On the Relationship between Hysteresis Loop under Low Cycle Fatigue and Meyer Hardness

Abstract

It is the object of this paper to make it clear that the form of hysteresis loops and its changes, which were obtained during the cyclic tension compression, were numerically related by a simple rule to the Meyer hardness values of the cyclically strained material.(1) The Meyer indices n of the cyclically strained carbon steels and copper were nearly equal to x+2, where x was the value of the strain hardening indices determined from the hysteresis loop. The value x was almost constant during the cycling of constant strain amplitude.(2) The cyclic softening of work hardened copper as well as the cyclic hardening of annealed copper, expressed by the change of stress amplitude of hysteresis loop, corresponded numerically to the change of the Meyer hardness values which were measured under constant‘hardness strain’1).(3) When the materials were subjected to tension compression, the following rule was obtained not only over the hardening or softening period but also over stable state of cycling. Namely, Meyer hardness Pm vs. hardness strain eh relationships of the cyclically stressed materials coincide with the relationships between the Ya value, true stress Y multiplied by material constants a (2.95≤a≤3.3), and true strain e of hysteresis loops.(4) The Meyer hardness measured of the specimens unloaded from the tension side during the cycling was slightly lower than the value measured after the unloading from the compression side.It will be concluded from these results of the present investigation that the cyclic hardening (Or softening) of the material can be determined either by the change of stress (Or strain) amplitude under constant strain (Or stress) amplitude or by the change of Meyer hardness values or of Vickers hardness values.