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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.
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
Figure 2: Right Knee
Traction-free macrocrack Bridging zone Microcrack zone
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
1u1v
2v
2u
3u3v
4u4v
tw
nwCohesive ElementsCohesive Elements are located in FEM model
Cohesive Law with Unloading-Reloading
Hysteresis
Loading Incremental stiffness
Fig 1 Cyclic Cohesive Law with unloading –reloading hysteresis. (Nguyen , Cohesive models of Fatigue crack growth and stress corrosion cracking,2000)
Unloading Incremental stiffness
T = K-δ, if δ < 0 = K+ δ, if δ >0
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 ampli tude tensile load cycles.
Figure 5: Comparison of theoretical and experimental crack growth rates (Aluminum alloys)
Fig 4 : Schematic of a center-crack panel test.
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 =0Where 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
Figure 10. Fringes indicating the presence of plasticity induced crack closure in the crack wake
Figure 11 Fringes indicating the occurrence of crack closure caused by mismatching fracture surfaces
Crack closure video and Images
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 ScopeA 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 Engng Sci 2004;5(2):91–102.
Thank You
Questions ???