Mecanica

ANNALS of the ORADEA UNIVERSITY. Fascicle of Management and Technological Engineering, Volume VII (XVII), 2008

AN ANALYSIS OF THE STRESS INTENSITY FACTOR MODE II VARIATION UNDER INFLUENCES OF RESIDUAL TENSIONS AND THE POSITION OF THE CRACK CENTRE FOR AN INTERNAL CRACK SITUATED IN THE HERTZIAN STRESSES FIELD OF GEAR TEETH
Claudiu Ovidiu POPA, Lucian Mircea TUDOSE Technical University of Cluj –Napoca Keywords: fatigue cracks, stress intensity factor KII, crack centre depth, residual tensions
Abstract: The parameter that governs the crack fatigue growth in the case of compression stresses field is the stress intensity factor mode II, KII. The main goal of this paper is to present the KII variation with respect to the contact stresses, the residual tensions and the crack centre depth ofan existent internal crack in the sub-surface of the pinion tooth in the Hertzian stresses field with friction, for digitized (with the step π/6) values of the inclination angle α of the crack. As result of this study, some particular factors favorable to the future development of cracks towards the surface were identified.

1.

INTRODUCTION

Fracture failure of engineering structures iscaused by cracks that extend beyond a safe size. It is a catastrophic event that takes place very rapidly and is preceded by crack growth which develops slowly during normal service conditions, mainly by fatigue due to cyclic loading. Since fatigue involves failure of the “weakest link” of the material, the fatigue strength is very closely coupled with the microstructural integrity and purity of thematerial. For example, larger inclusions or voids can be regarded as initiated cracks (at the surface or in the substrate) and the reduced fatigue life of the component has to be evaluated by the use of a crack propagation model. The first stage of the crack growth [8][10][14] corresponds to nucleation and, then, to a growth on a small scale with a growth rate in order of 10-6 mm/cycle. Itdepends on the material microstructure, the applied stress ratio and the environment. For many loading conditions, the highest loads are at the surface. But even the nominal stress is constant throughout, crack tend to nucleate at the surface because deformation of each grain is allowed to concentrate on a crystallographic plan [7]. The second stage of fatigue crack propagation was named [1][2] thestable crack growth. Here, in concordance with the Linear Elastic Fracture Mechanics (LEFM) outlook, the linear elastic crack growth is modeled using the Paris law representation of a surface crack in a semi infinite body subjected to a constant stress cycle. Stress intensity factor (SIF) is one the most important parameter that governs stage II. It reflects the whole stress field at the tip of thecrack when the size of the plastic zone at the crack tip is small compared to the crack length. We considered two mashing spur gears, in which any point of the material is subjected to normal and shear stresses due to Hertzian and frictional stresses which act on the contact zone. Here, the normal tensions (if no residual tensions exist) are of compression. This case corresponds to a crack growthunder mode II, also named sliding mode. According to the Paris Law, the parameter that governs the stable crack growth in this case is stress intensity factor mode II, KII. Its values are strongly depending, apart to the mentioned tensions, with the values of residual tensions, the size of the initiated crack and the crack centre coordinates. The last stage (instability) corresponds to a dramaticgrowing of the crack that has as result, eventually, the fracture of the component.
1018

ANNALS of the ORADEA UNIVERSITY. Fascicle of Management and Technological Engineering, Volume VII (XVII), 2008

The main goal of this paper is to present the KII variation with respect to the contact stresses, the residual tensions and the crack centre depth of an existent internal crack in the...