Análise por método de diferenças finitas da propagação dinâmica de trinca em uma haste em queda livre chocando-se transversalmente contra um apoio rígido

Abstract

Brazil is one of major producers of iron ore in the world. After the ore is explored, the first process of the production is to triturate iron ore. A rods mill is most common grinding equipment. These machines are of high maintenance costs due to constant failure in the milling bars caused by the chock when the bar drops down and impacts on the ores. To reduce such costs, mathematical and mechanical analysis for the bar failure is necessary. The aim of this study is to analyze the crack propagation in a bar, subjected to the shock inside the rod mill barrel. It is considered that the bar falls down freely on a rock (hard support) positioned exactly at the center. The dynamic analysis was performed by the finite difference method (FDM). At first the algorithm based on the FDM was compared with the results performed in ANSYS LS-DYNA and with analytical solution without crack propagation. It was verified FDM efficiency. The numerical analysis is to check when crack onset occurs and if there are conditions for the crack propagation, in other words, when the stress exceeds the ultimate strength of the material initiating crack, thereafter, using the energy balance Griffith at each instant of time to check the conditions of crack continue propagation. By analyzing the results we conclude that: the bar can break into several pieces; in materials with elevated hardness may not onset crack; the fracture toughness influences the speed and length of the crack propagation; the work hardening coefficient of the material is efficient to arrest crack propagation and decrease the speed of crack propagation. This work has laid the foundation for analyzing multi-cracks propagation in a bar with a profile of variable hardness.