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Hollomon's equation is a power law relationship between the stress and the amount of plastic strain: [10] = where σ is the stress, K is the strength index or strength coefficient, ε p is the plastic strain and n is the strain hardening exponent.
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.
where represents the applied true stress on the material, is the true strain, and is the strength coefficient. The value of the strain hardening exponent lies between 0 and 1, with a value of 0 implying a perfectly plastic solid and a value of 1 representing a perfectly elastic solid.
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).
The stress of the flat region is defined as the lower yield point (LYP) and results from the formation and propagation of Lüders bands. Explicitly, heterogeneous plastic deformation forms bands at the upper yield strength and these bands carrying with deformation spread along the sample at the lower yield strength.
The yield strength or yield stress is a material property and is the stress corresponding to the yield point at which the material begins to deform plastically. The yield strength is often used to determine the maximum allowable load in a mechanical component, since it represents the upper limit to forces that can be applied without producing ...
The yield strength is the point at which elastic deformation gives way to plastic deformation. Deformation in the plastic range is non-linear, and is described by the stress-strain curve . This response produces the observed properties of scratch and indentation hardness, as described and measured in materials science.
The quadratic Hill yield criterion for thin rolled plates (plane stress conditions) can be expressed as + (+) (+) + = where the principal stresses , are assumed to be aligned with the axes of anisotropy with in the rolling direction and perpendicular to the rolling direction, =, is the R-value in the rolling direction, and is the R-value perpendicular to the rolling direction.