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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.
For elastomers, such as rubber, the elastic limit is much larger than the proportionality limit. Also, precise strain measurements have shown that plastic strain begins at very low stresses. [11] [12] Yield point The point in the stress-strain curve at which the curve levels off and plastic deformation begins to occur. [13]
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:
Depending on the type of material, size and geometry of the object, and the forces applied, various types of deformation may result. The image to the right shows the engineering stress vs. strain diagram for a typical ductile material such as steel.
The work-hardened steel bar has a large enough number of dislocations that the strain field interaction prevents all plastic deformation. Subsequent deformation requires a stress that varies linearly with the strain observed, the slope of the graph of stress vs. strain is the modulus of elasticity, as usual.
At the same strain, the higher the rate of strain the higher the stress; A change in the rate of strain during the test results in an immediate change in the stress–strain curve. The concept of a plastic yield limit is no longer strictly applicable.
In such situations, if the shear stress reaches the yield limit then the material enters the plastic domain. Figure 2 shows the Tresca–Guest yield surface in two-dimensional stress space, it is a cross section of the prism along the σ 1 , σ 2 {\displaystyle \sigma _{1},\sigma _{2}} plane.
The linear-elastic region is either below the yield point, or if a yield point is not easily identified on the stress–strain plot it is defined to be between 0 and 0.2% strain, and is defined as the region of strain in which no yielding (permanent deformation) occurs. [11]