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The Interaction of Mean or Weld Residual Stress with the Neuber Plasticity

Correction and the Effects on Fatigue Life Prediction

Copyright (C) 2012 F.A. Conle and Univ. of Waterloo

Permission is granted to copy, distribute and/or modify this document

under the terms of the GNU Free Documentation License, Version 1.3

or any later version published by the Free Software Foundation;

with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.

A copy of the license is available here:

"GNU Free Documentation License". ( "http://www.gnu.org/licenses/fdl.html" )

of the local cyclic stresses and strains experienced at the hot-spot of

many components subjected to fatigue loading. Most estimates of component stress however,

have been calculated elasticly, by means of either traditional manual calculations

or elastic FEA methods. It is then necessary to translate the elastic

calculated stress at the critical locations into estimates of elastic-plastic

stress and strain behavior. Of the several methods of accomplishing this

translation, the one most popularly adopted by most software methods is the

Neuber [1-3] plasticity correction.

** Fig. 1 :** Correcting an Elastic Stress Calculation for Material Plasticity

As depicted in Fig._1, the Neuber correction can be set into three steps:

- Using elastic calculation methods compute the stress and strain

at the fatigue hot-spot.

- Compute the energy or product of elastic stress multiplied by

elastic strain.

- Using the stabilized cyclic stress-strain curve of the material

at the hot-spot find the cyclic stress and cyclic strain that

give the same energy product as in Step 2.

One can find examples of the stabilized cyclic stress-strain curve

in fatigue databases such as here. When you find the material of interest

e.g.:

A36 Merged File of two above files __ | __ Fitted __ | __ Calculator

Click on the**"Fitted"**link and using either "View Page Source" in your

browser or "cut and paste", extract the stress and strain columns

from the data section.

the initial stress-strain origin with subsequent straining through a series of

simple fluctuating strain (or stress) cycles. It is apparent that the

of cyclically stabilized aluminum

initial loading path from the origin is different in size than the loading path

of the subsequent hysteresis loops. A commonly used approximation is that the

cyclic path is a factor of two larger than the initial path. Generally this is

referred to as "Masing" type behavior[4,5]. Similar behavior is exhibited in

multiaxial cyclic conditions[6,7], but for many fatigue problems a one-dimensional

approach suffices. An example of a strain sequence for HSLA 350 steel:

Try your own strain sequence.

plasticity correction is shown in Fig._3 and their application to two half cycles

are shown in Fig._4.

** Fig. 3 :** (a) Initial stress-strain curve (b) Hysteresis loop stress-strain curve

There are two similar curves shown in figure_3. The one on the left side is the

stabilized cyclic stress-strain curve generally derived from uniaxial fatigue test

samples, while on the right is the same curve with co-ordinates multiplied by a factor

of two. Both curves use the equivalent elastic energy product to solve for the

stress-strain magnitudes of each half-cycle of the loading history.

** Fig. 4:** Application of Initial and Cyclic Neuber Solutions.

More details of how these features are modelled for fatigue purposes can be

found in reference_[8].

data set. An example:

The first item, on the left is a text display and of the "raw" fatigue

test data. Data can be added to these files, either on-line or locally, and plots

created by clicking on the "Send" button.

The second item "_Fitted_" is a html file of a median line fit of the raw data.

It would be an input file for any software that performs a plasticity correction

and calculates the life based on the resulting local stress-strain hysteresis loops.

The third item, "_Calculator" is a html form which incorporates the "Fitted" file above,

and when submitted (click on Send), will calculate and display the local stress-strain

response to the nominal stress inputs as predicted by the Neuber plasticity correction.

Life is computed by using the local stress-strain loops maximum and minimum stresses and strains.

The software that performs these calculations is available in a link under the topic
**Other Links** below.

A screen shot image of how to use the calculators is
available here.

For an example set of screen shots of a typical usage with explanations:

- Entering the Cycle Set information

- The resulting Local Stress-Strains & Damage

- Percent Damage per Cycle Set Graphic

- FEA Fatigue Analysis: Case 1
- FEA Fatigue Analysis: Case 2
- Calculation Software that includes Neuber Plasticity Correction
- How to do a quick Fatigue Analysis
- Interaction of Neuber Plas. Corr. in Welded Components

in creating this publication.

- Neuber, H., "Theory of Stress Concentration for Shear Strained Prismatical

Bodies with Arbitrary Non Linear Stress Strain Law," J.Appl.Mech., Dec. 1961, pp. 544-550.

- Topper, T.H., R.M.Wetzel, J.Morrow, "Neuber's Rule Applied to Fatigue of

Notched Specimens," ASTM, J.of Materials V4 N1, March 1969, pp.200-209.

- Tipton, S., "A Review of the Development and Use of Neuber's Rule for Fatigue

Analysis," SAE Paper 910165, 1991.

- Jenkin, C.F."Fatigue in Metals," The Engineer, Vol.134, No.3493, Dec. 1922, pp.612-614.

- Masing, G., "Eigenspannungen und Verfestigung beim Messing," in Proc. of 2nd Int.

Congress of Appl. Mech., Zurich, 1926.

- Mroz, Z., "On the Description of Anisotropic Work-Hardening," J.of Mech. Phys

of Solids, Vol.15 1967, pp.163-175.

- Chu, C.-C., "A Three-Dimensional Model of Anisotropic Hardening in Metals

and Its Application to the Analysis of Sheet Metal Formability," J.of Mech. Phys.

of Solids, Vol.32, 1984, pp.197-212.

- Conle, A., T.R.Oxland, T.H.Topper, "Computer-Based Prediction of Cyclic Deformation

and Fatigue Behavior,"*Low Cycle Fatigue*ASTM STP 942, 1988, pp.1218-1236

- Chu, C.-C, "Incremental Multiaxial Neuber Correction for Fatigue Analysis,"

SAE Technical Paper 950705, 1995

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