notch sensitivity corrections in msc fatigue and fe … sensitivity corrections in msc fatigue and...

MSC.Software VPD Conference | July 17-19, 2006 | Huntington Beach, California

Notch Sensitivity Corrections in MSC Fatigue and FE-Fatigue

Jeff MentleyMark Pompetzki

nCode International

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MSC.Software VPD Conference | July 17-19, 2006 | Huntington Beach, California

ABSTRACT

Notch Sensitivity Corrections in MSC Fatigue and FE-Fatigue (2006-54)

Jeff Mentley, Mark PompetzkinCode International Southfield, MI 48076(248) 945-4368jeff.mentley@ncode.commark.pompetzki@ncode.com

In the prediction of fatigue lives at geometric stress risers, the notch sensitivity of the material becomes important. When the stresses are calculated from a finite element model, traditional notch sensitivity corrections are difficult to use because they rely on knowing the stress concentration factor. A methodology has been introduced in MSC Fatigue, and FE-Fatigue that uses stress gradients to estimate correction factors across the model that account for the notch sensitivity of the material. The results of these corrections will be compared to empirical corrections and to physical test data.

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MSC.Software VPD Conference | July 17-19, 2006 | Huntington Beach, California

INTRODUCTION

• Definition of Notch Sensitivity• Approaches to Compensate for Notch Sensitivity• Implementation in MSC Fatigue and FE-Fatigue• Comparison to Test Data• Questions

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MSC.Software VPD Conference | July 17-19, 2006 | Huntington Beach, California

NOTCHES ARE STRESS RISERS

Elastic Stress Concentration Factor

Kt = σmax/σnom

Kt depends on:• Geometry• Mode of Loading

-Stress Concentration Factors,- R. E. Peterson, John Wiley, New York, 1953

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MSC.Software VPD Conference | July 17-19, 2006 | Huntington Beach, California

FATIGUE OF NOTCHES

Mechanical Behavior of Materials, Dowling, N., 1993

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MSC.Software VPD Conference | July 17-19, 2006 | Huntington Beach, California

FATIGUE STRENGTH REDUCTION

Fatigue Strength Reduction Factor

Kf = Sf/S’fKf depends on:• Geometry• Mode of Loading• Material Type

104 105 106

Cycles, N

Stre

ss A

mp.

400

200

600

800

un-notched

notched

Sf

S’f

tf

f

KKK

≤≤1 K thanlessusually is t

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MSC.Software VPD Conference | July 17-19, 2006 | Huntington Beach, California

NOTCH SENSITIVITY FACTOR

)(1)(10

1011

effectnotchFullKKthenqifeffectnotchNoKthenqif

qwhereKK

q

tf

f

t

f

==

==

<<−−

=

Empirical Approximations

r

q α+=

1

1

Peterson

⎟⎟⎠

⎞⎜⎜⎝

⎛+

=

r

qρ1

1where

r - notch root radiusα, ρ - material constants

Neuber

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MSC.Software VPD Conference | July 17-19, 2006 | Huntington Beach, California

STRESS GRADIENT CALCULATION

z’

∆z’

∆σvm

σvm Gσ= ∆σvm∆z’( ) σvm/

Normalized stress gradient

• Calculated by MSC Patran or FE2FES

• At every node on the surface

• Stress tensor history on surface

(σx’, σy’, τxy’ )

• Normalized stress gradient history into surface

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MSC.Software VPD Conference | July 17-19, 2006 | Huntington Beach, California

MATERIAL CORRECTION FACTORS

nσ = Kt/Kf

Using normalized Von Mises stress gradient Gσ, along with material type and strength, a correction factor nσ is calculated.

Available Materials•Steel•Cast steel•Grey Cast Iron•Nodular Cast Iron•Malleable Cast Iron•Aluminum•Cast Aluminum•UserAnalytical Strength Assessment of Components in

Mechanical Engineering, 5th ed., Haibach, T. E , 2003

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MSC.Software VPD Conference | July 17-19, 2006 | Huntington Beach, California

MODIFICATION OF STRESS HISTORY

Computed Stress Histories(σx’, σy’, τxy’)

Normalized σvm gradient

Correction factor fornodular cast iron

Corrected Stress Histories(σx’, σy’, τxy’)

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MSC.Software VPD Conference | July 17-19, 2006 | Huntington Beach, California

COMPARISON OF STRESS HISTORIES

Computed Stress History

Corrected Stress HistoryUniaxial fatigue: corrected surface stress tensor history converted into a combined stress

Multiaxial fatigue: corrected surface stress tensor history is used directly.

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MSC.Software VPD Conference | July 17-19, 2006 | Huntington Beach, California

FATIGUE COMPARISON WITH TEST DATA

Kt = 4.0Test data of notched and un-notched specimens used to validate stress gradient notch sensitivity correction.

MIL-HDBK-5•Un-notched SN curves•Notched SN curves•Notch geometries•Stress-strain curves

MIL-HDBK-5J, 31 January 2003

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MSC.Software VPD Conference | July 17-19, 2006 | Huntington Beach, California

FATIGUE COMPARISON WITH TEST DATA

Test specimen used for notched fatigue data is analyzed by detailed MSC Nastran model to produce:

• Stress tensor at surface

• Stress gradient at surface

Multiple FE-Fatigue analyses performed at varying load levels to produce a load life curve.

Load life curve is converted into a nominal stress life curve and compared to the notched test data.

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MSC.Software VPD Conference | July 17-19, 2006 | Huntington Beach, California

FATIGUE COMPARISON WITH TEST DATA

Un-notched

Notched, Kt=4

Using stress data from FE model and un-notched material data• Predict notched fatigue life• Correlate with notched test data

MIL-HDBK-5J, 31 January 2003

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MSC.Software VPD Conference | July 17-19, 2006 | Huntington Beach, California

Summary

• A notch sensitivity correction procedure has been added to MSC Fatigue and FE-Fatigue.

• The correction uses:• Surface stress gradients calculated from the model geometry and stresses• Material dependent correction curves built into MSC Fatigue and FE-

Fatigue

• Improves the accuracy of fatigue life predictions of notch sensitive materials and geometries with sharp stress risers.

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MSC.Software VPD Conference | July 17-19, 2006 | Huntington Beach, California

REFERENCES

1) Haibach, T. E., Analytical Strength Assessment of Components in Mechanical Engineering, 5th ed., VDMA, Frankfurt, 2003.

2) Peterson, R. E., Stress Concentration Factors, John Wiley, 1953.3) Dowling, N. E., Mechanical Behavior of Materials, Prentice-Hall, 19934) MIL-HDBK-5J, 31 January 2003

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MSC.Software VPD Conference | July 17-19, 2006 | Huntington Beach, California

SYMBOLS

Kt - theoretical elastic stress concentration factorσmax - maximum stress in cross sectionσnom - stress in nominal cross section without stress riserKf - fatigue reduction factor, notch factorNf - life in cyclesSf - fatigue strength of un-notched specimenS’f - fatigue strength of notched specimenq - notch sensitivity coefficientr - radius of notchα - material constant for notch sensitivity relationship by Petersonρ - material constant for notch sensitivity relationship by Neuberσvm - Von Mises stressGσ - normalized stress gradientnσ - stress correction factor