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EPOXY composites under static and fatigue loads
Composite Structures 81 (2007) 606–613 www.elsevier.com/locate/compstruct
Behavior of notched and unnotched [0/±30/±60/90]s GFR/EPOXY composites under static and fatigue loads U.A. Khashaba *, A.I. Selmy, I.A. El-Sonbaty, M. Megahed Mechanical Design and Production Engineering Department, Faculty of Engineering, Zagazig University, P.O. Box 44519, Zagazig, Egypt Available online 3 January 2007
Abstract The main objective of the present paper is to study the bending behavior of notched and unnotched angle-ply, [0/±30/±60/90]s, glass fiber reinforced epoxy (GFRE) composites under static and fatigue loads. Static and fatigue bending properties have been determined for notched and unnotched angle-ply specimens. For this purpose different circular notch sizes (2, 4.5, 7, 9 mm) were drilled at the specimen center. Constant-deflection bending fatigue tests were performed at zero mean stress and 25 Hz. A 15% reduction of the initial applied moment was taken as a failure criterion. S–N diagrams for notched GFRE specimens have been constructed based on gross and net cross-section area. The results show that the ultimate bending strength of notched GFRE specimens decreased linearly with increasing notch diameter. Based on gross-section the fatigue life increases with decreasing notch size and the longer fatigue life was for the unnotched specimens. On the other hand, the S–N diagrams based on net-section indicate the insensitivity of angle-ply composites to the notch size. This is considered to be a peculiar phenomenon to composite materials. The results also show that the S–N diagrams have not any fatigue limit rigorous within 107 cycles. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Bending fatigue; Notched and unnotched; Gross-section; Net-section; Angle-ply composites; Glass fiber
1. Introduction The design of composite materials to resist fatigue loads is a complicated problem and a large research effort is being spent on it today. However, there is still a need for extensive experimental testing because numerical simulations of the fatigue damage behavior of fiber-reinforced composites are often found to be unreliable [1]. Drilled holes in composite laminates are necessary to facilitate bolting or riveting to the main load-bearing structures. The demand for improving performance of structural materials in transportation industries, particularly in aircraft, makes fatigue analysis of notched composites as important consideration [2]. Many investigators [3–12] have studied the fatigue behavior of notched fiber reinforced composites. To the author’s knowledge, the effect of using the gross-section *
Corresponding author. Fax: +055 230 4987. E-mail address: [email protected] (U.A. Khashaba).
0263-8223/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruct.2006.11.005
or net-section, in the calculation of the applied stress amplitude, on the fatigue behavior has not yet been reported. Some of these investigators [3–6] do not specify the type of cross-section area (gross or net) that is used in the calculation of notched stress. Many researchers [7–10] calculated the notched stress based on the net -section, while the gross-section was used in calculating the notched stress in Refs. [11,12]. Special attention will be given in this paper to the assessment of the effect of using the gross-section and net-section in the calculation of stress amplitude on the fatigue behavior of notched specimens. Fatigue failure in composite laminates involves combination of several damage modes including matrix cracking, delamination, interfacial debonding and fiber fracture [13]. The order in which each type of damage occurs may vary depending on the constituent materials, material properties, stacking sequence, type of fatigue loading, etc. Chen et al. [14] examined the failure mechanisms of unidirectional glass fiber/polyphenylene sulfide composites in 4-point bending test. They found that the test specimen
U.A. Khashaba et al. / Composite Structures 81 (2007) 606–613
failed either in shear along the neutral plane or bending failure associated with cracks on the compression side between the inner loading points. Choi et al. [15] investigated the flexure-response and fracture behavior of notched unidirectional carbon fiber /Polyamide-6 composite. Four kinds of notch direction were adopted: edgewise notches parallel (L) and transverse (T) to the major direction of fiber bundles and flatwise notches parallel (ZL) and perpendicular (ZT) to this direction. Nominal strength for L and ZL specimens exhibited a high sensitivity to notching. However, T and ZT specimens showed less sensitivity. Palmer et al. [16] investigated the behavior of notched carbon/epoxy composites under tension and bending loads. They found that the strains due to bending were larger at failure than those for pure tension. Several studies show that a larger failure stress (strain) was measured in bending specimens because much less material is under the maximum tension stress [16,17]. Khashaba et al. [2,18–20] extensively studied the behavior of pultruded GFR/polyester composites with different fiber volume fraction subjected to pure bending fatigue loads [18,19], torsion fatigue loads [20], rotating bending fatigue loads [2], and combined (torsion/bending) fatigue loads [20]. Their results show that the S–N diagrams have not any fatigue limit rigorous within 107 cycles. The unidirectional glass fiber reinforced polyester composites have poor torsional fatigue strength compared with the bending fatigue strength. The endurance limit of combined fatigue strength approximately half the fatigue limit of pure bending fatigue strength. The widest scatter was observed at the life range of 105 and 106 cycles. This tendency in the dispersion of fatigue life at varying stress levels is extremely important and deserves much attention for the design and application of GFRP composites. Wang and Shin [21] studied notch fatigue behavior of [0/90]4s AS4/PEEK under different tension–tension cyclic stress levels (65%, 75% and 85% ru). A 6.3 mm diameter central hole was drilled in each specimen. Fatigue