Halping-Tsai is a widely used model for the prediction of tensile modulus of composite. What is shape factor value for cylindrical fillers.
It depends on what way your filler particles are oriented.
Halpin and Kardos [1] recommend that a shape factor of 2w/t be used when the filler particles are oriented with the loading direction. In this case w is the width of the particles and t is the thickness. If the particles are oriented perpendicular then a shape factor of 2 is recommended.
For randomly oriented particles, the situation will lie somewhere between these two bounds, but closer to a shape factor of 2. In my experience, unless you have very high asset ratio fillers a value of 2 gives very reasonable agreement with experimental observation.
[1] Halpin JC, Kardos JL. Polym Eng Sci 1976;16(5):344e52
Following the Carolan 's answer it is usual using the following equation for random "in plane" filler distribution:
Ec=3/8*E11+5/8*E22
where Ec= modulus of composite
E11=modulus obtained using H-T with the shape factor =2w/t
E22= modulus obtained using H-T with the shape factor=2
However, as pointed out by Carolan, Ec gets values close to E22 because of the formation of clusters of fillers that decrease the effectiveness of the reinforcing phase.
If the dispersion is good (i.e. filles do not aggregate) then the above equation is a reliable estimation of composite's modulus.
One more equation is used when the filler is three-dimensionallly dispersed
Ec = 0.184 E11 + 0.816 E22
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