PSI - Issue 5

Valeriy Lepov et al. / Procedia Structural Integrity 5 (2017) 777–784 Valeriy Lepov et al / Structural Integrity Procedia 00 (2017) 000 – 000

782

6

N

K

M

1

1

1

f i     l k 

 

       

,

(1)

fr j

F

L

Fr

N

K

M

i

j

k

1

1





1



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:

U     

0  T

  

( ) U t dt kT t     ( )

1

1

M 



i

exp

exp







,

(2)

 

 

Fr

kT



1  





j

i

where T – wheel resource, U – activation energy,  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 ·  3,5·365 = 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:

1 exp 

   

U     

M 



i

p T

,  







  

 

 

,

(3)

Fr

j

j

j

kT

1  

j

i

, j p T   - probability of j -damage at extreme uncertainty conditions. j j

where

The stress-strain state analysis is based on the models of linear elasticity, which are described by Lame equations for displacement. The discretization of the system of equations is done through the finite element method, and the numerical realization of the method is performed on collection of free software FEniCS. The result obtained shows that, the distribution of displacement in all samples are almost the same. Between the welded zone, the heat affected zone and the external elliptic zone, the Von Mizes stress is almost the same in all three samples (see Fig.4). Numerical results of Von Mizes stress for tension around the welded zone of three samples are presented in fig. 4. The maximum value located around the boundary between heat affected and welded zones is significantly lesser than total maximum value of Von Mizes stress. 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 provide the crack propagation proposed by Broberg (1990) and modified by Lepov (2007). The model could visualize the crack propagation in heterogeneous media in real time. It is assumed that the length of the crack is a mean value of fraction and has a stochastic nature and normal distribution. The distance between cracks is the mean value also.