tests were terminated at one million cycles if no failure occurred. It was found that even at the lowest stress level of 65%, longitudinal splitting started to appear to the naked eye after 500 cycles. The split length increased quickly in the first 100,000 cycles. Above 500,000 cycles, the split length remained nearly constant with increasing cycle. Jen et al. [3,4] investigated experimentally the initiation and propagation of delamination in centrally notched graphite/epoxy composite laminates subjected to tension and cyclic tension–tension loads. They found that stacking sequence affects the damage initiation and growth in composite laminates, and also may result in different failure modes. The main objective of this work is to investigate the behavior of notched and unnotched angle-ply [0/±30/ ±60/90]s glass fiber reinforced epoxy (GFRE) composites under static and fatigue bending loads. Four point static bending tests will implement to investigate the influence of notch size on bending strength of the composite specimens. Constant-deflection plane bending fatigue tests will
607
carry out on the notched and unnotched composite specimens at zero mean stress and 25 Hz. A 15% reduction of the initial applied moment will be taken as a failure criterion. 2. Experimental work 2.1. Specimen fabrication The angle-ply [0/±30/±60/90]s glass fiber reinforced epoxy (GFRE) composite laminates with 6 ± 0.1 mm thickness were fabricated using hand lay-up technique. The constituent materials of the composite laminates are illustrated in Table 1. The details about the manufacturing technique are illustrated elsewhere [22–24]. Fiber volume fraction (Vf) was determined experimentally by physical removing the matrix using the ignition technique according to ASTM D3171-99. The average value of Vf was 40 ± 0.5%. 2.2. Bending test Bending properties of notched and unnotched angle-ply GFRE composites were determined experimentally using four-point bending test according to JIS K7055. The dimensions of the test specimens are 160 mm length total length, 135 mm span length (L), 6 mm thickness (h), and 19 mm width (w). For notched specimens, circular holes with different sizes (D = 2, 4.5, 7, 9 mm) were drilled at the specimen center. A four-point bending test jig is attached to the grips of the universal testing machine (Testometric 200 kN). The dimensions between the supporting points along the test specimen are illustrated in Fig. 1. The cross-head speed of the loading member was 2 mm/min. Five specimens are tested for each notch size. The strength values are determined based on the average value. The load-displacement diagram are monitored for all test specimens and printed through the PC of the testing machine. The bending fracture strength (rb) was calculated at the fracture load, Pb, as following: rb ¼ P b L=wh2 ¼ P b L=hA
ð1Þ
where ‘‘A’’ is the cross-section area of test specimen; for notched specimens the net-section is A = h(w D), while the gross-section is A = h(w). The bending modulus (Eb) of elasticity was calculated from the slope of the initial linear portion of the loaddeflection diagram, P/d, as following:
Table 1 Composition of GFRP composite laminates Material
Type
Matrix Hardener Reinforcement
Epoxy: araldite LY5138-2 (100 part by weight) HY5138 (23 part by weight) E-roving glass; linear density = 1150 g/Km.
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2.0
0.0
Eb ¼
23 L3 p 108 wh3 d
ð2Þ
2.3. Bending fatigue tests Bending fatigue tests were carried out on constant deflection bending fatigue machine type AVERY 7305. Fig. 2 shows the dimensions of test specimen. Fatigue specimens were cut from the laminate such that the 0° fiber orientation was parallel to the specimen axis. The stress cycles were 1500 CPM (25 HZ) that recommended by the standards, JIS K7119 and ASTM D671-71. The stress ratio (minimum applied stress/maximum applied stress) was equal to ‘‘1’’. This means that mean stress is equal to zero and fatigue tests were performed under reverse loading. Notched fatigue tests were carried out on specimens with different central holes that machined at its center (4.5, 7, 9 mm). Many researchers [2,10,18–20] considered the failure is said to occur when the specimen stiffness reduced to a certain limit, where fatigue cracks does not always result in a complete separation. In the present work, the reduction of the applied moment by 15% of the initial applied value was taken as a failure criterion, ASTM D671-71. Seven specimens are tested for each test conditions and the average life was used to construct the S–N diagram. 3. Results and discussion
0
2
4
6
8
10
D=2
D=7
D = 4.5
1.0 0.5
Fig. 1. Dimensions of 4-point bending test specimen.
Unnotched
1.5
D=9
Load, P, (kN)
2.5
12
Deflection, δ, (mm)
14
16
18
20
Fig. 3. Load-deflection diagrams of notched and unnotched bending specimens.
in this figure represents the movement of the loading member of the testing machine. Fig. 3 shows that the final failure of the bending specimens was catastrophic. This behavior was due to the presence of the unidirectional plies (that have maximum strength than the other layers) at the surfaces of tension and compression sides. Therefore the failure of these layers leads to catastrophic failure. Fig. 3 also shows that as the notch size increases the value of the ultimate load decreases. The bending strength of notched (rN) and unnotched (ro) specimens was calculated from load-deflection curves, Fig. 3, using Eq. (1) and the results are illustrated in Fig. 4. This figure shows the behavior of rN/ro as a function of D/ w for notched specimen. The results in this figure indicate that the net and gross notched strengths decrease, in a linear relationship, with increasing D/w. As expected, the values of notched strength based on the net-section were higher than that of gross-section strength. Decreasing the notched strength with increasing D/w ratio was due to the stress-concentration ahead of the notch as discussed by many investigators [25–28]. Several models have been developed to predict the effect of notches, either circular holes or slits, upon the tensile strength of composites. The notched strength in these models was based on the gross-section [25–28].
