Fracture Process Zone -1

1. Fracture Process Zone -1 crack Body under study Separation distance Separation Length • Crack is the material separation with separation distance substantially smaller than the separation length, the crack length. • Separation distance is comparable to some microstructural length dimension, ex. Distance between inhomogeneities or inclusions • This distance can be as low as a few atomic distance while the crack length is considerable larger. • The length scales involved are typically smaller than the characteristic length scale of the material, e.g. grain sizes • The cracks at these length scales are called micro-cracks, and material separates at micro level and indicates micro separation. Refernce: Cracks and Fracture by K. B. Broberg

2. Fracture Process Zone -2 • The fracture process always takes place in a small region near the edge of the crack and is the process zone where the material separation occurs. • While continuum theories are valid in other region, the theory is not valid in the process zone. • Micromechanistic processes occurring in the process zone vary from material to material; even for the same material they vary under different temperatures and rates of loading • Micro separation is the decohesion on a microstructural level. • They can be classified as • Micro cracks (metals at low temperatures, ceramics) • Voids (metals at room temperatures) • Cavities at grain boundaries (metals at high temperature) • Rupture/disentaglement (polymers) • Rupture at atomic scale (ceramics like glass)

3. FPZ-3: Dominant kernels of micro-separation Large particles Small particles • Note that there are two populations of particles, large and small. Cracks nucleate in each case at a nucleating kernel. • Nucleating kernels can be the large or small particles. Typically it starts with the large and connects with the ones originating from the smaller ones.

4. FPZ 4- Intrinsic Material Length Parameter Let us suppose We know that depends on the crack length a. Thus, where the function f decreases with the argument. Suppose the failure occurs due to microseparation from void growth of particles, then d may be the average distance between particles, or the nucleating kernels.

5. FPZ-5 Micro separation in metals • Metals are polycrystalline in nature; and micro-separation occur as a rule after severe plastic flow. • Micro cracks are generated by high stresses (usually at lower temperatures). • Cleavage is a micro crack occuring along specific planes, and is promoted by lower plastic flow. Since high triaxial state suppress plasticity, cleavage is promoted by triaxial state. • Voids originate by large strains with a stong shear component.(typically above room temperature) • Typically microcracks and voids grow inside the grain leading to transgranular fracture. • Cavities occur at higher temperatures typically at grain boundaries and triple points, and lead to intergranular fracture.

6. FPZ 6- Micro cracks in metals • Various types of mechanisms are active in the formation of micro cracks within a grain.

7. FPZ 7- Cleavage fracture in metals Ligament that fails eventually Cleavage within a single grain • Micro cracks occur in different grains with different orientations. Once the ligaments are sheared off, the fractured surfaces contain glittering facets with fibrous borders

8. FPZ-8 Micro separation in ceramics • Crack is the material separation with separation distance substantially smaller than the separation length, the crack length.

9. FPZ-9 Micro separation in polymers Fibrils link the crack faces Crack mouth • Bond between macromolecules are very weak; they stretch/slide/disentangle under load. • Crazing at the edge of a crack in a polymer. Fibrils link the top and bottom of the crack surface. They break at the left.

10. FPZ-10 Cell Model of Materials • Cell Model permits the modeling of separation within the context of continuum mechanics.

11. FPZ-11 Cohesion-Decohesion curve • Crack is the material separation with separation distance substantially smaller than the separation length, the crack length.

12. FPZ-12 Model of forward and wake regions • Ahead of the crack tip the process zone has a forward region where the material undergoes separation. • Behind the crack tip we have elastic unloading.

13. FPZ-13 Model of a process zone • The top figure indicates the cell model while the bottom shows the traction-separation profile.

14. FPZ-12 The sequence of the fracture process • Crack is the material separation with separation distance substantially smaller than the separation length, the crack length.

15. FPZ-12 Model of forward and wake regions • Crack is the material separation with separation distance substantially smaller than the separation length, the crack length.

16. FPZ-12 Model of forward and wake regions • Crack is the material separation with separation distance substantially smaller than the separation length, the crack length.