Hypothesis of local determinability for five-dimensional strain trajectories

Summary Hypothesis of local determinabilily predicting the behavior of the angles between a stress vector and a Frenet's frame established on a strain trajectory in a five-dimensional vector space of strain deviator is discussed to formulate a plastic constitutive equation of metals under complex loadings. Namely, a set of equations giving the rates of angles at the relevant instant for arbitrary five-dimensional curved strain trajectories is derived first on the basis of the previously reported experiments for the deformation along three-dimensional orthogonal trilinear strain trajectories. Then, a simple constitutive equation is formulated by employing the above equations together with the relation between the magnitude of stress vector and the arc-length of strain trajectory for pure torsion. It is found that the resulting equation reproduced well the above experimental results.With 4 Figures