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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.
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.
where ˙ is the effective plastic strain-rate of the quasi-static test used to determine the yield and hardening parameters A,B and n. This is not as it is often thought just a parameter to make ε p ˙ ∗ {\displaystyle {\dot {\varepsilon _{\rm {p}}}}^{*}} non-dimensional. [ 35 ]
The strain can be decomposed into a recoverable elastic strain (ε e) and an inelastic strain (ε p). The stress at initial yield is σ 0 . Work hardening , also known as strain hardening , is the process by which a material's load-bearing capacity (strength) increases during plastic (permanent) deformation.
Strain energy density consists of two components - volumetric or dialational and distortional. Volumetric component is responsible for change in volume without any change in shape. Distortional component is responsible for shear deformation or change in shape.
The difference between the Cam Clay and the Modified Cam Clay [4] (MCC) is that the yield surface of the MCC is described by an ellipse and therefore the plastic strain increment vector (which is perpendicular to the yield surface) for the largest value of the mean effective stress is horizontal, and hence no incremental deviatoric plastic ...
This is not true since the actual area will decrease while deforming due to elastic and plastic deformation. The curve based on the original cross-section and gauge length is called the engineering stress–strain curve, while the curve based on the instantaneous cross-section area and length is called the true stress–strain curve. Unless ...
Where is flow stress, is a strength coefficient, is the plastic strain, and is the strain hardening exponent. Note that this is an empirical relation and does not model the relation at other temperatures or strain-rates (though the behavior may be similar).