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The effect of stitching on FRP cylindrical shells under axial compression
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International Journal of Impact Engineering 30 (2004) 923–938
The effect of stitching on FRP cylindrical shells under axial compression R. Velmurugana,*, N.K. Guptab, S. Solaimuruganc, A. Elayaperumalc a
Aerospace Engineering Department, IIT Madras, Chennai 600 036, India b Applied Mechanics Department, IIT Delhi, 110 016, India c Mechanical Engineering Department, CEG, Anna University, Chennai 600 025, India Received 8 July 2003; received in revised form 7 April 2004; accepted 9 April 2004 Available online 13 July 2004
Abstract FRP composites have usually poor through-thickness mechanical properties and, therefore, are able to sustain more loads in tension than in compression and fail as a consequence of buckling. The throughthickness reinforcement is carried out by stitching to improve the delamination strength and to reduce the in-plane crack growth rate. Experiments were performed on both stitched and unstitched laminated plates which were prepared by using woven roving glass fibre mat and chopped strand glass fibre mat with polyester resin, and the effect of stitching was studied. It is observed that stitching increases delamination strength to a great extent. There are losses in the in-plane mechanical properties due to in-plane fibre damage and creation of resin-rich pockets. Various energy-absorbing modes observed during progressive crushing of both stitched and unstitched FRP cylindrical shells under axial compression were studied both experimentally and theoretically. Analytical expressions for the calculation of energy absorption in various modes and average crush stress were derived, and the results thus obtained were compared with the experiments. r 2004 Elsevier Ltd. All rights reserved. Keywords: Progressive crushing; Stitching; Through-thickness reinforcement; Peel strength
1. Introduction Cylindrical tubes of metals and composites are efficient energy-absorbing components and their deformation behaviour under quasi-static conditions as well as under the drop hammer has *Corresponding author. E-mail address: [email protected] (R. Velmurugan). 0734-743X/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijimpeng.2004.04.007
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Nomenclature h crush length M plastic bending moment P applied load R; t and D mean radius, thickness and diameter of the cylindrical shell Sf; Si, S flexural and impact strengths and stiffness Wb ; Wh ; Wm ; Wf and WT energy terms Greek so sm ss y m d
symbols ultimate strength in uni-axial tension Peel or delamination strength short beam shear strength bending angle of the ply coefficient of friction between debris and crushing plate vertical deformation
received considerable attention in the past [1–4]. It is seen in experiments that under axial compressive loads the metallic tubes undergo progressive folding, whereas the composite tubes undergo progressive crushing occurring over the micro-fracture zones, which are successively formed. It is observed that the energy absorption in progressive crushing in the case of composite tubes is relatively more efficient [4]. Micro-fracture in the form of delamination and transverse shearing of delaminated plies moves towards the other end of tube with the same speed as that of the crosshead. Hamada and Ramakrishna [5] have shown that the tubes of t=D ratio less than 0.015 fail by brittle fracture while those of t=D ratios in the range of 0.015–0.25 crush progressively. Specific energy absorption capacity depends on absolute value of t; rather than the t=D ratio and it increases with an increase in thickness up to a certain value, above which it decreases. Highest value of specific energy absorption has been observed in the case of tubes with thickness values in the range of 2–3 mm. The energy-absorbing capacity of cylindrical tubes is seen to increase [6] between 20% and 45% for an increase in crushing speed from 0.01–12 m/s. Farley and Jones [7] carried out experimental and theoretical studies to predict the energy-absorbing characteristics of Kevlar/epoxy and graphite/epoxy tubes. A commercially available FE code was used for the analysis. The different factors influencing the energy-dissipating system have been studied in detail by Fairfull and Hull [8]. The frictional energy dissipated between the platen and debris of the tubes for surfaces of different roughness has also been discussed. The energy absorption characteristics of laminated composites have been studied by Daniel et al. [9,10]. They observed that there is a clear relationship between the interlaminar shear strength and energy absorption. Fibre-reinforced composite laminates have a considerable advantage over metals particularly in applications where the fibre directions are aligned with primary stresses in either tension or bending. Initial delamination in such materials may, however, be caused due to imperfections in
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their fabrication, such as air entrapment or regions of insufficient resin. It is also known that the layered composites have less strength in the thickness direction, which leads to premature failure of the structure and hence, a suitable mechanism is essential to increase the delamination strength in the thickness direction. A simple method to achieve this is stitching of composites in the thickness direction. Stitching can be plain, lock or chain. Of these plain stitching is quite simple and commonly employed. Stitching can be used for composite through-thickness reinforcement and joining. It can also be used to improve the delamination resistance of a composite structure. Dransfield et al. [11] observed from experiments that under compressive loading, stitched laminates failed in a brittle manner via kink band formation in the stitches after the formation of matrix cracks. The paper gives an overview of the stitching of 2D laminates, in which the advantage and disadvantage of stitching along with the different stitching commonly available are discussed in detail. The study reveals that there is an improvement of interlaminar strength and reduction in the in-plane properties of the CFRP laminates. Earlier studies have shown that through thickness reinforcement done by stitching delays delamination propagation [12] and provides improved interlaminar strength and delamination resistance by producing a more integrated composite structure. In the present work the effect of stitching of the cylindrical shells subjected to axial compression has been studied theoretically and experimentally. The cylindrical tubes are made with alternative layers of woven roving glass fibre mats and chopped strand glass fibre mats of densities 610 and 450 gms/m2, respectively, with polyester resin. It is seen that through-thickness stitching improves delamination strength of composites significantly and consequently, the energy-absorbing capability of cylindrical tubes in the progressive crushing mode increases. Experimental results are compared with the theoretical values and these match well.
2. Progressive crushing of cylindrical tubes It has been observed in earlier studies [4, 13] that energy is absorbed in the following four modes during the formation of crush zone in progressive crushing of cylindrical tubes: – – – –
Work required for cracking the matrix in the vertical direction, i.e. along the height. Work required for straining the material in the circumferential direction. Work required for bending the fibre layers, which bend both inside and outside the shell radius. Work required for overcoming the frictional forces between the debris and crushing plate.
