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ABAQUS connects your stress-strain data pairs with a series of straight line segments to form a continuous, piecewise-linear plasticity curve. The first data pair defines the initial yield stress and the corresponding initial plastic strain, which must have a value of zero. The data pairs on the *PLASTIC option define the true stress as a function of true plastic strain. Use the *PLASTIC option in ABAQUS to define the post-yield behavior for most metals. Replacing nominal stress,, and nominal strain,, with alternative stress and strain measures allows us to account for the change in area during the finite deformations. A mathematical model describing the plastic behavior of metals must be able to account for differences in the compressive and tensile behavior independent of the structure's geometry or the nature of the applied loads. For example, testing the same material in compression produces a stress-strain curve that does not have a necking region because the specimen does not thin as it deforms in compression. This material behavior is caused by the geometry of the test specimen, the nature of the test itself, and the stress and strain measures used. During necking the nominal stress (force per unit original area) drops well below the ultimate strength, as the nominal strain (length change per unit original length) continues to increase. Often plastic deformation increases a material's yield stress upon subsequent loadings, a behavior called work hardening.Ī metal deforming plastically under a tensile load may experience highly localized deformation, called necking, after reaching its ultimate strength. If the material is loaded again after unloading, its stiffness is equal to the Young's modulus until its stress-strain curve on reloading once again intersects the hardening curve, at which point the material yields and continues loading along the hardening curve. Once the metal yields, the stiffness for continued loading decreases dramatically, while the Young's modulus still defines the stiffness when unloading. Even after yielding, the elastic strains continue to increase according to the original elastic modulus, so that any additional straining contains both elastic and plastic components. Strains associated with plastic deformation are called plastic strains. However, once the stress in the metal exceeds the yield stress, permanent or plastic deformation begins to occur. The deformation of the metal prior to reaching the yield point creates only elastic strains, which are recovered fully if the applied load is removed. In most metals the stress at the yield point, called the yield stress, is 0.05 to 0.1% of the material's elastic modulus. At a point on the stress-strain curve known as the elastic limit or the yield point, the behavior changes from elastic to plastic. Figure 5≢ shows a stress-strain curve for a ductile metal with all the important regions labeled.
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The plastic behavior of a material is described by its yield point and its post-yield hardening. 5.2.1 Characteristics of plasticity in ductile metals