A Study of Hysteresis Loops in Strain Cycling Fatigue and Life Estimation

Abstract

Hysteresis loops were recorded intermittently but periodically during completely reversed, strain-controlled low cycle fatigue tests of four kinds of steel : a mild steel and three high strength steels. The longitudinal strain amplitude e±a was controlled over the gauge length of 12.5 mm on 8 mm diameter test section of the smooth, solid cylinder type specimen. After the conversion of the loops to true stress versus natural strain hysteresis loops, cyclic characteristics were studied on true stress amplitude, hysteresis energy and hysteresis loop shape.Main conclusions obtained are as follows : (1) The transition strain amplitude e*ta, on which neither cyclic hardening nor cyclicsoftening is occurred, is expressed as a function of ultimate tensile strength σu (kgf/mm2).log e*ta =0.0478 σu -4.544(2) Although plastic strain hysteresis energy per cycle ΔW behaves irregular and remarkable change in the beginning stage of cycling, that is approximately less than 2 percent of the crack initiation life, the change of ΔW is neglegible order after the beginning stage.The fatigue toughness Wf (kgf/mm2) is expressed as a function of ultimate tensile strength σu and visible crack initiation life Nc.Wf= (94.93-0.347σu) Nc0.335 (3) The ratio of ΔW to the product of true stress range and plastic strain range is not constant during the fatigue cycling, and the mean value of the ratio over the total cycling for a specimen is expressed as a function of the total strain amplitude.(4) The constants a and n in the n-th power strain hardening formula are expressed as a function of N and eta for the nearly total range of cycling excluding the beginning stage.An empirical formula was found between a and 1/n.1/n= (log a+1.623+0.376log σu)/(0.1539-1.169 logσu)(5) An estimation procedure for crack initiation life was proposed on the basis of the fatigue toughness, showing an estimation error less than 28 percent.