Ratcheting and Rolling Contact Fatigue Crack Initiation Life of Rails under Service Loading Wenyi YAN Monash University, Australia Chung Lun PUN Peter Mutton Qianhua Kan Guozheng Kang
Contents Introduction Research objectives A comprehensive approach Experimental study Development of ratcheting model for rail steels Determination of contact pressure and traction distribution Prediction of crack initiation life Summary 2
Heavy haul railway in Australia Iron ore and coal High axle load Iron ore (35-40 t) Coal (30 t) passenger trains (18-20 t) Rail Steel High strength, e.g. eutectoid grade Example Rio Tinto in Pilbara Track Services 14 mines 1,400 km A single train 2.4 km long 234 ore cars (31,000 t) 3
Rail degradation Rolling contact fatigue Stress level > plastic shakedown limit Kapoor and Johnson (1994) ratcheting Ratcheting strain > ductility limit Std C Std HH HE HT Initiation of rail degradation. i.e. fatigue cracks Wessels L, Oswald S, Welsby D and Mutton P (2015), Managing the transition from wear to rolling contact fatigue in a heavy haul environment, Proc. International Heavy Haul Conference (IHHA 2015), Perth 4
Research objectives 1. Evaluate the ratcheting behaviour of three high strength rail steels currently used in heavy haul railways in Australia 2. Develop a ratcheting-based approach to predict crack initiation life of those rail steels 5
A Comprehensive approach 1.Experimental program 2.Material model development 4. Ratcheting and crack initiation life 3. Pressure & traction distributions 6
Hardness HV (kg/mm 2 ) Hardness HV (kg/mm 2 ) 1. Materials Three high strength pearlitic rail steels Rail C (%) Si (%) Mn (%) P (%) S (%) Cr (%) LAHT 0.8 0.74 0.95 0.02 0.02 0.41 HE1 1.0 0.49 0.70 0.016 0.014 0.21 HE2 0.85 0.52 1.17 0.014 0.005 0.25 500 500 450 450 400 350 300 h LAHT HE1 HE2 250 0 7 14 21 28 35 400 350 0 LAHT 180 HE1 HE2 300 0 90 180 270 360 Depth below gauge corner h (mm) Angular displacement (degree) 7
Experimental Program Monotonic Tensile Tests Uniaxial Strain Cycling Uniaxial Stress Cycling MTS 809-250kN machine Bi-axial Compression- Torsion Stress Cycling 8
Axial Stress (MPa) Monotonic Tensile Test 1500 1200 900 1100 600 1000 300 900 800 700 0.0 0.5 1.0 1.5 2.0 0 0 3 6 9 12 Axial Strain (%) LAHT HE1 HE2 D ln L L ln o 1 1 R Elastic Modulus (GPa) Nominal yield strength (MPa) Ultimate tensile strength (MPa) Reduction of area R (%) Ductility D (%) LAHT 212 1000 1446 35.9 44.43 HE1 203 850 1429 14.7 15.91 HE2 212 905 1384 39.5 50.25 9
Uniaxial symmetrical strain cycling, a = 0.8% 1200 1050 Stress amlitude a Mean Stress m LAHT HE1 HE2 (MPa) 900 100 0 σ a = 1 2 (σ max σ min ) σ m = 1 2 (σ max + σ min ) -100 0 20 40 60 80 100 N (cycles) All three materials features cyclic softening a with N LAHT & HE2 m HE1 m 10
Equivalent shear strain 3-1/2 (%) Equivalent shear strain 3-1/2 (%) Biaxial stress cycling Rectangular loading path Elliptical loading path 0.50 HE2 Loading cycle, N 0.50 HE2 Loading cycle, N 0.25 0.25 0.00 0.00-0.25-0.25-0.50-3.5-2.8-2.1-1.4-0.7 0.0 Axial Strain (%) -0.50-1.5-1.2-0.9-0.6-0.3 0.0 Axial Strain (%) 11
Biaxial stress cycling 0.0 LAHT 0.0 HE1-0.5-0.7 r (%) r (%) -1.0-1.5 Loading Path: -2.0 Linear Oblique Rectangular Butterfly Elliptical -2.5 0 20 40 60 80 100 0.0-0.7-1.4-2.1 N (cycles) Loading Path: -2.8 Linear Oblique Rectangular Butterfly Elliptical -3.5 0 20 40 60 80 100 N (cycles) HE2 r (%) Loading Path: -2.8 Linear Oblique Rectangular Butterfly Elliptical -3.5 0 20 40 60 80 100 N ε r N dε r dn Loading paths influence ratcheting Elliptical loading paths lowest axial ratcheting strain -1.4-2.1 N (cycles) ε r = ε max + ε min 2 12
2. Ratcheting model for rail steels Abdel-Karim and Ohno model Modification of non-proportional parameter Φ proposed by Tanaka, 1994 by fourth order tensor C. tr( C : C) n : C : C : n 2 tr( C : C) Pun CL, Kan Q, Mutton PJ, Kang G and Yan W (2014). Ratcheting Behaviour of High Strength Rail Steels under Bi-axial Compression-Torsion Loadings: Experiment and Simulation. International Journal of Fatigue 66, 138-154. 13
Verification of the ratcheting model 0.0 LAHT 0.0 HE1-0.7-0.9-1.4-1.8 r (%) r (%) -2.1-2.8-3.5 0.0-0.9-1.8 Exp. Simu. Linear Oblique Rectangular Butterfly Elliptical 0 20 40 60 80 100 N (cycles) Exp. Simu. -2.7 Linear Oblique -3.6 Rectangular Butterfly Elliptical -4.5 0 20 40 60 80 100 N (cycles) HE2 r (%) Exp. Simu. -2.7 Linear Oblique -3.6 Rectangular Butterfly Elliptical -4.5 0 20 40 60 80 100 N (cycles) Quantification of ratcheting with acceptable accuracy Overprediction / underprediction < 10% 14