2.1. Work required to propagate the central crack in the matrix (delamination work) Delamination (Peel) load per unit width of the planar-laminated specimen, sm ; was obtained by conducting a Peel test as per B.S.4994: 1987 standard and the details are given in Sections 3 and 4.6 (Peel test). Referring to Fig. 1, we write the delamination load for circumferential length=sm 2pRt. Delamination force acts in the outward radial direction (dx =h sin y).
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Fig. 1. Idealised model of cylindrical shell for analysis.
Work required for crack propagation or delamination work is Wm ¼ 2pRsm ht sin y;
ð1Þ
where sm is the Peel or delamination strength. 2.2. Work required to strain the material in the circumferential direction Variation of hoop strain at any point between A and B with distance X from A (see Fig. 1) is Ai ¼ X sin y=R: Work required to circumferentially (hoop) strain the material, which bends inside is Z h Z h Whi ¼ so Ai dv ¼ so ðX =RÞ sin y 2pRt1 dx; 0
0 2
Whi ¼ so pt1 sin y h ; where, t1 is the thickness of the layer material bending inside the shell radius. Similarly work required to circumferentially strain the material, which bends outside is Who ¼ so pt1 sin y h2 : Total work required to circumferentially strain the material, which bends both inside and outside the wall is Wh ¼ so ph2 t sin y;
ð2Þ
where t is the thickness of the shell. 2.3. Work required to bend the fibre layers, which bend both inside and outside the shell radius Bending moment capacity of the fibre layers when the stress is beyond the yield stress, i.e., in plastic state [1] is written as t 2 1 per unit deflection; M ¼ so b 2
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where, b is the width of the beam, equal to 2pR and so is the uniaxial ultimate tensile strength of the laminate. Work required to bend the fibre layers, which bend inside the shell radius t2 Wbi ¼ pRso y 1 : 2 Similarly, work required to bend the fibre layers, which bend outside the shell radius t2 Wbo ¼ pRso y 1 : 2 Total work required to bend the fibre layers, which bend both inside and outside the shell radius is given by t2 Wb ¼ Wbi þ Wbo ¼ pRso y : 4
ð3Þ
2.4. Work required to overcome the frictional forces between the debris and the crushing plate Wf =frictional force rubbing distance travelled by hoop-strained fibres on the crushing plate in single progression, and is written as Wf ¼ mPdx :
ð4Þ
Total energy required for single progression in axial crushing is the sum of all energy terms and is given by WT ¼ Wm þ Wh þ Wb þ Wf ; WT ¼ 2pRsm ht sin y þ so ph2 t sin y þ pRso y
t2 þ mPdx : 4
ð5Þ
Total work done by the crushing plate is given by W = load distance travelled by crushing plate in single progression W ¼ Pd:
ð6Þ
Total energy required for single progression in axial crushing is equal to the total work done by the crushing plate. Hence Pd ¼ 2pRsm ht sin y þ so ph2 t sin y þ pRso y
t2 þ mPdx ; 4
2pRt so h2 sin y so ty þ P¼ sm h sin y þ ; ðd mdx Þ 2R 8 where 2pRt is the area of cross-section of the shell.
ð7Þ
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2.5. Average crushing stress during the crushing process Average crushing stress, sav may be written as 1 so h2 sin y so ty sav ¼ þ : sm h sin y þ ðd mdx Þ 2R 8
ð8Þ
when the bending angle y is 90 , bending moment will be maximum. 2.6. Average crush length in a single progression h After substituting the values d=h(1cos y) and dx=h sin y in the above equation and minimising it with respect to crush length we get crush length, h; in a single progression as Rty 1=2 : ð9Þ h¼ 4 sin y
3. Fabrication and testing of stitched composite specimens The cylindrical tubular specimens were prepared by laying alternative layers of woven roving glass fibre mat and chopped strand glass fibre mat of densities 610 and 450 gms/m2, respectively, with polyester resin. The fibre layers were stitched with polyester thread (diameter=0.17 mm) in a sewing machine. The stitched layers were wound on wooden mandrels of 40, 50, 60 and 70 mm diameters and the just overlapped longitudinal joint was made by hand stitching. The stitched cylindrical fabrics were impregnated with polyester resin. The cured tubes were cut with height equal to three times the diameter. Stitched and unstitched laminated tubular specimens with 4 layers (2WRM, 2CSM) and 6 layers (3WRM, 3CSM) were made for each diameter. The tubes were made such that the D=t ratio was between 15 and 40 in order to avoid overall buckling or catastrophic failure during axial crushing. One end of the tube was chamfered with an external angle of 30 (see Fig. 2), which provided triggering mechanism for its progressive crushing. Chamfering also avoids catastrophic brittle failure because average progressive crushing stress is lower than brittle failure stress [7,9].
Fig. 2. Triggering mechanism at one end of the tube.
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Tubular specimens were subjected to axial compression in compression-testing machine. The tubes were crushed with a crosshead speed of 2 mm/min. The load–displacement curves obtained from the compression test results were plotted. Stitched and unstitched laminates of dimension 300 mm 300 mm and same layer sequence, fibre orientation and materials, as used in the cylindrical tubes, were made. Standard tensile test specimens with dimensions 230 mm 25 mm were cut from the planar laminate and tested in UTM as per ISO 3268-75. Similarly inter-laminar shear test specimens of width 10 mm and length equal to 6 times the thickness of the specimen were cut from the planar laminate and tested for short beam shear strength in a 3-point bending test as per standard BSM 341A. Standard stitched and unstitched specimens of dimensions 60 mm length and 20 mm width, as shown in Fig. 3, were cut from the planar laminate and tested for Peel (delamination) strength as per B.S.4994: 1987. Ultimate uni-axial tensile strength, % elongation from tensile test and average delamination strength from Peel strength test were obtained. These values are used in the analytical expressions to find the average crush load. The tested specimens under uniaxial tension are shown in Fig. 4.
Fig. 3. Peel (delamination) strength test specimen.
Fig. 4. Tested specimens of tension test.
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The test methods used to determine the flexural and impact strengths include ISO 178-75/ ASTM D 790-86 and ISO 180-82 (E)/ASTM D 256-8, respectively. The flexural and impact test specimens of dimensions 85 mm 12 mm and 65 mm 13 mm, respectively, were cut from planar laminate and tested. For each test three sample specimens were tested. All the tests in UTM were carried out under quasi-static loading with a crosshead speed of 2 mm/min. The specimens were prepared with equal amount of fibre and resin using hand lay up. Dry fabrics were stitched together, laid on a suitable mandrill and then resin was applied.
