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0° crack interface
Materials Science and Engineering A 529 (2011) 265–269
Contents lists available at SciVerse ScienceDirect
Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea
Effect of stacking sequence on R-curve behavior of glass/epoxy DCB laminates with 0◦ //0◦ crack interface M.M. Shokrieh ∗ , M. Heidari-Rarani Composites Research Laboratory, Center of Excellence in Experimental Solid Mechanics and Dynamics, School of Mechanical Engineering, Iran University of Science and Technology (IUST), Tehran 16846-13114, Iran
a r t i c l e
i n f o
Article history: Received 4 July 2011 Received in revised form 7 September 2011 Accepted 8 September 2011 Available online 16 September 2011 Keywords: Delamination toughness R-curve Multidirectional DCB
a b s t r a c t In this study, the influence of stacking sequence on mode I delamination resistance (R-curve) behavior of E-glass/epoxy laminated composites with an initial delamination between 0◦ //0◦ interface is experimentally investigated. To this end, symmetric double cantilever beam (DCB) specimens of stacking sequences; [0◦ 12 ]s , [(0◦ /90◦ )3 ]2s and [0◦ /90◦ / ± 45◦ /90◦ /0◦ ]2s with two initial crack lengths are used. A pronounced R-curve behavior is observed on all stacking sequences due to locating delamination between two similar layers. Comparison of R-curve behavior of cross-ply and quasi-isotropic DCB specimens with unidirectional (UD) one reveals the significant effect of the non-dimensional coupling parame2 ter, Dc = D12 /D11 D22 , on the R-curves. Thus, three main outputs of R-curves could be summarized as; (a) the initiation delamination toughness (GIc-init ) of multidirectional (MD) laminates are much lower than that of UD one, (b) stacking sequence has no effect on the fiber bridging length in DCB specimens, and (c) the greater the Dc value of a laminate, the higher the steady-state propagation toughness (GIc-prop ) is. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Delamination is a typical fracture mechanism in fiber reinforced composite laminates occurs due to low interlaminar strength. Some well-known sources of delamination under different loadings are free edges, cut out, low-velocity impact and fabrication defects. These damages may considerably reduce the global stiffness and strength and then leads to a catastrophic structure failure. Therefore, characterization of delamination resistance based on the fracture mechanics is of great importance in engineering design. Over the last two decades, much attention has been devoted to the mode I delamination. The double cantilever beam (DCB) is commonly used for this purpose. All these efforts have led to the establishment of standard test methods for mode I [1,2], which concern only mode I delamination initiation for unidirectional (UD) composites [3], while laminates widely used in industrial applications are multidirectional (MD). Comprehensive reviews by Andersons and König [4], Tay [5] and Brunner et al. [6], concerning delamination onset and growth in laminated composites under various mode loadings, show the importance of delamination behavior of MD laminates. Also, extensive researches have been recently carried out to characterize the mode I interlaminar fracture
∗ Corresponding author. Tel.: +98 21 77240540, fax: +98 21 77491206. E-mail address: [email protected] (M.M. Shokrieh). 0921-5093/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2011.09.027
toughness of laminated composites with delaminating interfaces such as 0◦ //0◦ , 0◦ // ◦ , ◦ // ◦ and ◦ //− ◦ [7–13]. It is currently believed [12–14] that initiation fracture toughness (GIc ) is a material property, i.e., the critical energy release rate is independent of the specimen size and delamination length. Whereas in the case of large-scale bridging, Suo et al. [15] and Jacobsen and Sørensen [16,17] have shown that the delamination resistance (R-curve) is not only a material property but also is dependent on the specimen geometry. The effect of bridging fibers on the interlaminar fracture toughness is quantitatively investigated by cutting the bridging fibers by de Moura et al. [18]. It was found that interlaminar fracture toughness without fiber-bridging has a constant value during the crack propagation. However, if the fiber-bridging occurs in the wake of delamination front, the strain energy release rate is no longer a constant value and rises with increasing the delamination length. Therefore, as well as the initiation fracture toughness, the other two parameters, i.e., the fiber-bridging zone and steady-state delamination toughness, or generally R-curve behavior is important in order to accurately predict the response of fiber-reinforced composites during the damage propagation. From the above literature, it is found that the R-curve effects are pronounced in laminated composites and most of these researches are related to resistance behavior of laminated composites with a special initial crack length (a0 ) and different delaminating interfaces. Therefore, the influence of stacking sequence on the R-curve
266
M.M. Shokrieh, M. Heidari-Rarani / Materials Science and Engineering A 529 (2011) 265–269
Table 1 Mechanical properties of unidirectional E-glass/ML-506 epoxy.
illumination is used under the specimen to better detection of the crack tip. Three tests are carried out for each initial crack length in order to check the repeatability of the results.
