By Sol R. Bodner (auth.)
Considerably simplified types of macroscopic fabric habit, equivalent to the idealization for metals of elastic-time self sustaining plastic reaction with a yield (onset) criterion, have served the engineering career good for a few years. they're nonetheless easy to the layout and research of such a lot structural purposes. within the have to use fabrics extra successfully, there are situations the place these conventional versions aren't sufficient, and constitutive legislation which are extra bodily practical need to be hired. this can be particularly suitable to stipulations the place the inherent time dependence of inelastic deformations, known as "viscoplasticity", is mentioned equivalent to at increased temperatures and for top pressure charges. Unified theories of elastic-viscoplastic fabric habit, that are basically appropriate for metals and metal alloys, mix all elements of inelastic reaction right into a set of time established equations with a unmarried inelastic pressure cost variable. For such theories, creep lower than consistent rigidity, tension leisure less than consistent pressure, and stress-strain family at consistent premiums are each one specified situations of a common formula. these equations mayor would possibly not contain a yield criterion, yet versions which don't separate a completely elastic quarter from the final reaction should be thought of "unified" in a extra normal feel. The theories have reached a degree of improvement and adulthood the place they're getting used in a couple of subtle engineering purposes. although, they've got now not but turn into a regular approach to fabric illustration for common engineering practice.
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Additional resources for Unified Plasticity for Engineering Applications
With respect to that state, damage could be interpreted as deterioration in the ability of a material to support stress thereby magnifying the effect of stress on the response. A specific definition of "damage" is elusive but it is often considered to be the presence of geometrical discontinuities in the material such as voids, cracks or debonding of components which reduce the effective load carrying area. These defects are presumed to be small in size compared to the dimensions of the object under discussion but larger than the atomic scale; a level sometimes referred to as the "mesoscale".
He performed both extension (constant velocity) and constant load (creep) tests on tin which is reasonably viscoplastic at room temperature and moderate strain rates. For the extension tests, the stresses were at about the maximum of the stress-strain relation. Ludwik's proposed empirical relations were in the forms of a power law and an exponential (logarithmic) law, (41) (42) UNIFIED PLASTICITY 48 In these equations, So would correspond to a stress at zero strain rate. These equations are actually relations between certain stress levels obtained under particular conditions and were not intended to be general viscoplastic constitutive laws such as Eq.
One of the first proposals of this kind was that of Bodner and Rubin (1986) who suggested the angle 8 between the direction of l3ij and its rate Pij as the measure for non-proportionality. This choice includes aspects of the history of loading. A factor a determined by a separate evolution equation a. (8, Wp) is then added to the saturation value Zl for isotropic hardening. That separate evolution equation would provide for the dependence of the additional hardening effect on the history of nonproportional loading, and whether a return to proportional loading leads to permanent or reduced hardening.