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Fatigue behaviour of alumina-fibre-reinforced epoxy resin composite pipes under tensile and compressive loading conditions
Composites Science and Technology 61 (2001) 2393–2403 www.elsevier.com/locate/compscitech
Fatigue behaviour of alumina-fibre-reinforced epoxy resin composite pipes under tensile and compressive loading conditions V.K. Srivastavaa,*, Hiroyuki Kawadab a Department of Mechanical Engineering, Institute of Technology, BHU, Varanasi-221005, India Department of Mechanical Engineering, School of Engineering and Science, Waseda University, Okubo 3-4-1, Shinjuku-Ku, Tokyo 169-8555, Japan
b
Received 7 March 2001; received in revised form 17 July 2001; accepted 26 July 2001
Abstract Fatigue tests have been conducted on composites consisting of epoxy resin reinforced with alumina fibres (AFRP) under cyclic tensile and compressive loading conditions with the variation of fibre orientation. The behaviour of the stress/strain curve for a 45 sample is different from those for the 15 and 25 composite specimens, whereas, the monotonic strength decreases with increase in fibre angle for all specimens, which satisfies the maximum stress failure criterion. Fatigue results show that the applied stress decreases with an increase in the number of cycles to failure under both loading conditions for all composite pipes, but for the 45 sample the decrease was slow. The results of fatigue tests on a macroscopic level indicate that the matrix crack density slowly increased with increase in the normalized number of cycles to failure in all the specimens. The normalized apparent stiffness therefore falls with an increase of the normalized number of cycles to failure. However, the maximum stress decreased with the increase in the number of cycles to failure in the case of the 45 pipe. Finally, it is observed that matrix cracking and delaminations are occurring in the 45 sample whereas delamination and fibre buckling are appearing in the 15 and 25 samples. # 2001 Elsevier Science Ltd. All rights reserved. Keywords: Alumina-fibre-reinforced epoxy composites; B. Fatigue
1. Introduction Fibre-reinforced plastic (FRP) composites are now widely accepted as structural materials within the aerospace and automotive industries. The use of FRP laminates is rapidly increasing on account of their excellent properties, especially their high strength-to-weight ratio. Alumina-fibre-reinforced epoxy composites (AFRP) are one of these materials, which have high strength-toweight ratio and low thermal and electrical conductivity [1]. Recently, various composite laminates have been used in aerospace vehicles in the form of circular cylindrical shells as primary load-carrying structures. These structures are often required to operate under critical conditions and, therefore, the dependence of the mechanical properties of such composites in the critical loading condition needs to be carefully visualised. The * Corresponding author. Tel.: +91-542-315619; fax: +92-542-368174. E-mail addresses: [email protected] (V.K. Srivastava), [email protected] (H. Kawada).
advantages of high stiffness and strength of composite laminates can be fully utilized in the area of pressure vessels and pipes. When the vessel or pipe is constructed by filament winding over a metal liner, in more than one direction, the wall usually is no longer symmetric and first ply failure does not necessarily mean total failure of the system. The choice of metal for the liners is required whenever the vessel or pipe is designed to contain gas or acid under high pressure, in order to prevent permeation through the wall, or when it is designed to contain or supply the fluid under severe temperature conditions. In both cases elastomeric liners are not suitable [2]. On the other hand when composite laminate cylinders are applied in critical aircraft application, fatigue behaviour becomes very important. Many authors have done very extensive work on the fatigue behaviours of composite materials [3–6]. Their results show that fatigue is one of the loading parameters, which governs the damage of fibre composites under the action of various stresses. The damage appears in the form of delamination, matrix cracking and crazing, fibre failure, etc., all
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of which depend on the basic lamina properties as well as the interaction between adjacent lamina within the laminated composite. However, as composites technology approaches its maturity, more attention is directed toward the so-called matrix-controlled failure modes, such as off-axis ply failure and delamination. It is now well established that the failure in multidirectional composite laminates initiates in the ply whose fibres run normal to the applied tensile load. This ply failure manifests itself as cracks in the matrix and along the matrix/fibre interface. The ply failure occurs because unidirectional composites are much weaker along the transverse direction of the fibres [7]. Cracks form parallel to the fibres and multiply as fatigue proceeds. The number of cracks reaches equilibrium only when stresses in the ply are sufficiently reduced by the formation of the cracks themselves. Furthermore, these cracks frequently grow along the interfaces between plies, leading to delamination prior to failure. In all fibrous composites, the ply failure occurs long before the final failure, which usually coincides with final fracture of the fibres. Generally, transverse failure strain of unidirectional ply and longitudinal failure strain affects the ply failure of fibre composite pipe. Ply failure in fatigue has received more attention in recent years; therefore, the purpose of this paper is to study the fatigue behaviour of an alumina-fibre-reinforced epoxy resin composite under the action of cyclic tensile and compressive loading conditions.
