Static versus. dynamic elastic moduli of multiphase polymeric composite materials.

Luca, Dana Motoc ; Cerbu, Camelia ; Soica, Adrian 等

1. INTRODUCTION

The experimental data presented herein are natural consequences of an elaborated work in the field of advanced materials development, manufacturing and characterizing with the aim of providing a working frame for further material combinations with controlled mechanical, electrical or thermal properties (Curtu & Motoc Luca, 2008). These properties can be tailored knowing deeply the material behaviour in different circumstances and rely on extensive experimental research. These materials were developed with the aim to be used in structural applications such as force/pressure sensors, electromagnetic shields, boat hulls, automotive components.

Technical literature provide relatively numerous references with respect to the elastic moduli evaluation, both statically and dynamically, theoretically and experimental, in case of polymeric composite materials, particle or fibber reinforced, but when a multiphase combination is considered the references are scarcely, not necessarily due to the researchers' unfocusing on the subject but mostly due to the time consuming issue (Motoc Luca & Teodorescu, 2008); (Ramadan, 2008).

The paper herein approaches the theoretical and experimental issues on a particular class of polymeric multiphase composite materials, namely particle-fiber combination with the aim of retrieving the mechanical properties such as elastic coefficients. The experimental works were carried out using both statical and dynamical measuring principles and the data will be used to compare the material behaviour under given circumstances and underline the main influencing factors on the aimed property.

2. THEORETICAL APPROACH

The micromechanics of composite materials represent the best environment for the elastic moduli prediction in case of these combinations. It is beyond the purpose of this article to present an extended approach on the subject. Nonetheless, a small direction will be given in order to have an overall idea about the theoretical frame. Furthermore, a homogenization scheme was applied to retrieve the elastic moduli of the multiphase composites studied herein, using in the 1st step the well known Mori-Tanaka expressions, followed in the 2nd step by the Halpin-Tsai ones.

With respect to the last step, applied to the homogenized matrix and to the unidirectional, long fibres, the complex elastic moduli on longitudinal and transversal directions have the following expressions:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

where

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

respectively,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

In the previous relations, the complex modulus is in the form of [E.sup.*] = E' + i x E", E' being the storage modulus and E" the loss modulus. The f and m indices correspond to the fibers and matrix, respectively, [xi] being a shape factor defined as a ratio between the fibers lenght, l, and its diameter, d.

In case of long, random fibers the complex effective elastic moduli can be expressed as follows:

[E.sup.*.sub.c = 3/8 x [E.sup.*.sub.L] + 5/8 x [E.sup.*.sub.T (5)

and after replacing with the previous formulae:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)

where

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

representing the loss factor of the overall composite.

In the previous expression:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (10)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (11)

3. EXPERIMENTAL RESEARCH

The polymeric composite samples were manufactured using different volume fractions of ceramic particles ([Al.sub.2][O.sub.3]) embedded along with a glass fiber mat into a polymeric matrix. The volume fraction ranges from 0%, 5% to 10%. The static measurements were carried out in 3 point bending mode with a free bending lenght of 50 mm, at room temperature on a Lloyd LR 5K measuring device. The dynamic measurements were carried out in 3 point bending mode with a free bending length of 50 mm, at frequency of 1 Hz, temperature range from -30[degrees] C to 200[degrees] C using a measurement device from Netzsch (Germany) -DMA 242 C.

Figure 1 shows the DMA curves of a sample with 5 % volume fraction of ceramic particles at a frequency of 1 Hz in a temperature range from -30[degrees]C to 200[degrees]C. During the first heating two transitions can be measured. An onset in the storage modulus curve at 60[degrees]C with corresponding values at 74[degrees]C (E"-curve, onset). The second transition appears at 95[degrees]C in the storage modulus curve, at 97[degrees]C in the loss modulus curve and at 109[degrees]C in the loss factor curve.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

In figure 2 is being represented the storage moduli variation with temperature in case of a multiphase composite sample reinforced with ceramic particles embedded as having 10% as their volume fraction and subjected to successive heating processes (blue--1st heating, red--2nd heating). As it can be seen there are no huge differences among the values.

Two transition can be measured while the first heating run at 59[degrees]C for the storage modulus corresponding at 69[degrees]C for the loss modulus, respectively at 83[degrees]C in the storage modulus curve, at 85[degrees]C in the loss modulus curve. While the second heating run the first transition disappears, phenomenon corresponding to a post-curing stage.

In figure 3 is being plotted the theoretical and experimentally retrieved data for further comparison. As it can be seen the values corresponding to the measured dynamical data are closely to the theoretical ones.

[FIGURE 3 OMITTED]

4. CONCLUSION

The theoretical predicted and experimental retreived data reveal relatively small differences among the elastic coefficients either statical or dynamic measured. The experimental data retrieved from dynamic measurements are slighly lower than the ones from static bending tests. For this behaviour can account the differences bretween the measurement parameters even the same measuring principle was involved. Other influencing parameter can be assigned to the frequency applied, an increase giving rise to different dynamic spectra derived by different molecular, intermolecular and atomic oscillations that appear in combination to the inertial phenomena.

5. ACKNOWLEDGEMENTS

The research was supported from grant ID_135, 108/1/10/2007, CNCSIS, Romania. Thank to the Netzsch family for technical assistance and help.

6. REFERENCES

Curtu, I. & Motoc Luca, D. (2008). Theoretical-experimental comparisons of multi-phase composite materials elastic coefficients retrieved from tensile, compressive and bending tests. Influencing factors. Plastic Materials, Vol. 45, No. 4, 366-371, ISSN 0025/5289

Motoc Luca, D. & Teodorescu, H. (2008). Fillers' content influence on the mechanical properties of the glass mat reinforced polymeric composite, Proceedings of 19th International DAAAM Symposium "Intelligent Manufacturing & Automation: Focus on next generation of intelligent systems and solutions", Katalinic, B. (Ed.), pp. 00913-00914, ISSN 1726-9679, Trnava, October 2008

Torquato, S. (2002). Random heterogeneous materials, Springer, ISBN 0-387-95167-9, U.S.A.

Ramadan, M. (2008). Temperature dependence of dynamic modulus and damping in continuous fiber-reinforced Al--alloy matrix composites at elevated temperature, Jordan J. of Mech. And Ind. Eng., Vol. 2, No. 1, ISSN 1995-6665