On the Constitutive Equations of the Orthotropic Theory of Creep

Abstract

Creep equations have been formulated for the multi-axial state of stress for an orthotropic medium, based on an invariant proposed by Hill for theory of plasticity. Any one of the numerous creep laws suggested from time to time by different investigators on the basis of experiments can then be used in these equations giving a complete set of equations for the solution of creep problems in orthotropic medium. Two simple applications are also discussed. As an example in which principal axes of stress do not coincide with axes of anisotropy, tension of a bar is discussed. Another example, that of compression under conditions of plane strain, illustrates variation of stress with time when load is kept constant. It is shown that in this case σ z relaxes to the final value \(\frac{G\sigma_{x}+F\sigma_{y}}{F+G}\) after a few times the retardation time.