On the basis of laminated theory, the stress axis and fibre axis of the composite are shown in Fig. 1 and can be formulated as [9]: 11 x 22 ¼ ½T y ð1Þ 12 xy where cos2 4 ½T ¼ sin2 cos sin
sin2 cos2 cos sin
12 ¼ x ðsincos þ l0 Gxy0 cos2Þ
3 2sin cos 2sin cos 5 cos2 sin2
ð2Þ
Since, laminate is loaded along the axial direction (y ¼ xy ¼ 0), after considering the coupling effect, the stresses can be written as 11 ¼ x ðcos2 þ l0 Gxy0 sin2Þ
ð3Þ
22 ¼ x ðcos2 l0 Gxy0 sin2Þ
ð4Þ
ð5Þ
where "
1 2ð1 þ L l0 ¼ cos2 GLT EL # 1 2ð1 þ T 2 sin sin cos GLT ET
1 1 þ L 1 þ T 1 ¼ þ cos2 2 sin2 2 þ Gxy0 GLT EL ET
2. Basic governing equation
2
Fig. 1. Schematic illustration of stresses along normal and transverse direction of fibre.
1 1 1 þ x 1 þ y ¼ þ sin2 2 GLT cos4 Ex Ey 1 þ cos2 2 Gxy
ð6Þ
ð7Þ
ð8Þ
L T ¼ EL ET
"
y 4 1 ¼ cos þ sin4 4sin2 cos2 cos4 Ey
1 1 1 2 2 sin cos Gxy Ex Ey
ð9Þ
where , , E, G and are the stress, shear stress, modulus of elasticity, shear modulus and Poisson’s ratio along the respective directions. Now, using the simple criterion of maximum stress failure, it is assumed that failure occurs when a stress, parallel or normal to the fibre axis, reaches the
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Fig. 2. Geometry of AFRP composite pipe.
appropriate critical value, that is if one of the following is satisfied;
3. Experimental programme 3.1. Materials and specimen
j11 j 5 11u j22 j 5 22u j22 j 5 12u
ð10Þ
Monitoring of 11, 22 and 12 as the applied stress is increased, allows the failure of the system, when one of the inequalities in 11, 22 and 12 is satisfied. However, the longitudinal and transverse strength are related to the fibre angle and static fibre strength Fx for each of the three failure modes, FL ¼ Fxcos2 FT ¼ Fxsin2 FLT ¼ Fxsin cos
3.2. Static and fatigue tests ð11Þ
In the present case, FL, FT and FLT are calculated on the basis of the relation; F ¼ FxVf
The materials chosen for this study are g-alumina fibre, bisphenol epoxy resin and aromatic amine hardener. The specification of g-alumina is listed in Table 1. Using the above materials, alumina-fibre-reinforced epoxy resin (AFRP) composite pipes were manufactured by the filament winding method with three different winding angles, 15, 25 and 45 . Arisawa Company, Niigatta Pref. Japan supplied the composite pipes for the present study. The fibre volume fraction of the specimens was between 50 and 55%. The geometry of the composite pipe is shown in Fig. 2.
ð12Þ
where Vf is the fibre volume fraction.
All the static tests were conducted on a Servo Pulser Fatigue test machine with the crosshead speed of 0.3 mm/min to determine the tensile and compressive strength values. The specimens were firmly fixed in the lower and upper holder of the machine. The longitudinal stress and longitudinal strain values were recorded for the entire composite pipe under tensile and compressive loading condition.
Table 1 Specification of g-alumina fibre Chemical composition
Al2O3 85% SiO2 15%
Roving designation Diameter Filament/yarn Density Tensile strength Tensile modulus
SX-11-1K 15 mm 1000 3.3 g/cm3 2 GPa 210 GPa
Fig. 3. Definition of matrix crack density.
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The fatigue tests were also done on a Servo Pulser machine. The specimens were loaded in the machine and the number of cycles to failure were recorded carefully with the following test conditions; frequency, f=10 Hz, stress ratio, R=0.1–10, load wave form sine curve and stress level, max ¼ 0:40:9. With this specification, u applied stress and the number of cycles to failure of each type of composite pipe were recorded for further analysis of the experimental data. 3.3. Fractography studies Each of the composite pipes were scanned on the microscopic and macroscopic scale by using a scanning electron microscope and digital camera after fatigue failure test. On the basis of the SEM micrograph ( 50), matrix crack density was measured for each fatigue failure pipe from Eq. (13) as shown in Fig. 3.
