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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.
[2] [4] Tytus Maksymilian Huber (1904), in a paper written in Polish, anticipated to some extent this criterion by properly relying on the distortion strain energy, not on the total strain energy as his predecessors. [5] [6] [7] Heinrich Hencky formulated the same criterion as von Mises independently in 1924. [8]
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.
The normalized strain-rate and temperature in equation (1) are defined as ... is the effective plastic strain-rate of the quasi-static test used to determine the ...
The quadratic Hill yield criterion [1] has the form : + + + + + = . Here F, G, H, L, M, N are constants that have to be determined experimentally and are the stresses. The quadratic Hill yield criterion depends only on the deviatoric stresses and is pressure independent.
The exact equation to represent flow stress depends on the particular material and plasticity model being used. Hollomon's equation is commonly used to represent the behavior seen in a stress-strain plot during work hardening: [2] =
In materials science and engineering, the yield point is the point on a stress–strain curve that indicates the limit of elastic behavior and the beginning of plastic behavior. Below the yield point, a material will deform elastically and will return to its original shape when the applied stress is removed.
The Ramberg–Osgood equation was created to describe the nonlinear relationship between stress and strain—that is, the stress–strain curve—in materials near their yield points. It is especially applicable to metals that harden with plastic deformation (see work hardening ), showing a smooth elastic-plastic transition.