Similitude Law of Prefracture Hysteresis of Steel Members

A hypothesis, which is called similitude law of prefracture hysteresis, is advocated in this paper. The similitude law is as follows: the relationships anlong ductility amplitude ${\mu }_p\text{,}$ cumulative ductility ${\eta }_p\text{,}$ and number of cycles $N_f$ prior to fracture are represented by invariant functions for any type of steel member which can be fabricated from different materials, welding processes, and connections. Several invariant functions in accordance with the law were proposed, where the invariant functions show that the amounts of ${\eta }_p$ and $N_f$ are reduced with an increase of ${\mu }_p$ in plastic hystereses. The law was applied to four independent series of experiments done in the past, or series 1 (brittle fracture of box-section beams), series 2 (brittle and pseudobrittle fracture of rectangular solid bars), series 3 (pseudobrittle fracture of round bars), and series 4 (ductile fracture of H-section beams with welded connections), from which it was found that the invariant functions fit consistently for all of the experimental results. Since the similitude law allows us to calculate any combination of ${\mu }_p\text{,}$ ${\eta }_p\text{,}$ and $N_f$ from a single set of them, the law has significance for engineering application when we need to reduce the number of specimens from an economic standpoint without losing confidence. The similitude law is expected to be applied to earthquake resistant design which relies on plastic deformation of steel members.