4. Results and discussion Longitudinal stress–strain curves for the three different composite specimens are shown in Fig. 4. The stress– strain behaviours of 15 and 25 composite pipes show almost similar deformation of fibre/matrix failure under tensile and compressive fatigue loading condition. Whereas stress–strain behaviour of a 45 composite pipe is different from that of the 15 and 25 composite pipes, the results show that the modulus of elasticity of 15 pipe (685 MPa), 25 pipe (500 MPa) and 45 pipe (125 MPa) decreases with an increase of woven angles. Therefore, ultimate strength and modulus of the 45 pipe gave lower values than the 15 and 25 pipes, as shown in Fig. 4. The fracture behaviour of each sample can be identified from the micrograph under the combined action of tensile and compressive stress. The static strength data as a function of winding
Fig. 4. Stress–strain curves of (a) 15 , (b) 25 and (c) 45 composite pipes along with macroscopic evidence under tensile and compressive loading conditions.
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angle are shown in Fig. 5. The result indicates that the static strength decreased with an increase of winding angle. Fig. 5(a)–(d) clearly show that the static strength is very much dependent on the winding angle, even if the condition of the stress changes. It defines an envelope in stress space. When cracks appear in the composite pipe under the cyclic loading condition, it means that the stress along the fibre direction is more dominant than the transverse fibre direction stress and shear stress. However, compressive load increases transverse fibre direction stress compared to axial load. As the crack is initiated, sudden transverse stress rises very frequently with the decrease of winding angle. The above results are parallel to the observation by Hull [8]. The results shown in Fig. 6, which were obtained using the maximum stress criterion and xi, was measured. This result demonstrates how the stresses in the plies, and the failure stress, vary with the winding angle in the AFRP composite pipes. The stress distribution ratio in tensile loading is very different from the compressive loading. The differences are due to the action of the applied load, which affects the ratio of stress along
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each direction. The transverse stress, 22 is more negative and insignificant in comparison to 11 in tensile loading of the 45 sample, whereas 11 is more negative and insignificant in comparison to 22 in compressive loading of the 45 sample. Fig. 7 indicates that the applied stress decreases with an increase of the number of cycles to failure. The result of 15 and 25 pipes shows the clear difference between the S–N curves under both condition ( 22 < 0 and 22>0). However the 45 pipes have similar values under both conditions. As the number of fatigue cycles increase crack is propagated from the resin area and diverted along the fibre direction. The rate of crack propagation is totally dependent on the winding angles. Under the action of applied load and winding angles the damage modes interfacial debonding and matrix crack dividing layers are changed as can be seen from Fig. 8(b) and (c). The change in matrix density is also effected by the normalized number of cycles to failure of the composite pipes. In each stage of fatigue cycle, the matrix density is changed due to an increase of the crack area. This type of behaviour is obtained in both cases, 15
Fig. 5. Comparison between static strength and winding angle of AFRP composite pipes (a) static loading (b) 22>0 (c) 22>0 and (d) 22 <0, after crack initiation.
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(Fig. 8) and 25 (Fig. 9) pipes, as well as tensile and compressive load. When the number of cycles to failure increased, the amount of crack population increased very rapidly. In the initial stage of cycles, the matrix cracks and then the fibre is debonded/delaminated followed by fibre fracture. Therefore, normalized apparent stiffness of the composite is affected by the increase of crack density. Figs. 10–12 show that the normalized apparent stiffness reduces gradually with an increase of the normalized number of cycles to failure. It was observed that the 45 pipe is severely damaged by the action of fatigue cycles under tensile as well as compressive loading conditions because of the optimal
values of stress ratio. It is evident from the fractographic Fig. 13 that the amount of crack density of 45 pipe is higher than for the 15 and 25 pipes. The results clearly indicate that the rate of crack propagation in the 45 pipe is dominated by the stress ratio because of high specific strength and low modulus of elasticity. Fig. 14 indicates the overall view of the 45 pipe that the maximum stress decreased with the increase of the number of cycles to failure as already discussed in Fig. 7. The enlarge view of the S–N curve in Fig. 14 shows almost the same behaviour in tensile as well as compressive loading conditions. The optimum fatigue cycles of the 45 pipe is below 103 cycles which
Fig. 6. Comparison between stress distribution ratio and winding angle of AFRP pipe (a) tensile loading, x>0 and (b) compressive loading x < 0.
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Fig. 7. Comparison between applied stress and number of cycles to failure 15, 25 and 45 composite pipes.
Fig. 8. Definition of matrix crack density in the 15 pipe (a) tensile (b) compressive loading and (c) effect of matrix crack density on normalized number of cycles to failure.
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Fig. 9. Definition of matrix crack density in the 25 pipe (a) tensile (b) compressive loading and (c) effect of matrix crack density on normalized number of cycles to failure.
Fig. 10. Comparison of normalized apparent stiffness, matrix crack density and normalized number of cycles to failure of the 15 pipe.
