession No. AD B8080182L, Wright-Patterson AFB, OH, 1983 Chapra, S.C. and Canale, R.P. 'Numerical Methods for Engineers', McGraw-Hill Book Company, Inc., New York, 1988
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UTTE E I N
RWQR E M A
Composites 26 (1995) 291 301 9 1995 Elsevier Science Limited Printed in Great Britain. All rights reserved 0010-4361/95/$10.00
TH N N
Energy absorption in composite stiffeners A.O. Bolukbasi McDonnell Douglas Helicopter Systems, Mesa, AZ 85205-9797, USA and D.H. Laananen* Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ 85287-6106, USA (Received 15 February 1994; revised 11 August 1994) The energy absorption behaviour of composite stiffeners subjected to axial compression has been investigated. A semi-empirical analysis methodology has been developed for prediction of the energy absorption capability of composite stiffeners based on crush tests of flat plate specimens and an understanding of the fundamentals of the energy absorption process. Flat plate, angle and channel specimens were fabricated from T650-35/F584 graphite/epoxy plain-weave fabric using five different lay-ups that consisted of varying percentages of 450 and 0~ plies. The specimens were crush tested under axial compression, and measured levels of sustained crushing stress were compared with model predictions. (Keywords: composite stiffeners; energy absorption; crush initiators)
INTRODUCTION The overall objective of designing an aircraft for crash protection is to minimize the number of injuries and fatalities in survivable crash impacts. The crashworthy design of aircraft involves a systems approach with the fuselage structure, landing gear and seats working together to absorb the aircraft kinetic energy and slow the occupants to rest without injurious loading. An important part of this energy absorption system is the structure below the fuselage floor, which may absorb up to 80% of the aircraft's kinetic energy. Application of composite materials to aircraft fuselage structures offers potentially significant weight and cost reductions relative to metallic structures. However, because composite materials are typically brittle and do not exhibit either plasticity or high elongation prior to failure, special design approaches are required to provide energy absorption capability comparable to that of metal structures. The energy absorption characteristics of various composite structural elements have been experimentally studied by several researchers. Circular tube specimens have been the most extensively studied structural elements I s, but experiments have also been conducted with square tubes 9J~ flat plates 11 and sine-wave beams 12'13. The results obtained with the tube specimens have indicated that the energy absorbed depends on such design parameters as the material system, lay-up and cross-section geometry. The tests have also demonstrated that when controlled stable crushing is produced through selection of appropriate design parameters, the composite tubes can yield a higher specific crushing efficiency than aIuminium tubes. * T o w h o m c o r r e s p o n d e n c e s h o u l d be a d d r e s s e d
In spite of the considerable work done on the energy absorption of composite materials, reliable analytical methods are not yet available to predict the energy absorption capability of practical composite aircraft fuselage structures. The current practice is to conduct expensive and time-consuming design support tests at the element and sub-assembly level prior to fabrication of the fuselage structure. Therefore, additional research is needed to study the energy absorption behaviour of practical composite structural elements and to develop analysis tools to support the design of composite fuselage structures in a timely and cost-effective manner. The objective of this research effort has been to study the energy absorption behaviour of composite stiffeners, specifically angle and channel sections, in order to develop a design technique for such components. Selection of the stiffeners over other structural elements such as sine-wave beams or tubes was based on widespread use of such elements in semi-monocoque fuselage structures. The following section describes experiments that were conducted with flat plate specimens of graphite/epoxy composite that were crushed by uniaxial in-plane loading. Axial crush tests of angle and channel stiffeners fabricated with the same material and lay-ups are then described. Finally, a semi-empirical analysis method, which uses the flat plate crush test data, is described and applied to the angle and channel stiffeners. EXPERIMENTS
Test specimens The crust test specimens were flat plates, angle stiffeners and channel stiffeners, the geometries of which are illustrated in Figure 1. Three different lay-ups were used for most of the specimens: [45]~0, [452/0/452]~ and
COMPOSITES Volume 26 Number 4 1995 291
Energy absorption in stiffeners: A.O. Botukbasi and D.H. Laananen
..%
Machined chamfer crush initiator
19
19
150
I
O0
J'----.... Flat plate
Channel stiffener
Angle stiffener
Dimensions in rnm
All radii = 3 mm
Figure 1 Crush test specimens
