PSI - Issue 13

Valeriy Lepov et al. / Procedia Structural Integrity 13 (2018) 1201–1208 Valeriy Lepov et al/ Structural Integrity Procedia 00 (2018) 000 – 000

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where  f i – damage during fatigue i -cycle,  l k – damage during contact impact k -cycle,  fr j – damage during j -cycle of wear, N, K – appropriate cycles value. For operation at low temperatures the fatigue and friction damage of tire and rail way has been reduced, but the impact damage significantly grown. In summer contrariwise the contact impact damage low-to-nonexistent. The calculation of  F and  F is known before by Lepov et al (2016), but the contact wear damage was very hard to estimate due to complex process in contact spot and necessity of coherent thermal and mechanical problem solution. Here the thermal kinetic of interaction model used for two rough surfaces by Goryacheva (2013) and averaging of stress in contact spot of wheel-rail system. So the contact wear damage will be calculated by: where T – wheel resource, U – activation energy of steel,  and  – material parameters, k – Boltzmann constant,  (t) – stress in contact spot of wheel-rail system in point of time t , T(t) – temperature-time cycle, j =1,2… M – number of months when the wheel was exploited, <  > – averaging stress in contact spot. Summation in (2) is performed by months with the known average temperature on railway spot. The stress value <  > in this case will be equal to strength of steel and could be calculated by microhardness value. Here for locomotive tire  b ·  ·365 = 1277,5 MPa.  and  calculated by initial and boundary data for damage accumulation: t = 0,  Fr = 0; t = T ,  Fr = 1. The condition of extreme uncertainty of tire stress and temperature state is defined by lack of information during operation of locomotive. The calculation shows that the locomotive tire lifetime de facto is three times as little in extreme conditions. To taking into account another undefined factors the some expert system and the Bayesian approach are need for most appropriate case of damage assessment by Al-Najjar and Weinstein (2015) approach: Stochastic model of crack growth and fracture in multiphase heterogeneous material is based on the mechanism triggered by stresses opening small cracks or pores on particles or ruptures of material, further viscoplastic growth and mutual coalescence of defects, asproposed by Broberg (1990) and modified by Lepov (2007). Thus all parameters to simulate the crack growth, observe the possible path and calculate the crack velocity as an averaged discrete propagation of the crack tip are known. But another aspect of the modelling is the scale problem. The macroscopic cracks (with length of 1 mm and more) here has the same mechanical behaviour as microscopic cracks (length 1 mkm and above) so the algorithm is right, but the size of calculation zone is significantly large. So for velocity of crack the dimension factor used was equal to 100. Crack growth visualization according to stochastic crack growth model in welded and heat affected zones shown on Fig. 7a and 7b subsequently. Despite of the stochastic character of crack size and distribution, and distance between cracks, the modeling result differs significantly. Taking into account the dimension factor, the velocity of crack propagation in welded zone of low-alloyed steel estimated as 64.59 m/s (see Fig. 6a and 7a), but in heat affected zone only as 0,354.1 m/s (Lepov et al, 2017). So the energy dissipation in welded steel seen to be much lesser than that in the heat affected zone or base metal. It is a reason for many failures of structures during the service life eligible by many faults also. The extreme environmental conditions such as corrosion due to acid rains, low temperature and thermal shock could worsen the failure possibility. Web-oriented visualization examples of crack growth on microdefects shown in Fig.5, with algorithm by modern version of Java script language (http://iptpn.ysn.ru/hdr). Further modification of the model connected with application to a wide range of phenomena, such as accumulation of damage in porous media, materials with multiple phase transitions, including evaporation, melting and freezing, as well as the second order phase transition at lower temperature. 1   0  T 1 ( ) U t dt kT t     ( ) 1 exp exp M  i j i Fr U      kT               , (2) 1   1 exp  ,   M  i j j j j i Fr U      p T kT                , (3) where , j p T   - probability of j -damage at extreme uncertainty conditions. j j