4. Results and discussion Stitching in composite reinforcement improves the delamination resistance and local shear strength. But it causes resin-rich regions, which will cause high stress concentration area, initiation of inter-planar cracks and fibre damage during stitching done with improper needle. Stitching decreases the inter-laminar crack initiation strength and improves the strength against crack propagation. This can be understood from load–displacement curves for peel strength. Modified lock-stitched, plain-stitched and unstitched planar-laminated specimens of standard dimensions were tested for uni-axial ultimate tensile strength, short beam shear strength, flexural strength, impact strength and Peel (delamination) strength. The results are discussed below. 4.1. Tensile strength (so ) Uni-axial ultimate tensile strength, so ; values determined from the tension test of unstitched, modified lock-stitched and plain-stitched 4-layered specimens are 151.02, 148.95 and 125.48 N/ mm2 and that of the 6-layer specimens are 167.39, 131.95 and 144.16 N/mm2, respectively. It is observed that stitching decreases the ultimate tensile strength of the specimen. Modified lock stitch decreases so by 1.36% in 4-layer specimens and 21.2% in 6-layer specimens, compared to its value in unstitched specimens. When the thickness of the specimen is increased, the percentage decrease of so increases. Plain stitch caused 16.9% decrease of so in 4-layer specimens and 13.88% decrease in 6-layer specimens. As the thickness of the specimen is increased, the percentage decrease of so also decreases. 4.2. Short beam shear strength (ss) The shear strength of the unstitched and stitched specimens was found from short beam 3-point bending test and the values are given in Table 1. The tested specimens are shown in Fig. 5. From the tested specimens it is seen that the failure was due to delamination of layers from the edges rather than by bending. It is observed that the shear strength is less in the modified lock stitch and is more in the plain stitch than the unstitched specimen values. It is clear that when the thickness of specimen is increased, the percentage decrease of ss due to modified lock stitch also decreases. Plain stitch causes 34% increase of ss in 4-layer specimens and 1.71% increase in ss in 6-layer specimens, i.e. as the thickness of specimen increases, the percentage increase of ss decreases.
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Table 1 Test results of planar-laminated specimens Strength
4-layers (2CSM,2WRM)
Ultimate tensile strength(N/mm2) Short beam shear strength (N/mm2) Flexural strength (N/mm2) Impact strength (J/cm) Stiffness (N/mm)
6-layers (3CSM,3WRM)
Unstitched
Plain stitched
Modified lockstitched
Unstitched
Plain stitched
Modified lockstitched
151.02
125.47
148.95
167.39
144.16
131.95
9.81
13.15
4.62
15.57
15.839
13.33
252.09 8.60 77.99
114.04 9.55 31.67
182.51 9.48 47.98
150.27 5.98 117.47
204.36 5.631 155.14
158.34 6.30 107.70
Fig. 5. Tested specimens of short beam shear test (3-point bending test).
4.3. Flexural strength (Sf ) Flexural tests are carried out for all the three cases and the results are given in Table 1. It is observed that stitching decreases flexural strength in 4-layered specimens and increases in 6layered specimens. In modified lock stitch the decreased value is 27.6% in 4-layered specimens and increase in 6-layered specimens is 5.37%, i.e. increase in thickness increases the bending strength. In plain stitch also there is 54.76% decrease in 4-layered specimens and 36% increase in 6-layered specimens in comparison with the unstitched specimens. The tested specimens are shown in Fig. 6.
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Fig. 6. Tested specimens of flexural test.
4.4. Impact strength (Si ) The specimens are subjected to the Izod impact test and the results are given in Table 1. The tested specimens are shown in Fig. 7. It is observed that stitching increases the impact strength of 4-layer stitched specimens. In case of 6-layer stitched specimens modified lock stitch increases Si value and plain stitch decreases the Si : In modified lock stitch there is an 10.25% increase of Si in 4-layer specimens and 5.35% increase in 6-layer specimens. When the thickness of specimen is increased, the percentage increase of Si due to modified lock stitch decreases. Plain stitch causes 11.10% increase of Si in 4-layer specimen and 5.84% decrease in 6-layer specimens. For higher thickness laminated specimens, plain stitch decreases the value of Si : This is due to lower stitch density and lower number of threads effecting impact strength. 4.5. Stiffness (S) The stiffness values of these specimens are also obtained from the flexural test and the results are given in Table 1. It is observed that stitching decreases the stiffness of 4-layer stitched specimens. In modified lock stitch the reduction is 38.5% in 4-layered specimens and is 8.32% in 6-layered specimens. As the thickness of specimen is increased, the percentage decrease of S is reduced. In plain stitch 59.39% decrease of S in 4-layer specimens and 32.06% increase of S in 6layer specimens are observed. Hence in plain stitch also there is an increase in stiffness as thickness of the specimen is increased. The decrease of S in 4-layer stitched specimens is due to damages
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Fig. 7. Tested specimens of impact test.
caused during stitching and in 6-layered specimens the damage is less and hence increased property values.
4.6. Peel (delamination) strength (sm ) Peel (delamination) strength of 4-layer, planar-laminated specimens were obtained from the mode-I failure (opening mode) test in UTM. The tested specimens are shown in Fig. 8. Peel strength was measured as delamination load per mm width of specimen. It is observed that for unstitched specimens delamination strength initial peak is 12.88 N/mm and in the progressive region it is 1.38 N/mm. After the first peak there is reduction in the load value but does not reach zero until complete failure. The deformation progresses in a controlled manner with the average load less than the first peak. This region is considered as a progressive region. Delamination crack initiation strength of modified lock-stitched specimen is 8.53 N/mm, in the progression region across the stitches it is 7.52 N/mm and in the unstitched zone the load level is 4.42 N/mm. In case of plain-stitched specimens delamination crack initiation strength is 11.77 N/mm, in the unstitched region it is 2.52 N/mm, and in the stitched zone it is 4.20 N/mm. It is clear that both modified lock-stitched and plain-stitched specimens absorb more energy than the unstitched specimens. Resin-rich pockets within the modified lock-stitched specimens cause greater decrease in initial peak value. But, in plain-stitched specimens few resin-rich pockets were formed and hence there is a small amount of decrease in initial peak. Figs. 9–11 show the load with crack opening displacement curves of unstitched, modified lock-stitched and plain-stitched specimens during Peel strength test. The average delamination propagation strengths of unstitched, modified
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Fig. 8. Tested specimens of Peel (delamination) test.
