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In the deformation of solids, surface energy can be treated as the "energy required to create one unit of surface area", and is a function of the difference between the total energies of the system before and after the deformation: = ().
Compute the change in the free energy (surface energy − elastic energy) as a function of the crack length. Failure occurs when the free energy attains a peak value at a critical crack length, beyond which the free energy decreases as the crack length increases, i.e. by causing fracture. Using this procedure, Griffith found that
Comparison of surface energy, creating new surface on the left, and surface stress due to elastic deformation. Surface stress was first defined by Josiah Willard Gibbs [1] (1839–1903) as the amount of the reversible work per unit area needed to elastically stretch a pre-existing surface. Depending upon the convention used, the area is either ...
The total deformation is related to the maximum contact pressure by = = The maximum ... is the total surface energy of both surfaces per unit contact area ...
Depending on the type of material, size and geometry of the object, and the forces applied, various types of deformation may result. The image to the right shows the engineering stress vs. strain diagram for a typical ductile material such as steel.
The stress tending to shrink voids that must be overcome is related to the surface energy and surface area-volume ratio of the voids. For a general void with surface energy γ and principle radii of curvature of r 1 and r 2 , the sintering limit stress is [ 27 ] σ s i n t = γ r 1 + γ r 2 {\displaystyle \sigma _{\rm {sint}}={\frac {\gamma }{r ...
Gibbs emphasized that for solids, the surface free energy may be completely different from surface stress (what he called surface tension): [14]: 315 the surface free energy is the work required to form the surface, while surface stress is the work required to stretch the surface. In the case of a two-fluid interface, there is no distinction ...
Ductile fracture surface of 6061-T6 aluminum. Because ductile rupture involves a high degree of plastic deformation, the fracture behavior of a propagating crack as modelled above changes fundamentally. Some of the energy from stress concentrations at the crack tips is dissipated by plastic deformation ahead of the crack as it propagates.