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 ???