Presentation For Fracture Mechanics

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 :
Modeling approach that defines cohesive stresses around the tip of a crack
Figure 2: Righ
Cohesive stresses are related to the crack opening width (w)
Crack will propagate, when s = σf

How can it be applied to design of any material?
The cohesive stresses are defined by a cohesive law that can be calculated for a given material
Material properties
Cohesive Elements
Cohesive Elements are located in FEM model

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
Nguyen used Six-node
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
Nguyen used a center-crack panel of
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
g > 0; p < 0; gp =0
Where g is gap function,
P is contact force
The crack faces experience contact
force whenever
Δn- - Δn* < 0.
The displacements of beam element
is given by equation
ΔUb =W (Kb+ IW )-1p
By increasing thickness of
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?
The potential to predict crack growth behavior under monotonic and fatigue load
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

Crack closure video and Images
Figure 11 Fringes indicating the occurrence of crack closure caused by mismatching fracture surfaces
Figure 10. Fringes indicating the presence
of plasticity induced crack closure
in the crack wake

SUMMARY
We have studied the use of cohesive theories of fracture, for the purpose of fatigue-life prediction..
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.

Future Scope
A worthwhile extension would be to consider cohesive laws in terms of three point displacement and therefore to capable of describing tension shear coupling.
To couple the model of fatigue crack growth and stress corrosion cracking to study corrosion fatigue for several systems / environment under various loading conditions.

References
[1] Brown EN. Fracture and fatigue of a self-healing polymer composite
material. PhD thesis, University of Illinois at Urbana-Champaign, 2003.
[2] Deshpande VS, Needleman A, Van der Giessen E. A discrete dislocation analysis of near-threshold fatigue crack growth. ActaMater 2001;49(16):3189–203.
[3] Geubelle PH, Baylor J. Impact-induced delamination of composites: a
2-D simulation. Composites B 1998;29:589–602.
[4] Knauss WG. Time dependent fracture and cohesive zones. J Engng
Mater Tech Trans ASME 1993;115:262–7.
[5] Lemaitre J. A course on damage mechanics. 2nd ed. Springer; 1996.
[6] Lin G, Geubelle PH, Sottos NR. Simulation of fiber debonding with
friction in a model composite pushout test. Int J Solids Struct 2001;38(46–
47):8547–62.
[7]Maiti S, Geubelle PH. Mesoscale modeling of dynamic fracture of ceramic materials. Comp Meth EngngSci 2004;5(2):91–102.

Thank You

Questions ???

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