23rd Nordic Seminar on Computational Mechanics NSCM-23 A. Eriksson and G. Tibert (Eds) KTH, Stockholm, 2010c
MECHANICAL RESPONSE AND FRACTURE OF
Harald Osnes, Dag McGeorge and Geir O. Guthu
2 EXPERIMENTAL STRENGTH MEASUREMENTS
In several recent research projects, the strength of adhesively bonded joints has been inves-tigated experimentally. Here we will present a set of results obtained within the context of a network of excellence on marine structures (MARSTRUCT), to which one of the authors be-longs. A set of double-lap shear joints was analysed. In all cases, the inner adherend was made of 10 mm steel, while the outer adherends consisted of 0/90 woven rowing glass fibre reinforced plastics (GFRP) or 0/90 uni-directional carbon fibre reinforced plastics (CFRP) laminates of various thicknesses. The composite laminates were bonded to the steel plate using an epoxy adhesive of the type Araldite 2015. More details are available from1.
The measured failure loads for various overlap lengths are shown in Fig. 1. It is seen that for short overlap lengths, the strength is proportional to the overlap length. This behaviour lasts until a plateau level is reached, from which the failure load is almost constant and does not depend on the overlap length. The same kind of strength behaviour of bonded steel-composite joints was obtained in a recent EUCLID project2.
0 50 100 150 200 250
0 10 20 30 40 50 60 70 80 90 100
Overlap length (mm) Failure load (Fmax ) (kN)
3mm CFRP overlaps 5mm GFRP overlaps 6mm GFRE overlaps
Figure 1: Failure loads of double-lap shear joints made of steel/CFRP and steel/GFRP.
In the experimental studies reported above, the thickness of the adhesive layer was the same for each set of test specimens. Thus, the effect of adhesive layer thickness on joint strength could not be studied. However, in a similar joint industry project on patch repair3, test specimens with different values of the adhesive thickness were produced. In that study it was shown that the adhesive layer thickness played a negligible role on the joint strength.
3 ANALYSIS USING STRENGTH OF MATERIALS APPROACH
3.1 Critical stress approach
The capacity of adhesive joints has traditionally been analysed using a strength of materials method, of which the critical stress approach is the simplest. This is an elastic stress-based
Harald Osnes, Dag McGeorge and Geir O. Guthu
method for predicting the strength, and it is assumed that fracture of the bondline will occur when the maximum shear stress in the adhesive layer reaches a critical level. The critical stress level is determined through comparison of theoretical stress analysis and the experimentally observed failure load of a selected joint with a specific overlap length. The distribution of the adhesive shear stresses in the joint is modeled using, e.g., the classical theory of Volkersen4, or the modified version developed by Tsai et al.5, in which adherend shear deformations are included. Analysing the joint subjected to the measured failure load, the critical stress level is defined as the maximum value of the shear stresses in the adhesive layer. Using this value as the maximum allowed stress level, the critical stress approach offers reasonable strength predictions for joints with overlap lengths close to the one selected, but the overall strength behaviour as illustrated in Fig. 1 is not offered.
3.2 Critical plastic strain approach
A slightly more complex analysis method is provided by the critical plastic strain approach.
This method is based on the assumption of elastic-plastic behaviour of the shear stresses in the bondline. Thus, plastic effects of the adhesive layer are included, and it is assumed that the joint fails when a critical plastic strain is reached. The theoretical foundation of the method might be provided by the well-known work of Hart-Smith6 or the extended theory derived by Osnes and McGeorge2. In the critical plastic strain approach, the yield stress and the maximum plastic strain of the adhesive layer must be determined. The former value is determined from the experimentally observed failure load of a joint with a short overlap length, while the latter critical property is obtained from the result of a joint at the plateau level. The method offers strength predictions that agree well with the results presented in Fig. 1. However, the theoretically obtained failure loads depend considerably on the adhesive layer thickness, a feature that is not supported by experimental strength measurements.
4 ANALYSIS USING INELASTIC FRACTURE MECHANICS APPROACH
4.1 Analytical derivations
Recently, McGeorge derived an energy release rate formulation accounting for plastic defor-mations7. It models the fracture process that causes failure of bonded joints and accounts for the energy released and consumed in the various parts of the bonded assembly during fracture. It is essential that the nonlinear inelastic behaviour of the adhesive bondline is taken into account.
The strength parameters to be determined from experiments is the adhesive yield stress and the fracture resistance. In the work of McGeorge7, certain closed form equations were derived for the fracture load of some simple joint geometries, and good agreement was demonstrated with experimental results.
4.2 Finite element analysis using cohesive elements
In the present study, the new energy release rate formulation7 has been investigated for more general joint geometries. Finite element analysis (FEA) using cohesive elements of the Abaqus software package has been conducted. The equations derived by McGeorge for simplified geometries have been confirmed. Furthermore, the general applicability of FEA has permitted
Harald Osnes, Dag McGeorge and Geir O. Guthu
comparison of theoretical predictions with experiments for a wider range of geometries. Again, very good agreement with experimental results has been obtained. The strength behaviour from Fig. 1 is excellently represented. In addition, the present fracture-based strength method predicts failure loads that are almost independent of the thickness of the adhesive layer. This contributes to gaining confidence in adhesive bonding technology, and this improved confidence will be important for implementation of adhesive bonding in the industry.
5 CONCLUSIONS
In this study, the strength of adhesively bonded double-lap shear joints has been investigated.
Experimentally measured failure loads have been presented and compared with predictions of-fered by theoretical analysis methods. The strategy is to apply the measured strength values for a few (typically one or two) joints to determine the critical strength parameters required in the theoretical models.
The capacity of adhesive joints has traditionally been modeled using a strength of materi-als approach. However, the results provided by such methods do not agree with experimental predictions. Thus, a new fracture-based energy release rate formulation has been derived. Ana-lytical relations have been developed for simplified geometries and FEA using cohesive elements has been conducted for more general joint geometries. In both cases, the results agree well with failure loads measured experimentally.
REFERENCES
[1] Hashim, S. et al. Fabrication, testing and analysis of steel/composite dls adhesive joints. In Soares, G. & Das (eds.) Analysis and design of marine structures, 379–385 (London: Taylor
& Francis Group, 2009).
[2] Osnes, H. & McGeorge, D. Experimental and analytical strength analysis of double-lap joints for marine applications. Composites: Part B 40, 29–40 (2009).
[3] McGeorge, D. et al. Repair of floating offshore units using bonded fibre composite materials.
Composites: Part A 40, 1364–1380 (2009).
[4] Volkersen, O. Die niektraftverteilung in zugbeanspruchten mit konstanten laschenquerschrit-ten. Luftfahrtforschung 15, 41–47 (1938).
[5] Tsai, M. Y., Oplinger, D. W. & Matthews, F. L. Improved theoretical solutions for adhesive lap joints. Int. J. Solids Structures 35, 1163–1185 (1998).
[6] Hart-Smith, L. J. Adhesive-bonded double-lap joints. NASA CR-112235 1–106 (1973).
[7] McGeorge, D. Inelastic fracture of adhesively bonded overlap joints. Eng. Fract. Mech. 77, 1–21 (2010).
23rd Nordic Seminar on Computational Mechanics NSCM-23 A. Eriksson and G. Tibert (Eds)
KTH, Stockholm, 2010