Stress Non-uniformity in Hollow Cylindrical Test Specimens

Different levels of stress non-uniformity usually occur in test specimens of different dimensions and aspect ratios. The effect of the choice of dimensions on the level of stress nonuniformity for hollow cylindrical specimens was studied using a linear elastic analysis during the development of a new hollow cylinder apparatus. Earlier researchers have assumed slightly different variations in the stress components that act across the thickness of the specimen wall in deriving the stress equations and these differences are discussed. The current analysis assumed a linear variation in the circumferential shear stress. Slightly different regions to those reported by the other researchers were identified in generalized stress space where unacceptable levels of stress non-uniformity could arise. The case for maintaining the confining pressures applied to the outer cell chamber and the inner bore cavity of the specimen equal to reduce the level of stress non-uniformity was also studied. It was found that stress non-uniformity could still arise when these confining pressures were maintained equal, for example when a torque was applied across the length of the specimen, with the magnitude of stress non-uniformity related to the assumed variation of the circumferential shear stress across the specimen wall. The magnitude of the calculated stress non-uniformity was shown to be related to the stress state, the specimen dimensions and the constitutive model adopted. INTRODUCTION The hollow cylinder apparatus (HCA) allows independent control of the magnitudes of the three principal stresses and rotation of the major-minor principal stress axes facilitating more generalized stress path testing. However, the use of the HCA in studying the constitutive behavior has often been criticized on account of the level of stress non-uniformity that may develop across the wall thickness of the hollow cylindrical test specimen. Stress non-uniformity arises due to the curvature of the specimen wall, the frictional restraint and stiffness of the annular loading platens, and whenever a torque or different confining pressures are applied across the specimen wall. The HCA used in the present study was developed at University College Dublin (UCD), Ireland [1,2,3]. The apparatus subjects a hollow cylindrical test specimen (35.5 mm inner radius, 50.0 mm outer radius and 200 mm high) to four surface tractions: an outer cell confining pressure (po), an inner bore confining pressure (pi), an axial load (W), and a torque (T), Figure 1a. Figure 1b presents the stress components (σz, σr, σθ, τzθ), and Figure 1c the principal stresses (σ1, σ2, σ3) induced in an element of the specimen wall. Torque application causes rotation ασ, of the σ1– σ3 stress axes. The relative value of the intermediate principal stress σ2, was quantified in terms of the intermediate principal stress parameter, b. The b parameter has a range of 0 to 1, with b = 0 for σ2 = σ3, and b = 1 for σ2 = σ1. The UCD HCA was closed-loop controlled [4] allowing independent and precise regulation of the system of applied loads and confining pressures. Figure 1. Stress state in hollow cylindrical specimen. (a) (b)