[45JOJ45]~. These lay-ups, which are typical of those used with fabric prepregs, were selected to contain 0-40% 0~ plies in order to evaluate their effect on the energy absorbing capability of the laminates. Results of previous studies have indicated that stable crushing can be achieved in tubes consisting entirely of bias plies, and that the addition of some axial pries can increase the specific crush stress for graphite/epoxy laminates2. However, as the percentage of 0 ~ plies is increased, at some point the failure mode may change to a less efficient mode. The 0 e plies tend to split longitudinally without crushing, and the tendency towards delamination increases, with a resulting drop in specific energy absorption capability. Hull 6 reported on the axial crushing of tubes fabricated from glass cloth with various warp to weft ratios that produced a range of ratios of hoop to axial plies. Results indicated that beyond a hoop to axial ratio of 1:1 the initial crash load increased, but the sustained crush stress was reduced. In addition to the 10-ply lay-ups, two channel and two angle specimens were also fabricated using [45]7 and [45]5 lay-ups to evaluate the effect, on the energy absorption capability of the stiffener, of different width to thickness aspect ratios for the stiffener web and flanges. Lay-ups for all specimens are listed in Table 1. All specimens were fabricated using T650-35/F584 Table 1 Test specimens Specimen number F1 F2 F3 A1 A2 A3 A4 A5 C1 C2 C3 C4 C5
292
Specimen type Flat plate Flat plate Flat p]ate Angle Angle Angle Angle Angle Channel Channel Channel Channel Channel
Quantity
graphite/epoxy plain-weave fabric, the mechanical properties of which, based on material supplier data, are listed in Table 2. The cured ply thickness was -0.203 mm. The stiffener specimens were fabricated using a male tool, and all specimens were cured in an autoclave under 690 kPa pressure. A crush initiator in the form of a 2.5 mm long chamfer was machined at one end of all crush test specimens. The unchamfered end of each angle and channel crush test specimen was potted in a 25 mm deep aluminium ring using an epoxy-based potting compound. The flat plate specimens were not potted but were tested in a special test fixture that provided lateral support along the unloaded edges. The dimensions of the flat plate crush test specimens were selected to fit an existing test fixture. The dimensions of the angle and channel stiffener crush specimens were selected based on elastic stability analyses to ensure that these specimens, except the specimens with the [45]5 lay-up, would not undergo local or global buckling during testing. The specimens with the [45]5 lay-up were designed to experience limited local buckling to investigate its effect on the energy absorption capability of the stiffeners. As indicated in Table 1, a total of nine flat plates, five angle stiffener and five channel stiffener specimens of five different lay-ups were fabricated and tested. Flat plate crush tests Flat plate specimens were selected for most of the crush experiments because they are less expensive and easier to fabricate than other types of test specimens such as stiffeners, tubes and sine-wave beams. A simple coupon configuration is also desirable for practical evaluation of material and laminate energy absorption capability. A problem with the fiat plate specimen is, however, the possibility of global buckling of the plate rather than the desired failure mode of sustained crushing. The buckling problem was eliminated by selection of the plate dimensions based on elastic stability analysis and by using a special text fixture that provided lateral support to the specimen during the test. The flat plate specimens were loaded using a special text fixture14, which is shown in Figure 2. The fixture consisted of eight steel rods and upper and lower platens. The four 25 mm diameter steel rods at the corners of the fixture served to guide the movable upper platen. The fixture provided lateral support to the specimen through four 13 mm diameter inner steel rods located at the centre of the platens. The inner support rods were positioned in pairs located 38 mm apart, so that the effective supported plate width was 38 mm. Each pair had a
Lay-up Table 2 Material properties for T650-35/F584 graphite/epoxy plainweave fabric
3 3 3 1 1 1 1 1 1 1 1 1 1
[45]~ [452/0/45z]s [452/02/45]~ [45]10 [45J0/452]s [45j02/45]s [45]7 [45]5 [45]10 [452/0/452]s [452/02/45]s [45]7 [45]5
COMPOSITES Volume 26 Number 4 1995
Material property
Value
Longitudinal Young's modulus, El (GPa) Transverse Young's modulus, E2 (GPa) Out-of-plane Young's modulus, E3 (GPa) Poisson's ratio, v12 In-plane shear modulus, G~2 (GPa) Longitudinal tensile strength, S, (MPa) Transverse tensile strength, S2t (MPa) Longitudinal compressive strength, $1~ (MPa) Transverse compressive strength, $2c (MPa) In-plane shear strength, SI2 (MPa)
70.3 70.3 8.27 0.028 5.65 855 855 848 848 152
Energy absorption in stiffeners: A.O. Bolukbasi and D.H. Laananen
Figure 3 Figure 2
Channel stiffener crush test
Flat plate crush test fixture
separation of 2 mm, the specimen thickness, so that the specimens could slide into the fixture from the side. The load was applied to the specimens and fixture through a 25 mm diameter steel ball which rested in a seat that was machined in the upper platen of the fixture. The displacement-controlled crosshead rate of the testing machine was 1.3 mm min 1. The load and crosshead displacement were digitally recorded during the test. The flat plate specimens were crushed for ~38 mm.
