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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) [email protected]@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