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Experimental studies of Mode I energy release rate in adhesively bonded width tapered composite DCB specimens
COMPOSITES SCIENCE AND TECHNOLOGY Composites Science and Technology 65 (2005) 9–18 www.elsevier.com/locate/compscitech
Experimental studies of Mode I energy release rate in adhesively bonded width tapered composite DCB specimens Aurodhya Jyoti, Ronald F. Gibson *, Golam M. Newaz Advanced Composites Research Laboratory, Department of Mechanical Engineering, 5050 Anthony Wayne Dr, Rm # 2100, Wayne State University, Detroit, MI 48202, USA Received 11 August 2003; received in revised form 19 April 2004; accepted 21 April 2004 Available online 13 August 2004
Abstract The Mode I energy release rate, GI, derived from conventional uniform width double cantilever beam (DCB) test data depends on crack length. Data acquisition and analysis from such experiments can be simplified if GI is independent of crack length, particularly at high loading rates. Previous research by others has shown that width tapered double cantilever beam (WTDCB) specimens made from aerospace grade carbon/epoxy composite laminates without adhesive layers exhibit critical energy release rates which are independent of crack length. The purpose of the present investigation was to determine whether or not adhesively bonded WTDCB specimens of automotive type sheet molding compound (SMC) composites show similar behavior. It was observed that the critical energy release rate was practically independent of crack length for unidirectional carbon/epoxy WTDCB specimens without adhesive layers but not for unidirectional carbon/epoxy, unidirectional E-glass/epoxy or automotive SMC WTDCB specimens with adhesive layers, and that self-similar crack growth only occurred in unidirectional carbon/epoxy WTDCB specimens without adhesive layers. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: A. Adhesive joints; A. Polymer matrix composites; A. Short fiber composites; B. Fracture toughness; D. Fractography
1. Introduction Adhesively bonded composite joints, which are often used within automotive vehicle structures, may experience dynamic loading as in vehicle crashes. For proper design of such joints, it is important to know the dynamic fracture toughness, which characterizes the resistance to crack propagation. The critical Mode I energy release rate, which is a measure of fracture toughness, is often measured using double cantilever beam (DCB) specimens such as those described in ASTM standard D5528 [1]. Data from such tests generally depend on the crack length. *
Corresponding author. Tel.: +1 313 5773702; fax: +1 313 5778789. E-mail address: [email protected] (R.F. Gibson). 0266-3538/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.compscitech.2004.04.006
Several studies of fracture in adhesively bonded composites using DCB and other specimens have been reported in the literature. The critical energy release rate GIc of graphite/epoxy composites with adhesive strips at the interface was determined by Norman and Sun [2] using the DCB test and it was found that delamination fracture toughness increases substantially when adhesive strips are added at the interface, reaching a limiting value as the adhesive widths are increased. In continued research by the same authors with similar materials [3], good agreement was also found between quasi-static and dynamic critical load and crack growth data. Mode I fracture of epoxy bonded CFRP joints under quasi-static loading at different temperatures was studied by Ashcroft et al. [4] and it was found that the critical strain energy release rate increases with temperature and the failure locus transferred from
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Table 1 Materials for different specimens Adherend
Adherend thickness (mm)
Adhesive thicknessa (mm)
Backing beam thickness (mm)
Initial crack length (mm)
SMC E-glass/epoxy Carbon/epoxy Carbon/epoxy
2.54 2.032 1.905 5.207
0.762 0.762 0.762 –
6.35 6.35 9.144 –
80 81 80 80
a
Adhesive layer thickness was controlled by mixing 0.762 mm glass beads in the adhesive.
predominantly in the composite substrate to predominantly in the adhesive layer. Mixed-mode fracture behavior of adhesively bonded carbon/epoxy composite joints was studied by Daghyani et al. [5] using a rubbermodified epoxy as the adhesive. It was found that Gc was dependent of bond thickness and the actual crack path in the joints. For poor bonding between the adhesive and the composite adherends, interfacial crackpropagation was observed for very thin bonds with alternating crack jumping from one interface to another across the bond line. However, for strong interfacial bonding, the crack was deviated from the precrack towards the composite adherend and propagated cohesively in the composite layer. Dynamic Mode-I delamination fracture toughness of a carbon/epoxy composite was studied by Guo and Sun [6] using a modified DCB specimen with an adhesive strip at the tip of the precrack. The adhesive strip substantially increased the crack initiation toughness so that after initiation an unstable crack-propagation was produced and high crack-propagation speed was achieved. In dynamic fracture toughness testing, however, it is difficult to measure the crack growth during testing. One possible solution to this problem is to use tapered double cantilever beam specimens having either tapered height or tapered width for which the calculated energy release rate is theoretically independent of crack length if pure bending is assumed. Daniel et al. [7] studied rate effects on delamination fracture toughness of toughened graphite/epoxy laminates. It was found that for a tapered width thin DCB specimen the energy release rate is independent of crack length. As explained in the next section, the tapered width design was selected for evaluation here due to its simplicity and ease of fabrication. The major objective of the current study is to investigate the quasi-static Mode I energy release rate of width tapered DCB (WTDCB) specimens of SMC (sheet molding compound), unidirectional E-glass/epoxy and carbon/epoxy composite materials (Table 1) with and without adhesive layers as a prelude to possible dynamic fracture tests of the same materials.
