Cohesive zone model

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The cohesive zone model (CZM) is a way to understand fracture where crack growth happens gradually across a cohesive zone at the crack tip. Instead of an abrupt jump, the two crack faces pull apart through cohesive forces that resist separation. The idea goes back to the 1960s with work by Dugdale and Barenblatt to describe nonlinear processes at the crack front.

Key ideas
- CZM does not pretend to be a real material. It describes the cohesive forces that occur as material elements are pulled apart.
- As the crack surfaces separate, the traction (pulling force per area) rises to a maximum and then drops to zero. The relation between traction and opening displacement is shown as a traction–displacement curve. The area under this curve represents the energy needed to create new surfaces (fracture energy).
- The model keeps mathematical continuity, so the displacement remains smooth even though the material separates. This makes stresses stay finite and limited by the material’s cohesive strength.
- The shape of the traction–displacement curve and the overall energy available influence how large the fracture process zone is—the region ahead of the crack tip where damage and inelastic processes occur. A smaller ratio of peak traction to yield stress generally leads to a longer process zone.

Dugdale and Barenblatt pictures
- Dugdale model: envisions a thin plastic zone ahead of a Mode I crack tip in an elastic–perfectly plastic material. The plastic traction equals the yield stress and helps balance the stress intensity so that stresses don’t blow up at the tip. This gives an estimate of the plastic zone size and how opening at the tip develops.
- Barenblatt model: for brittle solids, it treats the cohesive zone as a small region where the interatomic bonds are about to break. The traction equals the theoretical bond strength, and the fracture energy is linked to surface energy. From this, one can relate the energy release rate to a critical opening or cohesive zone size.

In short, CZM provides a practical way to model fracture by focusing on the cohesive forces at the crack front, explaining how energy is absorbed in the fracture process and how the process zone develops, without needing to simulate an actual material’s full failure.