On the Yielding Condition of Metals under Non-Uniform Stress Distribution (I)

Abstract

One of the most important problems in the field of the strength of materials is the yielding condition under non-uniform stress distribution. In order to determine the yielding condition of metals under non-uniform stress distribution, the authors performed the following experiments.(1) Torsion tests on cylindrical mild steel, brass and duralumin test specimens.(2) Combined torsion and tension tests on cylindrical test specimens.(3) Tension tests of plates having a circular hole.(4) Compression tests on two cylinders in contact.The results obtained as follows:(1) The twisted mild steel, brass and duralumin bars yield, when the mean value of the shearing stress acting in some proper region reaches the Mises's yielding condition.The proper region is determined from the nature of the materials and stress distribution.(2) The test specimens, subject to an arbitrary combination of twist and tension, yield when the mean value of stresses acting in the region as described above satisfies Mises's yielding condition.(3) A plate having a circular hole, which is subject to tension, comes to yield when the mean value of the tensile stress of the minimum section of the plate approaches the point of tensile yielding stress.(4) The two cylinders which is pressed in contact comes to yield when the mean value of the stress acting in a circle of diameter 7.5√R2-ρ2/R×b approaches the point where the stress satisfies Mises's yielding condition.The circle passes through the points on the surface of contact where there is no compressive stress.