2. Specimen design The original thin WTDCB specimen, which was used by Daniel et al. [7] to measure interlaminar fracture
toughness of composite laminates, was selected and modified for the testing of adhesively bonded composite joints. Tapered height backing beams have also been used [8,9], but a complex nonlinear taper geometry is required, and the linearly tapered WTDCB of constant thickness is easier to fabricate. Initial tests showed that the stiffness of the original thin WTDCB specimen with adhesive layer was too low to sustain the load needed to grow the crack; so aluminum backing beams were used to increase the stiffness of the specimen. These aluminum backing beams were adhesively bonded to the outer faces of the composite specimen with a secondary adhesive layer as shown in Fig. 1. The original thin WTDCB specimen was loaded by a hinge attachment, but the modified specimen required higher loads to initiate crack growth. It was found that such large loads could not be supported by the hinge attachment, so two clevis pins inserted through holes in the backing beams were used to introduce the load into the backing beams as shown in Fig. 1. Irwin [10] defined the energy release rate, G to be the rate of change of potential energy with respect to the crack extension area. Under the assumption of linear elastic fracture mechanics (LEFM) and geometric linearity, for both load and displacement controlled systems, the energy release rate, G, for a test specimen can be defined by G¼
P 2 dC ; 2b da
ð1Þ
where P is applied load, C is specimen compliance, b is the specimen width and a is the crack length. Using Timoshenko beam theory and considering bending and shear deformations, Mostovoy et al. [10] derived the Mode I energy release rate for a uniform cross sectional DCB specimen as 4P 2 3a2 1 GI ¼ þ ; ð2Þ h E11 b2 h3 where h is the half of the specimen thickness and E11 is the longitudinal modulus of the beam. In the above equation, the first term represents the effect of bending deformation and the second term represents the effect of shear deformation. But for a thin, uniform cross-section DCB, h is very small and if h a, the shear contribution may be neglected. Then the above equation can be written as
A. Jyoti et al. / Composites Science and Technology 65 (2005) 9–18
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Fig. 1. Specimen with backing beams and adhesive layers.
GI ¼
12P 2 a2 : E11 b2 h3
ð3Þ
For a properly designed tapered width specimen, the beam width b at crack length a will increase linearly with increasing crack length a, so k = a/b = constant. So for a WTDCB specimen, Daniel et al. [7] showed that Mode I energy release rate can be expressed as GI ¼
12P 2 k 2 ; E11 h3
ð4Þ
which is independent of crack length. For a constant width DCB specimen the load increases up to a peak where the crack initiates and then the load drops gradually as the crack propagates. But for a WTDCB specimen the load remains constant after crack initiation. A typical load–displacement curve for a WTDCB specimen is shown in Fig. 2. The above equations represent the energy release rate of a homogenous DCB or WTDCB but do not include the effect of an adhesive layer. The effect of the adhesive layer was first considered by Penado [11] based on the Winckler foundation model. Penado considered the uncracked portion of the adhesive and the adherend as an elastic foundation. Olson [12] analyzed the uncracked part of a composite laminate DCB specimen by including the Saint-Venant effect. Considering bending, shear, elastic foundation and Saint-Venant effects, Liu et al. [13] showed that an improved model for the compliance
of an adhesively bonded composite DCB specimen with an adhesive layer along its middle surface is given by ( P2 12 GI ¼ 2 ½k3 a2 þ 2k2 a þ k 3 0 b EF k ðh þ tÞ3 ) 1 24va þ þ ; ð5Þ lGT ðh0 þ tÞ EF ðh0 þ tÞ3 where EF is the flexural modulus of the composite laminate or adherend, GT the transverse shear modulus of the composite laminate or adherend, h 0 the thickness of the adherend, t the half of thickness of the adhesive layer, k4 = 3K/[EFb(h 0 + t)3], K = 1/[(1/Kadherend) + (1/ Kadhesive)] the stiffness of the foundation per unit length, Kadherend = 2ETb/h 0 the stiffness of the adherend per unit length, Kadhesive = (b/t)[Ea/(1 ma2)] the stiffness of the adhesive per unit length, ET the transverse modulus of the adherend, Ea the YoungÕs modulus of the adhesive, ma the pPoissonÕs ratio of the adhesive, ffiffiffiffiffiffiffiffiffiffiffiffiffiffi v ¼ ðh=2pÞ EF =GT is the decay length of the Saint-Venant effect. By substituting k = a/b, we can rewrite Eq. (5) as ( 12 1 24 þ þ GI ¼ P 2 k 2 0 3 3 2 0 lG ðh þ tÞa T EF ðh þ tÞ EF kðh0 þ tÞ a ) 12 24v þ : ð6Þ þ 3 2 3 2 0 EF k ðh þ tÞ a EF ðh0 þ tÞ a
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Fig. 2. Load versus crack opening deflection for WTDCB specimen loaded at a crosshead rate of 0.0085 mm/s (0.02 in./min). From Daniel et al. [7].
For thin beams, the bending energy is the dominant portion of the total energy and the other energy terms can be neglected. But when thick backing beams and an adhesive layer are used, the effective specimen thickness increases and the other energy terms may be significant. Figs. 3 and 4 were generated by applying Eq. (6) and the properties in Table 2 to the case of adhesively bonded SMC with and without aluminum backing beams, respectively. However, as shown in Figs. 3 and 4, with the larger values of initial crack length, the bending energy term dominates the shear, elastic foundation and Saint-Venant energy terms. Similar conclusions were reached regarding the unidirectional E-glass/epoxy and carbon/epoxy materials with and without backing beams. Although thin backing beams may contribute a dominant portion of bending energy, which is desired
for this study, the backing beams may also exhibit yielding due to high bending stresses. Also there should be a hole in each backing beam in order to insert the clevis pins. Considering both effects, it is necessary to optimize the backing beam thickness so the bending energy is dominant and yielding can be avoided. For this study the thickness of the aluminum backing beam was selected to be 6.35 mm. The initial crack length was selected in such a way that at least 60% of the total energy is due to bending. Materials and material properties which are used to calculate the percentage contribution of the different energy terms at different crack lengths are tabulated in Tables 1 and 2. So for a thin WTDCB specimen having a sufficiently long pre-crack, the Mode I energy release rate mainly depends on the energy due to bending, which is inde-
Fig. 3. Variation of energy components with crack length for adhesively bonded SMC specimen without backing beam.
