Incremental plastic deformation

It is important to appreciate that plasticity is different in kind from elasticity, where there is a unique relationship between stress and strain defined by a modulus or stiffness constant. Once we achieve the combination of stresses required to produce yield in an idealized rigid plastic material, deformation can proceed without altering stresses and is determined by the movements of the external constraints, e.g. the displacement of the jaws of the tensometer in a tensile test. This means that there is no unique relationship between the stresses and the total plastic deformation. Instead, the relationships that do exist relate the stresses and the incremental plastic deformation, as was first recognized by St Venant, who proposed that for an isotropic material the principal axes of the strain increment are parallel to the principal axes of stress. 

But the two curves still do not exactly match, as Fig. 8.7 shows. The reason is a displacement of (for example) u = l f2 in tension and compression gives different strains) it represents a drawing out of the tensile specimen from 1q to 1.5 1q, but a squashing down of the compressive specimen from /q to 0.5/q. The material of the compressive specimen has thus undergone much more plastic deformation than the material in the tensile specimen, and can hardly be expected to be in the same state, or to show the same resistance to plastic deformation. The two conditions can be compared properly by taking small strain increments... 

For the case of LiF crystals, both the dislocation concentration and the incremental stress caused by plastic deformation are proportional to the amount of deformation. This indicates that the hardening is caused by impediments created by dislocations and dipoles to the motion of subsequent dislocations. 

Excessive plastic deformation—The primary and secondary stress limits as outlined in ASME Section Vlll, Division 2, are intended to prevent excessive plastic deformation and incremental collapse. 

Plastic instability—Incremental collapse incremental collapse is cyclic strain accumulation or cumulative cyclic deformation. Cumulative damage leads to instability of vessel by plastic deformation. 

Different model for rutting owing to structural deformation, plastic deformation or surface wear (studded tyres). Incremental change of sand patch texture depth during analysis year. 

It was indicated in the above curves that strain hardening is related to an increase in the yield stress, which can be observed after unloading, followed by an increment of plastic deformation and upon reloading the specimen. The slope of the stress-strain curve, being a measure of the increase in the stress on a stress-strain curve, usually defines the strain hardening rate. The slope, at a constant stress rate, is expressed as ... 

Because the assumption of small strains is not always valid in plastic deformation, equation (6.11) becomes more and more imprecise with increasing strains. To circumvent this problem, we can consider only strain increments ... 

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