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The strain can be decomposed into a recoverable elastic strain and an inelastic strain (). The stress at initial yield is σ 0 {\displaystyle \sigma _{0}} . For strain hardening materials (as shown in the figure) the yield stress increases with increasing plastic deformation to a value of σ y {\displaystyle \sigma _{y}} .
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.
The Lankford coefficient (also called Lankford value, R-value, or plastic strain ratio) [1] is a measure of the plastic anisotropy of a rolled sheet metal. This scalar quantity is used extensively as an indicator of the formability of recrystallized low-carbon steel sheets.
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.
Under tensile stress, plastic deformation is characterized by a strain hardening region and a necking region and finally, fracture (also called rupture). During strain hardening the material becomes stronger through the movement of atomic dislocations. The necking phase is indicated by a reduction in cross-sectional area of the specimen.
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:
The stress-strain behavior exhibits four characteristic regions. The first region is the linear-elastic regime, where the stress-strain behavior is elastic with no plastic deformation. The characteristic deformation mechanism in the second region is yielding, where plastic deformation can occur in the form phenomena such as twinning.
They are present when a material's plastic deformation is accompanied by internal plastic strain gradients. [2] They are in contrast to statistically stored dislocations, with statistics of equal positive and negative signs, which arise during plastic flow from multiplication processes like the Frank-Read source.