Fig. 9. Load–displacement curve for unstitched planar laminate (Peel test).
lock-stitched and plain-stitched planar-laminated specimens are 1.38, 5.97 and 3.36 N/mm, respectively. 4.7. Progressive crushing of tubular specimens The experimental values of uni-axial ultimate tensile strength, percentage elongation and delamination strength of 4-layer unstitched and modified lock-stitched planar-laminated
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Fig. 10. Load–displacement curve for modified lock-stitched planar laminate (Peel test).
Fig. 11. Load–displacement curve for plain-stitched planar laminate (Peel test).
specimens were used in Eqs. (8) and (9). The average crush load and crush length are calculated and are given in Table 2. Four-layer stitched and unstitched tubular specimens of 60 and 70 mm in diameter were crushed axially. Fig. 12 shows typical tested specimen. Typical load–displacement curves are shown in Figs. 13 and 14. From the experimental results, it is observed that stitched tubes carry more load than the corresponding unstitched tubes. Average crush load of unstitched and stitched tubes for 70 mm diameter are 27.78 and 33.8 KN, respectively with an increase of 21.66% in stitched specimens. From the load–displacement curve of unstitched tubular specimen with 70 mm diameter, we can
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Table 2 Average crush load of the 4-layered composite tubes R (mm)
t (mm)
h (mm)
Type
D=t
Crush load (KN) Experimental
Theoretical
70 mm inner diameter tubular specimens 36.65 3.30 5.55 36.80 3.60 5.86
Unstitched Stitched
27.78 33.80
22.91 26.89
22.9 20.9
60 mm inner diameter tubular specimens 31.80 3.60 5.46 31.90 3.80 5.65
Unstitched Stitched
28.15 29.26
24.34 26.87
18.5 17.7
Fig. 12. Crushed tube–front view.
see that the initial load is higher than the average load in the progressive region and the crush propagation part of the curve shows the uniform zigzag variation of load. But in stitched specimens the load–displacement curve shows an increase in load level whenever the circumferential delamination propagates across the circumferential stitches. For 60 mm tubular specimens the average crush load of stitched tube is 29.26 KN and that of unstitched tube is 28.15 KN. There is an increase of 3.95% in stitched specimens. The increase in average crush load is due to the increase in delamination strength. The average crush values are given in Table 2. These values are compared with the theoretical results obtained from Eqs. (8) and (9) and match well.
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35000
Crush Load (N)
30000 25000 20000 15000 10000 5000 0 0
10
20
30
40
50
60
70
80
Axial Displacement (mm)
Fig. 13. Load–displacement curve of unstitched four layers and 70 mm diameter, cylindrical tube under progressive crushing.
40000
Crush Load (N)
35000 30000 25000 20000 15000 10000 5000 0 0
10
20
30 40 50 Axial displacement (mm)
60
70
80
Fig. 14. Load–displacement curve of stitched four layers and 70 mm diameter cylindrical tube under progressive crushing.
5. Conclusion The through-thickness reinforcement of stitched laminated composites significantly improves delamination strength and thus increases the energy-absorbing capability of cylindrical tubes in the progressive-crushing mode under axial compression. But stitching causes in-plane fibre damage and resin-rich pockets which degrade the tensile and bending properties. It is also observed that with suitable stitching and fabrication parameters we can maximise the delamination resistance with minimum loss of in-plane mechanical properties. The central crack propagation in progressive crushing of stitched tubes, unlike in unstitched samples, occurred gradually by the continuous loss of individual stitches. Stitching reduces the crack initiation load due to in-plane fibre damage and resin-rich pockets near the thread of the laminate. When crack propagation passes through stitches, higher load is required to damage the stitches than in unstitched region. Stitching greatly reduces the extent of delamination growth. The damage caused by stitching is more in 4-layered composites than 6-layered laminates. Plain stitch is better than modified stitches in thin laminates and in thick laminates modified stitch gives better results.
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References [1] Alexander JM. An approximate analysis of the collapse of thin cylindrical shells under axial loading. Quart J Mech Appl Maths Pt1/1960; XIII. p. 10–15. [2] Abramowicz W, Jones N. Dynamic axial crushing of circular tubes. Int J Impact Eng 1984;2(3):263–81. [3] Gupta NK, Velmurugan R. Consideration of internal folding and non-symmetric fold formation in axial collapse of round tubes. Int J Solids Struct 1997;34(20):2611–33. [4] Gupta NK, Velmurugan R, Gupta SK. An analysis of axial crushing of composite tubes. J Compos Mater 1997;31(13):1262–86. [5] Hamada H, Ramakrishna S. Scaling effect in the energy absorption of carbon fibre/peek composite tubes. Compos Sci Technol 1995:211–21. [6] Farley GL. Effect of crushing speed on the energy absorption capability of composite tubes. J Compos Mater 1991;25:1314–29. [7] Farley GL, Jones RM. Prediction of energy absorption capability of composite tubes. J Compos Mater 1992;26(3):388–404. [8] Fairfull AH, Hull D. Energy absorption of polymer matrix composite structures: frictional effects. In: Wierzbicki T, Jones N, editors. Structural failure. New York: Wiley; 1989. p. 255–79. [9] Daniel L, Hogg PJ, Curtis PT. The crush behaviour of carbon fibre angle-ply reinforcement and the effect of interlaminar shear strength on energy absorption capability. Composites Part B: Eng 2000;31(5):435–40. [10] Daniel L, Hogg PJ, Curtis PT. The relative effects of through-thickness properties and fibre orientation on energy absorption by continuous fibre composites. Composites Part B: 1999;30(3):257–66. [11] Dransfield K, Baillie C, Mai Y. Improving the delamination resistance of CFRP by stitching—a review. Compos Sci Technol 1994;50:305–17. [12] Shu D, Mai Y. Effect of stitching on interlaminar delamination extension in composite laminates. Compos Sci Technol 1993;49:165–71. [13] Hull D. A unified approach to progressive crushing of fibre-reinforced composite tubes. Compos Sci Technol 1991;40:377–421.
