Prediction of the Flexural Modulus of Fibre Reinforced Thermoplastics as used for Kayak Paddle Blades. P.D. EWART* AND CJR VERBEEK The Department of Materials and Process Engineering. The University of Waikato, Hamilton, New Zealand. E-mail: *p.ewart@waikato.ac.nz

Overview Introduction Composite materials and their interactions The model accounting for the interfacial layer Experimental Results and discussion Conclusion

Introduction A strong link between paddler performance and paddle stiffness [1] Modelling mechanical properties of composite materials to aid product design Inaccuracies inherent in theory due to assumptions

Introduction (cont) Discrete layers seen within a composite An improved model accounting for a non-bonded layer at the interface

Composite materials and their interactions Modelling component interaction Surfaces between components, interface Intermediate third layer, interphase Three interphases and two interfaces Non-contact region to account for the interface

The model with account for the interfacial layer From previous work a model based on simple beam theory gave a reasonable prediction for flexural modulus [2] To account for non-contact regions the equivalent section is reduce to an effective section [3]

The model with account for the interfacial layer (cont) Where;

The model with account for the interfacial layer (cont)

Experimental Test samples: Injection moulded, glass fibre/ LLDPE wood fibre/ LLDPE Kayak paddle blades, glass fibre/ PP carbon/ PA

Results and discussion The improved model shows similar trend to experimental values with excellent approximation for modulus values using 2μm non-contact depth

Results and discussion (cont) Sample Experimental modulus Predicted modulus Glass/ PP (Aplax) 5.8 GPa (σ = 0.02) 5.3-8.0 GPa Carbon/ PA (Duralon) 20.2 GPa (σ = 1.35) 19.1-27.1 GPa Manufacturers only provide limited data on many commodity materials Non-contact values may be better gained by density measurement to account for voidage

Conclusion The assumption of perfect bonding using the elemental approach is greatly improved when some account is made for non-contact regions The model shows sensitivities to both non-contact value and elastic modulus value.

References Carreira, R.P., Q.H. Ly, and G. Lagante. A bicycle frame Finite Element Analysis: standard tests and common cycling situations simulation. in The 4th International Conference on the Engineering of Sport. 2002: Blackwell Science. Ewart, P. D. and C. J. R. Verbeek (2005). Prediction of the Flexural Modulus of Composite Materials for Sporting Equipment. Asia-Pacific Conference on Sports Technology., Tokyo, Japan, Australian Sports Technology Alliance Pty Ltd. Moore, D. R. and M. J. Ironman (1973). “The prediction of the flexural rigidity of sandwich foam mouldings.” Journal of Cellular Plastics 10 (5). Throne, J. L. (1972). “A note on the mechanical strength of self-skinning foams.” Journal of Cellular Plastics 8(4). Wu, J.-S. and Y. Tsong-Ming (1994). “Studies on the Flexural Modulus of Structural Foams.” Journal of Polymer Research (1): 61-68.

Acknowledgments New Zealand Lottery Grants Board Lottery Ministers discretionary fund The Department of Materials Engineering The University of Waikato, Hamilton, New Zealand. Waikato Centre of Advanced Materials