E1 (GPa)
E2 (GPa)
12
G12 (GPa)
Efx (GPa)
33.5 (±1.3)
10.23 (±0.83)
0.27 (±0.01)
4.26 (±0.45)
29.54 (± 1.1)
2.2. Test procedure behavior of a symmetric glass/epoxy composite with 0◦ //0◦ crack interface is investigated in present study. Due to specimen dependency of R-curve [7], the DCB specimen geometry (i.e., overall length, width and thickness) and the initial crack length are supposed to be constant. Also, the 0◦ //0◦ delaminating interface is selected to prevent deviation of initial crack from the mid-plane and propagation in a zigzag fashion. Pereira et al. [11] showed that the intra-ply damage causes the GIc values of MD-DCB specimens with different delaminating interface to be 3–4 times higher than those of unidirectional [0◦ ]n specimens. 2. Experimental procedure 2.1. Materials and specimen preparation Twenty-four plied DCB test specimens of [0◦ ]24 (LS1), (LS2) and [0◦ /90◦ / ± 45◦ /90◦ /0◦ ]2s (LS3) stacking sequences are fabricated from E-glass/epoxy by hand lay-up method. E-glass quasi-unidirectional fabric with 5% fiber in the 90◦ direction of density 2.564 g/cm3 and ML-506 epoxy resin based on bisphenol F of density 1.11 g/cm3 with a polyamine hardener (HA-12) which are produced by Mokarrar Industrial Group (Iran) are used. The laminates are cured at the room temperature for 7 days followed by post-curing at 80 ◦ C for 2 h. Average fiber volume fraction is obtained 47.5% from the burn-out test of DCB specimens. In-plane mechanical properties of glass/epoxy laminates are reported in Table 1. The above stacking sequences are selected to result in a desirable crack propagation behavior, i.e., there is no change of delamination plane and an acceptable crack front profile. Table 2 shows the features of LS1, LS2 and LS3 laminates. Effective flexural modulus (Efx ) is calculated by the classical lamination theory (CLT) [19]: [(0◦ /90◦ )3 ]2s
Efx =
−1 12 , [d] = ([D] − [B][A]−1 [B]) d11 h3
(1)
where [A], [B] and [D] are the extensional, coupling and bending stiffness of a laminate. In Table 2, the Dc indicates the curvature due to the longitudinal-transverse bending coupling, which is intro2 /D D duced by Davidson [20] and defined as Dc = D12 11 22 where Dij are components of the bending stiffness matrix. In the mentioned laminates, the initial crack is located at the mid-plane and is made by inserting a Teflon film of thickness of 20 m. Using a diamond saw, DCB test specimens are cut from the center plates, with a width of b = 25 mm, a total length of L = 150 mm and the initial crack lengths of a0 = 35 and 55 ± 0.2 mm. Specimen edges are sanded to remove imperfections that may interfere with the crack growth or a clear image of the crack tip position. The aluminum piano hinges are adhesively bonded to the ends of specimen arms to provide the loading points. A measurement scale with 1 mm divisions is attached to the lower edge of the specimen for measuring the crack length from the photos taken during the test by using a digital camera with CANON MACRO lens of 150 mm. An Table 2 Calculated features of E-glass/epoxy laminates. Lay-up
LS1
LS2
LS3
h, mm Efx -CLT, GPa Dc
4.2 33.5 0.022
4.43 24.93 0.016
4.65 21.3 0.041
A universal testing machine (SANTAM STM-150) is used to conduct the DCB tests. A high precise load cell with a capacity of 50 kg is utilized for recording the load. The hinges on the specimen are mounted in the grips of the loading machine to make sure that the specimen is aligned and centered. Quasi-static mode I tests are performed under the displacement control condition. The crosshead speed is set at 0.75 mm/min to ensure steady crack propagation and recorded easily. A graph of load (P) versus displacement (ı) is recorded by the tensile machine. The onset of the crack growth from the starter insert is determined by a carefully inspection of the specimen edge with a camera and by observation of the load–displacement curve. Authors have written a program to print screen the load–displacement curve during the test, which is synchronized with digital camera connected to a computer for a live viewing of the crack propagation. After visual inspection of the first initiation of the crack growth, the camera starts to capture delamination images and displays in real time on the monitor. This set-up allows recording various crack lengths, corresponding loads and displacements at any arbitrary time interval from the crack initiation. The crack lengths were measured directly from highresolution photos. The crack is extended approximately 30 mm from the initial crack length. The DCB test setup is shown in Fig. 1. One of the main advantages of this new test setup is the capability of measuring the crack front with the corresponding edge crack during the delamination growth process. Fig. 2 shows procedure of measuring the crack length during the crack propagation. 2.3. Calculation of delamination toughness, GIc The mode I critical energy release rate can be experimentally determined by various methods mentioned in ASTM standard [1], namely; modified beam theory (MBT) method, compliance calibration (CC) method and modified compliance calibration (MCC) method. In this study, the fracture toughness is calculated using the compliance calibration method. That is; GIc =