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Fig. 4. Variation of energy components with crack length for SMC with aluminum backing beam (SMC thickness = 2.54 mm).
Table 2 Material properties for different components of specimens Material
YoungÕs modulus (MPa)
PoissonÕs ratio
SMC (DMS 951)a Aluminuma Pliogripa Glass–epoxyb Carbon–epoxyb
10,300 69,000 517 38,620 148,285
0.3 0.3 0.3 0.3 0.3
Tensile strength (MPa) 72.5 21 2750
Note: Superscript ÔaÕ is for isotropic and superscript ÔbÕ is for orthotropic material. For orthotropic material the YoungÕs modulus is the longitudinal modulus.
pendent of crack length. For a properly designed specimen of this type, the other energy terms due to the through-the-thickness shear contribution, elastic foundation effect and Saint-Venant end effect, which depend on crack length, are negligible. For adhesively bonded composite joints, the other energy terms are not necessarily negligible, but they diminish at large initial crack lengths [14].
3. Test procedure As shown in Table 1, three types of composite materials were tested. Those materials were: (i) randomly oriented short E-glass fiber reinforced polyester sheetmolding compound (Budd Company – Plastic division SMC type DSM951), (ii) unidirectional continuous E-glass fiber reinforced epoxy (3M Scotchply 1002), and (iii) unidirectional continuous carbon fiber reinforced epoxy (Toray Composites America P2254-20305). Unidirectional E-glass/epoxy and carbon/epoxy laminates were made from 3M Scotchply 1002 E-glass/ epoxy prepreg tape and Toray P2254-20-305 carbon/ epoxy prepreg tape, respectively, by molding the prepreg tapes in a TMP composite vacuum press machine (manufactured by Technical Machine Products Corporation) [14]. For specimens with adhesive layers and backing
beams, shown in Fig. 1, a tough urethane adhesive (Ashland Pliogrip) was used for adhesive bonding (termed as primary adhesive layer) of tapered width DCB specimens made from each type of composite material. Following the automotive industry practice, no surface preparation was used prior to adhesive bonding. Aluminum plates of 6.35 mm thickness were used as backing beams on both sides of the specimen bonded by same adhesive (termed as secondary adhesive layers) to make it stiffer. Pre-cracks were introduced by placing Teflon film within the primary adhesive layer. Specimens without any adhesive layer, shown in Fig. 5, were made from unidirectional carbon/epoxy laminates by placing Teflon film in the middle of the laminates at one end to make the pre-crack. Three SMC specimens, two E-glass/epoxy specimens and one carbon/epoxy specimen, all with adhesive layers and backing beams were tested. For all specimens pre-cracks of length 80 mm and crack length to width (taper) ratio k = 2.4 were selected. Two carbon/epoxy specimens without any adhesive layers or backing beams were tested. The specimens with adhesive layers and backing beams were loaded at a quasi-static displacement controlled rate of 0.051 mm/s in an Endura Tec Smart Test servo-pneumatic testing machine. The maximum displacement of the actuator of this machine is limited to ±25.4 mm. The bending stiffness of the carbon/epoxy specimens without any
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Fig. 5. Specimens without any adhesive layers or backing beams.
adhesive layers was such that a larger MTS servo-hydraulic machine was required to produce the desired displacement at failure. The Mode I energy release rate was calculated by using Eq. (4), considering P as crack initiation load (where the crack growth started).
4. Results and discussion The crack initiation loads, calculated critical Mode I energy release rates from experiments and the fracture surface descriptions for the different specimens are given in Table 3. The first two adhesively bonded SMC
specimens failed with mixed composite/interfacial failure. Crack initiation started through the interface and then grew into the composites. The load increased very slightly at the end, where the failure was mainly within the composite. A typical load–displacement curve and fracture surfaces for this type of specimen are shown in Fig. 6. The third SMC specimen failed with fully interfacial failure. The load dropped suddenly with the crack started and the load increased again with the crack growth and the specimen failed, i.e., the load–displacement curve was stepwise. The load–displacement curve and the fracture surfaces for the third SMC specimen are shown in Fig. 7. The crack initiation
Table 3 Mode I critical energy release rates for different specimens Specimen no. a
Adherend
Crack initiation load (N)
Critical Mode I energy release rate (N/m)
1 2a 3a 4a
SMC SMC SMC E-glass/epoxy
578 170 332 778
365.95 31.66 120.74 763.55
5a 6a 7b 8b
E-glass/epoxy Carbon/Epoxy Carbon/epoxy Carbon/epoxy
1175 628 108 120
1741.62 432.89 407.78 594.31
a b
Specimen with adhesive layer and backing beams (Fig. 1). Specimen without adhesive layer or backing beam (Fig. 5).
Fracture surface Composite/interface Interface/composite Interface Mixed of adhesive, interface/ composite Interface Mid-surface Mid-surface
A. Jyoti et al. / Composites Science and Technology 65 (2005) 9–18
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Fig. 6. (a) Load–displacement curve and (b) failure surfaces for adhesively bonded SMC specimen with mixed composite/interfacial failure.
