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

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)

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.

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.

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.

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

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

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

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.

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

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

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.

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

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.

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.

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.