Angle and channel stiffener crush tests The angle and channel stiffeners were placed between the platens of the test machine with the stiffeners free standing on the potted ring, as shown for one of the channel stiffeners in Figure 3. The lower surface of each potted ring was precision machined to ensure that the stiffener was vertically aligned between the platens. A smooth steel plate was also placed between the upper end of the specimens containing the failure initiator and the movable platen of the test machine. As in the case of the flat plate specimens, the stiffener specimens were crushed using a displacement-controlled crosshead rate of 1.3 mm rain i. The angle and channel stiffener crush test specimens were crushed for ~38 and 64 ram, respectively. EXPERIMENTAL RESULTS The test results for the flat plate, angle and channel stiffener crush tests consist of force and deflection values, which were analysed to identify loads for initiation of crushing as well as the loads associated with the sustained crushing process for each of the specimens. In addition, photomicrographs of the specimens were prepared to obtain data on the delaminations and material failures associated with the crushing process.
Flat plate crush tests The flat plate specimens, which are shown in Figure 4, crushed between the lateral support rods of the text fixture in what has been called by Hull 6 a 'splaying' mode and by Farley and Jones 8 a 'lamina bending' mode. Each specimen tore against the lateral support rods and exhibited a central crack, which split the plate into a Y-shaped cross-section with multiple lamina bundles in each leg. The crushing force was reacted through bending and compression of the lamina bundles. The load versus crosshead displacement response for specimen F2-1, which is typical of the flat plate specimen data, is shown in Figure 5. The response curves for the flat plate specimens show an initial peak force associated with initiation of the fracture process followed by sustained crushing of the specimen. For crashworthiness applications, it is desirable that the initial peak load should not significantly exceed the average load during steady crushing. The initial peak, maximum and average crushing loads for all flat plate specimens tested are listed in Table 3, where the initial peak load is seen to be less than the maximum crushing load for all specimens and is comparable to the average crushing load. This indicates that the machined chamfer at one end of the specimens was a very effective crush initiator. The experimental data were also repeatable for specimens with identical lay-ups with the exception of specimen F1-2, which experienced a premature delamination. A good indicator of the crushing performance is the specific sustained crushing stress (SSCS), which is a measure of the energy absorption capability of the material: SSCS = r
P
COMPOSITES Volume 26 Number 4 1995
(1)
293
Energy absorption in stiffeners: A.O. Bolukbasi and D.H. Laananen in which p is the material density and o-~:is the sustained crushing stress given by
P~V
o'~ = ~ A
(2)
where Pa,~is the average crushing load and A is the crosssectional area. Experimental data in Table 3 indicate that the SSCS of the laminates tested increased with increasing percentage of 0~ plies in the laminate. To study the crush regions in more detail, the crushed flat plate specimens were sliced using a diamond saw, and photomicrographs of the plate segment edge surfaces were made. Typical photomicrographs of edge surfaces at the centre of the plate and near one of the lateral supports are shown in Figure 6. The photomicrographs indicate that the principal crack occurred at or close to the centre of the cross-section. The depth of this central crack was about twice the thickness of the plate and tended to be longer in the middle of the plate span away from the lateral supports. The photomicrographs also show interlaminar cracks in the legs of the Y-shaped cross-section, present between all plies. The depths of the interlaminar cracks were less than that of the central crack and extended slightly beyond the lamina surface in contact with the crush surface.