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Fig. 11. Comparison of normalized apparent stiffness, matrix crack density and normalized number of cycles to failure of the 25 pipe.
Fig. 12. Comparison of normalized apparent stiffness, matrix crack density and normalized number of cycles to failure of the 45 pipe.
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is not significantly affected by the fatigue stress. The average endurance limits are 130 MPa in compressive mode and 115 MPa in tensile mode, which corresponds very closely to previous data. It is clear that the filament wound composite pipes fail at appreciably lower loads than the crossply or unidirectional laminates [5].
5. Discussion The results obtained from the static and fatigue tests on alumina-fibre-reinforced epoxy resin clearly indicate that the static strength and fatigue strength are very much dominated by the action of the applied load and winding angles. The static strength and stress distribution ratio data as a function of winding angle are shown in Figs. 5 and 6 together with predictions based on the
maximum stress failure criteria. The value of static strength of the 45 pipe is less than the 15 and 25 pipes. However, the average stress ratio of the 45 pipe is higher than the 15 and 25 pipes. This difference arises, basically, from the consideration of the interface bond strength along the biaxial direction, between the fibre and matrix, and also due to the matrix shear strain energy. However, during progressive matrix cracking and debonding, there will be a substantial stress acting on the plane of the crack tip inside the matrix which gives rise to a high corresponding fibre stress [10]. As the experiment progresses to fatigue tests under tensile and compressive cyclic loading conditions of AFRP composite pipes, one can observe a significant fatigue strength difference between the three different composite pipes because of the winding angles. As
Fig. 13. Comparison between microscopic and macroscopic observation in the 45 pipe after fatigue damage.
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Fig. 14. S–N curve of the 45 pipe under tensile and compressive loading conditions.
shown in Figs. 8, 9 and 13, it can be seen that fatigue damage, in the form of several cracks parallel to each other along the fibre direction, is initiated in the plies. As the number of cycles increases, the other plies and small regions between the cracks, parallel to each other, are rapidly affected by the initial stage of fatigue damage due to the interlacing structures. However, the damage still develops always along the fibre direction until the final fracture. One can also observe the density of matrix cracking through the thickness by Eq. (13). The increase of matrix crack density shows that the normalized apparent stiffness decreases with the increase of cycles to failure in the entire specimen. However, the 45 pipe looses the stiffness very rapidly with the increase of fatigue cycles, because, maximum shear stress develops along the 45 angle. Many transverse microcracks are observed in the different lamina as can be seen from Fig. 13. These microcracks are in the direction of the specimen thickness (normal to the fibre) and indicate actual cracking of the matrix during fatigue loading. However, the fatigue cyclic failure of the 45 pipe may be more complex, because of severe and extensive microscopic damage.
6. Conclusions The fatigue behaviour of alumina fibre reinforced epoxy resin composite pipes was been studied with stress ratio of 0.1, 10 and a frequency of 10 Hz under the tensile and compressive loading conditions. The influence of the winding angle on the fatigue behaviour has also been studied. The results strongly suggest that
the normalized apparent stiffness and number of cycles to failure are affected by the winding angle. However, the present observation conclude that the 45 AFRP pipe can be used below 103 cycles and at the level of maximum stress 140 MPa without any damage. Fracture surfaces include a combination of several interdependent failure modes such as matrix cracking, fibre delamination and debonding.
References [1] Gu YH. Fracture behaviour of continuous alumina fibre reinforced epoxy. J Comp Mater 1994;28(13):1227–36. [2] Lifshitz JM, Dayan H. Filament-wound pressure vessel with thick metal liner. Comp Struct 1995;32:313–23. [3] Miller KJ. Fatigue under complex stress. J Mater Sci 1977;11: 432–8. [4] Wang SS, Chim ESM, Socie DF. Biaxial fatigue of fibre-reinforced composites at cryogenic temperatures. Part-I: fatigue fracture life and mechanisms. ASME, J Eng Mater Technol 1982; 104:128–36. [5] Tsangarakis N. Fatigue failure of an orthotropic plate with a circular hole. J Comp Mater 1984;18:47–57. [6] Tsangarakis N, Nunes JJ. Nondestructive evaluation of fatigue damage in alumina fibre reinforced aluminium. J Comp Mater 1985;19:250–68. [7] Owen MJ. In: Broutman LJ, editor. Composite materials, fracture and fatigue, Vol. 5. New York: Academic Press, 1974. p. 313– 40. [8] Hull D. A unified approach to progressive crushing of fibre reinforced composite tubes. Comp Sci Technol 1991;40:377–421. [9] Hull D, Clyne TW. An introduction to composite materials. Cambridge, UK: Cambridge University Press, 1996. [10] Jonathan A, Hahn HT. Off-axis fatigue of graphite/ epoxy composite, fatigue of fibrous composite materials, ASTM STP 723. USA: American Society for Testing and Materials, 1981.