International Journal of Impact Engineering 30 (2004) 923–938
The effect of stitching on FRP cylindrical shells under axial compression R. Velmurugana,*, N.K. Guptab, S. Solaimuruganc, A. Elayaperumalc a
Aerospace Engineering Department, IIT Madras, Chennai 600 036, India b Applied Mechanics Department, IIT Delhi, 110 016, India c Mechanical Engineering Department, CEG, Anna University, Chennai 600 025, India Received 8 July 2003; received in revised form 7 April 2004; accepted 9 April 2004 Available online 13 July 2004
Abstract FRP composites have usually poor through-thickness mechanical properties and, therefore, are able to sustain more loads in tension than in compression and fail as a consequence of buckling. The throughthickness reinforcement is carried out by stitching to improve the delamination strength and to reduce the in-plane crack growth rate. Experiments were performed on both stitched and unstitched laminated plates which were prepared by using woven roving glass fibre mat and chopped strand glass fibre mat with polyester resin, and the effect of stitching was studied. It is observed that stitching increases delamination strength to a great extent. There are losses in the in-plane mechanical properties due to in-plane fibre damage and creation of resin-rich pockets. Various energy-absorbing modes observed during progressive crushing of both stitched and unstitched FRP cylindrical shells under axial compression were studied both experimentally and theoretically. Analytical expressions for the calculation of energy absorption in various modes and average crush stress were derived, and the results thus obtained were compared with the experiments. r 2004 Elsevier Ltd. All rights reserved. Keywords: Progressive crushing; Stitching; Through-thickness reinforcement; Peel strength
1. Introduction Cylindrical tubes of metals and composites are efficient energy-absorbing components and their deformation behaviour under quasi-static conditions as well as under the drop hammer has *Corresponding author. E-mail address: [email protected] (R. Velmurugan). 0734-743X/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijimpeng.2004.04.007
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Nomenclature h crush length M plastic bending moment P applied load R; t and D mean radius, thickness and diameter of the cylindrical shell Sf; Si, S flexural and impact strengths and stiffness Wb ; Wh ; Wm ; Wf and WT energy terms Greek so sm ss y m d
symbols ultimate strength in uni-axial tension Peel or delamination strength short beam shear strength bending angle of the ply coefficient of friction between debris and crushing plate vertical deformation
received considerable attention in the past [1–4]. It is seen in experiments that under axial compressive loads the metallic tubes undergo progressive folding, whereas the composite tubes undergo progressive crushing occurring over the micro-fracture zones, which are successively formed. It is observed that the energy absorption in progressive crushing in the case of composite tubes is relatively more efficient [4]. Micro-fracture in the form of delamination and transverse shearing of delaminated plies moves towards the other end of tube with the same speed as that of the crosshead. Hamada and Ramakrishna [5] have shown that the tubes of t=D ratio less than 0.015 fail by brittle fracture while those of t=D ratios in the range of 0.015–0.25 crush progressively. Specific energy absorption capacity depends on absolute value of t; rather than the t=D ratio and it increases with an increase in thickness up to a certain value, above which it decreases. Highest value of specific energy absorption has been observed in the case of tubes with thickness values in the range of 2–3 mm. The energy-absorbing capacity of cylindrical tubes is seen to increase [6] between 20% and 45% for an increase in crushing speed from 0.01–12 m/s. Farley and Jones [7] carried out experimental and theoretical studies to predict the energy-absorbing characteristics of Kevlar/epoxy and graphite/epoxy tubes. A commercially available FE code was used for the analysis. The different factors influencing the energy-dissipating system have been studied in detail by Fairfull and Hull [8]. The frictional energy dissipated between the platen and debris of the tubes for surfaces of different roughness has also been discussed. The energy absorption characteristics of laminated composites have been studied by Daniel et al. [9,10]. They observed that there is a clear relationship between the interlaminar shear strength and energy absorption. Fibre-reinforced composite laminates have a considerable advantage over metals particularly in applications where the fibre directions are aligned with primary stresses in either tension or bending. Initial delamination in such materials may, however, be caused due to imperfections in
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their fabrication, such as air entrapment or regions of insufficient resin. It is also known that the layered composites have less strength in the thickness direction, which leads to premature failure of the structure and hence, a suitable mechanism is essential to increase the delamination strength in the thickness direction. A simple method to achieve this is stitching of composites in the thickness direction. Stitching can be plain, lock or chain. Of these plain stitching is quite simple and commonly employed. Stitching can be used for composite through-thickness reinforcement and joining. It can also be used to improve the delamination resistance of a composite structure. Dransfield et al. [11] observed from experiments that under compressive loading, stitched laminates failed in a brittle manner via kink band formation in the stitches after the formation of matrix cracks. The paper gives an overview of the stitching of 2D laminates, in which the advantage and disadvantage of stitching along with the different stitching commonly available are discussed in detail. The study reveals that there is an improvement of interlaminar strength and reduction in the in-plane properties of the CFRP laminates. Earlier studies have shown that through thickness reinforcement done by stitching delays delamination propagation [12] and provides improved interlaminar strength and delamination resistance by producing a more integrated composite structure. In the present work the effect of stitching of the cylindrical shells subjected to axial compression has been studied theoretically and experimentally. The cylindrical tubes are made with alternative layers of woven roving glass fibre mats and chopped strand glass fibre mats of densities 610 and 450 gms/m2, respectively, with polyester resin. It is seen that through-thickness stitching improves delamination strength of composites significantly and consequently, the energy-absorbing capability of cylindrical tubes in the progressive crushing mode increases. Experimental results are compared with the theoretical values and these match well.
2. Progressive crushing of cylindrical tubes It has been observed in earlier studies [4, 13] that energy is absorbed in the following four modes during the formation of crush zone in progressive crushing of cylindrical tubes: – – – –
Work required for cracking the matrix in the vertical direction, i.e. along the height. Work required for straining the material in the circumferential direction. Work required for bending the fibre layers, which bend both inside and outside the shell radius. Work required for overcoming the frictional forces between the debris and crushing plate.
2.1. Work required to propagate the central crack in the matrix (delamination work) Delamination (Peel) load per unit width of the planar-laminated specimen, sm ; was obtained by conducting a Peel test as per B.S.4994: 1987 standard and the details are given in Sections 3 and 4.6 (Peel test). Referring to Fig. 1, we write the delamination load for circumferential length=sm 2pRt. Delamination force acts in the outward radial direction (dx =h sin y).
