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Beyond the Lüders strain, the stress increases due to strain hardening until it reaches the ultimate tensile stress. During this stage, the cross-sectional area decreases uniformly along the gauge length, due to the incompressibility of plastic flow (not because of the Poisson effect , which is an elastic phenomenon).
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.
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 ...
A phenomenological uniaxial stress–strain curve showing typical work hardening plastic behavior of materials in uniaxial compression. For work hardening materials the yield stress increases with increasing plastic deformation. The strain can be decomposed into a recoverable elastic strain (ε e) and an inelastic strain (ε p).
The point in the stress-strain curve at which the curve levels off and plastic deformation begins to occur. [13] Offset yield point (proof stress) When a yield point is not easily defined on the basis of the shape of the stress-strain curve an offset yield point is arbitrarily defined.
Stress-strain curve showing typical plastic behavior of materials in uniaxial compression. The strain can be decomposed into a recoverable elastic strain ( ε e {\displaystyle \varepsilon _{e}} ) and an inelastic strain ( ε p {\displaystyle \varepsilon _{p}} ).
On a stress-strain curve, the flow stress can be found anywhere within the plastic regime; more explicitly, a flow stress can be found for any value of strain between and including yield point and excluding fracture (): <.
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 ...