nPc ıc 2ba
(2)
where a represents the crack length, b the specimen width, ıc the load point displacement and Pc is the critical load. The n value represents the slope of the logC–loga plot. The point of deviation from the linearity in the load–displacement curve (nonlinearity point = NL) owning to giving the lowest of the GIc , is considered for determination of the initiation point of the delamination growth. 3. Results and discussion The typical load–displacement curves for three different layups (LS1, LS2 and LS3) with two initial crack lengths are illustrated in Fig. 3. The load–displacement curves of each lay-up with initial crack lengths of a0 = 35 mm or 55 mm show the same trend. All curves indicate a linear behavior up to nonlinearity point where the delamination front grows at the middle of the DCB specimen width. The slopes of first linear parts are different due to various longitudinal flexural stiffness of the specimens. Consequently, the slope of P–ı curve starts to decrease from nonlinearity point due to crack propagation and monotonically continued up to a maximum value due to fiber bridging. At the peak of P–ı curve (Pmax ), the fiber-bridging phenomenon vanishes and abruptly drops are
M.M. Shokrieh, M. Heidari-Rarani / Materials Science and Engineering A 529 (2011) 265–269
267
Fig. 1. Experimental setup for DCB testing.
Table 3 Results of average compliance and maximum load values for MD DCB specimens (±standard deviation). Crack length
Critical values at NL
mm 35
55
LS1 LS2 LS3 LS1 LS2 LS3
Compliance,
Maximum load,
Displacement, mm
Load, N
m/N
N
2.02 (±0.03) 1.43 (±0.01) 1.62 (±0.11) 4.82 (±0.23) 3.27 (±0.09) 3.77 (±0.21)
32.15 (±0.35) 21.54 (±0.82) 20.46 (± 1.65) 22.77 (±1.67) 14.6 (±0.16) 13.89 (±0.44)
62.82 (±1.53) 66.39 (±2.2) 79.18 (±1.1) 211.69 (±5.66) 223.97 (±3.78) 271.45 (±6.1)
60.3 52.7 62.9 43.5 36.7 46.1
observed in the load values in each crack extension. Fig. 4 represents a fiber-bridging phenomenon in LS3 before and after reaching to the Pmax value in the P–ı curve. An occasional stick-slip behavior is observed for all DCB specimens during the crack propagation. However, this behavior is more sensible for the unidirectional laminates (LS1) than the cross-ply (LS2) and quasi-isotropic (LS3) ones (Fig. 3b). It is shown that the crack propagation is more stable for LS2 and LS3 laminates than LS1. The critical load and displacement at the nonlinearity point as well as the corresponding compliance are reported in Table 3. The results confirm that changing the stacking sequences from the unidirectional to the cross-ply and quasi-isotropic, would increase the compliance of DCB specimens.
As shown in Table 3, the maximum and minimum loads belong to the quasi-isotropic and cross-ply lay-ups, respectively, confirming the effect of stacking sequence on the fiber-bridging phenomenon or R-curve behavior. On the other hands, the crossply laminate (LS2) with the lowest value of Dc has the minimum value of peak load in the P–ı curves. Fig. 5 represents the R-curve (GI versus crack extension) behavior of LS1, LS2 and LS3 for two different initial crack lengths. Three regions would be discussed in Fig. 5 as the initiation fracture toughness values, the fiber-bridging region and the propagation region. The summaries of Fig. 5 results are tabulated in Table 4. Results in Table 4 show that the initial crack length between 35 and 55 mm does not affect the initiation fracture toughness (GIc-init ), fiber-bridging length (lbr ) and steady-state toughness (GIc-prop ) of each individual lay-up. Also, a considerable change in GIc-init and GIc-prop values can be observed by moving from UD to MD
Table 4 Average initiation and steady-state values of fracture toughness and fiber-bridging length for MDDCB specimens. Crack length, mm 35
55 Fig. 2. Measurement of crack length at the edge of DCB specimen.
LS1 LS2 LS3 LS1 LS2 LS3
GIc-init at NL, J/m2 (±SDV)
lbr , mm
GIc-prop , J/m2 (±SDV)
101.6 (±1.25) 49.24 (±2.05) 52.78 (±3.41) 108.23 (±5.85) 49.37 (±1.15) 52.42 (±0.38)
9.5 9.1 10.4 9.7 9.3 11.0
541.9 (±20.3) 466.5 (±31.2) 729.2 (±21.5) 550.2 (±17.5) 481.9 (±10.2) 808.65 (±2.3)
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Fig. 5. Effect of lay-up on R-curve behavior of DCB specimens with delamination between 0◦ //0◦ interface. Fig. 3. Load–displacement curves of MD DCB specimens with 0◦ //0◦ interface.