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Fig. 1. Idealised model of cylindrical shell for analysis.
Work required for crack propagation or delamination work is Wm ¼ 2pRsm ht sin y;
ð1Þ
where sm is the Peel or delamination strength. 2.2. Work required to strain the material in the circumferential direction Variation of hoop strain at any point between A and B with distance X from A (see Fig. 1) is Ai ¼ X sin y=R: Work required to circumferentially (hoop) strain the material, which bends inside is Z h Z h Whi ¼ so Ai dv ¼ so ðX =RÞ sin y 2pRt1 dx; 0
0 2
Whi ¼ so pt1 sin y h ; where, t1 is the thickness of the layer material bending inside the shell radius. Similarly work required to circumferentially strain the material, which bends outside is Who ¼ so pt1 sin y h2 : Total work required to circumferentially strain the material, which bends both inside and outside the wall is Wh ¼ so ph2 t sin y;
ð2Þ
where t is the thickness of the shell. 2.3. Work required to bend the fibre layers, which bend both inside and outside the shell radius Bending moment capacity of the fibre layers when the stress is beyond the yield stress, i.e., in plastic state [1] is written as t 2 1 per unit deflection; M ¼ so b 2
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where, b is the width of the beam, equal to 2pR and so is the uniaxial ultimate tensile strength of the laminate. Work required to bend the fibre layers, which bend inside the shell radius t2 Wbi ¼ pRso y 1 : 2 Similarly, work required to bend the fibre layers, which bend outside the shell radius t2 Wbo ¼ pRso y 1 : 2 Total work required to bend the fibre layers, which bend both inside and outside the shell radius is given by t2 Wb ¼ Wbi þ Wbo ¼ pRso y : 4
ð3Þ
2.4. Work required to overcome the frictional forces between the debris and the crushing plate Wf =frictional force rubbing distance travelled by hoop-strained fibres on the crushing plate in single progression, and is written as Wf ¼ mPdx :
ð4Þ
Total energy required for single progression in axial crushing is the sum of all energy terms and is given by WT ¼ Wm þ Wh þ Wb þ Wf ; WT ¼ 2pRsm ht sin y þ so ph2 t sin y þ pRso y
t2 þ mPdx : 4
ð5Þ
Total work done by the crushing plate is given by W = load distance travelled by crushing plate in single progression W ¼ Pd:
ð6Þ
Total energy required for single progression in axial crushing is equal to the total work done by the crushing plate. Hence Pd ¼ 2pRsm ht sin y þ so ph2 t sin y þ pRso y
t2 þ mPdx ; 4
2pRt so h2 sin y so ty þ P¼ sm h sin y þ ; ðd mdx Þ 2R 8 where 2pRt is the area of cross-section of the shell.
ð7Þ
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2.5. Average crushing stress during the crushing process Average crushing stress, sav may be written as 1 so h2 sin y so ty sav ¼ þ : sm h sin y þ ðd mdx Þ 2R 8
ð8Þ
when the bending angle y is 90 , bending moment will be maximum. 2.6. Average crush length in a single progression h After substituting the values d=h(1cos y) and dx=h sin y in the above equation and minimising it with respect to crush length we get crush length, h; in a single progression as Rty 1=2 : ð9Þ h¼ 4 sin y
3. Fabrication and testing of stitched composite specimens The cylindrical tubular specimens were prepared by laying alternative layers of woven roving glass fibre mat and chopped strand glass fibre mat of densities 610 and 450 gms/m2, respectively, with polyester resin. The fibre layers were stitched with polyester thread (diameter=0.17 mm) in a sewing machine. The stitched layers were wound on wooden mandrels of 40, 50, 60 and 70 mm diameters and the just overlapped longitudinal joint was made by hand stitching. The stitched cylindrical fabrics were impregnated with polyester resin. The cured tubes were cut with height equal to three times the diameter. Stitched and unstitched laminated tubular specimens with 4 layers (2WRM, 2CSM) and 6 layers (3WRM, 3CSM) were made for each diameter. The tubes were made such that the D=t ratio was between 15 and 40 in order to avoid overall buckling or catastrophic failure during axial crushing. One end of the tube was chamfered with an external angle of 30 (see Fig. 2), which provided triggering mechanism for its progressive crushing. Chamfering also avoids catastrophic brittle failure because average progressive crushing stress is lower than brittle failure stress [7,9].
Fig. 2. Triggering mechanism at one end of the tube.
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Tubular specimens were subjected to axial compression in compression-testing machine. The tubes were crushed with a crosshead speed of 2 mm/min. The load–displacement curves obtained from the compression test results were plotted. Stitched and unstitched laminates of dimension 300 mm 300 mm and same layer sequence, fibre orientation and materials, as used in the cylindrical tubes, were made. Standard tensile test specimens with dimensions 230 mm 25 mm were cut from the planar laminate and tested in UTM as per ISO 3268-75. Similarly inter-laminar shear test specimens of width 10 mm and length equal to 6 times the thickness of the specimen were cut from the planar laminate and tested for short beam shear strength in a 3-point bending test as per standard BSM 341A. Standard stitched and unstitched specimens of dimensions 60 mm length and 20 mm width, as shown in Fig. 3, were cut from the planar laminate and tested for Peel (delamination) strength as per B.S.4994: 1987. Ultimate uni-axial tensile strength, % elongation from tensile test and average delamination strength from Peel strength test were obtained. These values are used in the analytical expressions to find the average crush load. The tested specimens under uniaxial tension are shown in Fig. 4.
Fig. 3. Peel (delamination) strength test specimen.
Fig. 4. Tested specimens of tension test.
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The test methods used to determine the flexural and impact strengths include ISO 178-75/ ASTM D 790-86 and ISO 180-82 (E)/ASTM D 256-8, respectively. The flexural and impact test specimens of dimensions 85 mm 12 mm and 65 mm 13 mm, respectively, were cut from planar laminate and tested. For each test three sample specimens were tested. All the tests in UTM were carried out under quasi-static loading with a crosshead speed of 2 mm/min. The specimens were prepared with equal amount of fibre and resin using hand lay up. Dry fabrics were stitched together, laid on a suitable mandrill and then resin was applied.