Fatigue behaviour of alumina-fibre-reinforced epoxy resin composite pipes under tensile and compressive loading conditions V.K. Srivastavaa,*, Hiroyuki Kawadab a Department of Mechanical Engineering, Institute of Technology, BHU, Varanasi-221005, India Department of Mechanical Engineering, School of Engineering and Science, Waseda University, Okubo 3-4-1, Shinjuku-Ku, Tokyo 169-8555, Japan
b
Received 7 March 2001; received in revised form 17 July 2001; accepted 26 July 2001
Abstract Fatigue tests have been conducted on composites consisting of epoxy resin reinforced with alumina fibres (AFRP) under cyclic tensile and compressive loading conditions with the variation of fibre orientation. The behaviour of the stress/strain curve for a 45 sample is different from those for the 15 and 25 composite specimens, whereas, the monotonic strength decreases with increase in fibre angle for all specimens, which satisfies the maximum stress failure criterion. Fatigue results show that the applied stress decreases with an increase in the number of cycles to failure under both loading conditions for all composite pipes, but for the 45 sample the decrease was slow. The results of fatigue tests on a macroscopic level indicate that the matrix crack density slowly increased with increase in the normalized number of cycles to failure in all the specimens. The normalized apparent stiffness therefore falls with an increase of the normalized number of cycles to failure. However, the maximum stress decreased with the increase in the number of cycles to failure in the case of the 45 pipe. Finally, it is observed that matrix cracking and delaminations are occurring in the 45 sample whereas delamination and fibre buckling are appearing in the 15 and 25 samples. # 2001 Elsevier Science Ltd. All rights reserved. Keywords: Alumina-fibre-reinforced epoxy composites; B. Fatigue
1. Introduction Fibre-reinforced plastic (FRP) composites are now widely accepted as structural materials within the aerospace and automotive industries. The use of FRP laminates is rapidly increasing on account of their excellent properties, especially their high strength-to-weight ratio. Alumina-fibre-reinforced epoxy composites (AFRP) are one of these materials, which have high strength-toweight ratio and low thermal and electrical conductivity [1]. Recently, various composite laminates have been used in aerospace vehicles in the form of circular cylindrical shells as primary load-carrying structures. These structures are often required to operate under critical conditions and, therefore, the dependence of the mechanical properties of such composites in the critical loading condition needs to be carefully visualised. The * Corresponding author. Tel.: +91-542-315619; fax: +92-542-368174. E-mail addresses: [email protected] (V.K. Srivastava), [email protected] (H. Kawada).
advantages of high stiffness and strength of composite laminates can be fully utilized in the area of pressure vessels and pipes. When the vessel or pipe is constructed by filament winding over a metal liner, in more than one direction, the wall usually is no longer symmetric and first ply failure does not necessarily mean total failure of the system. The choice of metal for the liners is required whenever the vessel or pipe is designed to contain gas or acid under high pressure, in order to prevent permeation through the wall, or when it is designed to contain or supply the fluid under severe temperature conditions. In both cases elastomeric liners are not suitable [2]. On the other hand when composite laminate cylinders are applied in critical aircraft application, fatigue behaviour becomes very important. Many authors have done very extensive work on the fatigue behaviours of composite materials [3–6]. Their results show that fatigue is one of the loading parameters, which governs the damage of fibre composites under the action of various stresses. The damage appears in the form of delamination, matrix cracking and crazing, fibre failure, etc., all
0266-3538/01/$ - see front matter # 2001 Elsevier Science Ltd. All rights reserved. PII: S0266-3538(01)00132-4
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of which depend on the basic lamina properties as well as the interaction between adjacent lamina within the laminated composite. However, as composites technology approaches its maturity, more attention is directed toward the so-called matrix-controlled failure modes, such as off-axis ply failure and delamination. It is now well established that the failure in multidirectional composite laminates initiates in the ply whose fibres run normal to the applied tensile load. This ply failure manifests itself as cracks in the matrix and along the matrix/fibre interface. The ply failure occurs because unidirectional composites are much weaker along the transverse direction of the fibres [7]. Cracks form parallel to the fibres and multiply as fatigue proceeds. The number of cracks reaches equilibrium only when stresses in the ply are sufficiently reduced by the formation of the cracks themselves. Furthermore, these cracks frequently grow along the interfaces between plies, leading to delamination prior to failure. In all fibrous composites, the ply failure occurs long before the final failure, which usually coincides with final fracture of the fibres. Generally, transverse failure strain of unidirectional ply and longitudinal failure strain affects the ply failure of fibre composite pipe. Ply failure in fatigue has received more attention in recent years; therefore, the purpose of this paper is to study the fatigue behaviour of an alumina-fibre-reinforced epoxy resin composite under the action of cyclic tensile and compressive loading conditions.
