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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 ...
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 ...
For elastic-perfectly viscoplastic materials, the elastic strain is no longer considered negligible but the rate of plastic strain is only a function of the initial yield stress and there is no influence of hardening. The sliding element represents a constant yielding stress when the elastic limit is exceeded irrespective of the strain.
The strain can be decomposed into a recoverable elastic strain and an inelastic strain (). The stress at initial yield is σ 0 {\displaystyle \sigma _{0}} . For strain hardening materials (as shown in the figure) the yield stress increases with increasing plastic deformation to a value of σ y {\displaystyle \sigma _{y}} .
The stress is proportional to the strain, that is, obeys the general Hooke's law, and the slope is Young's modulus. In this region, the material undergoes only elastic deformation. The end of the stage is the initiation point of plastic deformation. The stress component of this point is defined as yield strength (or upper yield point, UYP for ...
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 elastic components, as previously mentioned, can be modeled as springs of elastic constant E, given the formula: = where σ is the stress, E is the elastic modulus of the material, and ε is the strain that occurs under the given stress, similar to Hooke's law.
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]