1. November 14, 2013 Mechanical Engineering Tribology Laboratory (METL) Arnab Ghosh Ph.D. Research Assistant Analytical Modeling of Surface and Subsurface Initiated Fretting Wear

2. 2 November 14, 2013 Mechanical Engineering Tribology Laboratory (METL) Outline Motivation & Background Surface Initiated Fretting Wear –Simulation of fretting –Stress based wear model (Damage Mechanics) –Effect of friction, hardness and Young’s modulus Subsurface Initiated Fretting Wear –Use of Linear Elastic Fracture Mechanics (LEFM) –Crack propagation criteria –Crack paths and life calculations –Effect of friction and normal load on life

3. 3 November 14, 2013 Mechanical Engineering Tribology Laboratory (METL) Motivation and Background Subsurface crack initiation - Ductile fracture initiated by formation of microcracks at interface between precipitates - Subsequent removal of material in fretting wear happens due to delamination (Waterhouse, 1977) Crack formation underneath the wear track of annealed copper (Suh, 1973) Cracks caused by alteration of the friction forces acting on surfaces of actual contact (Hirano & Goto, 1967) Intergranular fracture of ball bearing steel due to hydrogen embrittlement (Scott, 1968) Cross section of specimen showing surface cracks. (Nishioka & Hirakawa, 1969) Fracture surface showing crack extension by alternating shear (wavy slip region) – (Pelloux, 1970) Surface Crack Initiation Alternating tensile and compressive stresses induce fatigue crack formation around the regions of surface contact. The direction of propagation of these cracks is clearly associated with the direction of the contact stresses.

4. 4 November 14, 2013 Mechanical Engineering Tribology Laboratory (METL) Simulation of Fretting in FEA A 2 dimensional Hertzian line contact with plain strain condition is simulated in FEA to study the stress states at different stages of fretting. Partial Slip Gross Slip Von Misses stress and fretting loops at the interface It can be observed that high contact stresses are observed in the slip regions and therefore, surface damage (wear) can be related to these stresses. Steel microstructure Voronoi Tessellation Each Voronoi cell is divided into Constant Strain Triangle elements 2D Voronoi tessellations incorporate randomness in the microstructure and geometrically simulate the grain morphology observed in reality. FEA mesh

5. 5 November 14, 2013 Mechanical Engineering Tribology Laboratory (METL) Stress based Wear Model ENERGY BASED WEAR EQUATION DAMAGE EVOLUTION Generalized damage equation: Damage Law derived for Wear equation: INTERGRANULAR CRACK PROPAGATION Crack Propagtes along the grain boundary in CCW direction Simulating wear by removing grains at the contact interface D  D c Crack at grain boundary Grain removal (Crack surrounds a grain) (Fouvry et al) (Amonton) (E Rabinowicz)

6. 6 November 14, 2013 Mechanical Engineering Tribology Laboratory (METL) Wear Propagation Evolution of contact pressure as wear progresses Comparison of wear scars with experiments Archard’s Law: From the Damage Mechanics model: The coefficient k GS thus obtained is compared to Archard’s wear coefficients found in literature

7. 7 November 14, 2013 Mechanical Engineering Tribology Laboratory (METL) Effect of Coefficient of Friction H=4GPa, E=200 GPaH=2.5GPa, E=200 GPaH=1GPa, E=200 GPa A critical value of µ was observed between 0.25 and 0.5 for the mentioned input parameters. Increasing µ beyond 0.5 doesn’t change wear rate considerably. V@10,000 : Wear Volume after 10000 cycles calculated using the equation H (GPa)E (GPa)µVwrVwoV(@10000)k 42000.255.12264199.4470271.14E-02 42000.58.525385.9798141.89E-02 42000.758.474716.2799841.88E-02 420016.73586634141.49E-02 Wear rate vs Coefficient of Friction

8. 8 November 14, 2013 Mechanical Engineering Tribology Laboratory (METL) Effect of Hardness µ=0.5, E=200 GPaµ=0.75, E=200 GPaµ=1.0, E=200 GPa H (GPa)E (GPa)µVwrVwoV(@10000N)k 42000.58.525385.9798141.89E-02 42000.758.474716.2799841.88E-02 420016.73586634141.49E-02 2.52000.51357341242661.81E-02 2.52000.7513.3845291292711.86E-02 2.5200113.6146321314681.89E-02 12000.530.9148123042881.72E-02 12000.7533.494547.73303521.86E-02 1200133.2554504.33280461.85E-02 Wear rate vs Hardness

