A Study of the Equivalent Stress-Equivalent Strain Relation of Titanium Sheets

Abstract

From the results of tensile tests of titanium sheets which have an intensity maximum of the basal pole at an angle θ inclined from the sheet normal to the transverse direction, the equivalent stress-equivalent strain relation has been discussed. The results are as follows.
(1) When several slip systems and/or twin systems are activated simultaneously, the yield criterion for titanium sheet is given by
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Here σ_X, σ_Y…τ_YZ are related to the principal axes of anisotropy and the axis (Z-axis) can be assumed to be located at the maximum intensity of the basal pole on the basal pole figure.
(2) The above equation coincides with the criterion of Hill that is introduced when yielding occurs symmetric ally about the axis.
(3) When the parameters in the above equation vary without the rotation of the principal axis of anisotropy as deformation proceeds, the ratio of the contribution of each activated system to the deformation varies.
(4) In analyzing the equivalent stress-equivalent strain relation obtained from the above criterion by the same method as Hill did, a good agreement between the equivalent stress-equivalent strain curves, plotted for the tensile directions in the plane of the titanium sheet is observed in those in the 45, 67.5 and 90° directions; the curves in the 0 and 22.5° directions did not agree with each other nor did with those in the directions mentioned above. As this inconsistency is due to the difference of parameters in the above cditerion by the tensile directions, it can be said that the anisotropy of work hardening exists among those directions.