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5.1 Generalized notation

In the generalized stress tensor notation, the tensor component are written "σ_ij" where i and j are in {1;2;3}.

The first step is to number the sides of the cube. When the lines are parallel to a vector base , then :

the sides perpendicular to ares called "j" and "-j" ;
point from the center of the cube, points towards the j side, the -j side is at the opposite.

σ_ij is then the component along the i axis that applies on the j side of the cube.

This generalized notation allows an easy writing of equations of the continuum mechanics, such as the generalized Hooke's law :

the correspondance with the former notation is thus :

x	→	1
y	→	2
z	→	3
σ_xx	→	σ₁₁
τ_xy	→	σ₂₁
τ_xz	→	σ₃₁
...

6 Stress measurement

As with force, stress cannot be measured directly but is usually inferred from measurements of strain and knowledge of elastic properties of the material.

7 Units

The SI unit for stress is the pascal (symbol Pa); in US Customary units, stress is expressed in pounds per square inch ( PSI). See also: Pressure (physics)

8 Residual stress

Residual stress occures in un-loaded structures for a variety of reasons. Heat from welding may cause localized expansion, which is taken up during welding by either the molten metal or the placement of parts being welded. When the finished weldment cools, some areas cool and contract more than others, leaving residual stresses. Castings may also have large residual stresses due to uneven cooling.

Another example are certian types of gun barrles, which are made with two tubes forced together. The inner tube is compressed and the outer tube streched. This has the effect of better stress distribution when the gun is fired. Parts are often heated or dunked in liquid nitrogen to aid assembly.

Press fits are the most common intentional use of residual stress. Automotive wheel studs, for example are pressed into holes on the wheel hub. The holes are smaller than the studs, requiring force to drive the studs into place. The residual stresses fasten the parts together. Nails are another example.

9 See also

10 Books

Dieter, G. E. (1988) Mechanical Metallurgy, BooksEnthsiast.com
Love, A. E. H. (1944) A Treatise on the Mathematical Theory of Elasticity BooksEnthsiast.com
Marsden, J. E. & Hughes, T. J. R. (1983) Mathematical Foundations of Elasticity BooksEnthsiast.com

11 External links

Stress analysis, Wolfram Research

Continuum mechanics

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