4. Results and discussion Stitching in composite reinforcement improves the delamination resistance and local shear strength. But it causes resin-rich regions, which will cause high stress concentration area, initiation of inter-planar cracks and fibre damage during stitching done with improper needle. Stitching decreases the inter-laminar crack initiation strength and improves the strength against crack propagation. This can be understood from load–displacement curves for peel strength. Modified lock-stitched, plain-stitched and unstitched planar-laminated specimens of standard dimensions were tested for uni-axial ultimate tensile strength, short beam shear strength, flexural strength, impact strength and Peel (delamination) strength. The results are discussed below. 4.1. Tensile strength (so ) Uni-axial ultimate tensile strength, so ; values determined from the tension test of unstitched, modified lock-stitched and plain-stitched 4-layered specimens are 151.02, 148.95 and 125.48 N/ mm2 and that of the 6-layer specimens are 167.39, 131.95 and 144.16 N/mm2, respectively. It is observed that stitching decreases the ultimate tensile strength of the specimen. Modified lock stitch decreases so by 1.36% in 4-layer specimens and 21.2% in 6-layer specimens, compared to its value in unstitched specimens. When the thickness of the specimen is increased, the percentage decrease of so increases. Plain stitch caused 16.9% decrease of so in 4-layer specimens and 13.88% decrease in 6-layer specimens. As the thickness of the specimen is increased, the percentage decrease of so also decreases. 4.2. Short beam shear strength (ss) The shear strength of the unstitched and stitched specimens was found from short beam 3-point bending test and the values are given in Table 1. The tested specimens are shown in Fig. 5. From the tested specimens it is seen that the failure was due to delamination of layers from the edges rather than by bending. It is observed that the shear strength is less in the modified lock stitch and is more in the plain stitch than the unstitched specimen values. It is clear that when the thickness of specimen is increased, the percentage decrease of ss due to modified lock stitch also decreases. Plain stitch causes 34% increase of ss in 4-layer specimens and 1.71% increase in ss in 6-layer specimens, i.e. as the thickness of specimen increases, the percentage increase of ss decreases.
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Table 1 Test results of planar-laminated specimens Strength
4-layers (2CSM,2WRM)
Ultimate tensile strength(N/mm2) Short beam shear strength (N/mm2) Flexural strength (N/mm2) Impact strength (J/cm) Stiffness (N/mm)
6-layers (3CSM,3WRM)
Unstitched
Plain stitched
Modified lockstitched
Unstitched
Plain stitched
Modified lockstitched
151.02
125.47
148.95
167.39
144.16
131.95
9.81
13.15
4.62
15.57
15.839
13.33
252.09 8.60 77.99
114.04 9.55 31.67
182.51 9.48 47.98
150.27 5.98 117.47
204.36 5.631 155.14
158.34 6.30 107.70
Fig. 5. Tested specimens of short beam shear test (3-point bending test).
4.3. Flexural strength (Sf ) Flexural tests are carried out for all the three cases and the results are given in Table 1. It is observed that stitching decreases flexural strength in 4-layered specimens and increases in 6layered specimens. In modified lock stitch the decreased value is 27.6% in 4-layered specimens and increase in 6-layered specimens is 5.37%, i.e. increase in thickness increases the bending strength. In plain stitch also there is 54.76% decrease in 4-layered specimens and 36% increase in 6-layered specimens in comparison with the unstitched specimens. The tested specimens are shown in Fig. 6.
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Fig. 6. Tested specimens of flexural test.
4.4. Impact strength (Si ) The specimens are subjected to the Izod impact test and the results are given in Table 1. The tested specimens are shown in Fig. 7. It is observed that stitching increases the impact strength of 4-layer stitched specimens. In case of 6-layer stitched specimens modified lock stitch increases Si value and plain stitch decreases the Si : In modified lock stitch there is an 10.25% increase of Si in 4-layer specimens and 5.35% increase in 6-layer specimens. When the thickness of specimen is increased, the percentage increase of Si due to modified lock stitch decreases. Plain stitch causes 11.10% increase of Si in 4-layer specimen and 5.84% decrease in 6-layer specimens. For higher thickness laminated specimens, plain stitch decreases the value of Si : This is due to lower stitch density and lower number of threads effecting impact strength. 4.5. Stiffness (S) The stiffness values of these specimens are also obtained from the flexural test and the results are given in Table 1. It is observed that stitching decreases the stiffness of 4-layer stitched specimens. In modified lock stitch the reduction is 38.5% in 4-layered specimens and is 8.32% in 6-layered specimens. As the thickness of specimen is increased, the percentage decrease of S is reduced. In plain stitch 59.39% decrease of S in 4-layer specimens and 32.06% increase of S in 6layer specimens are observed. Hence in plain stitch also there is an increase in stiffness as thickness of the specimen is increased. The decrease of S in 4-layer stitched specimens is due to damages
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Fig. 7. Tested specimens of impact test.
caused during stitching and in 6-layered specimens the damage is less and hence increased property values.
4.6. Peel (delamination) strength (sm ) Peel (delamination) strength of 4-layer, planar-laminated specimens were obtained from the mode-I failure (opening mode) test in UTM. The tested specimens are shown in Fig. 8. Peel strength was measured as delamination load per mm width of specimen. It is observed that for unstitched specimens delamination strength initial peak is 12.88 N/mm and in the progressive region it is 1.38 N/mm. After the first peak there is reduction in the load value but does not reach zero until complete failure. The deformation progresses in a controlled manner with the average load less than the first peak. This region is considered as a progressive region. Delamination crack initiation strength of modified lock-stitched specimen is 8.53 N/mm, in the progression region across the stitches it is 7.52 N/mm and in the unstitched zone the load level is 4.42 N/mm. In case of plain-stitched specimens delamination crack initiation strength is 11.77 N/mm, in the unstitched region it is 2.52 N/mm, and in the stitched zone it is 4.20 N/mm. It is clear that both modified lock-stitched and plain-stitched specimens absorb more energy than the unstitched specimens. Resin-rich pockets within the modified lock-stitched specimens cause greater decrease in initial peak value. But, in plain-stitched specimens few resin-rich pockets were formed and hence there is a small amount of decrease in initial peak. Figs. 9–11 show the load with crack opening displacement curves of unstitched, modified lock-stitched and plain-stitched specimens during Peel strength test. The average delamination propagation strengths of unstitched, modified
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Fig. 8. Tested specimens of Peel (delamination) test.