3.1. Bending behavior 1.5
Fig. 3 shows the load-deflection diagrams of notched and unnotched 4-point bending specimens. The deflection
Net-Section; N/ o = 1.005 – 1.244(D/w) Gross-Section; N/ o = 1.045 – 0.537(D/w) 1.0 N/ o
o
90
4 holes 7 Dia.
R38
19
17
30
0.5 0o
63 89
Fig. 2. Fatigue test specimen.
0.0 0.0
0.2
0.4
0.6
D/w Fig. 4. Variation of rN/ro vs D/w of angle-ply GFRE composites.
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The apparent bending modulus of elasticity (Eb) for unnotched GFRE composites was calculated from the slope of the initial portion of load-deflection curve, Fig. 3, using Eq. (2). The value of Eb equals 19.61 GPa. 4. Failure mode of GFR/Epoxy specimens in bending
Fig. 6. Failure modes of notched specimen.
concentrated near the boundary of the hole than in case of large hole [25–28]. 4.1. Fatigue behavior Fig. 7 shows the S–N diagram of unnotched GFRE specimens. The ordinate denotes the initial stress applied while the abscissa denotes the fatigue life (number cycles to failure, Nf). The experimental results were curve fitted by the Power function. Although this function has been extensively used for constructing the S–N diagrams for metallic materials, it is also used by many investigators [2,5,18,19] for presenting the S–N diagrams of polymeric composite materials. Figs. 8–10 show the S–N diagrams of GFRE specimens with different notch sizes, D = 4.5, 7, and 9 mm, respectively. The stresses in these figures are calculated based on the gross-section and net-section.
Initial stress amplitude (MPa)
(i) Unnotched Specimens Fig. 5 shows the failure modes of unnotched specimens. The failure was initiated in the tension side with inclined cracks accompanied with delamination at the outer layers, Fig. 5a. An erratic crack initiated at the midspan of the compression side and propagated by an angle towards the edges of the specimen, Fig. 5b. Most of GFRE specimens were failed due to the failure of tension side at its midspan, Fig. 5c, while few specimens failed due to interlaminar shear resulting in delamination between the layers, Fig. 5d. (ii) Notched Specimens Fig. 6 shows the failure modes of GFRE specimens with different notch sizes. The specimens with different notch sizes approximately failed in the same manner. The failure was initiated at the tension side with an inclined crack initiated ahead of the hole and propagated to the free edges of the specimen, Fig. 6a and b. This inclined crack is accompanied by delamination occurred around the hole. Some of the notched specimens have delamination extended longitudinally parallel to the specimen edge, Fig. 6b and c. The delamination size around the hole was decreased with increasing notch size, Fig. 6d. This result was due to the stress in case of small hole is considerably high and more
150 a
= 188.44(Nf)-0.06
120
90
60
30
10 3
10 4
10 5
10 6
10 7
10 8
Nf
Fig. 5. Failure modes of unnotched specimen.
Fig. 7. S–N curve for unnotched specimens.
150
Initial stress amplitude (MPa)
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Net-Section; a = 158.62(Nf)-0.04 Gross-Section; a = 119.84(Nf)-0.039
120
90
60
30
10 3
10 4
10 5 Nf
10 6
10 7
10 8
Initial stress amplitude (MPa)
Fig. 8. S–N curve for notched specimens, D = 4.5 mm.
150
Unnotched D = 4.5 mm D = 7 mm D= 9 mm
110
70
30 3 10
10 4
10 5
Nf
10 6
10 7
10 8
Fig. 11. S–N diagrams for unnotched and notched specimens based on gross-section stress.
180 150
Net-Section; a = 200.13(Nf)-0.058 Gross-Section; a = 121.9(Nf)-0.056
120 90 60 30
10 3
10 4
10 5 Nf
10 6
10 7
10 8
Fig. 9. S–N curve for notched specimens, D = 7 mm.
Initial stress amplitude (MPa)
Initial stress amplitude (MPa)
610
150
Unnotched D = 4.5 mm D = 7 mm D= 9 mm
110
70 a
30 3 10
4
10
= 176.3(Nf)-0.05
10
5
10
6
10
7
10
8
Nf
Initial stress amplitude (MPa)
Fig. 12. S–N diagrams for unnotched and notched specimens based on net-section stress. 150
Net-Section; a = 181.67(Nf)-0.049 Gross-Section; a = 88.25(Nf)-0.034
120 90 60 30 10 3
10 4
105
106
107
108
Nf Fig. 10. S–N curve for notched specimens, D = 9 mm.
