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Cohesive Modeling of Fatigue crack growth and retardation By , Aniket Suresh Waghchaure. Graduate Student, Mechanical Engineering Department, Michigan Tech University,Houghton.
Figure 2: Right Knee Traction-free macrocrack Bridging zone Microcrack zone What is the Cohesive Zone Model?   Definition  : ,[object Object],Figure 2: Righ ,[object Object]
Crack will propagate, when s = σf,[object Object]
Cohesive Law with  Unloading-Reloading Hysteresis T =   K-δ,  if δ < 0     =  K+ δ, if δ >0 Loading Incremental stiffness Unloading Incremental stiffness Fig 1 Cyclic Cohesive  Law with             unloading –reloading hysteresis.          (Nguyen , Cohesive models of Fatigue crack             growth and stress corrosion cracking,2000)
Finite Element Implementation ,[object Object],    Iso pararnetric  quadratic     elements  Fig 2.0 Geometry of a six-node cohesive element bridging two six-node triangular elements. Fig. 3: Initial mesh, overall view ad near--tip detail (crack length a0 = 10 mm).
Comparison with Experiment ,[object Object],    aluminum 2024-T351 subject to constant       ampli­tude tensile load cycles. Fig  4 : Schematic of a center-crack panel test.  Figure 5:  Comparison of theoretical and experimental crackgrowth rates (Aluminum alloys)
Crack closure effect in Polymers Fig  7  Crack Closure Effect in polymers (A. S. Jones Life extension of  self-healing polymers  with rapidly growing fatigue cracks,Dec  2006)
A Cohesive modeling of wedge effect ,[object Object],Where g is gap function,             P is contact force ,[object Object],     force whenever  Δn- - Δn* < 0. ,[object Object],    is given by equation  ΔUb =W (Kb+ IW )-1p ,[object Object],    inserted wedge we can reduce      crack extension rate. Fig..8 Schematic of the wedge and the cracked portion of the DCB specimen in contact showing contacting nodes with link element between them Fig 9 Crack closure due to a wedge of varying thickness inserted after the crack has propagated by  1 mm
Why is CZM better for fracture?  ,[object Object]
The cohesive relation is a Material  Property
Predict fatigue using a cohesive relation  that is sensitive to applied cycles, overloads, stress ratio, load history.
Allows to simulate real loads,[object Object]
SUMMARY ,[object Object]
The  unloading-reloading hysteresis of the cohesive law simulates simply dissipative mechanisms such as crystallographic slip and frictional interactions between asperities.
Cohesive theory is capable of a unified treatment of long cracks under constant-amplitude loading, short cracks and overloads.,[object Object]

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Presentation For Fracture Mechanics

  • 1. Cohesive Modeling of Fatigue crack growth and retardation By , Aniket Suresh Waghchaure. Graduate Student, Mechanical Engineering Department, Michigan Tech University,Houghton.
  • 2.
  • 3.
  • 4. Cohesive Law with Unloading-Reloading Hysteresis T = K-δ, if δ < 0 = K+ δ, if δ >0 Loading Incremental stiffness Unloading Incremental stiffness Fig 1 Cyclic Cohesive Law with unloading –reloading hysteresis. (Nguyen , Cohesive models of Fatigue crack growth and stress corrosion cracking,2000)
  • 5.
  • 6.
  • 7. Crack closure effect in Polymers Fig 7 Crack Closure Effect in polymers (A. S. Jones Life extension of self-healing polymers with rapidly growing fatigue cracks,Dec 2006)
  • 8.
  • 9.
  • 10. The cohesive relation is a Material Property
  • 11. Predict fatigue using a cohesive relation that is sensitive to applied cycles, overloads, stress ratio, load history.
  • 12.
  • 13.
  • 14. The unloading-reloading hysteresis of the cohesive law simulates simply dissipative mechanisms such as crystallographic slip and frictional interactions between asperities.
  • 15.
  • 16.
  • 18. Questions ???