laminates whereas the fiber-bridging lengths are relatively close to each other in all the lay-ups. The noticeable point in the obtained experimental results is that three main parameters in the R-curves (i.e.; GIc-init , lbr and GIc-prop ) have the lowest values for the cross-ply DCB specimen and the highest values for the quasi-isotropic DCB specimens. Although equivalent flexural modulus (Efx ) of LS1, LS2 and LS3 (shown in Table 2) continuously decrease from LS1 to LS3, the GIc-init and GIc-prop values decrease for LS2 and then increase for LS3. As a result, it can be concluded that the non-dimensional coupling parameter, Dc , may affect the R-curve behavior of DCB specimens. For instance, Dc values of LS1 and LS2 are near to each other and therefore the corresponding R-curves (Fig. 5a and b) show the same behavior. However, for LS3 laminate, Dc value is approximately two times of the LS1 and the R-curve behavior is significantly different. It should be finally declared when engineers design composite structures based on the fracture mechanics, they should pay attention to the pronounced R-curve behaviors for MD laminates. As shown in this research, the coupling parameter may remarkably affect the delamination behavior of laminated composites. For example, R-curve of a DCB specimen with lower longitudinal flexural stiffness (LS3) is not essentially the same or lower than that of the specimen with higher flexural stiffness (LS1). 4. Conclusions
Fig. 4. Fiber-bridging phenomenon in LS3 specimen.
The effect of the stacking sequence on mode I delamination resistance (R-curve) behavior of glass/epoxy composites has been investigated by DCB tests. Due to specimen dependency of Rcurve, the DCB specimen geometry (i.e., overall length, width and thickness) and the initial crack length (a0 ) are supposed to be
M.M. Shokrieh, M. Heidari-Rarani / Materials Science and Engineering A 529 (2011) 265–269
constant. Also, delamination is located between 0◦ //0◦ to prevent an unexpected change of the delamination plane to adjacent layers. To eliminate the complex behavior of any multidirectional (MD) sequence, lay-ups with the least possible effect of coupling parameter are selected. The analysis of R-curves of MD composite laminates shows: • Crack propagation behavior of a stick-slip type is more observed for the UD DCB specimens than the MD ones. On the other hands, crack at MD laminates grows in a more stable manner. • Initiation fracture toughness (GIc-init ) and steady-state toughness (GIc-prop ) are independent of initial crack length for any MD stacking sequence. • In spite of locating delamination between 0◦ //0◦ interface in all DCB specimens, a large-scale of fiber-bridging is occurred for the quasi-isotropic laminates. In other words, R-curve behavior of quasi-isotropic lay-ups is significantly different from the similar unidirectional and cross-ply lay-ups. Although the GIc-init value of quasi-isotropic laminate is lower than that of the UD laminates, the GIc-prop value is much higher. This is due to the bending-bending and bending-twisting coupling effects. • Stacking sequence does not affect the fiber-bridging length of DCB specimens, whereas it has pronounced effect on the maximum load value in the load–displacement curves.
