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8/11/2019 MAE 4353 - Fall 2014 - Module 3 Part 1
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MAE 4353 Mechanical Design IIDr James A. Kidd
Module 3, Part 1: 8/25/14
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Statistics & Fatigue Statistics Review
Fatigue Fatigue in Metals Fatigue Failures Fatigue Life Methods ( Stress-Life, Strain-Life, Linear-Elastic Fracture Mechanics) Endurance Limit Fatigue Strength Modifying Factors Stress Concentration and Notch Sensitivity Fluctuating Stress Characterization Fatigue Failure Criteria Loading Mode Combinations Fluctuating Stresses and Cumulative Fatigue Damage Problems
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Probability Distribution - Normal
Normal (Gaussian) Probability Density Function (PDF)
Shorthand:
Probability Distribution: Measure of uncertainty of a given quantity or measurement
Fatigue life and component wear data are noisy and must be treated accordingly forgood design and analysis
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Probability Distribution Normal, cont
Transforming into standardvariable z permits use CPD tables:
No closed form for Cumulative ProbabilityDistribution (CPD) for Gaussian:
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Empirical Distribution Rule
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Weibull DistributionVariable shape; Highly useful for reliability estimates based on experimental or field data
3-Parameter Weibull Distribution:
x 0 is the minimum guaranteed valued of x
Characteristic Value of x below which lie 63.2%
of observations
Shape parameter b >0Controls skew(large to right, small to left)
Reliability is complement to CPD:
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Weibull Distribution, cont
Solving for x:
x - Value at which specified reliability could be expected(given distribution defined by x0 , and b )
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Error Propagation
=Coefficient of Variation:
Table 20-6
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Error Propagation ExampleGiven force and area measurements of a rod under tension with normalprobability distributions and means of F = 20,000 psi and A = 0.5 in 2 andcoefficients of variation of CF = 0.05 and CA = 0.05, determine the mean andstandard deviation of the resulting direct stress. If the material has a yield stressallowable of 43,000 psi, comment on the implications of the results.
Going further: What are the implications of material property statistical variation?MMPS Handbook properties:
A Basis 99% samples exceed value to 95% confidenceB Basis 90% samples exceed value to 95% confidence
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Fatigue
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Fatigue in MetalsFailure - Under varying load
- Well below ultimate strength
- Possible with little structural deformation, i.e., suddenly
Cracks typically begin at discontinuities, for example:Rapid cross section changesKeywaysStress concentration pointsTool marks, scratches, etc.
Surface pits from contact or corrosionMaterial flaws
General fatigue classifications:Low Cycle: N10 3 cyclesHigh Cycle: N>10 3 cycles
Progression:Stage I: Micro-crack initiation and initial growthStage II: Micro-crack to macro-crack, beach mark bandsStage III: Rapid growth to failure
http:// youtu.be/DykiHVrVkKgTWI Fatigue Testing
http:// youtu.be/GPYw8hRkyVAFatigue Crack Propagation
http://youtu.be/DykiHVrVkKghttp://youtu.be/DykiHVrVkKghttp://youtu.be/GPYw8hRkyVAhttp://youtu.be/GPYw8hRkyVAhttp://youtu.be/GPYw8hRkyVAhttp://youtu.be/DykiHVrVkKg8/11/2019 MAE 4353 - Fall 2014 - Module 3 Part 1
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Fatigue-Life Methods - Introduction Stress-Life Method
Most traditional and represents high-cycle fatigue adequately Least accurate for low-cycle fatigue Strain-Life Method
More detailed analysis of localized plastic deformations Better for low-cycle fatigue estimates Multiple compounding idealizations so significant
uncertainties Discuss due to insight into nature of fatigue
Linear-Elastic Fracture Mechanics (LEFM)
Fracture mechanics crack growth as function of stressintensity Typically implemented via computer codes
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Stress-Life Method Fatigue strength from test data Widely used method:
Moores rotating beam for pure bending ofclose tolerance, highly polished specimens
Note statistical nature of the results
Testing of material andcomponents may berequired
Example with endurancelimit, S e
If no clear endurance limit,
S e must include number ofcycles (say 10 8)
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Endurance Limit Strength
Simplified relationship
for endurance limitstrength in steels:
For test specimen NOT actual component!
Fig 6-17
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Endurance Limit Modifying Factors
Marin Equation:
Endurance strength in real life can (will!) differ from lab test data using carefullyprepared specimens in controlled environments
Real effects include: Material, manufacturing, environment, design,
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Factors, cont.Surface Factor k a : Test specimens are highly machined, highly polished and in a protected environment Real components may have a variety of finishes (ground, machined, etc.)
Finish a, kpsi bGround 1.34 -0.085
Machined or cold-drawn 2.70 -0.265
Hot-Rolled 14.4 -0.718
As-Forged 39.9 -0.995
Sut , kpsi150
k a
0.875
0.7160.394
0.273
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Factors, cont.Size Factor k b : Real components vary in size from the test specimens
For bending and torsion:
For axial loading (no effect):
Equivalent diameters:For non-rotating cylinders:
For rectangular cross-sections:
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Factors, cont.Loading Factor k c : Accounts for differences in component loading vs. test loading When torsion is combined with bending or axial, use k c=1
Temperature Factor k d : For reduced temperatures, brittle fracture is a higher risk For elevated temperatures a model for a steel is:
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Factors, cont.Reliability Factor k e : Fatigue strength values usually expressed as means
Data indicates an 8% typical standard deviationReliabilty, % z a k e
50 0 1
90 1.288 0.897
95 1.645 0.868
99 2.326 0.814
99.9 3.091 0.753
99.99 3.719 0.702
99.999 4.265 0.659
99.9999 4.753 0.620Miscellaneous Effects Factor k f : For anything else, like
Corrosion, coatings,
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Endurance Strength ExampleWhat is the endurance strength of the machined shaft given below if a 99.99%reliability is desired?
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Assignments Friday (8/22) by 2200:
Complete and submit Resume Slide Assignment to D2L Dropbox By class time Monday (8/25):
Read Shigley Chapters 20 (stats) and 6 (Fatigue) Complete online Stats & Fatigue Quiz Download Stats/Fatigue Problem set (conditional on quiz) Upload Problem Set #1 (Elasticity)
Wednesday (8/27): Fatigue, continued + guest Speaker
Friday (8/29): Jet Engine Cutaway Assessment at DML 3 groups: 0900, 0945, 1030 sign up Wednesday
Monday (9/1): Labor Day No Class! Wednesday (9/3): Finish Fatigue, Introduce Project Phase I By class time Friday (9/5):
Review brainstorming videos on D2L project Phase I folder
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