Modulus - Tensile and Flexural

One of the main reasons for adding mineral fillers to thermoplastics is to increase the modulus (stiffness). Tensile (under tension) modulus is the ratio of stress to strain, at some low amount of strain, below the elastic limit. Flexural (bending) modulus is also often measured. The most relevant modulus to measure depends upon the expected deformation mode of the part that will be made from the material. Often, the flexural modulus and tensile modulus are rather similar. The exception is the case of anisotropic fillers, which can become aligned in the flow direction when the test specimens are moulded. 

There is a good understanding of how addition of filler affects the modulus of a polymer. Chow has done an extensive review of the area, and the interested reader can consult that work for a more detailed description [61]. In fact, the simple rule of mixtures is fairly accurate at low strain levels (Equation 8.4). E, Ep and Ef are the moduli of the composite, polymer and filler, respectively, and is the volume fraction of filler. The moduli of thermoplastics are in the range 1-3 GPa [1, 32, 35, 34] whereas common fillers have much higher moduli [5, 22, 31] (calcium carbonate and dolomite 35 GPa, mica 17.2 GPa and wood flour 10 GPa). 

Equation 8.4 The dependence of composite modulus on volume fraction of filler 

In these theories, modulus is independent of particle size. However, Heikens [68] has found that when the polymer is strongly bonded to the plastic composite, modulus is 

The most important filler parameter affecting modulus is its shape. Unfortunately, when the filler is non-spherical theories become much more complicated and the reader is advised to refer to Chow s review [61]. Shape factors can be incorporated in the models mentioned previously but are only useful when applied to very high aspect ratio materials, e.g., fibres. There is also an almost insurmountable problem with particulate fillers the difficulty and effort to measure aspect ratios of micrometre sized particles. Pukansky examined the effects of 11 different fillers in polypropylene [69] and concluded that Young s modulus is affected by the amount of bonded polymer, which is in turn related to surface area, and therefore to both particle size and shape. That observation helps to explain the strong effect that nano-fillers have on the modulus of a composite. Schreiber and Germain showed that modulus depends on the strength of interaction between the polymer and the filler surface [62]. 

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