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# Presentation For Fracture Mechanics

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Review of Cohesive modelling of crack growth in polymers

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### Presentation For Fracture Mechanics

1. 1. Cohesive Modeling of Fatigue crack growth and retardation<br />By ,<br />Aniket Suresh Waghchaure.<br />Graduate Student,<br />Mechanical Engineering Department,<br />Michigan Tech University,Houghton.<br />
2. 2. Figure 2: Right Knee<br />Traction-free macrocrack<br />Bridging zone<br />Microcrack zone<br />What is the Cohesive Zone Model? <br /> Definition :<br /><ul><li>Modeling approach that defines cohesive stresses around the tip of a crack</li></ul>Figure 2: Righ<br /><ul><li>Cohesive stresses are related to the crack opening width (w)
3. 3. Crack will propagate, when s = σf</li></li></ul><li>How can it be applied to design of any material? <br /><ul><li>The cohesive stresses are defined by a cohesive law that can be calculated for a given material</li></ul>Material properties<br />Cohesive Elements<br />Cohesive Elements are located in FEM model <br />
5. 5. Finite Element Implementation<br /><ul><li>Nguyen used Six-node </li></ul> Iso pararnetric quadratic <br /> elements <br />Fig 2.0 Geometry of a six-node cohesive element bridging two six-node triangular elements.<br />Fig. 3: Initial mesh, overall view ad near--tip detail (crack length a0 = 10 mm).<br />
6. 6. Comparison with Experiment<br /><ul><li> Nguyen used a center-crack panel of </li></ul> aluminum 2024-T351 subject to constant <br /> ampli­tude tensile load cycles.<br />Fig 4 : Schematic of a center-crack panel test.<br /> Figure 5: Comparison of theoretical and experimental crackgrowth rates (Aluminum alloys)<br />
7. 7. Crack closure effect in Polymers<br />Fig 7 Crack Closure Effect in polymers (A. S. Jones Life extension of <br />self-healing polymers with rapidly growing fatigue cracks,Dec 2006)<br />
8. 8. A Cohesive modeling of wedge effect<br /><ul><li> g > 0; p < 0; gp =0</li></ul>Where g is gap function,<br /> P is contact force<br /><ul><li> The crack faces experience contact </li></ul> force whenever <br />Δn- - Δn* &lt; 0.<br /><ul><li>The displacements of beam element </li></ul> is given by equation <br />ΔUb =W (Kb+ IW )-1p<br /><ul><li> By increasing thickness of </li></ul> inserted wedge we can reduce <br /> crack extension rate.<br />Fig..8 Schematic of the wedge and the cracked portion of the DCB specimen in contact showing contacting nodes with link element between them<br />Fig 9 Crack closure due to a wedge of varying thickness inserted after the crack has propagated by<br /> 1 mm<br />
9. 9. Why is CZM better for fracture? <br /><ul><li>The potential to predict crack growth behavior under monotonic and fatigue load
10. 10. The cohesive relation is a Material Property
11. 11. Predict fatigue using a cohesive relation that is sensitive to applied cycles, overloads, stress ratio, load history.
12. 12. Allows to simulate real loads</li></li></ul><li>Crack closure video and Images<br />Figure 11 Fringes indicating the occurrence of crack closure caused by mismatching fracture surfaces<br />Figure 10. Fringes indicating the presence <br />of plasticity induced crack closure <br />in the crack wake<br />
13. 13. SUMMARY<br /><ul><li>We have studied the use of cohesive theories of fracture, for the purpose of fatigue-life prediction..