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"Neuber Stress" PlotsAISI Bar Fatigue Group

Mar. 29 2018

F.A. Conle

Some standard data sheets show

a "Neuber Stress" plotPart 1

This work is licensed under a

Creative Commons Attribution-ShareAlike 4.0 International License. Part 1 of this article explains how a "Neuber Stress" is calculated from unnotched axially loaded fatigue specimen tests to create the plot. Part 2 will explain how it is useful to fatigue design engineers. In brief a Neuber stress graph plots energy vs. fatigue life. Specifically which has units of stress. It represents the energy at a fatigue hot spot such as the region at the root of a stress concentration where the fatigue crack will initiate.

Background References: 1. H.Neuber, "Theory of stress concentration for shear strained prismatical bodies

with arbitrary non-linear stress-strain law," J. of Appl. Mech., Dec. 1961 pp.544-550

2. T.H.Topper, R.Wetzel and J.D.Morrow, "Neuber's rule applied to fatigue of notched

specimens," ASTM J.of Matls., V4 N1, Mar.1969, pp.200-209 The Neuber Plasticity Correction transforms Elastic Analysis Stresses into strains and stresses from the cyclic stress-strain curve

The transformation

is based on equal Energy i.e.:

Stress X Strain

Elastic

AnalysisElastic+Plastic

stress-strain curve

The first half-cycle has

a shape different from following fatigue half cycles. hysteresis loop half-cycles curve.The cyclic stress-strain curve is assumed

½ the size of

This is termed

"Masing's hypothesis"Note the feature of cyclic material deformation behavior : On-line: http://fde.uwaterloo.ca/Fde/Notches.new/neuber.html Solution for initial loading

Solution for subsequent

½ cycles

"Neuber" Stress( both sides have units of stress )If one accepts the previous plasticity correction analysis one can play with the equation and define an elastic stress term from the cyclic stress-strain axial test result terms

Elastic + Plastic

side of equationElastic side of equation

Hot Spot

Elastic

Stress

SPeterson's Kt

Sn

S = Sn * Kt

S = SFEA

SFEA Sn * Kt

Source: F.D.& E. Comm. 2014 Both elastic Finite Element and Stress

Concentration(Kt) methods yield an elastic

hot spot stress that needs plasticity correction: W d

Given a series of constant amplitude axial

specimen tests we can take the elastic modulus and the stable values of strain range, stress range and compute the energy term or "Neuber stress" to create a fatigue life plot.

We can now enter the Y axis of this plot

with the elastic analysis stress S to estimate a fatigue life.

The Neuber plasticity correction is

built into the graph.

Note that this does NOT include a

mean stress correction.Axial Specimen tests ksi

The advantage of this plot

over a simple stress vs. life or strain vs. life plot is that it contains a measure of three variables, Strain

Stress

Elas.Modulus

of a material vs. life.

Part 2 of this article will

show how this can be useful in a number of ways.quotesdbs_dbs33.pdfusesText_39