On the basis of laminated theory, the stress axis and fibre axis of the composite are shown in Fig. 1 and can be formulated as [9]: 11 x 22 ¼ ½T y ð1Þ 12 xy where cos2 4 ½T ¼ sin2 cos sin
sin2 cos2 cos sin
12 ¼ x ðsincos þ l0 Gxy0 cos2Þ
3 2sin cos 2sin cos 5 cos2 sin2
ð2Þ
Since, laminate is loaded along the axial direction (y ¼ xy ¼ 0), after considering the coupling effect, the stresses can be written as 11 ¼ x ðcos2 þ l0 Gxy0 sin2Þ
ð3Þ
22 ¼ x ðcos2 l0 Gxy0 sin2Þ
ð4Þ
ð5Þ
where "
1 2ð1 þ L l0 ¼ cos2 GLT EL # 1 2ð1 þ T 2 sin sin cos GLT ET
1 1 þ L 1 þ T 1 ¼ þ cos2 2 sin2 2 þ Gxy0 GLT EL ET
2. Basic governing equation
2
Fig. 1. Schematic illustration of stresses along normal and transverse direction of fibre.
1 1 1 þ x 1 þ y ¼ þ sin2 2 GLT cos4 Ex Ey 1 þ cos2 2 Gxy
ð6Þ
ð7Þ
ð8Þ
L T ¼ EL ET
"
y 4 1 ¼ cos þ sin4 4sin2 cos2 cos4 Ey
1 1 1 2 2 sin cos Gxy Ex Ey
ð9Þ
where , , E, G and are the stress, shear stress, modulus of elasticity, shear modulus and Poisson’s ratio along the respective directions. Now, using the simple criterion of maximum stress failure, it is assumed that failure occurs when a stress, parallel or normal to the fibre axis, reaches the
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Fig. 2. Geometry of AFRP composite pipe.
appropriate critical value, that is if one of the following is satisfied;
3. Experimental programme 3.1. Materials and specimen
j11 j 5 11u j22 j 5 22u j22 j 5 12u
ð10Þ
Monitoring of 11, 22 and 12 as the applied stress is increased, allows the failure of the system, when one of the inequalities in 11, 22 and 12 is satisfied. However, the longitudinal and transverse strength are related to the fibre angle and static fibre strength Fx for each of the three failure modes, FL ¼ Fxcos2 FT ¼ Fxsin2 FLT ¼ Fxsin cos
3.2. Static and fatigue tests ð11Þ
In the present case, FL, FT and FLT are calculated on the basis of the relation; F ¼ FxVf
The materials chosen for this study are g-alumina fibre, bisphenol epoxy resin and aromatic amine hardener. The specification of g-alumina is listed in Table 1. Using the above materials, alumina-fibre-reinforced epoxy resin (AFRP) composite pipes were manufactured by the filament winding method with three different winding angles, 15, 25 and 45 . Arisawa Company, Niigatta Pref. Japan supplied the composite pipes for the present study. The fibre volume fraction of the specimens was between 50 and 55%. The geometry of the composite pipe is shown in Fig. 2.
ð12Þ
where Vf is the fibre volume fraction.
All the static tests were conducted on a Servo Pulser Fatigue test machine with the crosshead speed of 0.3 mm/min to determine the tensile and compressive strength values. The specimens were firmly fixed in the lower and upper holder of the machine. The longitudinal stress and longitudinal strain values were recorded for the entire composite pipe under tensile and compressive loading condition.
Table 1 Specification of g-alumina fibre Chemical composition
Al2O3 85% SiO2 15%
Roving designation Diameter Filament/yarn Density Tensile strength Tensile modulus
SX-11-1K 15 mm 1000 3.3 g/cm3 2 GPa 210 GPa
Fig. 3. Definition of matrix crack density.
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The fatigue tests were also done on a Servo Pulser machine. The specimens were loaded in the machine and the number of cycles to failure were recorded carefully with the following test conditions; frequency, f=10 Hz, stress ratio, R=0.1–10, load wave form sine curve and stress level, max ¼ 0:40:9. With this specification, u applied stress and the number of cycles to failure of each type of composite pipe were recorded for further analysis of the experimental data. 3.3. Fractography studies Each of the composite pipes were scanned on the microscopic and macroscopic scale by using a scanning electron microscope and digital camera after fatigue failure test. On the basis of the SEM micrograph ( 50), matrix crack density was measured for each fatigue failure pipe from Eq. (13) as shown in Fig. 3.