Stiffener crush tests Examples of crushed angle and channel stiffener specimens are shown in Figures 7 and 8, respectively. Except for specimens A5 and C5, the stiffener specimens exhibited a crushing behaviour similar to the flat plate specimens. They tore at the corners, and each segment of the cross-section exhibited a central crack, which split the segment into a Y-shaped cross-section with multiple lamina bundles on each leg. Specimens A5 and C5 were [45]5 laminates. Due to the greater width to thickness ratio of the flanges, these specimens experienced limited local buckling, and their crushing behaviour was very different from that of the other stiffeners. The A5 and C5 specimens tore at the corners and did not exhibit a central crack. The crushing force was reacted through bending and compression of the torn flanges as a whole. As the crushing force increased, the flanges started to tear at the corners, and interlaminar cracks formed within the flanges. After the flanges were torn at the corners, the crush load decreased slightly and the flange lamina bundles slid laterally on
Figure 4 Crushed flat plate specimens: (a) side view of all specimens; (b) top view of specimen F2-1
Figure 5
Crush test results for specimen F2-1
Table 3
Summary of flat plate crush test results
Specimen
Initial peak load (kN)
Average load (kN)
Maximum load (kN)
Sustained crush stress (MPa)
Specific sustained crush stress (kJ kg 1)
FI-1 F1-2 Ft-3 F2-1 F2-2 F2-3 F3-1 F3-2 F3-3
15.3 16.4 16.4 15.1 16.1 15.1 13.8 15.3 15.5
14.9 10.5 14.3 15.4 15.1 15.4 16.0 15.4 15.8
19.8 16.5 22.2 20.9 20.9 20,7 20,5 20.4 20.3
144 102 138 150 147 149 155 149 153
91,1 64.6 87.3 94.9 93.0 94.3 98.1 94.3 96.8
294
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Energy absorption in stiffeners: A.O. Bolukbasi and D.H. Laananen
Figure7 Crushedanglestiffenerspecimens:(a) specimenA2; (b) specimen A5
Figure 6 Photomicrographsof flat plate specimenF2-1: (a) centre of plate; (b) near lateral support the crush surface. As the stiffeners were crushed further, the crush loads once again increased, and the flanges tore further, repeating the crushing process. The load versus crosshead displacement for the stiffener specimens A2 and C2, which are typical for their stiffener types, are shown in Figures 9 and 10. As noted previously for the flat plate specimens, the response curves show an initial peak force associated with initiation of the crushing process, followed by sustained crushing of the specimen. The initial peak, maximum and average crushing loads, and S S C S for all angle and channel specimens tested are listed in Tables 4 and 5, respectively. The experimental data in Tables 4 and 5 show that the initial peak load was less than the maximum crush load and is comparable to the average crushing load, indicating that the crush initiator was effective. The only exception was specimen A l, where the initiation load was about 5% higher than the maximum crushing load. The S S C S values for all specimens except A5 and C5 (the [4515 lay-ups) are comparable but somewhat less than those for the flat plate specimens. This is due to differences in boundary conditions between the flat plate
test fixture and the stiffener specimens. The flat plate specimens were supported at both edges, where they tore as they crushed. The stiffener specimens, however, had flanges with free edges and tore only on the corners. The S S C S tor both the angle and channel stiffener specimens shows an increase with increasing percentage of 0 ~ plies. The S S C S values for specimens A5 and C5 are much less than those of the other stiffener specimens. This indicates that energy absorbed with flange bending as a whole without the formation of a central crack is less efficient than energy absorption in the presence of a central crack. The formation and growth of the central crack significantly contributes to the crushing force and, consequently, to the energy absorbed during the crushing process. To study the crush regions in more detail, the crushed stiffener specimens were sliced using a diamond saw, and photomicrographs of the edge surfaces were made. The photomicrographs of all the stiffener specimens except specimens A5 and C5 showed failures similar to those of the flat plates. Photomicrographs of specimens A1 and C3, which are typical of these stiffeners, are shown in Figures I1 and 12. The photomicrographs indicate that the central crack occurred at or close to the middle of the cross-section. For the channel stiffener specimens, the depth of the central crack was about twice the thickness of the stiffener and tended to be longer at the free edge of the flange and at the centre of the web than near the corners of the stiffener where the web and flanges intersected. The photomicrographs also show inter/intralaminar cracks in the legs of the Y-shaped cross-section. The
COMPOSITES Volume 26 Number 4 1995
295
Energy absorption in stiffeners: A.O. Bolukbasi and D.H. Laananen 30 25
/,
2O
z 10
0
0
10
20
30 40 50 Displacement (mm)
60
70
Figure 10 Crush test result for channel stiffener specimen C2
