High density closed-cell HDPE foams (450–950 kg/m3) were prepared by compression molding, and torsion rectangular tests were performed to measure their shear modulus in order to study: (1) the relationship between the modulus as a function of the density, and (2) to determine the effect of thin skins. Based on the assumption that the twist stiffness (product of shear modulus and moment of inertia) of the foams is the sum of the twist stiffness of the skin layers and the core part, several structural foam models are proposed. We found that structural foam models give better results than uniform foam models, indicating that thin skins have an important effect of the shear modulus of polymer foams.
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References
1.
1. Zhang, Y., Rodrigue, D. and Aït-Kadi, A. (2003). High Density Polyethylene Foams I: Polymer and Foam Characterization, accepted by J Appl Polym Sci.
2.
2. Zhang, Y., Rodrigue, D. and Aït-Kadi, A. (2003). High Density Polyethylene Foams II: Elastic Modulus, accepted by J Appl Polym Sci.
3.
3. Zhang, Y., Rodrigue, D. and Aït-Kadi, A. (2003). High Density Polyethylene Foams III: Tensile Properties, accepted by J Appl Polym Sci.
4.
4. Zhang, Y., Rodrigue, D. and Aït-Kadi, A. (2003). High Density Polyethylene Foams IV: Flexural and Tensile Moduli of Structural Foams, accepted by J Appl Polym Sci.
5.
5. Throne, J.L. (1996). Mechanical Design of Foams, Thermoplastic Foams, p. 425-425, Sherwood Publishers, Hinckley, Ohio .
6.
6. Lu, H., Zhang, X. and Knauss, W.G. (1997). Uniaxial, Shear, and Poisson Relaxation and Their Conversion to Bulk Relaxation: Studies on Poly(methyl methacrylate) , Polym Eng and Sci, 37(6): 1053–1064 .
7.
7. Hou, J.P., Ruiz, C. and Trojanowski, A. (2000). Torsion Tests of Thermosetting Resins at Impact Strain Rate and under Quasi-Static Loading , Mater Sci Eng A Struct Mater Prop Microstruct Process, 283(1): 181–188 .
8.
8. Headifen, G.R. and Fahrenthold, E.P. (1991). Mechanical and Electrical Properties of Glass and Carbon Fiber-Reinforced Composites , J Energy Resources Tech Trans ASME, 113(3): 176–181 .
9.
9. Zhu, H.X., Knott, J.F. and Mills, N.J (1997). Analysis of the Elastic Properties of Open-Cell Foams with Tetrakaidecahedral Cells , J Mech Phys Solids, 45(3): 319–343 .
10.
10. Farshad, M., Wildenberg, M.W. and Flueler, P. (1997). Determination of Shear Modulus and Poisson’s Ratio of Polymers and Foams by the Anticlastic Plate-Bending Method , Mater Struct, 30(200): 377–382 .
11.
11. Gibson, L.J. and Ashby, M. (1997). The Mechanics of Foams: Basic Results in Cellular Solids: Structure and Properties, 2nd edn, pp. 189–197, Cambridge University Press, Cambridge .
12.
12. Throne, J.L. (1976). Mechanical Properties of Thermoplastic Structural Foams, In: Wendle, B.C. (ed.), Engineering Guide to Structural Foams, p. 97-97, Technomic Publishing Co., Westport. Conn .
13.
13. Zhang, Y., Rodrigue, D., Zhang, Z. and Aït-Kadi, A. (2001). The Control of Polyethylene Foam Morphology, PPS-17, Montreal .
14.
14. Rheometric Scientific Inc. Test Fixtures, Geometries and Formulas, Instrument Manual: Advanced Rheometric Expansion System ARES, p. 27–32.
15.
15. McLaughlin, R. (1977). A Study of the Differential Scheme for Composite Materials , Inter. J. Eng. Sci., 15: 237–244 .
16.
16. Farber, J.N. and Farris, R.J. (1987). Model for Prediction of the Elastic Response of Reinforced Materials Over Wide Range of Concentration , J Appl Polym Sci, 34: 2093–2104 .
17.
17. Eric, T., Roger, L. and Bernard, N. (1998). Quantitative Approach towards the Measurement of Polypropylene/(ethylene-propylene) Copolymer Blends Surface Elastic Properties by AFM , Nanotechnology, 9: 305–315 .
18.
18. Gonzalez, H. (1976). Efficiency of Foams in Stiffness Applications , J Cell Plast, 12(1): 49–58
19.
19. Cauchy, A. (1828). Sur les Équations qui expérimentent les Conditions d’équilibre ou les Lois de Mouvement Intérieur d’un Corps Solide, Exercices de Mathématique, Paris .
20.
20. Timoshenko, S. and Goodier, J.N. (1970). General Theorems, Theory of Elasticity, 3rd edn, p. 235–242, McGraw-Hill Book Co., New York .
21.
21. Boresi, A.P. and Chong, K.P. (1987). Three-Dimensional Equations of Elasticity, Elasticity in Engineering Mechanics, p. 527–537, Elsevier Science Publishing Co., Inc., New York .
22.
22. Hsu, T.T.C. (1984). Torsion of Homogeneous Members, Torsion of Reinforced Concrete, pp. 3–50, Van Nostrand Reinhold Company Inc., New York .
23.
23. Timoshenko, S. and Goodier, J.N. (1970). Torsion, Theory of Elasticity, 3rd edn, pp. 291–349, McGraw-Hill Book Co., New York .
24.
24. Boresi, A.P. and Chong, K.P.(1987). Prismatic Bar Subjected to End Load, Elasticity in Engineering Mechanics, pp. 318–335, Elsevier Science Publishing Co., Inc. New York .
25.
25. Nemat-Nasser, S. and Hori, M. (1999). Micromechanics: Overall Properties of Heterogeneous Materials, 2nd edn, p. 79-79, Elsevier .
26.
26. Maron, M.J. (1982). Numerical Methods for Ordinary Differential Equations, Numerical Analysis: A Practical Approach, 2nd edn, pp. 392–398, Macmillan Publishing Company .
