Neuber hyperbole

Neuber hyperbole
Theory

When solving problems, engineers typically use simplifications and assumptions, which allow them to get a response as quickly as possible with the minimum of fuss. One of the most common assumptions is the linearity of the material. The real non-linear diagram of material deformation is replaced by a linear one, in which the tensions can increase indefinitely while remaining "elastic".

But what if the concentrated tensions in some areas calculated with a simple linear material model, locally exceed the yield point. How do you know the "real" voltage value?

One possibility is to apply H. Neuber's principle. It is based on the assumption that if the yield point is exceeded in a small Stress concentration zone puts the load on the surrounding areas working in the elastic area is redistributed. This means that there is no destruction, but the deformation at the point where the yield point exceeded will continue to vary proportionally to the load.

Neuber carried out a detailed analysis of the stress concentration in the area of cuts, Grooves, roundings, tooth roots, threads, etc. through. and came to the conclusion that the concentration coefficient weakly depends on the shape of the surface of a component and the notch itself depends, but mainly on its depth and the minimum radius of curvature at the tip is determined. Because of its great practical importance, this phrase is used together with the resulting methods for calculating stress fields in the vicinity commonly referred to by concentrators as the Neuber theory.

Note: Linear elastic-ideal plastic material law
Note: All units can be changed

Input Values
Re
E
𝜀𝑝𝑙𝑎𝑠𝑡𝑖𝑠𝑐ℎ [ΔL/L]
𝜎𝑒𝑙𝑎𝑠𝑡𝑖𝑠𝑐ℎ
Format:   Std Sci +.0 -.0
Output Values
Yield strength Re - [GPa]
Modulus of elasticity E - [MPa]
plastic-elastic stretching 𝜀𝑝𝑙𝑎𝑠𝑡𝑖𝑠𝑐ℎ - [ΔL/L]
linear elastic tension 𝜎𝑒𝑙𝑎𝑠𝑡𝑖𝑠𝑐ℎ - [N/mm²]
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