Abstract
Effects of grain diameter distribution on the flow stress of mild steel were studied. The flow stress have been usually connected with an apparent average grain diameter which is determined by counting a number of grains appeared in the cross section of mild steel. The difference between a true flow stress calculated considering a distribution of grain diameters and an apparent flow stress connected directly with the apparent average grain diameter was obtained in some distribution of grain diameters.
The following results were obtained:
(1) A stress calculated by the strain continuity model and a stress calculated by the stress continuity model coincided well for all the adopted distribution types of grain diameters.
(2) In Gauss distribution (f (x) = (1/ 2πS)·exp (-(x-μ) 2/2S2), x: grain diameter (mm)), the difference mentioned above increased with S.
(3) In the uniform distribution (f (x) =1/ 2P), the difference increased with P.
(4) In Poisson distribution (f (x) =exp (-R)·RX/X!, X=100x), the difference decreased with R and gradually came close to that of Gauss distribution.
(5) A metallurgical meaning of the equation (σ=g (x, ε)) used in the calculations was discussed using work hardening theory.
In summary the difference was remarkable in Poisson distribution, but those in Gauss distribution and in the uniform distribution might be neglected except in the case where the flow stress is discussed with an accuracy of the order of 10-1 kg/mm2.
