Theory for material toughness

What is it about?

A brittle solid suddenly cleaves by the growth of a crack. If we rejoin the macroscopic parts of the broken solid, it completely regains its original shape. However, perfectly brittle solids do not exist. Even in very brittle materials such as iron at low temperatures, there are dislocations. The motion of these defects is associated with plastic flow. The plastic deformation contrasts with the elastic deformation because it does not disappear after unloading. As a result, in strong ductile materials, the resistance to fracture, which is called material toughness, is orders of magnitude higher than that of brittle solids. A theory derives the material toughness. It shows that a dimensionless variable controls the behaviour of different solids from brittle to ductile. At the tip of the crack, there is always an elastic region. A relationship for the size of this elastic region is derived in terms of the macroscopic and microscopic parameters that govern the fracture.

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Photo by timJ on Unsplash

Photo by timJ on Unsplash

Why is it important?

The findings present a theoretical framework for material toughness. As a result, a unified criterion of crack growth is formulated for brittle, intermediate and ductile solids. This framework joins seemingly uncorrelated works under one single umbrella. Also, it predicts that an elastic region of variable size always surrounds the tip of the crack.

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