4. Results and discussion Longitudinal stress–strain curves for the three different composite specimens are shown in Fig. 4. The stress– strain behaviours of 15 and 25 composite pipes show almost similar deformation of fibre/matrix failure under tensile and compressive fatigue loading condition. Whereas stress–strain behaviour of a 45 composite pipe is different from that of the 15 and 25 composite pipes, the results show that the modulus of elasticity of 15 pipe (685 MPa), 25 pipe (500 MPa) and 45 pipe (125 MPa) decreases with an increase of woven angles. Therefore, ultimate strength and modulus of the 45 pipe gave lower values than the 15 and 25 pipes, as shown in Fig. 4. The fracture behaviour of each sample can be identified from the micrograph under the combined action of tensile and compressive stress. The static strength data as a function of winding
Fig. 4. Stress–strain curves of (a) 15 , (b) 25 and (c) 45 composite pipes along with macroscopic evidence under tensile and compressive loading conditions.
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angle are shown in Fig. 5. The result indicates that the static strength decreased with an increase of winding angle. Fig. 5(a)–(d) clearly show that the static strength is very much dependent on the winding angle, even if the condition of the stress changes. It defines an envelope in stress space. When cracks appear in the composite pipe under the cyclic loading condition, it means that the stress along the fibre direction is more dominant than the transverse fibre direction stress and shear stress. However, compressive load increases transverse fibre direction stress compared to axial load. As the crack is initiated, sudden transverse stress rises very frequently with the decrease of winding angle. The above results are parallel to the observation by Hull [8]. The results shown in Fig. 6, which were obtained using the maximum stress criterion and xi, was measured. This result demonstrates how the stresses in the plies, and the failure stress, vary with the winding angle in the AFRP composite pipes. The stress distribution ratio in tensile loading is very different from the compressive loading. The differences are due to the action of the applied load, which affects the ratio of stress along
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each direction. The transverse stress, 22 is more negative and insignificant in comparison to 11 in tensile loading of the 45 sample, whereas 11 is more negative and insignificant in comparison to 22 in compressive loading of the 45 sample. Fig. 7 indicates that the applied stress decreases with an increase of the number of cycles to failure. The result of 15 and 25 pipes shows the clear difference between the S–N curves under both condition ( 22 < 0 and 22>0). However the 45 pipes have similar values under both conditions. As the number of fatigue cycles increase crack is propagated from the resin area and diverted along the fibre direction. The rate of crack propagation is totally dependent on the winding angles. Under the action of applied load and winding angles the damage modes interfacial debonding and matrix crack dividing layers are changed as can be seen from Fig. 8(b) and (c). The change in matrix density is also effected by the normalized number of cycles to failure of the composite pipes. In each stage of fatigue cycle, the matrix density is changed due to an increase of the crack area. This type of behaviour is obtained in both cases, 15
Fig. 5. Comparison between static strength and winding angle of AFRP composite pipes (a) static loading (b) 22>0 (c) 22>0 and (d) 22 <0, after crack initiation.
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(Fig. 8) and 25 (Fig. 9) pipes, as well as tensile and compressive load. When the number of cycles to failure increased, the amount of crack population increased very rapidly. In the initial stage of cycles, the matrix cracks and then the fibre is debonded/delaminated followed by fibre fracture. Therefore, normalized apparent stiffness of the composite is affected by the increase of crack density. Figs. 10–12 show that the normalized apparent stiffness reduces gradually with an increase of the normalized number of cycles to failure. It was observed that the 45 pipe is severely damaged by the action of fatigue cycles under tensile as well as compressive loading conditions because of the optimal
values of stress ratio. It is evident from the fractographic Fig. 13 that the amount of crack density of 45 pipe is higher than for the 15 and 25 pipes. The results clearly indicate that the rate of crack propagation in the 45 pipe is dominated by the stress ratio because of high specific strength and low modulus of elasticity. Fig. 14 indicates the overall view of the 45 pipe that the maximum stress decreased with the increase of the number of cycles to failure as already discussed in Fig. 7. The enlarge view of the S–N curve in Fig. 14 shows almost the same behaviour in tensile as well as compressive loading conditions. The optimum fatigue cycles of the 45 pipe is below 103 cycles which
Fig. 6. Comparison between stress distribution ratio and winding angle of AFRP pipe (a) tensile loading, x>0 and (b) compressive loading x < 0.
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Fig. 7. Comparison between applied stress and number of cycles to failure 15, 25 and 45 composite pipes.
Fig. 8. Definition of matrix crack density in the 15 pipe (a) tensile (b) compressive loading and (c) effect of matrix crack density on normalized number of cycles to failure.
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Fig. 9. Definition of matrix crack density in the 25 pipe (a) tensile (b) compressive loading and (c) effect of matrix crack density on normalized number of cycles to failure.
Fig. 10. Comparison of normalized apparent stiffness, matrix crack density and normalized number of cycles to failure of the 15 pipe.
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Fig. 11. Comparison of normalized apparent stiffness, matrix crack density and normalized number of cycles to failure of the 25 pipe.