Fig. 7. (a) Load–displacement curve and (b) failure surfaces for adhesively bonded SMC specimen with fully interfacial failure.
load was about 300 N for SMC specimens. The load– displacement curve for E-glass/epoxy specimen shown in Fig. 8(a) was also stepwise but at the end it was
nearly constant. The fracture surfaces consisted of mixed adhesive, interfacial and composite failure, as shown in Fig. 8(b). The crack initiation load was the
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Fig. 8. (a) Load–displacement curve and (b) failure surfaces for adhesively bonded E-glass/epoxy specimen with composite/interfacial failure.
Fig. 9. (a) Load–displacement curve and (b) failure surfaces for carbon/epoxy specimen with adhesive layers.
highest for E-glass/epoxy specimens. The load–displacement curves for carbon/epoxy specimen with adhesive layers, shown in Fig. 9(a), was also stepwise and fracture surfaces were interfacial with changing
interface, shown in Fig. 9(b). For carbon/epoxy specimens without any adhesive layer, the failure occurred through the pre-cracked surface and a reasonably flat load–displacement curve after crack initiation was ob-
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Fig. 10. (a) Load–displacement curve and (b) failure surfaces for carbon/epoxy specimen without any adhesive layer.
served, as shown in Fig. 10(a). Of all the specimens tested, only the carbon/epoxy specimens without adhesive layer exhibited self-similar crack growth and gave a substantially flat load–displacement curve after crack growth initiation as in Fig. 2. The load increased very slightly with larger displacements due to the shortening of the moment arm at large flexural deformations. The failure surfaces are also shown in Fig. 10(b). If the crack growth occurs along the composite–adhesive interface or switches from interface to composite material, then the load required for crack initiation is very low, the crack growth is stepwise and with each increment of crack growth the load drops quickly. For such failure modes the crack growth was not self-similar and neither the Mode I fracture toughness of the composite nor the adhesive can be obtained from these experiments. If the adhesive bonding is good enough to force the crack growth to occur in the composite or in the adhesive layer, then the crack growth is self-similar and the load does not drop too much and the desired flat load–displacement curve after crack initiation can be achieved. It is clear from Table 3 that the crack initiation loads, the critical energy release rates and the appearance of the fracture surfaces were substantially different for supposedly identical specimens. As indicated earlier, the standard automotive industry practice of not using surface preparation procedures before adhesive bonding was followed here, and this may be a contributing factor to the scatter in the data. Further
research is needed on the effect of surface preparation on fracture toughness of adhesively bonded joints.
5. Conclusions The following observations were made from the experimental results: For adhesively bonded SMC specimens, the crack growth occurred along the composite–adhesive interface or in the composite. This means that the fracture toughness of the SMC composite is lower than that of the Pliogrip adhesive. The load–displacement curve was flat after crack initiation only for the pre-cracked carbon/epoxy composite laminates without adhesive layer whose fracture toughness is low enough that self-similar crack growth occurs through the same layer which includes the pre-crack. But for adhesively bonded composite joints, that type of curve was not achieved as the crack growth occurred along the composite–adhesive interface, in the composite, in the adhesive or in combinations of these modes. Energy release rate was independent of crack length for specimens without adhesive layers but not for specimens with adhesive layers, and self-similar crack growth only occurred in specimens without adhesive layers.
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The use of the WTDCB composite specimen with a tough adhesive like the Pliogrip urethane appears to be not a valid test method for measuring fracture toughness of the bonded joint. Significant scatter in the crack initiation loads, the corresponding critical energy release rates and the appearance of the fracture surfaces was observed for nominally identical specimens. The lack of surface preparation prior to adhesive bonding was a likely contributing factor, and further research on the role of surface preparation is needed. Finally, the relatively flat load–displacement curve after crack initiation indicates that the fracture toughness for crack propagation is independent of crack length. One of the main reasons for not achieving the desired flat displacement curve for adhesively bonded composite joints was that selfsimilar crack growth did not occur (i.e., the crack growth occurred along the composite–adhesive interface, in the composite, in the adhesive or in a combination of these modes). The use of a brittle adhesive layer with poor fracture toughness would probably cause the behavior of the adhesively bonded specimen to be similar to that of the carbon/epoxy composite laminate without adhesive layer, but the overall performance of the adhesively bonded structure would probably be degraded as well. Details of this work may be found in the thesis by Jyoti [14].
Acknowledgement This work was performed with the financial support of Ford Motor Company, and the technical advice of Carl Johnson, Matt Zaluzec and John Hill of the Ford Research Lab is gratefully acknowledged.
