Fracture strength theoretical

Orowan (1949) suggested a method for estimating the theoretical tensile fracture strength based on a simple model for the intermolecular potential of a solid. These calculations indicate that the theoretical tensile strength of solids is an appreciable fraction of the elastic modulus of the material. Following these ideas, a theoretical spall strength of Bq/ti, where Bq is the bulk modulus of the material, is derived through an application of the Orowan approach based on a sinusoidal representation of the cohesive force (Lawn and Wilshaw, 1975). 

The scaling behaviour of the most probable fracture strength (jf, expressed by the fracture exponent Tf near the percolation threshold, has been investigated extensively. The theoretical results compare well with those observed experimentally, and in computer simulations. Although considerable progress has been made here, experimental results for continuum percolation are scarce, and more investigations are clearly necessary. 

The theoretical fracture strength of a material can be deduced from the cohesive forces between the component atoms in the plane under consideration from a simple energy balance between the work to fracture and the energy require to create two new surfaces. It can be shown that the theoretical cohesive strength is given by... 

Engineering materials, including polymers, generally have low fracture strengths relative to their theoretical capacity. The lower-than-ideal fracture strengths of engineering materials are generally attributed to the presence of flaws such as cracks, scratches, and notches inherent in these materials. 

Metallic Glasses. Electrically conducting glasses can be prepared from combinations of predominantly metallic elements by rapid cooling or vapour deposition. Their magnetic properties make them suitable for low-loss transformer cures, and their mechanical strengths approach theoretical fracture strength, as local dislocation fracture mechanisms do not operate. 

This should lead to a reduced sensitivity to delaminations, as the CNTs, having a diameter which is a couple of hundred times smaller than that of carbon fibers, can reinforce the tiny area in between the fibers of a laminated composite. They should also improve the elastic modulus of the matrix material Itself. This last statement is mainly based on theoretical calculations and simulations, which predict a high fracture strength and elastic modulus for carbon nanotubes. ... 

In general, it is found that the tensile strengths of materials are very much lower than E/10 because brittle materials fracture prematurely due to the presence of flaws (Section 5.6.2) and ductile materials undergo plastic deformation through the motion of dislocations. However, fine whiskers of glass, silica and certain polymer crystals which do not contain any flaws and are not capable of plastic deformation have values of fracture strength which are close to the theoretically predicted ones. 

All brittle materials contain a population of small cracks and flaws that have a variety of sizes, geometries, and orientations. When the magnitude of a tensile stress at the tip of one of these flaws exceeds the value of this critical stress, a crack forms and then propagates, which results in fracture. Very small and virtually defect-free metallic and ceramic whiskers have been grown with fracture strengths that approach their theoretical values. 

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