The results in these figures show that, for the same number of cycles the stress amplitude based on net-section is higher than that based on gross-section. The results also show that the S–N diagrams have not any fatigue limit rigorous within 107. In practice the gross stress is useful for simulating the behavior of composite materials after damaging by impact loads. While net-section stress is used for calculating the bolted joint strength especially for net tension failure mode. Therefore a fruitful comparison was made, using the data in Figs. 7–10, to illustrate the effect of notch size on the fatigue life of GFRE composites based on gross-section and net-section stresses. Fig. 11 shows the effect of notch size on S–N diagrams of GFRE composites based on gross-section. The results in this figure indicate that at the same initial stress ampli-
tude fatigue life increases with decreasing notch size and the longer fatigue life was for the unnotched specimens. Fig. 12 illustrates the effect of notch size on S–N diagrams of GFRE composites. The stresses in this figure are calculated based on the net-section of the test specimen. The results in this figure indicate that fatigue life of angleply [0/±30/±60/90]s composites are insensitive to notch size. This is considered to be a peculiar phenomenon to composite materials. Similar results were found in Refs. [8,10,29,30]. During the manufacturing of the composite laminates the generated temperature (more than 150 °C) left residual stresses. These thermal stresses, macroscopically, are responsible for dimensional change, part warpage, and delamination. Microscopically, they can cause microcracking and fiber breakage, all of which affect a composite’s mechanical performance [31]. Machining holes cause relief to the thermal stresses through microcracks at the hole boundary resulting in improving fatigue properties. The improvement due to machining holes may compensate the stress concentration ahead of the hole and the final results show an insignificant effect of the hole size on the fatigue life based on net-section stress. In additions, Tanimoto and Amijima [29] show that the static strength of GFRP after cyclic loading to N/Nf = 0.02 retains the original value in spite of many cracks occurring in the specimen. Sturgeon [30] has pointed out that the residual static strength of carbon fiber reinforced plastics subjected to
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cyclic load to moderate number of cycles is greater than that of virgin material. They attributed this behavior to the presence of large number of cracks formed in the resin phase after a few cycles that leads to relieving the local high stress concentration without a loss in the strength of composite materials. 4.1.1. Failure mode of fatigue specimens The damage related to 15% reduction in the stiffness of fatigue specimens was visible at the specimen center and has the same general appearance on both surfaces. The following sub-sections illustrate the failure of unnotched and notched specimens. (i) Unnotched Specimens The failure of the specimens (15% stiffness reduction) that tested at low stress level (rmax = 73.63 MPa) was due to matrix cracking, debonding between fibers/matrix interfaces, and edge delamination. Delamination was observed at the edges of specimen waist, after certain number of cycles depending on the stress amplitude, due to the machining process that left short discontinuous fibers. Matrix cracking at the free end of machined fibers was initiated and propagated along fiber-matrix interface resulting in fiber depending followed by edge delamination. No visible transverse cracks were observed on the surfaces, Fig. 13a. The different elastic properties of the adjacent layers result in interlaminar shear stresses followed by delaminations of the outer layers that have maximum stress compared with the inner layers. These delaminations were clearly observed when testing at high stress amplitude, Fig. 13b. Specimens that tested at a high stress amplitude failed due to transverse visible cracks at the specimen waist, delamination the longitudinal layers (top and bottom layers), and complete fracture of the delaminated layers, Fig. 13b. (ii) Notched Specimens Fig. 14 shows photographs of some failed GFRE specimens with different notched sizes subjected to low stress amplitudes. The delaminations in these specimens are not only around the notches but also at the specimen edges. The failure of the specimens was initiated with matrix microcracking, these cracks were extended to fiber/matrix interface leading to debonding between them. The specimens with small notch diameter (D = 4.5 mm) have excessive delaminations compared with the other notch sizes
Fig. 14. Failure modes of notched specimens tested at a low stress amplitude.
(D = 7 and 9 mm). This behavior because, at the same number of cycles, specimens with small notch size subjected to higher stress amplitude compared with specimens that have a large notch size, Fig. 11. Fig. 15 shows the photographs of some failed GFRE specimens with different notched sizes subjected to high stress amplitudes. The failure of the test specimens was due to transverse cracks in the outer layers. The specimens with maximum notch diameter (D = 9 mm) have longitudinal cracks parallel to the fibers in the outer layer. No delamination was observed at the edges of GFRE specimens with different notch sizes.
Fig. 13. Failure modes of unnotched specimens tested at (a) rmax = 73.63 MPa and (b) rmax = 107.5 MPa.
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imens. The failure of tension side, of the static bending specimens, is the responsible for the complete fracture of the specimens. Few specimens were failed due to interlaminar shear stress associated with visible delamination between the layers. The failure modes of fatigue specimens significantly depend on stress amplitude, and notch size. The complete fracture of test specimens was not observed in all fatigue tests, while the delaminated outer layers are completely failed at high stress amplitudes. Acknowledgements The authors acknowledge the financial support of Dr. F. El-Refaie, President of Academy of Scientific Research and Technology, Egypt. Where the composite laminated are prepared from the budget of US–Egypt Joint Science and Technology Program. References
Fig. 15. Failure modes of notched specimens tested at high stress amplitude.
