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Figure 7.1 Plane stress state in a continuum. In continuum mechanics, a material is said to be under plane stress if the stress vector is zero across a particular plane. When that situation occurs over an entire element of a structure, as is often the case for thin plates, the stress analysis is considerably simplified, as the stress state can be represented by a tensor of dimension 2 ...
The chief advantage of critical plane analysis over earlier approaches like Sines rule, or like correlation against maximum principal stress or strain energy density, is the ability to account for damage on specific material planes. This means that cases involving multiple out-of-phase load inputs, or crack closure can be treated with high ...
The advantages of the Watts-Ford test are that it is convenient for testing thin sheets or strips, it is similar to a rolling process (in manufacturing analyses), frictional effects may be minimized, there is no 'barrelling' as would occur in a cylindrical compression test, and the plane strain deformation eases the analysis. Stress-strain curve
For two-dimensional, plane strain problems the strain-displacement relations are = ; = [+] ; = Repeated differentiation of these relations, in order to remove the displacements and , gives us the two-dimensional compatibility condition for strains
Schematic of the loading on a plane by force P at a point (0, 0) A starting point for solving contact problems is to understand the effect of a "point-load" applied to an isotropic, homogeneous, and linear elastic half-plane, shown in the figure to the right. The problem may be either plane stress or plane strain.
Total strain energy theory – This theory assumes that the stored energy associated with elastic deformation at the point of yield is independent of the specific stress tensor. Thus yield occurs when the strain energy per unit volume is greater than the strain energy at the elastic limit in simple tension.
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.
In essence, in some problems including plane strain and plane stress elastic-plastic problems, elastic part of the material prevent unrestrained plastic flow but in many metal-forming processes, such as rolling, drawing, gorging, etc., large unrestricted plastic flows occur except for many small elastic zones. In effect we are concerned with a ...