Elastic limit point

This ambiguity in the stress space loading criterion may be illustrated by considering a stress-strain plot corresponding to simple tension, as shown schematically in Fig. 5.3. With each point on the stress-strain curve past the initial elastic limit point A, there is associated a point on the elastic limit surface in stress space and a point on the elastic limit surface in strain space. On the hardening portion of the stress strain curve AB, both the stress and the strain are increasing, and the respective elastic limit surfaces are moving... 

Three significant characteristic points of the stress-strain curve are distinguishable. The first kink describes the elastic limit, the second kink is the yield strength and the third point describes the breaking point of the foil for uniaxial short term exposure. Up to the elastic limit, ETFE-foU shows an almost linear elastic behaviour. Ftooke s law prevails (at least for shortterm loads). From the elastic limit point up to the yield strength, ETFE... 

Here, F is the force applied to the dragline, S is the cross sectional area of the double filament, L is the initial length of the dragline, and AL is the elongation of the dragline when the F is applied. The F and AL are determined from the force-elongation curve within the elastic limit point and the S from the electron scanning microscopy. 

Stretching velocity of 3.3x10 m/s was plotted against spider weight W in Fig. 4.51. The ES, defined as the mechanical strength at the elastic limit point, increased linearly with increasing W. Experimentally, we may express ES as... 

In six-dimensional strain space, may be viewed as the inner produet of the normal to the elastic limit surface and the tangent to the strain history , see Fig. 5.1. Its value is negative, zero, or positive depending on whether i, points inward, along the tangent, or outward to the elastic limit surface. Four cases may be distinguished. 

Unloading. The strain lies on the elastic limit surface = 0, but the tangent to the strain history points inward into the elastic region < 0. It is assumed that k — 0. The material is said to be unloading and the elastic limit surface is stationary. 

When the material is at the ultimate stress point B, inelastic loading will entail a positive strain rate, and the elastic limit surface in strain space will be moving outward. On the other hand, the stress rate at this point is zero, and the elastic limit surface in stress space will be stationary. If the material is perfectly inelastic over a range of strains, then the stress rate will be zero and the elastic limit surface in stress space will be stationary on inelastic loading throughout this range. 

When a shearing stress is imposed on a solid, deformation occurs, until a point is reached when the internal stresses produced balance the shearing stresses. Provided the elastic limit for the material is not exceeded the solid will return to its original shape when the load is removed. 

Elastic Strength Pressure (ESP). The gas pressure that will produce an equivalent stress (based on distortion-energy criteria) at some point in the gun that is equal to the min elastic limit of the material at ambient temp... 

It may be pointed out that the term yield point is sometimes erroneously used as a synonym for elastic limit and proportional limit As it has been described in the paragraphs above it is actually a phenomenon that occurs in only a very small number of cases in tensile testing. As it has also been observed in the description that graphically and experimentally, it is an anomalous behaviour in which there is a strain occurring with no increase in stress. 

This analysis is consistent with the conclusion of Gerk (1977) that the behavior that determines hardness is deformation-hardening not the yield stress. He was one of the first authors to point this out. For other types of materials, it is the maximum stress that the material can bear after deformation (plastic, or that associated with phase transitions in eluding twinning). Hardness is not directly related to the elastic limit, although there is an indirect connection with the offset plastic deformation of metals as demonstrated by Tabor (1951). 

After the transient shock load phase has damped out, the subsequent confined hot gas pressure can be considered as a steady state load from a structural dynamics point of view. Therefore the design criteria requires that these loadings do not exceed the elastic limit of the structure. Dynamic increase factors are not applicable since loading rate is no longer a consideration. 

The theoretical analysis for two-dimensional foams and emulsions has recently been expanded to three dimensions [38], with Kelvin s minimal tet-rakaidecahedron as the unit cell. The system is subjected to a uniaxial extensional strain. As the elastic limit, or yield point, is approached, the cell shape tends towards a rhombic dodecahedron however, at the yield point, the shrinking quadrilateral faces of the polyhedron have finite (albeit small) area. 

Using planar tetrakaidecahedra as the model, on the other hand, causes the square faces to shrink to zero area at the yield point. The unit cell therefore resembles a true rhombic dodecahedron. The elastic response was found to be anisotropic (i.e. dependent on initial cell orientation) for the planar model, up to the elastic limit. This is in contrast to the monodisperse 2D case, which is... 

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