Fig. 12. Comparison of normalized apparent stiffness, matrix crack density and normalized number of cycles to failure of the 45 pipe.
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is not significantly affected by the fatigue stress. The average endurance limits are 130 MPa in compressive mode and 115 MPa in tensile mode, which corresponds very closely to previous data. It is clear that the filament wound composite pipes fail at appreciably lower loads than the crossply or unidirectional laminates [5].
5. Discussion The results obtained from the static and fatigue tests on alumina-fibre-reinforced epoxy resin clearly indicate that the static strength and fatigue strength are very much dominated by the action of the applied load and winding angles. The static strength and stress distribution ratio data as a function of winding angle are shown in Figs. 5 and 6 together with predictions based on the
maximum stress failure criteria. The value of static strength of the 45 pipe is less than the 15 and 25 pipes. However, the average stress ratio of the 45 pipe is higher than the 15 and 25 pipes. This difference arises, basically, from the consideration of the interface bond strength along the biaxial direction, between the fibre and matrix, and also due to the matrix shear strain energy. However, during progressive matrix cracking and debonding, there will be a substantial stress acting on the plane of the crack tip inside the matrix which gives rise to a high corresponding fibre stress [10]. As the experiment progresses to fatigue tests under tensile and compressive cyclic loading conditions of AFRP composite pipes, one can observe a significant fatigue strength difference between the three different composite pipes because of the winding angles. As
Fig. 13. Comparison between microscopic and macroscopic observation in the 45 pipe after fatigue damage.
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Fig. 14. S–N curve of the 45 pipe under tensile and compressive loading conditions.
shown in Figs. 8, 9 and 13, it can be seen that fatigue damage, in the form of several cracks parallel to each other along the fibre direction, is initiated in the plies. As the number of cycles increases, the other plies and small regions between the cracks, parallel to each other, are rapidly affected by the initial stage of fatigue damage due to the interlacing structures. However, the damage still develops always along the fibre direction until the final fracture. One can also observe the density of matrix cracking through the thickness by Eq. (13). The increase of matrix crack density shows that the normalized apparent stiffness decreases with the increase of cycles to failure in the entire specimen. However, the 45 pipe looses the stiffness very rapidly with the increase of fatigue cycles, because, maximum shear stress develops along the 45 angle. Many transverse microcracks are observed in the different lamina as can be seen from Fig. 13. These microcracks are in the direction of the specimen thickness (normal to the fibre) and indicate actual cracking of the matrix during fatigue loading. However, the fatigue cyclic failure of the 45 pipe may be more complex, because of severe and extensive microscopic damage.
6. Conclusions The fatigue behaviour of alumina fibre reinforced epoxy resin composite pipes was been studied with stress ratio of 0.1, 10 and a frequency of 10 Hz under the tensile and compressive loading conditions. The influence of the winding angle on the fatigue behaviour has also been studied. The results strongly suggest that
the normalized apparent stiffness and number of cycles to failure are affected by the winding angle. However, the present observation conclude that the 45 AFRP pipe can be used below 103 cycles and at the level of maximum stress 140 MPa without any damage. Fracture surfaces include a combination of several interdependent failure modes such as matrix cracking, fibre delamination and debonding.
References [1] Gu YH. Fracture behaviour of continuous alumina fibre reinforced epoxy. J Comp Mater 1994;28(13):1227–36. [2] Lifshitz JM, Dayan H. Filament-wound pressure vessel with thick metal liner. Comp Struct 1995;32:313–23. [3] Miller KJ. Fatigue under complex stress. J Mater Sci 1977;11: 432–8. [4] Wang SS, Chim ESM, Socie DF. Biaxial fatigue of fibre-reinforced composites at cryogenic temperatures. Part-I: fatigue fracture life and mechanisms. ASME, J Eng Mater Technol 1982; 104:128–36. [5] Tsangarakis N. Fatigue failure of an orthotropic plate with a circular hole. J Comp Mater 1984;18:47–57. [6] Tsangarakis N, Nunes JJ. Nondestructive evaluation of fatigue damage in alumina fibre reinforced aluminium. J Comp Mater 1985;19:250–68. [7] Owen MJ. In: Broutman LJ, editor. Composite materials, fracture and fatigue, Vol. 5. New York: Academic Press, 1974. p. 313– 40. [8] Hull D. A unified approach to progressive crushing of fibre reinforced composite tubes. Comp Sci Technol 1991;40:377–421. [9] Hull D, Clyne TW. An introduction to composite materials. Cambridge, UK: Cambridge University Press, 1996. [10] Jonathan A, Hahn HT. Off-axis fatigue of graphite/ epoxy composite, fatigue of fibrous composite materials, ASTM STP 723. USA: American Society for Testing and Materials, 1981.