Plastic Deformation in Annealed Aluminium Bar Containing Circumferential Semicircular Notch

Abstract

The clarification of the plastic strain distributions in the notched portions of annealed aluminium bars containing the circumferential semicircular notch was made using the specimen bars which were cut into halves along the longitudinal axis and joined closely to each other before the test. The plastic strains were measured by the photograting method. And, using the experimental results, the stress distributions in the minimum cross section and the strength of the notched specimen under both the uniaxial tension and compression were analysed.
The results obtained are as follows:
(1) The plastic strains, radial, circumferential and axial, occur not uniformly in the minimum cross section, but are maximum at the notch root. The strain concentration factor becomes higher as the notch sharpens. The radial and circumferential strains in the minimum cross section are equal on the axis, and various at the other points. The tendency of the plastic strain distributions approximately agrees with that of the elastic strain distributions calculated by using Neuber's theory (Poisson's ratio is 0.5).
(2) The curvature 1/ρ of the principal strain lines at the minimum cross section is approximately represented in the following equations. If a/ρ_a≤1, 1/ρ=r/(aρ_a). If a/ρ_a>1, 1/ρ=0 for 0≤r≤(a-nρ_a) and 1/ρ={nρ_a-(a-r)}/(nρ_a²) for (a-nρ_a)≤r≤_a, where r is the distance from the axis, a the radius of the minimum cross section, ρ_a the radius of curvature at the notch root, and the factor n is dependent on the notch configuration.
(3) The radial stress is different from the circumferential stress at each point, except on the axis. In the region of the mean axial strain over 2∼5%, the maxima of the hydrostatic tension and compression are on the axis in the dull notched specimens and shift in the direction of the notch root as the notch becomes sharper. In the compressive deformation and the tensile deformation with a mean axial strain below ten-odd percent, the results of the calculated notch strength approximately agree with experimental ones, in case that the change in notch configuration is taken into consideration. In the calculation value of n=1 was taken in the above equation.