Stress–strain–temperature relation for cyclically-damaged structural mild steel

•Behavior of grade 300 mild steel with cyclically-induced damage is considered.•Relationship between stress, strain, temperature and damage is established.•2 and 3-dimensional Second degree Bezier curves are used.•Constant–stress relation between strain and temperature is calculated.

Experimental results suggest that the mechanical properties of mild steel at elevated temperatures are affected by the cyclic load history previously applied to the material. This has great implications when it comes to post-earthquake fire analyzes. Therefore, it is desirable to establish the relationship for each mechanical property, not only as a function of temperature but also the damage induced by the cyclic load history. To achieve this goal, a special class of functions known as Bézier curves have been utilized in this research. These functions are used for the construction of stress–strain curves that depend on temperature and the amplitude of the previously applied strain cycles. Actual experimental results are used throughout the process for calibration and validation purposes. The proposed model proves to be highly versatile in the sense that it can successfully take the effect of temperature and pre-induced strain cycles into account, making it applicable to post-earthquake fire analyzes.