9. 9 November 14, 2013 Mechanical Engineering Tribology Laboratory (METL) Effect of Young’s Modulus µ=0.5, H=4 GPaµ=0.5, H=2.5 GPaµ=0.5, H=1 GPa H (GPa)E (GPa)µVwrVwoV(@10000N)k 42000.58.525385.9798141.89E-02 43000.55.233131.5491691.16E-02 44000.54.142451.1389499.20E-03 2.52000.514.3557341377661.99E-02 2.53000.58.082981778191.12E-02 2.54000.56.42362.3616388.89E-03 12000.530.948123041881.72E-02 13000.520.2529871995131.13E-02 14000.516.332414.11608869.07E-03 It has been shown that for low cycle fatigue wear of dry and smooth contacts, the wear coefficients are of the order of 10 -3 to 10 -2 (Challen & Oxley, 1986) Wear rate vs Young’s Modulus

10. 10 November 14, 2013 Mechanical Engineering Tribology Laboratory (METL) Subsurface Crack Propagation Shear stress reversal at the 2 crack tips Detailed view of the Left crack tip LEFT CRACK TIP RIGHT CRACK TIP

11. 11 November 14, 2013 Mechanical Engineering Tribology Laboratory (METL) Use of Linear Elastic Fracture Mechanics (Mode II) Under compressive load (Hertzian Pressure), Mode I growth is suppressed and Mode II growth is more predominant. Linear Elastic Fracture Mechanics (LEFM) can be used to find the direction of crack growth Check for LEFM assumption The plastic zone size: CRACK MONOTONIC PLASTIC ZONE CYCLIC PLASTIC ZONE

12. 12 November 14, 2013 Mechanical Engineering Tribology Laboratory (METL) Crack Propagation Direction Stress Intensity Factors (SIFs) ~ Modified Crack Closure Technique The crack propagates in the direction of maximum alternating shear stress Possible crack paths

13. 13 November 14, 2013 Mechanical Engineering Tribology Laboratory (METL) Crack Tip Mesh Refinement CRACK CYCLIC PLASTIC ZONE Crack Tip mesh refinement and the von Mises stress field Regions around crack tip and crack extension Crack Growth showing adaptive meshing around crack tip

14. 14 November 14, 2013 Mechanical Engineering Tribology Laboratory (METL) Crack Paths and Life P H =0.5 GPa P H =1 GPaP H =2 GPa Growth of Initial Crack for different values of Coefficient of Friciton Growth of Initial Crack for different values of Hertzian Pressure

15. 15 November 14, 2013 Mechanical Engineering Tribology Laboratory (METL) Log-log plot of Life vs Shear Force Log(N) = -1.39 Log (Q) +11.3 Effect of Different variables on Life P H =0.5 GPa P H =1 GPa P H =2 GPa Life vs applied pressure at different values of coefficient of friction Life vs Shear Force (Q) PHPH Approaching partial slip Life decreases

16. 16 November 14, 2013 Mechanical Engineering Tribology Laboratory (METL) Summary Surface initiated fretting wear can be modeled by damage mechanics using only standard material properties –Wear rate decreases with increase in Hardness and Young’s modulus –Increasing coefficient of friction beyond 0.5 doesn’t impact wear rate –The wear coefficients obtained from the model are comparable to Archard’s wear coefficient Sub surface initiated fretting wear can be modeled by Linear Elastic Fracture Mechanics –Alternating shear stress at crack tips drives crack propagation. Crack direction is calculated using a Mode II criteria –Crack path is studied for different combinations of variables –Paris’s Law is used to calculate the Life –Life decreases with increase in applied load and coefficient of friction Future Work Incorporate plasticity effects and model hardness in the stress based damage mechanics model Study the effect of grain size and surface roughness Extend the LEFM model to study cracks at different depths from the contact surface Model stress risers (inclusions, void) in the domain and study its effect on crack path Combine Damage Mechanics and LEFM: Subsurface crack initiation using damage mechanics and propagation using LEFM