5. Conclusions The failure of angle-ply, [0/±30/±60/90]s, composite specimens under static bending loads was catastrophic due to the presence of the unidirectional plies (that have maximum strength) at the outer surfaces of the specimen (tension and compression sides). Therefore, the failure of the unidirectional layers leads to a sudden failure to the specimen. The normalized notched strength (rN/ro) based on net-section and gross-section decreases in a linear relationship with increasing D/w ratio. The values of notched strength based on the net-section were higher than that of gross-section strength. For the same initial stress amplitude, based on gross-section, the fatigue life increases with decreasing notch size and the longer fatigue life was for the unnotched specimens. In contrast the S–N diagram, based on the net-section, indicates that the fatigue life of angle-ply [0/±30/ ±60/90]s composites is insensitive to notch size. This is considered to be a peculiar phenomenon to composite materials. The results also show that the S–N diagrams have not any fatigue limit rigorous within 107 cycles. Failure modes of static and fatigue bending specimens were examined with the aids of photographs of failed spec-
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Behavior of notched and unnotched [0/±30/±60/90]s GFR/EPOXY composites under static and fatigue loads U.A. Khashaba *, A.I. Selmy, I.A. El-Sonbaty, M. Megahed Mechanical Design and Production Engineering Department, Faculty of Engineering, Zagazig University, P.O. Box 44519, Zagazig, Egypt Available online 3 January 2007
Abstract The main objective of the present paper is to study the bending behavior of notched and unnotched angle-ply, [0/±30/±60/90]s, glass fiber reinforced epoxy (GFRE) composites under static and fatigue loads. Static and fatigue bending properties have been determined for notched and unnotched angle-ply specimens. For this purpose different circular notch sizes (2, 4.5, 7, 9 mm) were drilled at the specimen center. Constant-deflection bending fatigue tests were performed at zero mean stress and 25 Hz. A 15% reduction of the initial applied moment was taken as a failure criterion. S–N diagrams for notched GFRE specimens have been constructed based on gross and net cross-section area. The results show that the ultimate bending strength of notched GFRE specimens decreased linearly with increasing notch diameter. Based on gross-section the fatigue life increases with decreasing notch size and the longer fatigue life was for the unnotched specimens. On the other hand, the S–N diagrams based on net-section indicate the insensitivity of angle-ply composites to the notch size. This is considered to be a peculiar phenomenon to composite materials. The results also show that the S–N diagrams have not any fatigue limit rigorous within 107 cycles. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Bending fatigue; Notched and unnotched; Gross-section; Net-section; Angle-ply composites; Glass fiber
1. Introduction The design of composite materials to resist fatigue loads is a complicated problem and a large research effort is being spent on it today. However, there is still a need for extensive experimental testing because numerical simulations of the fatigue damage behavior of fiber-reinforced composites are often found to be unreliable [1]. Drilled holes in composite laminates are necessary to facilitate bolting or riveting to the main load-bearing structures. The demand for improving performance of structural materials in transportation industries, particularly in aircraft, makes fatigue analysis of notched composites as important consideration [2]. Many investigators [3–12] have studied the fatigue behavior of notched fiber reinforced composites. To the author’s knowledge, the effect of using the gross-section *
Corresponding author. Fax: +055 230 4987. E-mail address: [email protected] (U.A. Khashaba).
0263-8223/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruct.2006.11.005
or net-section, in the calculation of the applied stress amplitude, on the fatigue behavior has not yet been reported. Some of these investigators [3–6] do not specify the type of cross-section area (gross or net) that is used in the calculation of notched stress. Many researchers [7–10] calculated the notched stress based on the net -section, while the gross-section was used in calculating the notched stress in Refs. [11,12]. Special attention will be given in this paper to the assessment of the effect of using the gross-section and net-section in the calculation of stress amplitude on the fatigue behavior of notched specimens. Fatigue failure in composite laminates involves combination of several damage modes including matrix cracking, delamination, interfacial debonding and fiber fracture [13]. The order in which each type of damage occurs may vary depending on the constituent materials, material properties, stacking sequence, type of fatigue loading, etc. Chen et al. [14] examined the failure mechanisms of unidirectional glass fiber/polyphenylene sulfide composites in 4-point bending test. They found that the test specimen
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failed either in shear along the neutral plane or bending failure associated with cracks on the compression side between the inner loading points. Choi et al. [15] investigated the flexure-response and fracture behavior of notched unidirectional carbon fiber /Polyamide-6 composite. Four kinds of notch direction were adopted: edgewise notches parallel (L) and transverse (T) to the major direction of fiber bundles and flatwise notches parallel (ZL) and perpendicular (ZT) to this direction. Nominal strength for L and ZL specimens exhibited a high sensitivity to notching. However, T and ZT specimens showed less sensitivity. Palmer et al. [16] investigated the behavior of notched carbon/epoxy composites under tension and bending loads. They found that the strains due to bending were larger at failure than those for pure tension. Several studies show that a larger failure stress (strain) was measured in bending specimens because much less material is under the maximum tension stress [16,17]. Khashaba et al. [2,18–20] extensively studied the behavior of pultruded GFR/polyester composites with different fiber volume fraction subjected to pure bending fatigue loads [18,19], torsion fatigue loads [20], rotating bending fatigue loads [2], and combined (torsion/bending) fatigue loads [20]. Their results show that the S–N diagrams have not any fatigue limit rigorous within 107 cycles. The unidirectional glass fiber reinforced polyester composites have poor torsional fatigue strength compared with the bending fatigue strength. The endurance limit of combined