References [1] ASTM Standard D5528-01, Standard Test Method for Mode I interlaminar fracture toughness of unidirectional fiber-reinforced polymer matrix composites. American Society for Testing Materials, West Conshohocken, PA, 2002. [2] Norman TL, Sun CT. Mechanical properties and interlaminar toughness of cross-plied laminates containing adhesive strips. AIAA J 1991;29(2):247–52. [3] Norman TL, Sun CT. Delamination growth in composite laminates with adhesive strips subjected to static and impact loading. Compos Sci Technol 1993;46(3):203–11. [4] Ashcroft IA, Hughes DJ, Shaw SJ. Mode I fracture of epoxy bonded composite joints: 1. Quasi-static loading. Int J Adhes Adhes 2001;21(2):87–99. [5] Daghyani HR, Ye L, Mai YW. Mixed-mode fracture of adhesively bonded CF/epoxy composite joints. J Compos Mater 1996;30(11):1248–65. [6] Guo C, Sun CT. Dynamic Mode-I crack-propagation in a carbon/epoxy composite. Compos Sci Technol 1998;58(9):1405–10. [7] Daniel IM, Shareef I, Aliyu AA. Rate effects on delamination fracture toughness of a toughened graphite/epoxy. In: Johnston Norman J, editor. Toughened composites. ASTM STP, 937. Philadelphia: American Society for Testing and Materials; 1987. p. 260–74. [8] Boeman RG, Warren CD. Fracture testing and analysis of adhesively bonded joints for automotive applications. In: Proceedings of the 10th annual ASM/ESD advanced composites conference, Dearborn, MI, USA; 1994. p. 473–81. [9] Mostovoy S, Crosley PB, Ripling EJ. Use of crack-line loaded specimens for measuring plane-strain fracture toughness. J Mater 1967;2(3):661–81. [10] Irwin GR. Onset of fast crack propagation in high strength steel and aluminum alloys. Sagamore Res Conf Proc 1956;2:289–305. [11] Penado FE. A closed form solution for the energy release rate of the double cantilever beam specimen with and adhesive layer. J Compos Mater 1993;27(4):383–407. [12] Olsson R. Discussion. Int J Fract 1996;77(2):R41–3. [13] Liu Z, Gibson RF, Newaz GM. Improved closed form analytical models for the mixed mode bending test of adhesively bonded joints. J Adhes 2002;78:245–68. [14] Jyoti A. Investigation of tapered width DCB specimens for Mode I fracture toughness testing of composite materials with and without adhesive layers. MS Thesis, Wayne State University; 2001.
Experimental studies of Mode I energy release rate in adhesively bonded width tapered composite DCB specimens Aurodhya Jyoti, Ronald F. Gibson *, Golam M. Newaz Advanced Composites Research Laboratory, Department of Mechanical Engineering, 5050 Anthony Wayne Dr, Rm # 2100, Wayne State University, Detroit, MI 48202, USA Received 11 August 2003; received in revised form 19 April 2004; accepted 21 April 2004 Available online 13 August 2004
Abstract The Mode I energy release rate, GI, derived from conventional uniform width double cantilever beam (DCB) test data depends on crack length. Data acquisition and analysis from such experiments can be simplified if GI is independent of crack length, particularly at high loading rates. Previous research by others has shown that width tapered double cantilever beam (WTDCB) specimens made from aerospace grade carbon/epoxy composite laminates without adhesive layers exhibit critical energy release rates which are independent of crack length. The purpose of the present investigation was to determine whether or not adhesively bonded WTDCB specimens of automotive type sheet molding compound (SMC) composites show similar behavior. It was observed that the critical energy release rate was practically independent of crack length for unidirectional carbon/epoxy WTDCB specimens without adhesive layers but not for unidirectional carbon/epoxy, unidirectional E-glass/epoxy or automotive SMC WTDCB specimens with adhesive layers, and that self-similar crack growth only occurred in unidirectional carbon/epoxy WTDCB specimens without adhesive layers. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: A. Adhesive joints; A. Polymer matrix composites; A. Short fiber composites; B. Fracture toughness; D. Fractography
1. Introduction Adhesively bonded composite joints, which are often used within automotive vehicle structures, may experience dynamic loading as in vehicle crashes. For proper design of such joints, it is important to know the dynamic fracture toughness, which characterizes the resistance to crack propagation. The critical Mode I energy release rate, which is a measure of fracture toughness, is often measured using double cantilever beam (DCB) specimens such as those described in ASTM standard D5528 [1]. Data from such tests generally depend on the crack length. *
Corresponding author. Tel.: +1 313 5773702; fax: +1 313 5778789. E-mail address: [email protected] (R.F. Gibson). 0266-3538/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.compscitech.2004.04.006
Several studies of fracture in adhesively bonded composites using DCB and other specimens have been reported in the literature. The critical energy release rate GIc of graphite/epoxy composites with adhesive strips at the interface was determined by Norman and Sun [2] using the DCB test and it was found that delamination fracture toughness increases substantially when adhesive strips are added at the interface, reaching a limiting value as the adhesive widths are increased. In continued research by the same authors with similar materials [3], good agreement was also found between quasi-static and dynamic critical load and crack growth data. Mode I fracture of epoxy bonded CFRP joints under quasi-static loading at different temperatures was studied by Ashcroft et al. [4] and it was found that the critical strain energy release rate increases with temperature and the failure locus transferred from
10
A. Jyoti et al. / Composites Science and Technology 65 (2005) 9–18
Table 1 Materials for different specimens Adherend
Adherend thickness (mm)
Adhesive thicknessa (mm)
Backing beam thickness (mm)
Initial crack length (mm)
SMC E-glass/epoxy Carbon/epoxy Carbon/epoxy
2.54 2.032 1.905 5.207
0.762 0.762 0.762 –
6.35 6.35 9.144 –
80 81 80 80
a
Adhesive layer thickness was controlled by mixing 0.762 mm glass beads in the adhesive.
