Analysis of resin-transfer-moulded single-lap joints

Composites Science and Technology 59 (1999) 1513±1518

Analysis of resin-transfer-moulded single-lap joints Lalit K. Jain a, Yiu-Wing Mai b,* a

Cooperative Research Centre for Advanced Composite Structures Ltd., 361 Milperra Road, Bankstown, NSW 2200, Australia Centre for Advanced Materials Technology, Department of Mechanical and Mechatronic Engineering, University of Sydney, Sydney, NSW 2006, Australia

b

Received 28 April 1998; received in revised form 27 November 1998; accepted 16 December 1998

Abstract This paper presents a fracture-mechanics-based approach to the prediction of the failure of single-lap joints manufactured by resin-transfer moulding. Since single-lap joints can undergo large deformation, a higher-order large-deformation theory is used to analyse the joint. Mode I and mode II components of energy release rate are determined from the loads and moments in the adherend and the overlap region at the end of the overlap. A linear failure criterion is used to predict the failure load. Comparison with experimental failure load data showed excellent agreement with theoretical prediction. # 1999 Elsevier Science Ltd. All rights reserved. Keywords: B. Fracture; C. Deformation; E. Resin transfer moulding (RTM); Single lap joint

1. Introduction Adhesively bonded composite lap joints are used extensively in aerospace structures. It has been observed that adherend delamination in the ply adjacent to the adhesive is a typical form of failure for adhesively bonded composite joints because of the weakness of the laminate in the through-thickness direction [1,2]. In the case of resin-transfer-moulded joints there is no adhesive layer at the joint and failure typically occurs at the interface of the adherends as a result of the peel stresses. Many investigators have analysed the failure of adhesively bonded joints. The failure criteria proposed in the literature are based either on the classical strength-of-materials approach or on the fracturemechanics approach. The strength-of-materials approach generally utilises a maximum stress or maximum strain failure criterion. Examples of these failure criteria can be found in Refs. [3±5]. Fracture-mechanics-based failure criteria have also been developed by many researchers and they have found that the strain energy release rate correlates well with joint fracture [6±11]. In summary, there are a large number of approaches and studies in the literature for adhesively bonded joints. With the advent of resin-transfer moulding techniques, it is possible to fabricate the complete composite * Corresponding author. Tel.: +61-2351-2290; fax: +61-2351-3760; e-mail: [email protected]

structure simultaneously, thereby avoiding the timeconsuming joining of various components. In such cases, a distinct layer of adhesive in the regions of overlap may not exist. Moreover, during co-curing of composite parts fabricated from pre-pregs, a layer of adhesive may not be required. Most of the failure criteria developed so far assume that the adhesive layer has a certain thickness. These failure criteria may not be applicable for joints where an adhesive layer does not exist. Therefore, a technique must be developed for analysing joints where an adhesive layer is nonexistent. In this paper, resin-transfer-moulded single-lap joint geometry is analysed by the use of large-deformation theory, and a fracture-mechanics-based failure criterion is proposed. This enabled us to predict failure without the detailed knowledge of stresses and strains in the joint region. The approach presented in this paper could easily be extended to other joint geometries. The theoretical results are compared with the experimental data to validate the model developed. 2. Analytical modelling 2.1. Analysis of single-lap joint geometry Fig. 1 shows the typical single-lap geometry where L1 is the free length and 2L2 is the overlap or joint length. During testing, at each end of the specimen an

0266-3538/99/$ - see front matter # 1999 Elsevier Science Ltd. All rights reserved. PII: S0266 -3 538(99)00006 -8

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Fig. 1. Con®guration of a single-lap joint subjected to tensile load.

aluminium end-tab was bonded. Aluminium tabs were used to provide a co-linear loading path for the specimens. It would also make it easier to grip the specimens without applying too much clamping force, which could otherwise cause damage in the matrix. An analytical model is developed for this geometry so that a comparison between the test results and model predictions can be provided. The adherends are assumed to have a symmetric lay up. It is also assumed that both adherends are of equal thickness, H. Since a single-lap joint can undergo large deformation when a tensile load is applied, a higher-order von Karman deformation theory [12] is employed to analyse the test geometry. In using this theory, the forces and bending moments are determined in the free length region of the adherends and in the overlap region. By using a fracture-mechanics-based approach proposed by Williams [8], the mode I and mode II components of the energy release rate are then determined. The failure of the joint is then predicted by the application of a suitable failure criterion. The free length region and the overlap region are analysed separately. The positive sign convention and the geometric axes used in the analysis are shown in Fig. 2. On account of the anti-symmetry of the specimen, only half of the test specimen needs to be analysed. The governing equilibrium equations and constitutive laws for the case of plane deformations (plane stress or plane strain) may be written as follows by using higherorder shear deformation laminated plate theory. The constitutive relationships for the free-length region are given by      A1 B1 N1x u10;x ‡ 12 …w1;x †2 ˆ …1† M1x B1 D1 1;x Q1x ˆ K1 … 1 ‡ w1;x †