fatigue strength approximately half the fatigue limit of pure bending fatigue strength. The widest scatter was observed at the life range of 105 and 106 cycles. This tendency in the dispersion of fatigue life at varying stress levels is extremely important and deserves much attention for the design and application of GFRP composites. Wang and Shin [21] studied notch fatigue behavior of [0/90]4s AS4/PEEK under different tension–tension cyclic stress levels (65%, 75% and 85% ru). A 6.3 mm diameter central hole was drilled in each specimen. Fatigue tests were terminated at one million cycles if no failure occurred. It was found that even at the lowest stress level of 65%, longitudinal splitting started to appear to the naked eye after 500 cycles. The split length increased quickly in the first 100,000 cycles. Above 500,000 cycles, the split length remained nearly constant with increasing cycle. Jen et al. [3,4] investigated experimentally the initiation and propagation of delamination in centrally notched graphite/epoxy composite laminates subjected to tension and cyclic tension–tension loads. They found that stacking sequence affects the damage initiation and growth in composite laminates, and also may result in different failure modes. The main objective of this work is to investigate the behavior of notched and unnotched angle-ply [0/±30/ ±60/90]s glass fiber reinforced epoxy (GFRE) composites under static and fatigue bending loads. Four point static bending tests will implement to investigate the influence of notch size on bending strength of the composite specimens. Constant-deflection plane bending fatigue tests will
607
carry out on the notched and unnotched composite specimens at zero mean stress and 25 Hz. A 15% reduction of the initial applied moment will be taken as a failure criterion. 2. Experimental work 2.1. Specimen fabrication The angle-ply [0/±30/±60/90]s glass fiber reinforced epoxy (GFRE) composite laminates with 6 ± 0.1 mm thickness were fabricated using hand lay-up technique. The constituent materials of the composite laminates are illustrated in Table 1. The details about the manufacturing technique are illustrated elsewhere [22–24]. Fiber volume fraction (Vf) was determined experimentally by physical removing the matrix using the ignition technique according to ASTM D3171-99. The average value of Vf was 40 ± 0.5%. 2.2. Bending test Bending properties of notched and unnotched angle-ply GFRE composites were determined experimentally using four-point bending test according to JIS K7055. The dimensions of the test specimens are 160 mm length total length, 135 mm span length (L), 6 mm thickness (h), and 19 mm width (w). For notched specimens, circular holes with different sizes (D = 2, 4.5, 7, 9 mm) were drilled at the specimen center. A four-point bending test jig is attached to the grips of the universal testing machine (Testometric 200 kN). The dimensions between the supporting points along the test specimen are illustrated in Fig. 1. The cross-head speed of the loading member was 2 mm/min. Five specimens are tested for each notch size. The strength values are determined based on the average value. The load-displacement diagram are monitored for all test specimens and printed through the PC of the testing machine. The bending fracture strength (rb) was calculated at the fracture load, Pb, as following: rb ¼ P b L=wh2 ¼ P b L=hA
ð1Þ
where ‘‘A’’ is the cross-section area of test specimen; for notched specimens the net-section is A = h(w D), while the gross-section is A = h(w). The bending modulus (Eb) of elasticity was calculated from the slope of the initial linear portion of the loaddeflection diagram, P/d, as following:
Table 1 Composition of GFRP composite laminates Material
Type
Matrix Hardener Reinforcement
Epoxy: araldite LY5138-2 (100 part by weight) HY5138 (23 part by weight) E-roving glass; linear density = 1150 g/Km.
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2.0
0.0
Eb ¼
23 L3 p 108 wh3 d
ð2Þ
2.3. Bending fatigue tests Bending fatigue tests were carried out on constant deflection bending fatigue machine type AVERY 7305. Fig. 2 shows the dimensions of test specimen. Fatigue specimens were cut from the laminate such that the 0° fiber orientation was parallel to the specimen axis. The stress cycles were 1500 CPM (25 HZ) that recommended by the standards, JIS K7119 and ASTM D671-71. The stress ratio (minimum applied stress/maximum applied stress) was equal to ‘‘1’’. This means that mean stress is equal to zero and fatigue tests were performed under reverse loading. Notched fatigue tests were carried out on specimens with different central holes that machined at its center (4.5, 7, 9 mm). Many researchers [2,10,18–20] considered the failure is said to occur when the specimen stiffness reduced to a certain limit, where fatigue cracks does not always result in a complete separation. In the present work, the reduction of the applied moment by 15% of the initial applied value was taken as a failure criterion, ASTM D671-71. Seven specimens are tested for each test conditions and the average life was used to construct the S–N diagram. 3. Results and discussion
0
2
4
6
8
10
D=2
D=7
D = 4.5
1.0 0.5
Fig. 1. Dimensions of 4-point bending test specimen.
Unnotched
1.5
D=9
Load, P, (kN)
2.5
12
Deflection, δ, (mm)
14
16
18
20
Fig. 3. Load-deflection diagrams of notched and unnotched bending specimens.
in this figure represents the movement of the loading member of the testing machine. Fig. 3 shows that the final failure of the bending specimens was catastrophic. This behavior was due to the presence of the unidirectional plies (that have maximum strength than the other layers) at the surfaces of tension and compression sides. Therefore the failure of these layers leads to catastrophic failure. Fig. 3 also shows that as the notch size increases the value of the ultimate load decreases. The bending strength of notched (rN) and unnotched (ro) specimens was calculated from load-deflection curves, Fig. 3, using Eq. (1) and the results are illustrated in Fig. 4. This figure shows the behavior of rN/ro as a function of D/ w for notched specimen. The results in this figure indicate that the net and gross notched strengths decrease, in a linear relationship, with increasing D/w. As expected, the values of notched strength based on the net-section were higher than that of gross-section strength. Decreasing the notched strength with increasing D/w ratio was due to the stress-concentration ahead of the notch as discussed by many investigators [25–28]. Several models have been developed to predict the effect of notches, either circular holes or slits, upon the tensile strength of composites. The notched strength in these models was based on the gross-section [25–28].