3. Determination of pressure & traction distributions Non-Hertzian pressure distribution More realistic Obtained from a static 3D FE simulation 15
Strip Theory Divide the contact area into thin strips Depends on traction coefficient ξ = P t fl ξ = 0 Free rolling 0 < ξ < 1 Partial slip ξ = 1 Full slip 16
Define the stick zone size Relationship between load and size of stick zone, a 0 (Haines and Ollerton (1963) Proc. IMechE) 3 ξ = 1 2 where 2K K 2 1 2 3 K + 1 3 K2 1 K sin 1 2K K 2 K - a 0 a0 a o semi width of the stick zone in x direction a o longest semi width of the contact area in x direction (measured from FEA) Define minor width of stick zone b 0 b 0 = b 0 2 a o a 0 a o a 0 2 where b 0 is the longest semi width of the contact area in y direction (measured from FEA) 17
Define stick zone for each strip Stick zone @ leading edge Slip zone @ trailing edge Define size of stick zone for each strip a i a i a i = a 0 a 0 where a i semi width of the contact area of each strip along x direction (measured directly from FEA) a i semi width of the stick zone of each strip along x direction 18
Longitudinal Tangential Traction Carter s theory: For stick zone, τ x x i, y i = fp x i, y i a i fp x a i, y i i For slip zone, τ x x i, y i = fp x i, y i 19
4. Numerical Model for Cyclic Rolling contact Fine mesh contact zone 60mm long 30mm wide 18mm depth 142581 degrees of freedom Cyclic rolling contact Translate from left to right within the fine mesh contact zone 20
Ratcheting strain ε r in rail head Both normal and shear plastic strains accumulate Ratcheting strain p ε r = ε eff max Effective Plastic strain p ε eff = 2 ε 3 ij P P ε ij Ratcheting strain rate dε r dn ε r N ε r N 1 21
Ratcheting behaviour dε r dn (a) d r / dn LAHT f = 0.2 f = 0.3 10-2 10-3 f = 0.4 f = 0.5 f = 0.6 L = 35 tonnes, = 0.5 10-4 10-5 10-6 10-7 (b) d r / dn 10-2 HE1 10-3 10-4 10-5 10-6 10-7 f = 0.2 f = 0.3 f = 0.4 f = 0.5 f = 0.6 L = 35 tonnes, = 0.5 (c) d r / dn 10-8 10-2 HE2 10-3 10-4 10-5 10-6 10-7 10-8 10 20 30 40 50 60 N (cycles) f = 0.2 f = 0.3 f = 0.4 f = 0.5 f = 0.6 L = 35 tonnes, = 0.5 10 20 30 40 50 N (cycles) 10-8 10 20 30 40 50 N (cycles) Non-zero ratcheting strain rate non-zero net plastic deformation Ratcheting occurs 22
Estimation of crack initiation life N i Based on dε r /dn & ductility of the material Stabilized max. dε r /dn of the entire model Criterion for stabilized max. dε r /dn dε r/dn i dε r /dn i 1 row dε r /dn i 1 Ductility ln ( L L 0 ) ln L L 0 = ln 1 1 R Crack initiation life N i N i = ln L L0 dε r /dn < 0.5 % for 5 cycles in a, R = reduction of area Materials ln L L 0 (%) LAHT 44.43 HE1 15.91 HE2 50.25 23
N i (10 6 cycles) Crack initiation life influence of 6.0 4.5 LAHT HE1 HE2 L = 35 tonnes, f = 0.4 Practical Crack Initiation Life for HE2 L = 35 tonnes, f = 0.4 with traction 3.0 1.5 ξ N i 0.0 0.00 0.25 0.50 0.75 1.00 When 0.5, the LAHT has the longest N i among all three rail steels When > 0.5, the HE2 has the longest N i 24
N i (10 6 cycles) Crack initiation life influence of friction 5 4 3 LAHT HE1 HE2 L = 35 tonnes, = 0.5 Practical Crack Initiation Life for HE2 L = 35 tonnes, f = 0.4 with traction 2 1 f N i 0 0.2 0.3 0.4 0.5 0.6 Rapid reduction of N i for LAHT when f > 0.4 f HE1 and HE2 more consistent decreasing rate 25
N i (10 6 cycles) Crack initiation life influence of axle load σ y (MPa) σ ys (MPa) σ ys/ σ y 5 4 LAHT HE1 HE2 f = 0.4, = 0.5 Practical Crack Initiation Life for HE2 L = 35 tonnes, f = 0.4 with traction LAHT 1000 535 0.54 HE1 850 562 0.66 HE2 905 554 0.61 3 2 1 L N i 0 30 35 40 45 L (tonnes) When L 35, the LAHT has the longest N i among all three rail steels When L > 35, the HE2 has the longest N i The HE1 steel has almost constant N i. 26
Summary 1.Experimental program 2.Material model development 4. Ratcheting and crack initiation life 3. Pressure & traction distributions 27
Acknowledgments Australian Research Council Linkage Project (LP110100655) Rio Tinto Iron Ore National Computational Infrastructure (NCI), Canberra, Australia Pun CL, Kan Q, Mutton PJ, Kang G and Yan W (2014). Ratcheting Behaviour of High Strength Rail Steels under Bi-axial Compression-Torsion Loadings: Experiment and Simulation. International Journal of Fatigue 66, 138-154. Pun CL, Kan Q, Mutton PJ, Kang G and Yan W (2015). An Efficient Computational Approach to Evaluate the Ratcheting Performance of Rail Steels under Cyclic Rolling Contact in Service. International Journal of Mechanical Sciences. Available online. 28