Modelagem matemática de propagação de trinca em uma haste em queda livre chocando-se transversalmente contra um apoio rígido

Abstract

Modeling crack propagation is always an important issue for the safety of structural components. This matter is very complex, due to crack propagation be influenced by several factors such as: mechanical properties of materials, type of loading, lamination in the crack region etc. When the structural component is subjected to an impact load, the situation is further complicated, for the impact of action time is extremely short. Initially this work developed a solution for the dynamic loading of a free falling bar crashing transverselly against a rigid support. Through this solution data as displacement, velocity, acceleration, bending moment and shear force at any point along its length can be obtained. By analyzing the numerical result, we denote the solution in serial form can be locked in the fifth term, for subsequent terms has no relevant influence on the result. We can see with the help of graphics, the maximum stress on the surface of the bar does not occur in the crack section until certain time has passed. Then this work has related yield stress and ultimate strength of the material with hardness. Through Palmeri and Cicirello’s method, crack propagation was modeled, in the bar section located over the support. The results show that the major contribution to the driving force in the crack propagation is the kinetic energy; the largest contribution to the crack propagation resistance is given by the work done by the spring elastic rotation, which represents the crack. When the driving force is less than the resistance crack propagation ceases. Still the results showed the need to improve the modeling, specifying: a way to get the stem flexibility coefficient containing the crack, and the processing of data concerning the instantaneous acceleration.