1. Fracture Process Zone -1
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.
Separation distance
Separation Length
crack
Body under study
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.