predominantly in the composite substrate to predominantly in the adhesive layer. Mixed-mode fracture behavior of adhesively bonded carbon/epoxy composite joints was studied by Daghyani et al. [5] using a rubbermodified epoxy as the adhesive. It was found that Gc was dependent of bond thickness and the actual crack path in the joints. For poor bonding between the adhesive and the composite adherends, interfacial crackpropagation was observed for very thin bonds with alternating crack jumping from one interface to another across the bond line. However, for strong interfacial bonding, the crack was deviated from the precrack towards the composite adherend and propagated cohesively in the composite layer. Dynamic Mode-I delamination fracture toughness of a carbon/epoxy composite was studied by Guo and Sun [6] using a modified DCB specimen with an adhesive strip at the tip of the precrack. The adhesive strip substantially increased the crack initiation toughness so that after initiation an unstable crack-propagation was produced and high crack-propagation speed was achieved. In dynamic fracture toughness testing, however, it is difficult to measure the crack growth during testing. One possible solution to this problem is to use tapered double cantilever beam specimens having either tapered height or tapered width for which the calculated energy release rate is theoretically independent of crack length if pure bending is assumed. Daniel et al. [7] studied rate effects on delamination fracture toughness of toughened graphite/epoxy laminates. It was found that for a tapered width thin DCB specimen the energy release rate is independent of crack length. As explained in the next section, the tapered width design was selected for evaluation here due to its simplicity and ease of fabrication. The major objective of the current study is to investigate the quasi-static Mode I energy release rate of width tapered DCB (WTDCB) specimens of SMC (sheet molding compound), unidirectional E-glass/epoxy and carbon/epoxy composite materials (Table 1) with and without adhesive layers as a prelude to possible dynamic fracture tests of the same materials.
2. Specimen design The original thin WTDCB specimen, which was used by Daniel et al. [7] to measure interlaminar fracture
toughness of composite laminates, was selected and modified for the testing of adhesively bonded composite joints. Tapered height backing beams have also been used [8,9], but a complex nonlinear taper geometry is required, and the linearly tapered WTDCB of constant thickness is easier to fabricate. Initial tests showed that the stiffness of the original thin WTDCB specimen with adhesive layer was too low to sustain the load needed to grow the crack; so aluminum backing beams were used to increase the stiffness of the specimen. These aluminum backing beams were adhesively bonded to the outer faces of the composite specimen with a secondary adhesive layer as shown in Fig. 1. The original thin WTDCB specimen was loaded by a hinge attachment, but the modified specimen required higher loads to initiate crack growth. It was found that such large loads could not be supported by the hinge attachment, so two clevis pins inserted through holes in the backing beams were used to introduce the load into the backing beams as shown in Fig. 1. Irwin [10] defined the energy release rate, G to be the rate of change of potential energy with respect to the crack extension area. Under the assumption of linear elastic fracture mechanics (LEFM) and geometric linearity, for both load and displacement controlled systems, the energy release rate, G, for a test specimen can be defined by G¼
P 2 dC ; 2b da
ð1Þ
where P is applied load, C is specimen compliance, b is the specimen width and a is the crack length. Using Timoshenko beam theory and considering bending and shear deformations, Mostovoy et al. [10] derived the Mode I energy release rate for a uniform cross sectional DCB specimen as 4P 2 3a2 1 GI ¼ þ ; ð2Þ h E11 b2 h3 where h is the half of the specimen thickness and E11 is the longitudinal modulus of the beam. In the above equation, the first term represents the effect of bending deformation and the second term represents the effect of shear deformation. But for a thin, uniform cross-section DCB, h is very small and if h a, the shear contribution may be neglected. Then the above equation can be written as
A. Jyoti et al. / Composites Science and Technology 65 (2005) 9–18
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Fig. 1. Specimen with backing beams and adhesive layers.
GI ¼
12P 2 a2 : E11 b2 h3
ð3Þ
For a properly designed tapered width specimen, the beam width b at crack length a will increase linearly with increasing crack length a, so k = a/b = constant. So for a WTDCB specimen, Daniel et al. [7] showed that Mode I energy release rate can be expressed as GI ¼
12P 2 k 2 ; E11 h3
ð4Þ
which is independent of crack length. For a constant width DCB specimen the load increases up to a peak where the crack initiates and then the load drops gradually as the crack propagates. But for a WTDCB specimen the load remains constant after crack initiation. A typical load–displacement curve for a WTDCB specimen is shown in Fig. 2. The above equations represent the energy release rate of a homogenous DCB or WTDCB but do not include the effect of an adhesive layer. The effect of the adhesive layer was first considered by Penado [11] based on the Winckler foundation model. Penado considered the uncracked portion of the adhesive and the adherend as an elastic foundation. Olson [12] analyzed the uncracked part of a composite laminate DCB specimen by including the Saint-Venant effect. Considering bending, shear, elastic foundation and Saint-Venant effects, Liu et al. [13] showed that an improved model for the compliance
of an adhesively bonded composite DCB specimen with an adhesive layer along its middle surface is given by ( P2 12 GI ¼ 2 ½k3 a2 þ 2k2 a þ k 3 0 b EF k ðh þ tÞ3 ) 1 24va þ þ ; ð5Þ lGT ðh0 þ tÞ EF ðh0 þ tÞ3 where EF is the flexural modulus of the composite laminate or adherend, GT the transverse shear modulus of the composite laminate or adherend, h 0 the thickness of the adherend, t the half of thickness of the adhesive layer, k4 = 3K/[EFb(h 0 + t)3], K = 1/[(1/Kadherend) + (1/ Kadhesive)] the stiffness of the foundation per unit length, Kadherend = 2ETb/h 0 the stiffness of the adherend per unit length, Kadhesive = (b/t)[Ea/(1 ma2)] the stiffness of the adhesive per unit length, ET the transverse modulus of the adherend, Ea the YoungÕs modulus of the adhesive, ma the pPoissonÕs ratio of the adhesive, ffiffiffiffiffiffiffiffiffiffiffiffiffiffi v ¼ ðh=2pÞ EF =GT is the decay length of the Saint-Venant effect. By substituting k = a/b, we can rewrite Eq. (5) as ( 12 1 24 þ þ GI ¼ P 2 k 2 0 3 3 2 0 lG ðh þ tÞa T EF ðh þ tÞ EF kðh0 þ tÞ a ) 12 24v þ : ð6Þ þ 3 2 3 2 0 EF k ðh þ tÞ a EF ðh0 þ tÞ a
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Fig. 2. Load versus crack opening deflection for WTDCB specimen loaded at a crosshead rate of 0.0085 mm/s (0.02 in./min). From Daniel et al. [7].
