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7/30/2019 6 Probalistic Introduction
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Introduction
Professor Darrell F. Socie
Department of Mechanical Science and Engineering
University of Illinois at Urbana-Champaign
© 2003-2011 Darrell Socie, All Rights Reserved
Probabilistic Aspects of Fatigue
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Contact Information
Darrell Socie
Mechanical Science and Engineering
1206 West Green
Urbana, Illinois 61801
Office: 3015 Mechanical Engineering Laboratory
dsocie@uiuc.edu
Tel: 217 333 7630
Fax: 217 333 5634
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Fatigue Calculations
Who really believesthese numbers ?
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SAE Specimen
Suspension
Transmission
Bracket
Fatigue Under Complex Loading: Analysis and Experiments, SAE AE6, 1977
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Analysis Results
1 10 100
48 Data Points
COV 1.27
99.9 %
99 %
90 %
50 %
10 %
1 %
0.1 %
C u m u l a t i v e P r o b a
b i l i t y
Analytical Life / Experimental Life
Strain-Life analysis of all test data
Non conservative
Conservative
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Material Variability
1 10 100
99.9 %
99 %
90 %
50 %
10 %
1 %
0.1 %
C u m u l a t i v e P r o b a
b i l i t y
Analytical Life / Experimental Life
Material Analysis
Strain-Life back calculation of specimen lives
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Probabilistic Models
Probabilistic models are no better than theunderlying deterministic models
They require more work to implement
Why use them?
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Quality and Cost
Taguchi
Identify factors that influence performance
Robust design – reduce sensitivity to noise
Assess economic impact of variation
Risk / Reliability
What is the increased risk from reduced testing ?
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Risk
10-9
10-8
10-7
10-6
10-5
10-4
10-3
R i s k
Time, Flights etc
Acceptable risk
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Reliability
99 %
80 %
50 %
10 %
1 %
0.1 %
E x p e c t e d F a
i l u r e s
106
Fatigue Life
105104
103
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Risk Contribution Factors
Operating Temperature
Analysis Uncertainty
Speed
MaterialProperties
Manufacturing
Flaws
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Uncertainty and Variability
customers
materials manufacturing
usage
107
Fatigue Life, 2Nf
1
10 102 103 104 105 106
0.1
10-2
1
10-3
10-4
S t r a i n A m p l i t u d e time
50%
100 %
F a i l u r e
s
Strength
Stress
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Deterministic versus Random
Deterministic – from past measurements the future positionof a satellite can be predicted with reasonable accuracy
Random – from past measurements the future position of a car can only be described in terms of probability andstatistical averages
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Deterministic Design
Stress Strength
SafetyFactor
Variability and uncertainty is accommodated by introducingsafety factors. Larger safety factors are better, but how much
better and at what cost?
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Probabilistic Design
Stress Strength
Reliability = 1 – P( Stress > Strength )
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3σ Approach
3σ contains 99.87% of the data
If we use 3σ on both stress and strength
The probability of the part with the lowest strength
having the highest stress is very small
P( s < S ) = 2.3 10-3
σ≈=≤≥Σ=− 5.4103.5)Sss(P)failure(P 6
For 3 variables, each at 3 σ:
σ≈=− 7.5102.1)failure(P 8
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Benefits
Reduces conservatism (cost) compared toassuming the “worst case” for every designvariable
Quantifies life drivers – what are the mostimportant variables and how well are theyknown or controlled ?
Quantifies risk
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Probabilistic Aspects of Fatigue
Introduction
Basic Probability and Statistics
Statistical Techniques
Analysis Methods
Characterizing Variability
Case Studies
FatigueCalculator.com
GlyphWorks
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