構成則に用いる応力速度と変形の局所化

抄録

The stress level of the incipience of localized deformation in ductile materials is shown to be considerably higher than the observed stress when it is estimated analytically by a bifurcation criterion with constitutive laws using the Jaumann stress rate of the Cauchy stress. In our investigation, we employed the Truesdell stress rate to predict the localization stress with the same criterion. While only the compressive localization stress can be predicted, the predicted stress level is smaller than that measured by the Jaumann stress rate by as much as a factor of ten. This is consistent with many experimental results. Even in three dimensional stress states, the localization stress is ten times smaller than the elastic moduli. Furthermore, the constitutive relation using the Truesdell stress rate yields straightforward results during simple shearing and uniaxial loading, indicating that the Truesdell stress rate should be preferably considered as a measure for describing material properties in rate form.