…2†

and the equilibrium equations are dN1x ˆ0 dx

…3†

Fig. 2. Positive sign convention and coordinate geometry used in the analysis.

where Nx is the in-plane force resultant, Mx is the moment, Qx is the shear force, u0 is the mid-plane displacement, is the bending rotation, and w1 is the out-of-plane displacement. A, D, K are the axial, bending and shear sti€ness and B is the extension-bending coupling term which is identically zero for symmetric laminates. Note that the subscript `1' represents the free length region. For the overlap region, the governing equilibrium and constitutive relations will be identical with subscript `1' replaced by subscript `2' and coordinate x replaced by co-ordinate x0 . Solution for the force balance relation [Eq. (3)] in x-direction results in N1x ˆ N2x ˆ Na

…6†

where Na is the applied load. On combining equilibrium equations with the constitutive equations, the moment balance equations can be re-written as follows in terms of out-of-plane displacement: 2 d4 w 2d w ÿ  ˆ0 dx4 dx2

…7†

where

d2 w1 dQ1x ˆ0 ˆ N1x dx2 dx

…4†

dM1x ÿ Q1x ˆ 0 dx

…5†

s Na
 ˆ ADÿB2 ÿNa A K ‡1

…8†

L.K. Jain, Y-W. Mai / Composites Science and Technology 59 (1999) 1513±1518

Note that in the above expressions, the subscripts have been dropped with the understanding that 1 refers to free length region and 2 refers to the overlap region. The solution for the governing moment Eq. (7) can be expressed as follows for the overlap and free length regions: w1 ˆ A1 sin h…1 x† ‡ A2 cos h…1 x† ‡ A3 x ‡ A4

…9†

w2 ˆ A5 sin h…2 x† ‡ A6 cos h…2 x† ‡ A7 x ‡ A8

…10†

where A1 ; ::; A8 are constants which can be determined by making use of the following boundary and matching conditions: w1 ˆ ˆ 0

0

w2 ˆ M2x ˆ 0 w1 ˆ w2

at x ˆ L2 at x ˆ L1 and x0 ˆ 0

1 ˆ 2 Q1x ˆ Q2x

at x ˆ L1 and x0 ˆ 0 at x ˆ L1 and x0 ˆ 0

M2x ˆ M1x ÿ N1x H2

at x ˆ L1 and x0 ˆ 0

…11†

Note that the bending moment, shear force and bending rotation can be expressed in terms of out-of-plane displacement as follows:  2   B AD ÿ B2 Na d w ‡1 Na ÿ A K A dx2 dMx Qx ˆ dx Qx dw ‡ ˆ dx K

Mx ˆ

…12†

2.2. Failure prediction Since the adherends have symmetric lay-up, the extension-bending coupling term, B, is identically zero. In addition, as the laminate is subjected to in-plane loading, the e€ect of shear deformation will be very small. The shear deformation e€ects can, therefore, be neglected by assuming the out-of-plane shear sti€ness, K, to be in®nite. On making use of these simpli®cations, following the approach adopted by Fernlund et al. [9] and Williams [8], the total energy release rate, G, at the end of the overlap (i.e. at x ˆ L1 and x0 ˆ 0) can be obtained from:

Gˆ

N2a M21x N2a M22x ‡ ÿ ÿ 2A1 2D1 2A2 2D2

where M1x is evaluated at x ˆ L1 and M2x is evaluated at x0 ˆ 0. The mode I and mode II components of the energy release rate can be obtained using the method proposed by Fernlund and Spelt [10] M21x 4D1 N 2 M2 N2 M2 GII ˆ a ‡ 1x ÿ a ÿ 2x 2A1 4D1 2A2 2D2 GI ˆ

…13†

…14†

Once the mode I and mode II components of the energy release rates are known, a simple linear failure criterion as proposed below can be used to predict failure. GI GII ‡ ˆ1 GIc GIIc

at x ˆ 0

1515

…15†

where GIc is the mode I critical energy release rate and GIIc is the mode II critical energy release rate. GIc and GIIc for any material or laminate can be determined from standard double-cantilever-beam (DCB) and endnotched-¯exure (ENF) tests, respectively. It should be added that while there are several other failure criteria based on fracture mechanics, the linear criterion of Eq. (15) has been shown to be most suitable for composite laminates and is demonstrated to give good agreement with experimental data. (See for example, Refs. [6,10].) We, therefore, believe the linear criterion is a reasonable choice but it should be further veri®ed with other joint geometry. An iterative approach needs to be adopted to predict failure load from Eq. (15). Initially a small load can be applied to the geometry. Based on this load the mode I and mode II components of the energy release rate can be determined. The new mode I component, GI,new can be determined as follows: GI;new ˆ

