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Work hardening is a consequence of plastic deformation, a permanent change in shape. This is distinct from elastic deformation, which is reversible. Most materials do not exhibit only one or the other, but rather a combination of the two. The following discussion mostly applies to metals, especially steels, which are well studied.
A break occurs after the material has reached the end of the elastic, and then plastic, deformation ranges. At this point forces accumulate until they are sufficient to cause a fracture. All materials will eventually fracture, if sufficient forces are applied.
Theoretically, the strength of a material with no dislocations will be extremely high because plastic deformation would require the breaking of many bonds simultaneously. However, at moderate dislocation density values of around 10 7 -10 9 dislocations/m 2 , the material will exhibit a significantly lower mechanical strength.
Specifically, for Zirconia, where it has three phases, the competition between phase transformation and plastic deformation has been found to be orientation dependent, [5] indicating the orientation dependence of activation energy of dislocation and nucleation. Therefore, for nanoscale materials suitable for superelasticity, one should research ...
The two plastic limit theorems apply to any elastic-perfectly plastic body or assemblage of bodies. Lower limit theorem: If an equilibrium distribution of stress can be found which balances the applied load and nowhere violates the yield criterion, the body (or bodies) will not fail, or will be just at the point of failure. [2] Upper limit theorem:
An idealized uniaxial stress-strain curve showing elastic and plastic deformation regimes for the deformation theory of plasticity There are several mathematical descriptions of plasticity. [ 12 ] One is deformation theory (see e.g. Hooke's law ) where the Cauchy stress tensor (of order d-1 in d dimensions) is a function of the strain tensor.
Plastic deformation of a thin metal sheet. Flow plasticity is a solid mechanics theory that is used to describe the plastic behavior of materials. [1] Flow plasticity theories are characterized by the assumption that a flow rule exists that can be used to determine the amount of plastic deformation in the material.
This is an ideal concept only; most materials which possess elasticity in practice remain purely elastic only up to very small deformations, after which plastic (permanent) deformation occurs.