Fracture Mechanics modeling of subsurface crack propagation

Arnab GhoshPh.D. Research AssistantAnalytical Modeling of Surface and Subsurface Initiated Fretting WearNovember 14, 2013Mechanical Engineering Tribology Laboratory (METL)#November 14, 2013Mechanical Engineering Tribology Laboratory (METL)OutlineMotivation & BackgroundSurface Initiated Fretting WearSimulation of fretting Stress based wear model (Damage Mechanics)Effect of friction, hardness and Youngs modulusSubsurface Initiated Fretting WearUse of Linear Elastic Fracture Mechanics (LEFM)Crack propagation criteriaCrack paths and life calculationsEffect of friction and normal load on life

#November 14, 2013Mechanical Engineering Tribology Laboratory (METL)Motivation and BackgroundSubsurface 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 InitiationAlternating 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. #November 14, 2013Mechanical 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 SlipGross 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 microstructureVoronoi TessellationEach Voronoi cell is divided into Constant Strain Triangle elements2D Voronoi tessellations incorporate randomness in the microstructure and geometrically simulate the grain morphology observed in reality.FEA mesh#November 14, 2013Mechanical Engineering Tribology Laboratory (METL)Stress based Wear Model

ENERGY BASED WEAR EQUATION

DAMAGE EVOLUTIONGeneralized damage equation:Damage Law derived for Wear equation: INTERGRANULAR CRACK PROPAGATION

Crack Propagtes along the grain boundary in CCW directionSimulating wear by removing grains at the contact interface

D DcCrack at grain boundary

Grain removal (Crack surrounds a grain)(Fouvry et al)(Amonton)(E Rabinowicz)#November 14, 2013Mechanical Engineering Tribology Laboratory (METL)

Wear Propagation

Evolution of contact pressure as wear progressesComparison of wear scars with experiments

Archards Law: From the Damage Mechanics model:

The coefficient kGS thus obtained is compared to Archards wear coefficients found in literature#November 14, 2013Mechanical Engineering Tribology Laboratory (METL)Effect of Coefficient of FrictionH=4GPa, E=200 GPaH=2.5GPa, E=200 GPaH=1GPa, E=200 GPaA critical value of was observed between 0.25 and 0.5 for the mentioned input parameters. Increasing beyond 0.5 doesnt change wear rate considerably.

V@10,000 : Wear Volume after 10000 cycles calculated using the equationH (GPa)E (GPa)VwrVwoV(@10000)k42000.255.12264199.4470271.14E-0242000.58.525385.9798141.89E-0242000.758.474716.2799841.88E-02420016.73586634141.49E-02

Wear rate vs Coefficient of Friction#November 14, 2013Mechanical Engineering Tribology Laboratory (METL)7Effect of Hardness

=0.5, E=200 GPa=0.75, E=200 GPa=1.0, E=200 GPaH (GPa)E (GPa)VwrVwoV(@10000N)k42000.58.525385.9798141.89E-0242000.758.474716.2799841.88E-02420016.73586634141.49E-022.52000.51357341242661.81E-022.52000.7513.3845291292711.86E-022.5200113.6146321314681.89E-0212000.530.9148123042881.72E-0212000.7533.494547.73303521.86E-021200133.2554504.33280461.85E-02

Wear rate vs Hardness#November 14, 2013Mechanical Engineering Tribology Laboratory (METL)Effect of Youngs Modulus

=0.5, H=4 GPa=0.5, H=2.5 GPa=0.5, H=1 GPaH (GPa)E (GPa)VwrVwoV(@10000N)k42000.58.525385.9798141.89E-0243000.55.233131.5491691.16E-0244000.54.142451.1389499.20E-032.52000.514.3557341377661.99E-022.53000.58.082981778191.12E-022.54000.56.42362.3616388.89E-0312000.530.948123041881.72E-0213000.520.2529871995131.13E-0214000.516.332414.11608869.07E-03It 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 Youngs Modulus#November 14, 2013Mechanical Engineering Tribology Laboratory (METL)Subsurface Crack Propagation

Shear stress reversal at the 2 crack tipsDetailed view of the Left crack tip

LEFT CRACK TIPRIGHT CRACK TIP

#November 14, 2013Mechanical 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 assumptionThe plastic zone size:CRACKMONOTONIC PLASTIC ZONECYCLIC PLASTIC ZONE

#November 14, 2013Mechanical Engineering Tribology Laboratory (METL)Crack Propagation DirectionStress Intensity Factors (SIFs)~ Modified Crack Closure Technique

The crack propagates in the direction of maximum alternating shear stressPossible crack paths#November 14, 2013Mechanical Engineering Tribology Laboratory (METL)Crack Tip Mesh Refinement

CRACKCYCLIC PLASTIC ZONECrack Tip mesh refinement and the von Mises stress fieldRegions around crack tip and crack extensionCrack Growth showing adaptive meshing around crack tip#November 14, 2013Mechanical Engineering Tribology Laboratory (METL)Crack Paths and Life

PH=0.5 GPaPH=1 GPaPH=2 GPaGrowth of Initial Crack for different values of Coefficient of FricitonGrowth of Initial Crack for different values of Hertzian Pressure#November 14, 2013Mechanical Engineering Tribology Laboratory (METL)Log-log plot of Life vs Shear ForceLog(N) = -1.39 Log (Q) +11.3Effect of Different variables on Life

PH=0.5 GPaPH=1 GPaPH=2 GPaLife vs applied pressure at different values of coefficient of frictionLife vs Shear Force (Q)PH Approaching partial slipLife decreases

#November 14, 2013Mechanical Engineering Tribology Laboratory (METL)SummarySurface initiated fretting wear can be modeled by damage mechanics using only standard material propertiesWear rate decreases with increase in Hardness and Youngs modulus Increasing coefficient of friction beyond 0.5 doesnt impact wear rateThe wear coefficients obtained from the model are comparable to Archards wear coefficientSub surface initiated fretting wear can be modeled by Linear Elastic Fracture MechanicsAlternating shear stress at crack tips drives crack propagation. Crack direction is calculated using a Mode II criteriaCrack path is studied for different combinations of variablesPariss Law is used to calculate the LifeLife decreases with increase in applied load and coefficient of frictionFuture WorkIncorporate plasticity effects and model hardness in the stress based damage mechanics modelStudy the effect of grain size and surface roughnessExtend the LEFM model to study cracks at different depths from the contact surfaceModel stress risers (inclusions, void) in the domain and study its effect on crack pathCombine Damage Mechanics and LEFM: Subsurface crack initiation using damage mechanics and propagation using LEFM#November 14, 2013Mechanical Engineering Tribology Laboratory (METL)16