3.1. Bending behavior 1.5
Fig. 3 shows the load-deflection diagrams of notched and unnotched 4-point bending specimens. The deflection
Net-Section; N/ o = 1.005 – 1.244(D/w) Gross-Section; N/ o = 1.045 – 0.537(D/w) 1.0 N/ o
o
90
4 holes 7 Dia.
R38
19
17
30
0.5 0o
63 89
Fig. 2. Fatigue test specimen.
0.0 0.0
0.2
0.4
0.6
D/w Fig. 4. Variation of rN/ro vs D/w of angle-ply GFRE composites.
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The apparent bending modulus of elasticity (Eb) for unnotched GFRE composites was calculated from the slope of the initial portion of load-deflection curve, Fig. 3, using Eq. (2). The value of Eb equals 19.61 GPa. 4. Failure mode of GFR/Epoxy specimens in bending
Fig. 6. Failure modes of notched specimen.
concentrated near the boundary of the hole than in case of large hole [25–28]. 4.1. Fatigue behavior Fig. 7 shows the S–N diagram of unnotched GFRE specimens. The ordinate denotes the initial stress applied while the abscissa denotes the fatigue life (number cycles to failure, Nf). The experimental results were curve fitted by the Power function. Although this function has been extensively used for constructing the S–N diagrams for metallic materials, it is also used by many investigators [2,5,18,19] for presenting the S–N diagrams of polymeric composite materials. Figs. 8–10 show the S–N diagrams of GFRE specimens with different notch sizes, D = 4.5, 7, and 9 mm, respectively. The stresses in these figures are calculated based on the gross-section and net-section.
Initial stress amplitude (MPa)
(i) Unnotched Specimens Fig. 5 shows the failure modes of unnotched specimens. The failure was initiated in the tension side with inclined cracks accompanied with delamination at the outer layers, Fig. 5a. An erratic crack initiated at the midspan of the compression side and propagated by an angle towards the edges of the specimen, Fig. 5b. Most of GFRE specimens were failed due to the failure of tension side at its midspan, Fig. 5c, while few specimens failed due to interlaminar shear resulting in delamination between the layers, Fig. 5d. (ii) Notched Specimens Fig. 6 shows the failure modes of GFRE specimens with different notch sizes. The specimens with different notch sizes approximately failed in the same manner. The failure was initiated at the tension side with an inclined crack initiated ahead of the hole and propagated to the free edges of the specimen, Fig. 6a and b. This inclined crack is accompanied by delamination occurred around the hole. Some of the notched specimens have delamination extended longitudinally parallel to the specimen edge, Fig. 6b and c. The delamination size around the hole was decreased with increasing notch size, Fig. 6d. This result was due to the stress in case of small hole is considerably high and more
150 a
= 188.44(Nf)-0.06
120
90
60
30
10 3
10 4
10 5
10 6
10 7
10 8
Nf
Fig. 5. Failure modes of unnotched specimen.
Fig. 7. S–N curve for unnotched specimens.
150
Initial stress amplitude (MPa)
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Net-Section; a = 158.62(Nf)-0.04 Gross-Section; a = 119.84(Nf)-0.039
120
90
60
30
10 3
10 4
10 5 Nf
10 6
10 7
10 8
Initial stress amplitude (MPa)
Fig. 8. S–N curve for notched specimens, D = 4.5 mm.
150
Unnotched D = 4.5 mm D = 7 mm D= 9 mm
110
70
30 3 10
10 4
10 5
Nf
10 6
10 7
10 8
Fig. 11. S–N diagrams for unnotched and notched specimens based on gross-section stress.
180 150
Net-Section; a = 200.13(Nf)-0.058 Gross-Section; a = 121.9(Nf)-0.056
120 90 60 30
10 3
10 4
10 5 Nf
10 6
10 7
10 8
Fig. 9. S–N curve for notched specimens, D = 7 mm.
Initial stress amplitude (MPa)
Initial stress amplitude (MPa)
610
150
Unnotched D = 4.5 mm D = 7 mm D= 9 mm
110
70 a
30 3 10
4
10
= 176.3(Nf)-0.05
10
5
10
6
10
7
10
8
Nf
Initial stress amplitude (MPa)
Fig. 12. S–N diagrams for unnotched and notched specimens based on net-section stress. 150
Net-Section; a = 181.67(Nf)-0.049 Gross-Section; a = 88.25(Nf)-0.034
120 90 60 30 10 3
10 4
105
106
107
108
Nf Fig. 10. S–N curve for notched specimens, D = 9 mm.