Fig. 9. Load–displacement curve for unstitched planar laminate (Peel test).
lock-stitched and plain-stitched planar-laminated specimens are 1.38, 5.97 and 3.36 N/mm, respectively. 4.7. Progressive crushing of tubular specimens The experimental values of uni-axial ultimate tensile strength, percentage elongation and delamination strength of 4-layer unstitched and modified lock-stitched planar-laminated
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Fig. 10. Load–displacement curve for modified lock-stitched planar laminate (Peel test).
Fig. 11. Load–displacement curve for plain-stitched planar laminate (Peel test).
specimens were used in Eqs. (8) and (9). The average crush load and crush length are calculated and are given in Table 2. Four-layer stitched and unstitched tubular specimens of 60 and 70 mm in diameter were crushed axially. Fig. 12 shows typical tested specimen. Typical load–displacement curves are shown in Figs. 13 and 14. From the experimental results, it is observed that stitched tubes carry more load than the corresponding unstitched tubes. Average crush load of unstitched and stitched tubes for 70 mm diameter are 27.78 and 33.8 KN, respectively with an increase of 21.66% in stitched specimens. From the load–displacement curve of unstitched tubular specimen with 70 mm diameter, we can
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Table 2 Average crush load of the 4-layered composite tubes R (mm)
t (mm)
h (mm)
Type
D=t
Crush load (KN) Experimental
Theoretical
70 mm inner diameter tubular specimens 36.65 3.30 5.55 36.80 3.60 5.86
Unstitched Stitched
27.78 33.80
22.91 26.89
22.9 20.9
60 mm inner diameter tubular specimens 31.80 3.60 5.46 31.90 3.80 5.65
Unstitched Stitched
28.15 29.26
24.34 26.87
18.5 17.7
Fig. 12. Crushed tube–front view.
see that the initial load is higher than the average load in the progressive region and the crush propagation part of the curve shows the uniform zigzag variation of load. But in stitched specimens the load–displacement curve shows an increase in load level whenever the circumferential delamination propagates across the circumferential stitches. For 60 mm tubular specimens the average crush load of stitched tube is 29.26 KN and that of unstitched tube is 28.15 KN. There is an increase of 3.95% in stitched specimens. The increase in average crush load is due to the increase in delamination strength. The average crush values are given in Table 2. These values are compared with the theoretical results obtained from Eqs. (8) and (9) and match well.
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35000
Crush Load (N)
30000 25000 20000 15000 10000 5000 0 0
10
20
30
40
50
60
70
80
Axial Displacement (mm)
Fig. 13. Load–displacement curve of unstitched four layers and 70 mm diameter, cylindrical tube under progressive crushing.
40000
Crush Load (N)
35000 30000 25000 20000 15000 10000 5000 0 0
10
20
30 40 50 Axial displacement (mm)
60
70
80
Fig. 14. Load–displacement curve of stitched four layers and 70 mm diameter cylindrical tube under progressive crushing.
5. Conclusion The through-thickness reinforcement of stitched laminated composites significantly improves delamination strength and thus increases the energy-absorbing capability of cylindrical tubes in the progressive-crushing mode under axial compression. But stitching causes in-plane fibre damage and resin-rich pockets which degrade the tensile and bending properties. It is also observed that with suitable stitching and fabrication parameters we can maximise the delamination resistance with minimum loss of in-plane mechanical properties. The central crack propagation in progressive crushing of stitched tubes, unlike in unstitched samples, occurred gradually by the continuous loss of individual stitches. Stitching reduces the crack initiation load due to in-plane fibre damage and resin-rich pockets near the thread of the laminate. When crack propagation passes through stitches, higher load is required to damage the stitches than in unstitched region. Stitching greatly reduces the extent of delamination growth. The damage caused by stitching is more in 4-layered composites than 6-layered laminates. Plain stitch is better than modified stitches in thin laminates and in thick laminates modified stitch gives better results.
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References [1] Alexander JM. An approximate analysis of the collapse of thin cylindrical shells under axial loading. Quart J Mech Appl Maths Pt1/1960; XIII. p. 10–15. [2] Abramowicz W, Jones N. Dynamic axial crushing of circular tubes. Int J Impact Eng 1984;2(3):263–81. [3] Gupta NK, Velmurugan R. Consideration of internal folding and non-symmetric fold formation in axial collapse of round tubes. Int J Solids Struct 1997;34(20):2611–33. [4] Gupta NK, Velmurugan R, Gupta SK. An analysis of axial crushing of composite tubes. J Compos Mater 1997;31(13):1262–86. [5] Hamada H, Ramakrishna S. Scaling effect in the energy absorption of carbon fibre/peek composite tubes. Compos Sci Technol 1995:211–21. [6] Farley GL. Effect of crushing speed on the energy absorption capability of composite tubes. J Compos Mater 1991;25:1314–29. [7] Farley GL, Jones RM. Prediction of energy absorption capability of composite tubes. J Compos Mater 1992;26(3):388–404. [8] Fairfull AH, Hull D. Energy absorption of polymer matrix composite structures: frictional effects. In: Wierzbicki T, Jones N, editors. Structural failure. New York: Wiley; 1989. p. 255–79. [9] Daniel L, Hogg PJ, Curtis PT. The crush behaviour of carbon fibre angle-ply reinforcement and the effect of interlaminar shear strength on energy absorption capability. Composites Part B: Eng 2000;31(5):435–40. [10] Daniel L, Hogg PJ, Curtis PT. The relative effects of through-thickness properties and fibre orientation on energy absorption by continuous fibre composites. Composites Part B: 1999;30(3):257–66. [11] Dransfield K, Baillie C, Mai Y. Improving the delamination resistance of CFRP by stitching—a review. Compos Sci Technol 1994;50:305–17. [12] Shu D, Mai Y. Effect of stitching on interlaminar delamination extension in composite laminates. Compos Sci Technol 1993;49:165–71. [13] Hull D. A unified approach to progressive crushing of fibre-reinforced composite tubes. Compos Sci Technol 1991;40:377–421.