Issue34

Yu.G. Matvienko et alii, Frattura ed Integrità Strutturale, 34 (2015) 255-260; DOI: 10.3221/IGF-ESIS.34.27 258 coefficients of friction the distribution of tangential contact loading q ( x ) due to relative sliding can be estimated with a simple Coulomb friction law within the Hertzian model [13] ( ) ( ) x q x p p x     , (9) where μ is the coefficient of friction between contacting elements. Following loading configurations have been considered to investigate the effect of a moving contact on the crack propagation angle (Fig. 2). All configurations have the same normal   p x and tangential   q x contact loading distributions which are applied at different positions with reference to the crack mouth. The pressure on the crack faces is considered to be equal to that at the crack mouth, and is equal to 2 0 0 ( ) 1 y x p x p p b          , (10) where 0 / x b is moving contact load position (Fig. 2). Figure 2 : Simulation of the moving contact. The following mechanical properties of carburized steel 16MnCr5 are used in the computational model: Young’s modulus 206 E GPa   , Poisson’s ratio 0.3   , yield strength 2200 Y МPа    and fracture toughness 521 mat K MPa m  [10]. The Hertzian contact pressure distribution p ( x ) has the following parameters, namely, maximum value of 0 1779 p MPa   and the half-length of the contact area 0.228 b mm  . The influence of different contact sliding is simulated with three different coefficients of friction ( μ =0 . 04, 0.065 and 0.1). Initial length of the crack is equal to 0 20 a m    with the initial inclination angle towards the contact surface 20 o   . The computational data published by Zafošnik et al. [10] is employed in calculation to illustrate the variation of observed parameters in the region of maximum stress intensity factors 0 I I K K p b   , 0 II II K K p b   and 0 T T p  for moving contact load over the crack mouth. The computational results (Fig. 3) determined by the MATS criterion illustrate the variation of crack propagation angle 0  in the region of maximum stress intensity factors I K , II K and T -stress for moving contact load over the crack mouth, which is given in terms of a relative position of the loading case with respect to the half-contact width b. It can be seen that the influence of coefficient of friction on crack propagation angle is negligible. To evaluate the analytical results obtained by the proposed maximum average tangential stress (MATS) criterion, the maximum tangential stress (MTS) criterion [10] is also employed. The obtained results illustrate the following. The MATS criterion gives slightly largest crack propagation angles as compared with the MTS criterion for load position corresponding to 0 / 0.94 x b   (Fig. 4). At the same time, the predicted crack propagation angles are smaller for contact load position corresponding to 0 / 0.94 x b   .