For thin beams, the bending energy is the dominant portion of the total energy and the other energy terms can be neglected. But when thick backing beams and an adhesive layer are used, the effective specimen thickness increases and the other energy terms may be significant. Figs. 3 and 4 were generated by applying Eq. (6) and the properties in Table 2 to the case of adhesively bonded SMC with and without aluminum backing beams, respectively. However, as shown in Figs. 3 and 4, with the larger values of initial crack length, the bending energy term dominates the shear, elastic foundation and Saint-Venant energy terms. Similar conclusions were reached regarding the unidirectional E-glass/epoxy and carbon/epoxy materials with and without backing beams. Although thin backing beams may contribute a dominant portion of bending energy, which is desired
for this study, the backing beams may also exhibit yielding due to high bending stresses. Also there should be a hole in each backing beam in order to insert the clevis pins. Considering both effects, it is necessary to optimize the backing beam thickness so the bending energy is dominant and yielding can be avoided. For this study the thickness of the aluminum backing beam was selected to be 6.35 mm. The initial crack length was selected in such a way that at least 60% of the total energy is due to bending. Materials and material properties which are used to calculate the percentage contribution of the different energy terms at different crack lengths are tabulated in Tables 1 and 2. So for a thin WTDCB specimen having a sufficiently long pre-crack, the Mode I energy release rate mainly depends on the energy due to bending, which is inde-
Fig. 3. Variation of energy components with crack length for adhesively bonded SMC specimen without backing beam.
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Fig. 4. Variation of energy components with crack length for SMC with aluminum backing beam (SMC thickness = 2.54 mm).
Table 2 Material properties for different components of specimens Material
YoungÕs modulus (MPa)
PoissonÕs ratio
SMC (DMS 951)a Aluminuma Pliogripa Glass–epoxyb Carbon–epoxyb
10,300 69,000 517 38,620 148,285
0.3 0.3 0.3 0.3 0.3
Tensile strength (MPa) 72.5 21 2750
Note: Superscript ÔaÕ is for isotropic and superscript ÔbÕ is for orthotropic material. For orthotropic material the YoungÕs modulus is the longitudinal modulus.
pendent of crack length. For a properly designed specimen of this type, the other energy terms due to the through-the-thickness shear contribution, elastic foundation effect and Saint-Venant end effect, which depend on crack length, are negligible. For adhesively bonded composite joints, the other energy terms are not necessarily negligible, but they diminish at large initial crack lengths [14].
3. Test procedure As shown in Table 1, three types of composite materials were tested. Those materials were: (i) randomly oriented short E-glass fiber reinforced polyester sheetmolding compound (Budd Company – Plastic division SMC type DSM951), (ii) unidirectional continuous E-glass fiber reinforced epoxy (3M Scotchply 1002), and (iii) unidirectional continuous carbon fiber reinforced epoxy (Toray Composites America P2254-20305). Unidirectional E-glass/epoxy and carbon/epoxy laminates were made from 3M Scotchply 1002 E-glass/ epoxy prepreg tape and Toray P2254-20-305 carbon/ epoxy prepreg tape, respectively, by molding the prepreg tapes in a TMP composite vacuum press machine (manufactured by Technical Machine Products Corporation) [14]. For specimens with adhesive layers and backing
beams, shown in Fig. 1, a tough urethane adhesive (Ashland Pliogrip) was used for adhesive bonding (termed as primary adhesive layer) of tapered width DCB specimens made from each type of composite material. Following the automotive industry practice, no surface preparation was used prior to adhesive bonding. Aluminum plates of 6.35 mm thickness were used as backing beams on both sides of the specimen bonded by same adhesive (termed as secondary adhesive layers) to make it stiffer. Pre-cracks were introduced by placing Teflon film within the primary adhesive layer. Specimens without any adhesive layer, shown in Fig. 5, were made from unidirectional carbon/epoxy laminates by placing Teflon film in the middle of the laminates at one end to make the pre-crack. Three SMC specimens, two E-glass/epoxy specimens and one carbon/epoxy specimen, all with adhesive layers and backing beams were tested. For all specimens pre-cracks of length 80 mm and crack length to width (taper) ratio k = 2.4 were selected. Two carbon/epoxy specimens without any adhesive layers or backing beams were tested. The specimens with adhesive layers and backing beams were loaded at a quasi-static displacement controlled rate of 0.051 mm/s in an Endura Tec Smart Test servo-pneumatic testing machine. The maximum displacement of the actuator of this machine is limited to ±25.4 mm. The bending stiffness of the carbon/epoxy specimens without any
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Fig. 5. Specimens without any adhesive layers or backing beams.
adhesive layers was such that a larger MTS servo-hydraulic machine was required to produce the desired displacement at failure. The Mode I energy release rate was calculated by using Eq. (4), considering P as crack initiation load (where the crack growth started).
