The measurement of shear modulus in highly anisotropic materials: the validity of St. Venant's principle

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Abstract
Torsion pendulum measurements of the longitudinal shear modulus in 'single-crystal' samples of an S-B-S block copolymer are reported. These samples consisted of a hexagonal array of polystyrene cylinders embedded in a matrix of polybutadiene, with the cylinder axes uniaxially aligned. Sample morphology and associated anisotropic physical properties resemble those of a miniature fibre-reinforced system. The shear modulus calculated from the torsional stiffness by conventional means, assuming St Venant's principle, is found to depend upon the sample length/width ratio, the results for short specimens being double those for very long specimens. It appears that St Venant's principle expressed in its usual form is not applicable to materials possessing a large mechanical anisotropy. An alternative interpretation of experimental results is given by invoking the shear-lag theory of fibre reinforcement.