Plastic flow limit

But at the present it (Bridgman s work) increases the presumption that the discontinuity in the shock wave is to be explained by something else. The whole question of what causes such discontinuities seems to be somewhat obscure. It is apparently recognized that such a phenomena as reaching the plastic limit may explain the discontinuity at 10,(X)0 (kg/cm ) mentioned above, but the precise mechanism by which reaching the plastic flow point may induce the discontinuity seems not to have been worked out. 

If we load a material in compression, the force-displacement curve is simply the reverse of that for tension at small strains, but it becomes different at larger strains. As the specimen squashes down, becoming shorter and fatter to conserve volume, the load needed to keep it flowing rises (Fig. 8.6). No instability such as necking appears, and the specimen can be squashed almost indefinitely, this process only being limited eventually by severe cracking in the specimen or the plastic flow of the compression plates. 

A metal tumbler would not crack because its elastic limit must be exceeded considerably before it fails. However, repetitions of thermal stress, when some plastic flow occurs on both heating and cooling cycles, can result in either cracking or so much deformation that a part becomes unserviceable. 

No one steel exceeds the tensile modulus of mild steel. Therefore, in applications in which rigidity is a limiting factor for design (e.g., for storage tanks and distillation columns), high-strength steels have no advantage over mild steel. Stress concentrations in mild steel structures are relieved by plastic flow and are not as critical in other, less-ductile steels. 

The second major assumption is that the material is elastic, meaning that the strains are directly proportional to the stresses applied and when the load is removed the deformation will disappear. In engineering terms the material is assumed to obey Hooke s Law. This assumption is probably a close approximation of the material s actual behavior in direct stress below its proportional limit, particularly in tension, if the fibers are stiff and elastic in the Hookean sense and carry essentially all the stress. This assumption is probably less valid in shear, where the plastic carries a substantial portion of the stress. The plastic may then undergo plastic flow, leading to creep or relaxation of the stresses, especially when the stresses are high. 

Fig. 2.1. Relationship of pressure Pv under indenter and the corresponding initial plastic flow and flow limit aT with uniaxial compression. (After Kelly, 1973)...

Fig. 18. Upon application of a localized heat to a TiNi wire which has been stretched uniaxially beyond its limit of easy plastic flow, the wire will bend abruptly at the point of heating to the fixed angle of 150 °C. By moving the heat down the wire, the bend will move along the wire with the flame. - reference [49]...

As a force is applied to the item through the die, the metal first becomes elastically strained and would return to its initial shape if the force were removed at this point. As the force increases, the metal s elastic limit is exceeded and plastic flow occurs via the motion of dislocations. Many of these dislocations become entangled and trapped within the plastically deformed material thus, plastic deformation produces crystals which are less perfect and contain internal stresses. These crystals are designated as cold-worked and have physical properties which differ from those of the undeformed metal. 

The mechanism of the indentation process has been clearly defined by Tabor (1947). When a ball presses on a metal surface, the material deforms elastically. As the load increases, the stresses soon exceed the elastic limit and plastic flow starts. By increasing the load still further the material directly beneath the penetrator becomes completely plastic. On release of the load there is an amount of elastic recovery. 

When the elastic limit of a metal has been exceeded, it will undergo plastic flow beginning at the yield point. It is this property of metals that is exploited for cold and hot working into desired shapes. When a metal is deformed permanently from the tension force, it exhibits a property known as ductility. By comparison, the term... 

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