interlaminar cracks were present between all plies. The depths of the interlaminar cracks were less than that of the central crack and extended slightly beyond the lamina surface in contact with the crush surface. Photomicrographs of specimens A5 and C5 are shown in Figures 13 and 14. These photomicrographs indicate that, as the flange was torn at the stiffener corner and then was bent, interlaminar cracks were formed in the flange between all plies, as observed in other stiffener specimens. The section of the flange undergoing bending and cracking was about three times the thickness of the specimen. ANALYSIS
Figure 8 Crushed channel stiffener specimens: (a) specimen C1; (b) specimen C5
Figure 9 Crush test results for angle stiffener specimen A2
Table 4
A semi-empirical analysis methodology, which has been developed for use in design of energy-absorbing composite structures, is based on observations of the energy absorption process during the experimental studies, on phenomenological failure criteria and on fiat plate crush test data. The concept behind this analysis method is to be able to predict the energy absorption capability of composite structural elements such as stiffeners based on crush tests of fiat plate specimens. The fiat plate specimens are relatively easy to fabricate and test using a specialized text fixture. Therefore, the fiat plate specimens potentially can be used to reduce or eliminate costly fabrication and testing of actual structural elements. The energy absorption capability of composite structures is strongly dependent on the crushing mode 8. Therefore, a fundamental requirement of the semiempirical analysis is that the crushing behaviour of the structural elements being analysed should be identical to that of the fiat plate specimens tested. The experimental studies that were described in the previous section have indicated that most of the angle and channel stiffeners crushed in a lamina bending crushing mode much like the fiat plate specimens. The only exceptions were the angle and channel stiffeners of [45]5
Summary of angle stiffener crush test results
Specimen
Initial peak load (kN)
Average load (kY)
Maximum load (kN)
Sustained crush stress (MPa)
Specific sustained crush stress (kJ kg-~)
A1 A2 A3 A4 A5
8.90 8.10 8.63 4.80 2.31
6.23 7.43 7.74 3.91 1.19
8.90 9.92 10.90 5.20 3.87
84.9 101.4 105.6 83.7 50.7
53.7 64.2 66.8 53.0 32.1
296
COMPOSITES Volume 26 Number 4 1995
Energy absorption in stiffeners: A.O. Bolukbasi and D.H. Laananen Table 5
Specimen
Summary of channel stiffcncr crush test results Initial peak load (kN)
Average load (kN)
Maximum load (kN)
Sustained crush stress (MPa)
Specific sustained crush stress (kJ kg ~) 67.7
C1
20,(1
18,5
24.2
lt)7
C2
22.7
22,1
27.4
128
81.0
C3
18.7
22.8
27,8
132
83.5
C4
14.9
10.6
14,9
C5
7.83
5.56
lqgure 11 I'hotomicrographs of angle stiffener specimen A l: (a) near free edge; (b) near corner
lay-up, which experienced local buckling and demonstrated much lower SSCS values than other specimens. Therefore, to ensure that the stiffeners crush in the same mode as the fiat plate specimens, it is necessary to develop a composite design criterion that will avoid local buckling of the stiffener cross-section. The design Of metal stiffeners is performed using a crippling analysis, which predicts compression failure due to the stress distribution associated with local buckling. This type of analysis tbr isotropic materials has traditionally been carried out using empirically derived design curves of the form shown in Figure 15. A similar approach has been developed for crippling of composite
8.14
96.9
61.3
63.0
39.9
Figure 12 Photomicrographs of channel stiflkner specimen C3 (flange): (a) near free edge; (b) near corner
plates 15and applied to postbuckling and crippling behaviour of composite stiffeners 16'17. To utilize the empirical crippling curves, the stiffener cross-section is divided into a number of rectangular plate segments of width b and thickness t with either oneedge free or no-edge free boundary conditions. Definitions of element dimensions and the distinctions between one-edge and no-edge free elements for angle and channel stiffeners are illustrated in Figure 16. Materials properties used are the elastic modulus E and the compressive yield strength ~roy. The parameter r is the crippling compressive stress. If all the parameters except crcc arc known, then the curves shown in Figure 15 can be used to calculate a crippling stress value for each element of a cross-section. The total cross-
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Energy absorption in stiffeners: A.O. Bolukbasi and D.H. Laananen
Figure 14 Photomicrographs of channel stiffener specimen C5: (a) flange near free edge; (b) web near corner Figure 13 Photomicrographs of angle stiffener specimen AS: (a) near free edge; (b) near corner
section crippling strength can then be found by a weighted average of the contributions of the individual elements as follows: n
Z (cr~c)iAiE; a,~ = i=1
(3)
Y. AiEI i=1
