Ultimate limit state fracture

Ductile properties such as crack pattern and deformations prefiguring the nearing failure are important characteristics regarding the fracture behavior of structural concrete members. The tests demonstrated that in general TRC members have a distinctive ductile behavior although the stress-strain-behavior of the fabrics is linear-elastic until a brittle tensile failure. While the deformations under service loads (SLS) are rather small, the load-bearing behavior of the specimens is characterized by a distinctive stabilized crack pattern as well as high deformations in ultimate limit state (ULS) of L/30 - L/20. 

At the same time the phenomenon of fracture reflects, in one way or another, the ultimate limit of deformation in a solid. It thus involves fundamental physical properties of the material such as its inter-atomic bonding, its surface energy and its crystal structure. It also involves crystallographic processes such as slip, stress induced phase transformations and twinning, whilst in molecular solids such as polymers other processes such as molecular relaxation behaviour may predominate. Fracture is clearly of great scientific interest and has attracted the attention of chemists and solid state physicists as well as engineers. 

The significance of the argument at this stage relates to the failure of plastics in the ductile state. Orowan [3] first pointed out that for ductile materials the ultimate stress is entirely determined by the stress-strain curve, i.e. by the plastic behaviour of the material, without any reference to its fracture properties provided that fracture does not occur before the load maximum corresponding to da/dl = a/A is reached. Yield stress is thus an important property in many plastics, and defines the practical limit of behaviour much more than the ultimate fracture, unless the plastic fails by brittle fracture. 

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