4. Results and discussion The crack initiation loads, calculated critical Mode I energy release rates from experiments and the fracture surface descriptions for the different specimens are given in Table 3. The first two adhesively bonded SMC
specimens failed with mixed composite/interfacial failure. Crack initiation started through the interface and then grew into the composites. The load increased very slightly at the end, where the failure was mainly within the composite. A typical load–displacement curve and fracture surfaces for this type of specimen are shown in Fig. 6. The third SMC specimen failed with fully interfacial failure. The load dropped suddenly with the crack started and the load increased again with the crack growth and the specimen failed, i.e., the load–displacement curve was stepwise. The load–displacement curve and the fracture surfaces for the third SMC specimen are shown in Fig. 7. The crack initiation
Table 3 Mode I critical energy release rates for different specimens Specimen no. a
Adherend
Crack initiation load (N)
Critical Mode I energy release rate (N/m)
1 2a 3a 4a
SMC SMC SMC E-glass/epoxy
578 170 332 778
365.95 31.66 120.74 763.55
5a 6a 7b 8b
E-glass/epoxy Carbon/Epoxy Carbon/epoxy Carbon/epoxy
1175 628 108 120
1741.62 432.89 407.78 594.31
a b
Specimen with adhesive layer and backing beams (Fig. 1). Specimen without adhesive layer or backing beam (Fig. 5).
Fracture surface Composite/interface Interface/composite Interface Mixed of adhesive, interface/ composite Interface Mid-surface Mid-surface
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Fig. 6. (a) Load–displacement curve and (b) failure surfaces for adhesively bonded SMC specimen with mixed composite/interfacial failure.
Fig. 7. (a) Load–displacement curve and (b) failure surfaces for adhesively bonded SMC specimen with fully interfacial failure.
load was about 300 N for SMC specimens. The load– displacement curve for E-glass/epoxy specimen shown in Fig. 8(a) was also stepwise but at the end it was
nearly constant. The fracture surfaces consisted of mixed adhesive, interfacial and composite failure, as shown in Fig. 8(b). The crack initiation load was the
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Fig. 8. (a) Load–displacement curve and (b) failure surfaces for adhesively bonded E-glass/epoxy specimen with composite/interfacial failure.
Fig. 9. (a) Load–displacement curve and (b) failure surfaces for carbon/epoxy specimen with adhesive layers.
highest for E-glass/epoxy specimens. The load–displacement curves for carbon/epoxy specimen with adhesive layers, shown in Fig. 9(a), was also stepwise and fracture surfaces were interfacial with changing
interface, shown in Fig. 9(b). For carbon/epoxy specimens without any adhesive layer, the failure occurred through the pre-cracked surface and a reasonably flat load–displacement curve after crack initiation was ob-
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Fig. 10. (a) Load–displacement curve and (b) failure surfaces for carbon/epoxy specimen without any adhesive layer.
served, as shown in Fig. 10(a). Of all the specimens tested, only the carbon/epoxy specimens without adhesive layer exhibited self-similar crack growth and gave a substantially flat load–displacement curve after crack growth initiation as in Fig. 2. The load increased very slightly with larger displacements due to the shortening of the moment arm at large flexural deformations. The failure surfaces are also shown in Fig. 10(b). If the crack growth occurs along the composite–adhesive interface or switches from interface to composite material, then the load required for crack initiation is very low, the crack growth is stepwise and with each increment of crack growth the load drops quickly. For such failure modes the crack growth was not self-similar and neither the Mode I fracture toughness of the composite nor the adhesive can be obtained from these experiments. If the adhesive bonding is good enough to force the crack growth to occur in the composite or in the adhesive layer, then the crack growth is self-similar and the load does not drop too much and the desired flat load–displacement curve after crack initiation can be achieved. It is clear from Table 3 that the crack initiation loads, the critical energy release rates and the appearance of the fracture surfaces were substantially different for supposedly identical specimens. As indicated earlier, the standard automotive industry practice of not using surface preparation procedures before adhesive bonding was followed here, and this may be a contributing factor to the scatter in the data. Further
research is needed on the effect of surface preparation on fracture toughness of adhesively bonded joints.
5. Conclusions The following observations were made from the experimental results: For adhesively bonded SMC specimens, the crack growth occurred along the composite–adhesive interface or in the composite. This means that the fracture toughness of the SMC composite is lower than that of the Pliogrip adhesive. The load–displacement curve was flat after crack initiation only for the pre-cracked carbon/epoxy composite laminates without adhesive layer whose fracture toughness is low enough that self-similar crack growth occurs through the same layer which includes the pre-crack. But for adhesively bonded composite joints, that type of curve was not achieved as the crack growth occurred along the composite–adhesive interface, in the composite, in the adhesive or in combinations of these modes. Energy release rate was independent of crack length for specimens without adhesive layers but not for specimens with adhesive layers, and self-similar crack growth only occurred in specimens without adhesive layers.
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The use of the WTDCB composite specimen with a tough adhesive like the Pliogrip urethane appears to be not a valid test method for measuring fracture toughness of the bonded joint. Significant scatter in the crack initiation loads, the corresponding critical energy release rates and the appearance of the fracture surfaces was observed for nominally identical specimens. The lack of surface preparation prior to adhesive bonding was a likely contributing factor, and further research on the role of surface preparation is needed. Finally, the relatively flat load–displacement curve after crack initiation indicates that the fracture toughness for crack propagation is independent of crack length. One of the main reasons for not achieving the desired flat displacement curve for adhesively bonded composite joints was that selfsimilar crack growth did not occur (i.e., the crack growth occurred along the composite–adhesive interface, in the composite, in the adhesive or in a combination of these modes). The use of a brittle adhesive layer with poor fracture toughness would probably cause the behavior of the adhesively bonded specimen to be similar to that of the carbon/epoxy composite laminate without adhesive layer, but the overall performance of the adhesively bonded structure would probably be degraded as well. Details of this work may be found in the thesis by Jyoti [14].
Acknowledgement This work was performed with the financial support of Ford Motor Company, and the technical advice of Carl Johnson, Matt Zaluzec and John Hill of the Ford Research Lab is gratefully acknowledged.
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