269
References [1] ASTM Standard D5528-94a, Standard test method for mode I interlaminar fracture toughness of unidirectional continuous fiber reinforced polymer matrix composites, Philadelphia, PA, 1994. [2] ISO 15024, Fibre-reinforced plastic composites – Determination of mode I interlaminar fracture toughness, GIc , for unidirectionally reinforced materials, 2001. [3] X.J. Gong, A. Hurez, G. Verchery, Polym. Test. 29 (2010) 658–666. [4] J. Andersons, M. König, Compos. Sci. Technol. 64 (2004) 2139–2152. [5] T.E. Tay, Appl. Mech. Rev. 56 (2003) 1–23. [6] A.J. Brunner, B.R.K. Blackman, P. Davies, Eng. Fract. Mech. 75 (2008) 2779–2794. [7] R. Gutkin, M.L. Laffan, S.T. Pinho, P. Robinson, P.T. Curtis, Int. J. Solids Struct. 48 (2011) 1767–1777. [8] M.R. Shetty, K.R. Vijay Kumar, S. Sudhir, P. Raghu, A.D. Madhuranath, J. Reinf. Plast. Compos. 19 (2000) 606–620. [9] H. Miyagawa, C. Sato, K. Ikegami, J. Appl. Polym. Sci. 115 (2010) 3295–3302. [10] P. Prombut, L. Michel, F. Lachaud, J.J. Barrau, Eng. Fract. Mech. 73 (2006) 2427–2442. [11] A.B. Pereira, A.B. de Morais, M.F.S.F. de Moura, A.G. Magalhães, Composites Part A 36 (2005) 1119–1127. [12] M.M. Shokrieh, M. Heidari-Rarani, M.R. Ayatollahi, Mater. Design 34 (2012) 211–218. [13] H. Chai, Composites 15 (1984) 277–290. [14] K.Y. Rhee, S.K. Koh, J.H. Lee, Polym. Compos. 21 (2000) 155–164. [15] Z. Suo, G. Bao, B. Fan, J. Mech. Phys. Solids 40 (1992) 1–16. [16] T.K. Jacobsen, B.F. Sørensen, Composites Part A 32 (2001) 1–11. [17] B.F. Sørensen, T.K. Jacobsen, Composites Part A 29A (1998) 1443–1451. [18] M.F.S.F. de Moura, R.D.S.G. Campilho, A.M. Amaro, P.N.B. Reis, Compos. Struct. 92 (2010) 144–149. [19] S.W. Tsai, Introduction to Composite Materials, Technomic Publishing Company, Pennsylvania, 1980. [20] B.D. Davidson, R. Krüger, M. König, Eng. Fract. Mech. 55 (1996) 557–569.
Contents lists available at SciVerse ScienceDirect
Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea
Effect of stacking sequence on R-curve behavior of glass/epoxy DCB laminates with 0◦ //0◦ crack interface M.M. Shokrieh ∗ , M. Heidari-Rarani Composites Research Laboratory, Center of Excellence in Experimental Solid Mechanics and Dynamics, School of Mechanical Engineering, Iran University of Science and Technology (IUST), Tehran 16846-13114, Iran
a r t i c l e
i n f o
Article history: Received 4 July 2011 Received in revised form 7 September 2011 Accepted 8 September 2011 Available online 16 September 2011 Keywords: Delamination toughness R-curve Multidirectional DCB
a b s t r a c t In this study, the influence of stacking sequence on mode I delamination resistance (R-curve) behavior of E-glass/epoxy laminated composites with an initial delamination between 0◦ //0◦ interface is experimentally investigated. To this end, symmetric double cantilever beam (DCB) specimens of stacking sequences; [0◦ 12 ]s , [(0◦ /90◦ )3 ]2s and [0◦ /90◦ / ± 45◦ /90◦ /0◦ ]2s with two initial crack lengths are used. A pronounced R-curve behavior is observed on all stacking sequences due to locating delamination between two similar layers. Comparison of R-curve behavior of cross-ply and quasi-isotropic DCB specimens with unidirectional (UD) one reveals the significant effect of the non-dimensional coupling parame2 ter, Dc = D12 /D11 D22 , on the R-curves. Thus, three main outputs of R-curves could be summarized as; (a) the initiation delamination toughness (GIc-init ) of multidirectional (MD) laminates are much lower than that of UD one, (b) stacking sequence has no effect on the fiber bridging length in DCB specimens, and (c) the greater the Dc value of a laminate, the higher the steady-state propagation toughness (GIc-prop ) is. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Delamination is a typical fracture mechanism in fiber reinforced composite laminates occurs due to low interlaminar strength. Some well-known sources of delamination under different loadings are free edges, cut out, low-velocity impact and fabrication defects. These damages may considerably reduce the global stiffness and strength and then leads to a catastrophic structure failure. Therefore, characterization of delamination resistance based on the fracture mechanics is of great importance in engineering design. Over the last two decades, much attention has been devoted to the mode I delamination. The double cantilever beam (DCB) is commonly used for this purpose. All these efforts have led to the establishment of standard test methods for mode I [1,2], which concern only mode I delamination initiation for unidirectional (UD) composites [3], while laminates widely used in industrial applications are multidirectional (MD). Comprehensive reviews by Andersons and König [4], Tay [5] and Brunner et al. [6], concerning delamination onset and growth in laminated composites under various mode loadings, show the importance of delamination behavior of MD laminates. Also, extensive researches have been recently carried out to characterize the mode I interlaminar fracture
∗ Corresponding author. Tel.: +98 21 77240540, fax: +98 21 77491206. E-mail address: [email protected] (M.M. Shokrieh). 0921-5093/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2011.09.027
toughness of laminated composites with delaminating interfaces such as 0◦ //0◦ , 0◦ // ◦ , ◦ // ◦ and ◦ //− ◦ [7–13]. It is currently believed [12–14] that initiation fracture toughness (GIc ) is a material property, i.e., the critical energy release rate is independent of the specimen size and delamination length. Whereas in the case of large-scale bridging, Suo et al. [15] and Jacobsen and Sørensen [16,17] have shown that the delamination resistance (R-curve) is not only a material property but also is dependent on the specimen geometry. The effect of bridging fibers on the interlaminar fracture toughness is quantitatively investigated by cutting the bridging fibers by de Moura et al. [18]. It was found that interlaminar fracture toughness without fiber-bridging has a constant value during the crack propagation. However, if the fiber-bridging occurs in the wake of delamination front, the strain energy release rate is no longer a constant value and rises with increasing the delamination length. Therefore, as well as the initiation fracture toughness, the other two parameters, i.e., the fiber-bridging zone and steady-state delamination toughness, or generally R-curve behavior is important in order to accurately predict the response of fiber-reinforced composites during the damage propagation. From the above literature, it is found that the R-curve effects are pronounced in laminated composites and most of these researches are related to resistance behavior of laminated composites with a special initial crack length (a0 ) and different delaminating interfaces. Therefore, the influence of stacking sequence on the R-curve
266
M.M. Shokrieh, M. Heidari-Rarani / Materials Science and Engineering A 529 (2011) 265–269
Table 1 Mechanical properties of unidirectional E-glass/ML-506 epoxy.
