Effective material properties of a hollow elastic sphere that undergoes a finite deformation under the action of external hydrostatic pressureThe effects of hydrostatic pressure on the torsional shear stress-strain behavior of polyoxymethylene (POM) and polypropylene (PP) have been investigated. The experimental data show that the shear modulus of polyoxymethylene increases linearly with pressure while the shear modulus of polypropylene increases bilinearly with pressure with the break, the glass transition pressure, occurring at 2.1 kbar. This value coincides with prior results obtained from Young's modulus-vs-pressure curve for polypropylene. The linear variation of the shear moduli with pressure is compared with the Birch's equation which was derived from finite strain theory of elasticity. The shear yield stress (2% offset) has been found to increase linearly with pressure for POM but increase nonlinearly with pressure for PP. The Pae yield criterion (J' 2)112 = ~k ~ oaJJ7 predicts accurately both the linear and the nonlinear variation of the shear stresses with hydrostatic pressure. Other proposed yield criteria, however, predict only linear or nonlinear, but not both. A new phenomenon, which is analogous to the necking in a tensile specimen, has been observed on the torsional shear specimens of polyoxymethylene and polypropylene. This phenomenon has been named girdling. Girdling is a constriction or a reduction of a cross-sectional area in a narrow band on the shear specimens.
SynopsisHollow and solid specimens of polypropylene and solid specimens of polyoxymethylene exhibited an effect under torsional shear which is analogous to the necking usually observed in tensile tests. After reaching some critical shear strain in the postyield region localized shear deformation developed on the gauge length. As twisting was continued a dramatic decrease in the diameter of the cross section was observed. This torsional shear induced phenomenon was named girdling. The superimposition of hydrostatic pressure u p to 6 kbar has a significant influence on the extent of girdle formation. Stress whitening, observed on the solid polyoxymethylene specimens was suppressed by the application of pressures greater than 1 kbar. Very large shear strains produced a ratchet-type fracture surface on the solid specimens which indicates the presence of axial, radial, and tangential strains. Qualitatively, these results are supported by the finite deformation theory of elasticity.
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