where o'cc is the critical compressive stress for the total cross-section, and A~ and Ei are the cross-sectional area and elastic modulus associated with each individual noedge or one-edge free element, for which the crippling stress is (o-=)i. The empirical crippling curves shown in Figure 15 indicate that, for relatively thick sections which lie on the horizontal line to the left of the empirical crippling curve, the cross-section will experience no local buckling and the element will fail due to a reduction in material stiffness after yielding. For thinner cross-sections, which lie on the sloped line to the right of the empirical crippling curve, the section will experience local buckling prior to reaching the yield strength under compressive load. It is possible to draw an analogy between metal and composite stiffeners. The sustained crushing stress o'so which was defined in equation (2) can be considered
298
COMPOSITES Volume 26 Number 4 1995
analogous to ~rcyfor metal stiffeners. Therefore, to avoid local buckling effects which may change the crushing mode, it is necessary to select the stiffener element dimensions so that the crippling stress lies on the horizontal part of the empirical curve. Beyond this analogy, however, the empirically derived crippling curves for isotropic materials are not directly applicable for laminated composite materials for several reasons. The traditional crippling curve has taken advantage of the fact that, for an isotropic material, the stiffness can be represented in terms of a single elastic modulus. This simplicity is not possible for laminated composite materials. For isotropic materials, there is also a direct proportionality relationship between bending and extensional stiffness given by the expression
T 0.8 Gc~ 0.6
Gcy 0.4
~
~ _ _ N o
Edge Free
b O~r
10
0,2
0.1 0.1
1
TVT Figure 15 Empirical crippling curves for isotropic materials
Energy absorption in stiffeners: A.O. Bolukbasi and D.H. Laananen ,,~jb
t
One end of the angle and channel specimens was potted and the other end was restrained by friction on the crosshead; the end conditions were assumed to be those of a column with one end fixed and the other end pinned. The effective length was then -0.7L (ref. 18), and c was set to a value of 2.04. Given that equation (5) is applicable, consider a noedge free stiffener cross-section for which crushing occurs at a load equal to or less than the load for which local elastic buckling of the cross-section as a whole occurs. This case can be represented mathematically as
"
b
L One-Edge Free Element
No-Edge Free Eleroeot
Figure 16 Definition of one-edge and no-edge frec elements acr 2> 1 G~frp.
El 3
D 12(1
(4)
vz )
where D is the isotropic bending stiffness; E is the elastic modulus; t is the thickness; and v is Poisson's ratio. The relationship between the bending and extensional stiffnesses for a composite laminate is not as straightforward, and the bending stiffness is defined by a 3 • 3 flexural stiffness matrix D. The approach taken in formulating the semi-empirical analysis model is, therefore, to develop expressions for local buckling of the elements of the stiffener crosssection with one-edge free and no-edge frcc boundary conditions using the coefficients of the D matrix.
fp, where o-~ is the sustained crushing stress of the flat plate specimen of identical material and lay-up, and ~re~is the critical buckling stress for the one-edge free stiffener element. Substituting for ~r~ from equation (5) into equation (7), the design criterion to ensure that the no-edge free stiffener element crushes in the same mode as the flat plate specimen, without local buckling of the cross section as a whole, can be written as
bZt \IDI1022+(D]2
+2D66)
(8)
One-edge free element
No-edge fi'ee element A no-edge free element with a length of at least twice the width b may be modelled as a rectangular plate simply supported on all four edges 18. An example of such an element is the web of the channel stiffeners tested. The critical buckling stress for a simply supported orthotropic plate can then be calculated by 19
Gcr
(7)
2rc2[-'D 11/9,
-2
+(/912+2/966)
]
Stability analysis of the one-edge free element is similar to that for the no-edge free element, except that one of the edges parallel to the loading direction is free rather than simply supported 18, Examples of one-edge free elements are the flanges of the angle and channel stiffeners tested. The critical buckling stress for a rectangular, orthotropic plate with one free, unloaded edge is given by 2~
(5) a~
where o-0~is the critical buckling stress; b is the width of the element; and Dll, D12, D22 and D06 are coefficients of the laminate flexural stiffness. This equation is strictly true only for specially orthotropic laminates. However, any balanced symmetric angle-ply laminate considered for structural applications will be approximately orthotropic, so that equation (5) will be applicable. The critical buckling stress given by equation (5) also does not take into account the stiffener length, other than assuming that the length is at least twice the width of the individual stiffener elements, but not long enough for the stiffener to fail in global column buckling. In general, a segment with a slenderness ratio (L'/p) less than 20 will not be subject to column buckling, and all of the stiffener specimens were designed to have a slenderness ratio below this limit. The effective length L' in the slenderness ratio is defined as
L ' = L/,,,;cc
(6)
where L is the actual length and c is the fixity coefficient, which takes into account the end support conditions.