illumination is used under the specimen to better detection of the crack tip. Three tests are carried out for each initial crack length in order to check the repeatability of the results.
E1 (GPa)
E2 (GPa)
12
G12 (GPa)
Efx (GPa)
33.5 (±1.3)
10.23 (±0.83)
0.27 (±0.01)
4.26 (±0.45)
29.54 (± 1.1)
2.2. Test procedure behavior of a symmetric glass/epoxy composite with 0◦ //0◦ crack interface is investigated in present study. Due to specimen dependency of R-curve [7], the DCB specimen geometry (i.e., overall length, width and thickness) and the initial crack length are supposed to be constant. Also, the 0◦ //0◦ delaminating interface is selected to prevent deviation of initial crack from the mid-plane and propagation in a zigzag fashion. Pereira et al. [11] showed that the intra-ply damage causes the GIc values of MD-DCB specimens with different delaminating interface to be 3–4 times higher than those of unidirectional [0◦ ]n specimens. 2. Experimental procedure 2.1. Materials and specimen preparation Twenty-four plied DCB test specimens of [0◦ ]24 (LS1), (LS2) and [0◦ /90◦ / ± 45◦ /90◦ /0◦ ]2s (LS3) stacking sequences are fabricated from E-glass/epoxy by hand lay-up method. E-glass quasi-unidirectional fabric with 5% fiber in the 90◦ direction of density 2.564 g/cm3 and ML-506 epoxy resin based on bisphenol F of density 1.11 g/cm3 with a polyamine hardener (HA-12) which are produced by Mokarrar Industrial Group (Iran) are used. The laminates are cured at the room temperature for 7 days followed by post-curing at 80 ◦ C for 2 h. Average fiber volume fraction is obtained 47.5% from the burn-out test of DCB specimens. In-plane mechanical properties of glass/epoxy laminates are reported in Table 1. The above stacking sequences are selected to result in a desirable crack propagation behavior, i.e., there is no change of delamination plane and an acceptable crack front profile. Table 2 shows the features of LS1, LS2 and LS3 laminates. Effective flexural modulus (Efx ) is calculated by the classical lamination theory (CLT) [19]: [(0◦ /90◦ )3 ]2s
Efx =
−1 12 , [d] = ([D] − [B][A]−1 [B]) d11 h3
(1)
where [A], [B] and [D] are the extensional, coupling and bending stiffness of a laminate. In Table 2, the Dc indicates the curvature due to the longitudinal-transverse bending coupling, which is intro2 /D D duced by Davidson [20] and defined as Dc = D12 11 22 where Dij are components of the bending stiffness matrix. In the mentioned laminates, the initial crack is located at the mid-plane and is made by inserting a Teflon film of thickness of 20 m. Using a diamond saw, DCB test specimens are cut from the center plates, with a width of b = 25 mm, a total length of L = 150 mm and the initial crack lengths of a0 = 35 and 55 ± 0.2 mm. Specimen edges are sanded to remove imperfections that may interfere with the crack growth or a clear image of the crack tip position. The aluminum piano hinges are adhesively bonded to the ends of specimen arms to provide the loading points. A measurement scale with 1 mm divisions is attached to the lower edge of the specimen for measuring the crack length from the photos taken during the test by using a digital camera with CANON MACRO lens of 150 mm. An Table 2 Calculated features of E-glass/epoxy laminates. Lay-up
LS1
LS2
LS3
h, mm Efx -CLT, GPa Dc
4.2 33.5 0.022
4.43 24.93 0.016
4.65 21.3 0.041
A universal testing machine (SANTAM STM-150) is used to conduct the DCB tests. A high precise load cell with a capacity of 50 kg is utilized for recording the load. The hinges on the specimen are mounted in the grips of the loading machine to make sure that the specimen is aligned and centered. Quasi-static mode I tests are performed under the displacement control condition. The crosshead speed is set at 0.75 mm/min to ensure steady crack propagation and recorded easily. A graph of load (P) versus displacement (ı) is recorded by the tensile machine. The onset of the crack growth from the starter insert is determined by a carefully inspection of the specimen edge