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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.
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.
Thus the basic influence parameters for the forming limits are, the strain hardening exponent, n, the initial sheet thickness, t 0 and the strain rate hardening coefficient, m. The lankford coefficient, r, which defines the plastic anisotropy of the material, has two effects on the forming limit curve. On the left side there is no influence ...
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]
In metal plasticity, the assumption that the plastic strain increment and deviatoric stress tensor have the same principal directions is encapsulated in a relation called the flow rule. Rock plasticity theories also use a similar concept except that the requirement of pressure-dependence of the yield surface requires a relaxation of the above ...
It provides the 3D coordinates of the component's surface as well as the distribution of major and minor strain on the surface and the material thickness reduction. In the Forming Limit Diagram, the measured deformations are compared to the material characteristics. The system supports optimization processes in sheet metal forming by means of;
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.
Generally, raising the temperature of an alloy above 0.5 T m results in the plastic deformation mechanisms being controlled by strain-rate sensitivity, whereas at room temperature metals are generally strain-dependent. Other models may also include the effects of strain gradients. [3]