The results in these figures show that, for the same number of cycles the stress amplitude based on net-section is higher than that based on gross-section. The results also show that the S–N diagrams have not any fatigue limit rigorous within 107. In practice the gross stress is useful for simulating the behavior of composite materials after damaging by impact loads. While net-section stress is used for calculating the bolted joint strength especially for net tension failure mode. Therefore a fruitful comparison was made, using the data in Figs. 7–10, to illustrate the effect of notch size on the fatigue life of GFRE composites based on gross-section and net-section stresses. Fig. 11 shows the effect of notch size on S–N diagrams of GFRE composites based on gross-section. The results in this figure indicate that at the same initial stress ampli-
tude fatigue life increases with decreasing notch size and the longer fatigue life was for the unnotched specimens. Fig. 12 illustrates the effect of notch size on S–N diagrams of GFRE composites. The stresses in this figure are calculated based on the net-section of the test specimen. The results in this figure indicate that fatigue life of angleply [0/±30/±60/90]s composites are insensitive to notch size. This is considered to be a peculiar phenomenon to composite materials. Similar results were found in Refs. [8,10,29,30]. During the manufacturing of the composite laminates the generated temperature (more than 150 °C) left residual stresses. These thermal stresses, macroscopically, are responsible for dimensional change, part warpage, and delamination. Microscopically, they can cause microcracking and fiber breakage, all of which affect a composite’s mechanical performance [31]. Machining holes cause relief to the thermal stresses through microcracks at the hole boundary resulting in improving fatigue properties. The improvement due to machining holes may compensate the stress concentration ahead of the hole and the final results show an insignificant effect of the hole size on the fatigue life based on net-section stress. In additions, Tanimoto and Amijima [29] show that the static strength of GFRP after cyclic loading to N/Nf = 0.02 retains the original value in spite of many cracks occurring in the specimen. Sturgeon [30] has pointed out that the residual static strength of carbon fiber reinforced plastics subjected to
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cyclic load to moderate number of cycles is greater than that of virgin material. They attributed this behavior to the presence of large number of cracks formed in the resin phase after a few cycles that leads to relieving the local high stress concentration without a loss in the strength of composite materials. 4.1.1. Failure mode of fatigue specimens The damage related to 15% reduction in the stiffness of fatigue specimens was visible at the specimen center and has the same general appearance on both surfaces. The following sub-sections illustrate the failure of unnotched and notched specimens. (i) Unnotched Specimens The failure of the specimens (15% stiffness reduction) that tested at low stress level (rmax = 73.63 MPa) was due to matrix cracking, debonding between fibers/matrix interfaces, and edge delamination. Delamination was observed at the edges of specimen waist, after certain number of cycles depending on the stress amplitude, due to the machining process that left short discontinuous fibers. Matrix cracking at the free end of machined fibers was initiated and propagated along fiber-matrix interface resulting in fiber depending followed by edge delamination. No visible transverse cracks were observed on the surfaces, Fig. 13a. The different elastic properties of the adjacent layers result in interlaminar shear stresses followed by delaminations of the outer layers that have maximum stress compared with the inner layers. These delaminations were clearly observed when testing at high stress amplitude, Fig. 13b. Specimens that tested at a high stress amplitude failed due to transverse visible cracks at the specimen waist, delamination the longitudinal layers (top and bottom layers), and complete fracture of the delaminated layers, Fig. 13b. (ii) Notched Specimens Fig. 14 shows photographs of some failed GFRE specimens with different notched sizes subjected to low stress amplitudes. The delaminations in these specimens are not only around the notches but also at the specimen edges. The failure of the specimens was initiated with matrix microcracking, these cracks were extended to fiber/matrix interface leading to debonding between them. The specimens with small notch diameter (D = 4.5 mm) have excessive delaminations compared with the other notch sizes
Fig. 14. Failure modes of notched specimens tested at a low stress amplitude.
(D = 7 and 9 mm). This behavior because, at the same number of cycles, specimens with small notch size subjected to higher stress amplitude compared with specimens that have a large notch size, Fig. 11. Fig. 15 shows the photographs of some failed GFRE specimens with different notched sizes subjected to high stress amplitudes. The failure of the test specimens was due to transverse cracks in the outer layers. The specimens with maximum notch diameter (D = 9 mm) have longitudinal cracks parallel to the fibers in the outer layer. No delamination was observed at the edges of GFRE specimens with different notch sizes.
Fig. 13. Failure modes of unnotched specimens tested at (a) rmax = 73.63 MPa and (b) rmax = 107.5 MPa.
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imens. The failure of tension side, of the static bending specimens, is the responsible for the complete fracture of the specimens. Few specimens were failed due to interlaminar shear stress associated with visible delamination between the layers. The failure modes of fatigue specimens significantly depend on stress amplitude, and notch size. The complete fracture of test specimens was not observed in all fatigue tests, while the delaminated outer layers are completely failed at high stress amplitudes. Acknowledgements The authors acknowledge the financial support of Dr. F. El-Refaie, President of Academy of Scientific Research and Technology, Egypt. Where the composite laminated are prepared from the budget of US–Egypt Joint Science and Technology Program. References
Fig. 15. Failure modes of notched specimens tested at high stress amplitude.
5. Conclusions The failure of angle-ply, [0/±30/±60/90]s, composite specimens under static bending loads was catastrophic due to the presence of the unidirectional plies (that have maximum strength) at the outer surfaces of the specimen (tension and compression sides). Therefore, the failure of the unidirectional layers leads to a sudden failure to the specimen. The normalized notched strength (rN/ro) based on net-section and gross-section decreases in a linear relationship with increasing D/w ratio. The values of notched strength based on the net-section were higher than that of gross-section strength. For the same initial stress amplitude, based on gross-section, the fatigue life increases with decreasing notch size and the longer fatigue life was for the unnotched specimens. In contrast the S–N diagram, based on the net-section, indicates that the fatigue life of angle-ply [0/±30/ ±60/90]s composites is insensitive to notch size. This is considered to be a peculiar phenomenon to composite materials. The results also show that the S–N diagrams have not any fatigue limit rigorous within 107 cycles. Failure modes of static and fatigue bending specimens were examined with the aids of photographs of failed spec-
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