with a camera and by observation of the load–displacement curve. Authors have written a program to print screen the load–displacement curve during the test, which is synchronized with digital camera connected to a computer for a live viewing of the crack propagation. After visual inspection of the first initiation of the crack growth, the camera starts to capture delamination images and displays in real time on the monitor. This set-up allows recording various crack lengths, corresponding loads and displacements at any arbitrary time interval from the crack initiation. The crack lengths were measured directly from highresolution photos. The crack is extended approximately 30 mm from the initial crack length. The DCB test setup is shown in Fig. 1. One of the main advantages of this new test setup is the capability of measuring the crack front with the corresponding edge crack during the delamination growth process. Fig. 2 shows procedure of measuring the crack length during the crack propagation. 2.3. Calculation of delamination toughness, GIc The mode I critical energy release rate can be experimentally determined by various methods mentioned in ASTM standard [1], namely; modified beam theory (MBT) method, compliance calibration (CC) method and modified compliance calibration (MCC) method. In this study, the fracture toughness is calculated using the compliance calibration method. That is; GIc =
nPc ıc 2ba
(2)
where a represents the crack length, b the specimen width, ıc the load point displacement and Pc is the critical load. The n value represents the slope of the logC–loga plot. The point of deviation from the linearity in the load–displacement curve (nonlinearity point = NL) owning to giving the lowest of the GIc , is considered for determination of the initiation point of the delamination growth. 3. Results and discussion The typical load–displacement curves for three different layups (LS1, LS2 and LS3) with two initial crack lengths are illustrated in Fig. 3. The load–displacement curves of each lay-up with initial crack lengths of a0 = 35 mm or 55 mm show the same trend. All curves indicate a linear behavior up to nonlinearity point where the delamination front grows at the middle of the DCB specimen width. The slopes of first linear parts are different due to various longitudinal flexural stiffness of the specimens. Consequently, the slope of P–ı curve starts to decrease from nonlinearity point due to crack propagation and monotonically continued up to a maximum value due to fiber bridging. At the peak of P–ı curve (Pmax ), the fiber-bridging phenomenon vanishes and abruptly drops are
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Fig. 1. Experimental setup for DCB testing.
Table 3 Results of average compliance and maximum load values for MD DCB specimens (±standard deviation). Crack length
Critical values at NL
mm 35
55
LS1 LS2 LS3 LS1 LS2 LS3
Compliance,
Maximum load,
Displacement, mm
Load, N
m/N
N
2.02 (±0.03) 1.43 (±0.01) 1.62 (±0.11) 4.82 (±0.23) 3.27 (±0.09) 3.77 (±0.21)
32.15 (±0.35) 21.54 (±0.82) 20.46 (± 1.65) 22.77 (±1.67) 14.6 (±0.16) 13.89 (±0.44)
62.82 (±1.53) 66.39 (±2.2) 79.18 (±1.1) 211.69 (±5.66) 223.97 (±3.78) 271.45 (±6.1)
60.3 52.7 62.9 43.5 36.7 46.1
observed in the load values in each crack extension. Fig. 4 represents a fiber-bridging phenomenon in LS3 before and after reaching to the Pmax value in the P–ı curve. An occasional stick-slip behavior is observed for all DCB specimens during the crack propagation. However, this behavior is more sensible for the unidirectional laminates (LS1) than the cross-ply (LS2) and quasi-isotropic (LS3) ones (Fig. 3b). It is shown that the crack propagation is more stable for LS2 and LS3 laminates than LS1. The critical load and displacement at the nonlinearity point as well as the corresponding compliance are reported in Table 3. The results confirm that changing the stacking sequences from the unidirectional to the cross-ply and quasi-isotropic, would increase the compliance of DCB specimens.
