Modeling the subcritical spread of cracks grown by fatigue / Modelando a propagação subcrítica de rachaduras crescidas por fadiga

The objective of this article is to mathematically model the subcritical propagation of fatigue-grown cracks. Three fatigue specimens were used, made of ASTM A 36 structural steel, which were notched in the center of the specimen to simulate a stress concentrator, and for the crack to propagate in the same plane. A three-point bending fatigue machine was used which is equipped with computer data acquisition equipment.The subcritical propagation of fatigue cracks was monitored, using the strain gage technique, and it was verified with the beach marking technique; which guaranteed the reliability of the method. With the data obtained, a vs N graph was made, and the empirical equation that governs this phenomenon was found; Likewise, derivatives were applied and the crack advance speed versus crack size was calculated; and to calculate the stress intensity factor, the Newman Raju method was applied, which is being verified by many researchers in recent years.In this way, it is possible to find a mathematical expression that modulates the fracto-mechanical behavior of the subcritical propagation of a crack, which relates the advance speed of the crack as a function of the fracture toughness evaluated as a function of the intensity factor of tensions K. With which a model similar to the one proposed for the Paris model is achieved, with the values for the parameters C = m / Cycle and m = 2.0252 that are close to the values obtained by researchers in similar materials.