-
12D66
- -
b2t
+
tc2Dll - -
L'2t
(9)
where L' is the effective length given by equation (6). Therefore, the design criterion that the one-edge free stiffener element should crush in the same mode as the flat plate specimen, without local buckling of the crosssection as a whole, can be written as a~r~ p _ 12/966 4 - Jv2Du -b2t L'2t
(10)
When the stiffener is designed to meet both these criteria for the one-edge and no-edge free elements, the experimental data indicate that the crushing modes of the stiffeners will be identical to those for the flat plates. However, the experimental data also indicate that the ~r~, values for one-edge free elements are less than those for the flat plate specimens. The no-edge free elements such as the webs of the channel specimen, on the other hand, have o-~ very close to that of the flat plate specimens. Therefore, taking into account the free edge effect,
COMPOSITES Volume 26 Number 4 1995
299
Energy absorption in stiffeners: A.O. Bolukbasi and D.H. Laananen the sustained crushing stress O'~cfor a stiffener designed to comply with the local buckling criteria of equations (8) and (10) is given by the following empirical relationship: nweb nflange A web + ~ Y~ A flange O~ ~ --i O-sc = O-sfP i:l i=1
(11)
A where A web and A/flange a r e the areas for the stiffener web and flange elements; nweb and nflange indicate the numbers of each element in the cross-section; A is the total stiffener cross-sectional area; and a and/3 are experimentally determined constants. ANALYSIS RESULTS An analysis of the energy absorption capability of the angle and channel stiffeners was performed using the semi-empirical analysis method described above. The critical buckling stresses for the web and flange elements of the stiffeners tested were calculated using equations (5) and (9). These critical stresses and the measured Crsc of the corresponding fiat plate specimens with the same lay-up are compared in Table 6. The flanges of the angle and channel stiffeners have different critical buckling stresses due to the fact that the angle and channel stiffener lengths were different, 100 and 150 mm, respectively. The data in Table 6 indicate that, for all stiffener elements except those with the [45]5 lay-up, the critical buckling stress O'er is greater than the fiat plate fp sustained crushing stress o-s~. Therefore, the semiempirical analysis predicts that these stiffener specimens will crush in the same crushing mode as the fiat plate specimens. On the other hand, for the stiffener elements with the [45]5 lay-up, Crcris less than O'SfPC, and the analysis predicts that they will suffer local buckling of the entire cross-section and will not crush in the same mode as the flat plate specimens. These predictions are consistent with the experimental observations where all the specimens crushed in the same mode as the flat plate
specimens except those with the [45]5 lay-up, which buckled locally. The energy absorption capability of the stiffeners that have crushed in the same mode as the fiat plate specimens can be calculated using equation (11), provided that the coefficients o~and/3 have been determined. Using the values of a -- 0.978 and /3 -- 0.680 determined by multiple linear regression of experimental data 22 and equation (11), the ~sc for the angle and channel stiffeners were calculated and are shown in Table 7. To evaluate the accuracy of the semi-empirical method to predict the energy absorption capability of the stiffeners using equation (11), a statistical error analysis of the data presented in Table 7 was performed. The average spread of the experimentally measured sustained crushing stress from that predicted by the multiple linear regression analysis of the semi-empirical method is 2.52 MPa, which represents less than 3% variation between test and analysis data. A coefficient of determination of 0.988 indicates that 98.8% of the original uncertainty in the data has been explained by the semi-empirical model using a multiple linear regression analysis. These results support the conclusion that the semi-empirical analysis method provides an accurate means of predicting the energy absorption capability of composite stiffeners. CONCLUSIONS The angle and channel stiffeners fabricated using T65035/F584 plain-weave graphite/epoxy fabric material with Table 7 Sustained crushing stress for angle and channel stiffeners Sustained crushing stress, cr~c(MPa) Specimen no.