1 GIc

‡

1   GII GI

1 GIIc

…16†

and the new mode II component is then given by: GII;new ˆ

  GII GI;new GI

…17†

The total energy release rate is then computed from Eqs. (16) and (17) and the load needed to give the required energy release rate is determined. The applied load is then adjusted accordingly and the process is repeated until the loads required in two successive steps reach convergence. Convergence was assumed to have

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been reached when the di€erence in failure load in two successive steps was less than 0.001%. 3. Experimental investigation 3.1. Materials and manufacturing The test panels used for the experimental programme were manufactured from Ciba Composites Injectex1 uniweave carbon fabric GU230E01 and GY260 epoxy resin/HY917 hardener/DY070 accelerator via the RTM technique. Uniweave material has the majority of its ®bres oriented in the warp direction, in this case in excess of 0.9 ®bre volume fraction, with the remaining ®bres in the weft direction to hold the warp ®bres in place for ease of handling. Single lap panels with an overlap length of 30 mm and measuring 250 mm360 mm were ®rst formed by overlaying two [0/‹45/90]s fabric stacks followed by debulking under vacuum and heat to produce a preform which was subsequently resin transfer moulded. The thickness of each adherend was 1.5 mm and the thickness of the overlap region was 3 mm. The panels were cured at a temperature of 80 C for 4 h and then post-cured at 160 C for a further 4 h. More information on the manufacturing and testing techniques can be found in Ref. [13]. 3.2. Specimen preparation Specimens were cut up from test panels after drying in the oven at 60 C for 4 h. As shown in Fig. 1, all specimens were 25.4 mm wide and had an overlap length of 30 mm. The free length L1 of each adherend was 90 mm for the specimens cut from panel No. 1 and was 70 mm for the specimens cut from panel No. 2. This allowed us to investigate the e€ect of free length on the strength of the joint. The specimen geometry conformed very well to the theoretical model. Because RTM technique was used to fabricate the specimens the quality control was excellent. The overlaps had square ends, as shown in Fig. 1, and they gave much less scatter in failure loads than taper ends. The specimens were identi®ed by two numbers. For example, the specimen numbered 2±1 refers to specimen No. 2 cut from panel No. 1. As mentioned previously, aluminium end tabs were bonded on one side of each adherend to facilitate a co-linear loading path. 3.3. Testing The specimens were tested in tension in an Instron machine at room temperature. A loading rate of 0.5 mm/min was used for all specimens. The applied load and the axial displacement between the two gripping points were measured by using a computer data logger.

4. Results and discussion For all test specimens, the tensile loads increased almost linearly with axial displacement up to ®nal failure with a loud bang. Failure typically occurred at the interface between the two adherends due to the absence of an adhesive layer. Normally, if an adhesive layer was present, failure would happen at the interface of the ®rst and second ply of the composite. Tables 1 and 2 give the ultimate failure loads for all specimens. The average failure loads were 11.22 and 12.37 kN for specimens with 90 and 70 mm free lengths, respectively. Relatively small scatter in the failure strength data indicates uniformity of structure in the panels. From these results it appears that the failure strength improves with the reduction in free length. To compare the test data with the analytical model predictions, mechanical properties of the material are required, which in turn means that the volume fraction of the laminate must be known. The volume fraction of the laminate was determined to be 67% from the thickness of the adherends (1.5 mm), areal density of the uniweave Injectex (220 g/m2) and the density of T300 carbon ®bres (1.75 g/cm3). The mechanical properties, as determined from micromechanics relations, are given in Table 3. In addition, to predict failure load, modes I and II critical energy release rates are required. The modes I and II critical energy release rates used in the model are also given in Table 3. These values are taken from Ref. [14] where experiments were conducted on the same ``uniweave'' material using DCB and ENF Table 1 Failure loads and displacements for specimens with L1=90 mm Specimen

Failure load (kN)

1±1 1±2 1±3 1±4 1±5 1±6 1±7

10.68 11.20 11.54 11.45 11.09 11.81 10.75

Average

11.22‹0.415

Table 2 Failure loads and displacements for specimens with L1=70 mm Specimen

Failure load (kN)

