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The two plastic limit theorems apply to any elastic-perfectly plastic body or assemblage of bodies. Lower limit theorem: If an equilibrium distribution of stress can be found which balances the applied load and nowhere violates the yield criterion, the body (or bodies) will not fail, or will be just at the point of failure. [2] Upper limit theorem:
To ensure that voids do not form between individually deforming grains, the GB constraint for the bicrystal is as follows: ε xx A = ε xx B (the x-axial strain at the GB must be equivalent for A and B), ε zz A = ε zz B (the z-axial strain at the GB must be equivalent for A and B), and ε xz A = ε xz B (the xz shear strain along the xz-GB ...
For elastomers, such as rubber, the elastic limit is much larger than the proportionality limit. Also, precise strain measurements have shown that plastic strain begins at very low stresses. [11] [12] Yield point The point in the stress-strain curve at which the curve levels off and plastic deformation begins to occur. [13]
In such situations, if the shear stress reaches the yield limit then the material enters the plastic domain. Figure 2 shows the Tresca–Guest yield surface in two-dimensional stress space, it is a cross section of the prism along the σ 1 , σ 2 {\displaystyle \sigma _{1},\sigma _{2}} plane.
PSB structure (adopted from [7]). Persistent slip-bands (PSBs) are associated with strain localisation due to fatigue in metals and cracking on the same plane. Transmission electron microscopy (TEM) and three-dimensional discrete dislocation dynamics (DDD [8]) simulation were used to reveal and understand dislocations type and arrangement/patterns to relate it to the sub-surface structure.
The Lankford coefficient (also called Lankford value, R-value, or plastic strain ratio) [1] is a measure of the plastic anisotropy of a rolled sheet metal. This scalar quantity is used extensively as an indicator of the formability of recrystallized low-carbon steel sheets.
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Thus, a point defining true stress–strain curve is displaced upwards and to the left to define the equivalent engineering stress–strain curve. The difference between the true and engineering stresses and strains will increase with plastic deformation. At low strains (such as elastic deformation), the differences between the two is ...