Test
A1
84.9 101 106 107 128 132
A2 A3 C1 C2 C3
Analysis 87.2 101 104 110 127 131
Table 6 Critical buckling stress for stiffener web and flange elements Stiffener element Web Flange Flange Web Flange Flange Web Flange Flange Web Flange Flange Web Flange Flange
300
(angle) (channel) (angle) (channel) (angle) (channel) (angle) (channel) (angle) (channel)
Lay-up
Element critical buckling stress, o'er (MPa)
[45]10 [45h0 [45]10 [45d0/452]s [452/0/452]s [452/0/452]s [452/0J45]s [45d0d45]s [45d0d45]s [45]7 [45]7 [45]7 [45]5 [45]5 [45]5
370 438 406 348 395 360 339 379 360 182 215 199 92.7 110 102
COMPOSITES Volume 26 Number 4 1995
Flat plate sustained crushing stress, o~ (MPa) 128 128 128 148 148 148 152 152 152 128 128 128 128 128 128
Energy absorption in stiffeners: A.O. Bolukbasi and D.H. Laananen
[45110, [45]7, [452/0/452]s and [45J02/45]s lay-ups all crushed in a lamina bending mode similar to the flat plate specimens of the same lay-ups. The stiffeners with the [45]5 lay-up and fabricated using the same material crushed in a local buckling mode and demonstrated an SSCS much lower than the other stiffeners. The SSCS values of the flat angle and channel specimens tested showed an increase with increasing number of 0 ~ plies in the laminate. However, the SSCS values for all stiffeners were lower than those of the flat plate specimens with identical lay-ups. The failure initiator, in the form of a 2.5 mm long chamfer machined at one of all crush specimens, was very effective. The initial peak crush loads for most specimens were at or below the maximum crush loads recorded during the sustained crushing phase of the specimens. Using the criterion that the sustained crushing stress ~rsc for the web and flange elements of the stiffener be less than a critical buckling stress ~rcr,the semi-empirical model successfully predicted that all stiffeners except the stiffeners with [45]5 would crush in a lamina bending mode similar to the flat plate specimens. These predictions were consistent with the experimental observations. The semi-empirical analysis method was also used to predict the energy absorption capability of the stiffeners based on data from flat plate crush tests of identical layups and multiple regression analysis. The multiple regression analysis successfully accounted for the free edge effects associated with stiffeners, and the predicted energy absorption capability was within 3% of the stiffener crush test results. The flat plate specimens are relatively easy to fabricate and test using a special test fixture. Therefore, the semi-empirical analysis method along with flat plate crush test data can potentially be used to eliminate or reduce costly fabrication and crush testing of actual composite structural elements.
State University, in whose laboratory the fiat plate crush tests were conducted.
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4
Thornton, P.H.J. Compos. Mater. 1979, 13, 247 Farley, G.L.J. Compos. Mater. 1983, 17, 267 Hull, D. in 'Structural Crashworthiness' (Eds N. Jones and T. Wierzbicki), Butterworths, London, 1983, pp. 118-135 Kindervater, C. in 'Proc. National Specialists Meeting on
5
Composite Structures', American Helicopter Society, Alexandria, VA, 1983 Schmueser, D.W. and Wickliffe, L.E.J. Eng. Mater. Technol.
1 2 3
6 7 8 9 10 11 12 13 14
National Aeronautics and Space Administration, Washington, 15
16 17
18 19 20 21
ACKNOWLEDGEMENT The authors wish to acknowledge the assistance of Professor J. Morton of Virginia Polytechnic Institute and
1987, 109, 72 Hull, D. Compos. Sci. Technol. 1991, 40, 377 Sigalas, I., Kumosa, M. and Hull, D. Compos. Sci. Technol. 1991, 40, 265 Farley, G.L. and Jones, R.M.J. Compos. Mater. 1992, 26, 59 Thornton, P.H. and Edwards, P.J.J. Compos. Mater. 1982, 16, 521 Czaplicki, M.J., Robertson, R.E. and Thornton, P.H. Compos. Sei. Technol. 1991, 40, 31 Jackson, K., Morton, J., Lavoie, J.A. and Boitnott, R. J. Am. Helicopter Soc. 1994, 39, 17 Kindervater, C.M. in 'Proc 30th National SAMPE Symposium, SAMPE, Covina, CA, 1985, pp. 1191-1201 Hanagud, S., Craig, J.I., Sriram, P. and Zhou, W. Z Compos. Mater. 1989, 23, 448 Lavoie, J.A. and Morton, J. NASA Contractor Report 4526,
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DC, 1993 Spier, E.E. and Klouman, F.L. in 'Composite Materials: Testing and Design (Fourth Conference), A S T M STP 617, American Society for Testing and Materials, Philadelphia, PA, 1977, pp. 255-271 Renieri, M.P. and Garrett, R.A. Report MDC A7091, McDonnell Aircraft Company, St Louis, MO, 1981 Reddy, A.D. and Rehfield, L.W. AIAA Paper No. 85~9672, 26th AIAA/ASME/SAE SDM Conference, American Institute of Aeronautics and Astronautics, Washington, DC, 1985 Timoshenko, S. 'Theory of Elastic Stability', McGraw-Hill Book Company, Inc., New York, 1961 Whitney, J.M. 'Structural Analysis of Laminated Anisotropic Plates,' Technomic Publishing Company, Inc., Lancaster, PA, 1987 Fogarty, J.H.J. Compos. Mater. 1992, 26, 991 US Air Force Flight Dynamics Laboratory, 'DOD/NASA Advanced Composites Design Guide', DTIC Accession No. AD B8080182L, Wright-Patterson AFB, OH, 1983 Chapra, S.C. and Canale, R.P. 'Numerical Methods for Engineers', McGraw-Hill Book Company, Inc., New York, 1988
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