As shown in Table 3, the maximum and minimum loads belong to the quasi-isotropic and cross-ply lay-ups, respectively, confirming the effect of stacking sequence on the fiber-bridging phenomenon or R-curve behavior. On the other hands, the crossply laminate (LS2) with the lowest value of Dc has the minimum value of peak load in the P–ı curves. Fig. 5 represents the R-curve (GI versus crack extension) behavior of LS1, LS2 and LS3 for two different initial crack lengths. Three regions would be discussed in Fig. 5 as the initiation fracture toughness values, the fiber-bridging region and the propagation region. The summaries of Fig. 5 results are tabulated in Table 4. Results in Table 4 show that the initial crack length between 35 and 55 mm does not affect the initiation fracture toughness (GIc-init ), fiber-bridging length (lbr ) and steady-state toughness (GIc-prop ) of each individual lay-up. Also, a considerable change in GIc-init and GIc-prop values can be observed by moving from UD to MD
Table 4 Average initiation and steady-state values of fracture toughness and fiber-bridging length for MDDCB specimens. Crack length, mm 35
55 Fig. 2. Measurement of crack length at the edge of DCB specimen.
LS1 LS2 LS3 LS1 LS2 LS3
GIc-init at NL, J/m2 (±SDV)
lbr , mm
GIc-prop , J/m2 (±SDV)
101.6 (±1.25) 49.24 (±2.05) 52.78 (±3.41) 108.23 (±5.85) 49.37 (±1.15) 52.42 (±0.38)
9.5 9.1 10.4 9.7 9.3 11.0
541.9 (±20.3) 466.5 (±31.2) 729.2 (±21.5) 550.2 (±17.5) 481.9 (±10.2) 808.65 (±2.3)
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Fig. 5. Effect of lay-up on R-curve behavior of DCB specimens with delamination between 0◦ //0◦ interface. Fig. 3. Load–displacement curves of MD DCB specimens with 0◦ //0◦ interface.
laminates whereas the fiber-bridging lengths are relatively close to each other in all the lay-ups. The noticeable point in the obtained experimental results is that three main parameters in the R-curves (i.e.; GIc-init , lbr and GIc-prop ) have the lowest values for the cross-ply DCB specimen and the highest values for the quasi-isotropic DCB specimens. Although equivalent flexural modulus (Efx ) of LS1, LS2 and LS3 (shown in Table 2) continuously decrease from LS1 to LS3, the GIc-init and GIc-prop values decrease for LS2 and then increase for LS3. As a result, it can be concluded that the non-dimensional coupling parameter, Dc , may affect the R-curve behavior of DCB specimens. For instance, Dc values of LS1 and LS2 are near to each other and therefore the corresponding R-curves (Fig. 5a and b) show the same behavior. However, for LS3 laminate, Dc value is approximately two times of the LS1 and the R-curve behavior is significantly different. It should be finally declared when engineers design composite structures based on the fracture mechanics, they should pay attention to the pronounced R-curve behaviors for MD laminates. As shown in this research, the coupling parameter may remarkably affect the delamination behavior of laminated composites. For example, R-curve of a DCB specimen with lower longitudinal flexural stiffness (LS3) is not essentially the same or lower than that of the specimen with higher flexural stiffness (LS1). 4. Conclusions
Fig. 4. Fiber-bridging phenomenon in LS3 specimen.
The effect of the stacking sequence on mode I delamination resistance (R-curve) behavior of glass/epoxy composites has been investigated by DCB tests. Due to specimen dependency of Rcurve, the DCB specimen geometry (i.e., overall length, width and thickness) and the initial crack length (a0 ) are supposed to be
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constant. Also, delamination is located between 0◦ //0◦ to prevent an unexpected change of the delamination plane to adjacent layers. To eliminate the complex behavior of any multidirectional (MD) sequence, lay-ups with the least possible effect of coupling parameter are selected. The analysis of R-curves of MD composite laminates shows: • Crack propagation behavior of a stick-slip type is more observed for the UD DCB specimens than the MD ones. On the other hands, crack at MD laminates grows in a more stable manner. • Initiation fracture toughness (GIc-init ) and steady-state toughness (GIc-prop ) are independent of initial crack length for any MD stacking sequence. • In spite of locating delamination between 0◦ //0◦ interface in all DCB specimens, a large-scale of fiber-bridging is occurred for the quasi-isotropic laminates. In other words, R-curve behavior of quasi-isotropic lay-ups is significantly different from the similar unidirectional and cross-ply lay-ups. Although the GIc-init value of quasi-isotropic laminate is lower than that of the UD laminates, the GIc-prop value is much higher. This is due to the bending-bending and bending-twisting coupling effects. • Stacking sequence does not affect the fiber-bridging length of DCB specimens, whereas it has pronounced effect on the maximum load value in the load–displacement curves.
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