2±1 2±2 2±3 2±4 2±5 2±6 2±7 2±8

11.18 12.5 12.6 12.97 13.95 10.46 12.12 13.22

Average

12.37‹1.120

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specimens. A comparison of model predictions and experimental data is given in Table 4. It can clearly be seen that the model predictions are slightly higher than the experimental data. This could be attributed to several factors; the sti€ness properties used in the model may be higher than the actual sti€ness properties as the micromechanics relations [15] do not adequately include tow waviness. Moreover, the mode I and II critical energy release rates used in the model may be higher. However, despite these uncertainties, the model is capable of predicting the failure with reasonable accuracy. The model predictions can be improved by including the precise mechanical and fracture properties. Fig. 3 shows the variation of failure load as a function of free length. The overlap length was kept constant at 30 mm. Experimental data is also included in this ®gure to further illustrate the comparison between experimental data and model predictions. It can be seen from this ®gure that at smaller free lengths, the failure load increases due to reduction in the bending moment at the edge of the overlap region. With increasing free length, the failure load reaches a plateau or a constant value. However, further tests are required to validate

the model predictions, particularly for short free lengths that show an increase in failure loads. Fig. 4 shows the e€ect of the overlap length on failure strength. The free length was kept constant here. It can clearly be seen that with increasing overlap length, the failure load also increases.

Table 3 Material properties of ``Uniweave'' carbon/epoxy RTM laminae

5. Conclusions

E11 E22 E33 G12 12 (GPa) (GPa) (GPa) (GPa) 126.8

20.23

7.66

3.6

13

23

GIIc GIc (kJ/m2) (kJ/m2)

0.086 0.251 0.251 0.41

1.3

Table 4 Comparison of analytical results and experimental data Free length (mm)

Test results (kN)

Analytical model predictions (kN)

70 90

12.37‹1.12 11.2‹0.42

12.326 12.326

Fig. 4. E€ect of overlap length on failure load prediction.

An analytical model based on a linear failure criterion has been developed to predict the failure strength of resin transfer moulded single lap joints. The model predictions agree quite well with a limited range of experimental data. But further work is required to verify the e€ect of short free lengths on failure load and the applicability of the linear criterion to other joint geometry. Acknowledgements The authors would like to thank A. Deveth, K. Houghton and P. Allatta of the CRC-ACS Ltd for their assistance in preparing the specimens for testing. References

Fig. 3. E€ect of free length on failure load prediction.

[1] Adams RD. Strength predictions for lap joints, especially with composite adherends. A review. International Journal of Adhesion 1989;30:219±42. [2] Kairouz KC, Matthews FL. Strength and failure modes of bonded single lap joints between cross-ply adherends. Composites 1993;24:475±84. [3] Harris JA, Adams RD. Strength prediction of bonded single lap joints by non-linear ®nite element methods. International Journal of Adhesion 1984;4:65±78. [4] Crocombe AD, Bigwood DA, Richardson G. Analysing structural adhesive joints for failure. International Journal of Adhesion and Adhesives 1990;10:167±78.

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[5] Czarnocki P, Piekarski K. Non-linear numerical stress analysis of a symmetric adhesive bonded lap shear joint. International Journal of Adhesion and Adhesives 1986;3:157±60. [6] Johnson WS. Stress analysis of the cracked-lap shear specimen: an ASTM round-robin. Journal of Testing and Evaluation 1987;15:303±24. [7] Suo Z, Hutchinson JW. Steady-state cracking in brittle substrates beneath adherent ®lms. International Journal of Solids and Structures 1989;25:1337±53. [8] Williams JG. On the calculation of energy release rates for cracked laminates. International Journal of Fracture 1988;36:101±19. [9] Fernlund G, Papini M, McCammond D, Spelt JK. Fracture load predictions for adhesive joints. Composites Science and Technology 1994;51:587±600. [10] Fernlund G, Spelt JK. Failure load prediction of structural

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[15]

adhesive joints. Part I: analytical method. International Journal of Adhesion and Adhesives 1991;11:213±20. Hamaush SA, Ahmad SH. Fracture energy release rate of adhesive joints. International Journal of Adhesion and Adhesives 1989;9:145±53. Von Karman T. Festigkeitsprobleme in maschinenbau. Encycklopadie der matimatischen wissenchaftenn 1910;4:339. Tong L, Jain LK, Leong KH, Kelly D, Herszberg I. Failure of transversely stitched RTM lap joints. Composites Science and Technology 1999;58:221±7. Jain LK. Improvement of interlaminar properties in advanced ®bre composites with through-thickness reinforcement. CRC-ACS-TM94012, Cooperative Research Centre for Advanced Composite Structures, 506 Lorimer Street, Fishermens Bend, VIC 3207, 1994. Ishikawa T, Chou T-W. Sti€ness and strength behaviour of fabric composites, vol. 17, 1982. p. 3211±20.