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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]
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 ...
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 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.
The strength of materials is determined using various methods of calculating the stresses and strains in structural members, such as beams, columns, and shafts. The methods employed to predict the response of a structure under loading and its susceptibility to various failure modes takes into account the properties of the materials such as its yield strength, ultimate strength, Young's modulus ...
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]