L9 Fatigue v1c
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Transcript of L9 Fatigue v1c
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ME366 Spring 2015 Professor Nathan Salowitz1
ME 366: Design of Machine Elements
Lecture 9: Introduction to Fatigue
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ME366 Spring 2015 Professor Nathan Salowitz2
Announcements & Reminders
HW 5 is posted and due Tuesday
Ok to use write a matlab script for repetitive problems
Include code in HW
Great to learn MatLab
Not good practice for exam
Book editions
Be sure to do the problems from 10th U.S. edition
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ME366 Spring 2015 Professor Nathan Salowitz3
Agenda
Review of Static Failure
Introduction to Fatigue Analysis
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ME366 Spring 2015 Professor Nathan Salowitz4
Ductile Static Failure Models
Tresca (maximum shear stress) Calculate max shear stresses (principle stress)
Yield if:
von Mises (distortion energy)
=1
2
2+
2+
2 +
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ME366 Spring 2015 Professor Nathan Salowitz5
Brittle Static Failure Models
Maximum Normal Stress 1 Sut or 3 Suc
Brittle Coulomb Mohr A B 0
1 A 0 B
0 A B Modified Mohr
A B 0
()
1 A 0 B
0 A B
Plane Stress:1 2 3A B & 0
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ME366 Spring 2015 Professor Nathan Salowitz6
Fatigue is Complicated
Can appear brittle or mixed mode
Failure regularly occurs well below Su or Sy Sudden failure common
No early deformation
Hard to detect
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ME366 Spring 2015 Professor Nathan Salowitz7
Case: SR-71 Blackbird
Fastest airplane in the world
18 months from initial design to first flight
After every test
What failed & why
What didnt fail & why
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ME366 Spring 2015 Professor Nathan Salowitz8
Case: Aloha Airlines Flight 243
Undetected multiple site fatigue cracking
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ME366 Spring 2015 Professor Nathan Salowitz9
Case Southwest Flight 812
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ME366 Spring 2015 Professor Nathan Salowitz10
Fatigue in Metals
Stage I: Initiation Microcracking due to cyclic plastic deformation
Not visable to the naked eye
Stage II: Growth Beach marks / clamshell marks
Easy to see, normal to crack growth direction
usually grow as crack progresses
Stage III: Failure Usually ductile or brittle as before
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ME366 Spring 2015 Professor Nathan Salowitz11
Fatigue Initiation
Fatigue cracks usually start at discontinuities:
Stress concentrations; holes, keyways, changes in cross section
Contact stresses
Stamp marks, tool marks, scratches, burrs, poor joint design
Microscopic material discontinuities (foreign material, voids, crystal discontinuities)
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ME366 Spring 2015 Professor Nathan Salowitz12
Fatigue Promoters
Residual Stresses
Elevated temperatures
Temperature cycling
Corrosive environment
Frequency
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ME366 Spring 2015 Professor Nathan Salowitz13
Analyzing Fatigue
a
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ME366 Spring 2015 Professor Nathan Salowitz14
Analyzing Failure
Where did fatigue start?
Identify Beach marks?
Final region of failure?
Ductile or brittle material?
Anything else unique?
Q&A
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ME366 Spring 2015 Professor Nathan Salowitz15
Analyzing Failure
Where did fatigue start?
Identify Beach marks?
Final region of failure?
Ductile or brittle material?
Anything else unique?
Q&A
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ME366 Spring 2015 Professor Nathan Salowitz16
Analyzing Failure
Where did fatigue start?
Identify Beach marks?
Final region of failure?
Ductile or brittle material?
Anything else unique?
Q&A
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ME366 Spring 2015 Professor Nathan Salowitz17
Examples in Text
z
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ME366 Spring 2015 Professor Nathan Salowitz18
Text table of Schematics
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ME366 Spring 2015 Professor Nathan Salowitz19
Models for Fatigue
Fatigue Life (section 6-3 to 6-6)
Fatigue Strength & Endurance Limit (6-7 to 6-8)
Modification Factors (6-9)
Stress Concentrations and Notch Sensitivity (6-10)
Fluctuating Stresses (6-11 to 6-13)
Combination of Loading Modes (6-14)
Varying, Fluctuating Stresses; Cumulative Fatigue Damage (6-15)
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ME366 Spring 2015 Professor Nathan Salowitz20
Fatigue Life Methods
Predict number of cycles (N) to failure for a specific loading level
low Cycle fatigue N < 1000 Stress Life
Easy Most common Least accurate (adequate for high cycle fatigue)
Strain Life Requires local analysis of plastic deformation Good for low cycle Requires assumptions and idealizations that lead to uncertainty in
results
Linear Elastic Fracture Mechanics Assumes a crack exists & is detected then predicts growth
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ME366 Spring 2015 Professor Nathan Salowitz21
Testing & Data Collection
Specimens Ground & polished (no surface imperfections)
Testing Machine rotates at high speed Constant moment applied (multiple tests with varying
moments)
Data Many specimens tested at each condition
https://www.youtube.com/watch?v=52knsY5AWIc https://www.youtube.com/watch?v=CVzK9V5WxRw
Video
Demo
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ME366 Spring 2015 Professor Nathan Salowitz22
Loading
Alternating load centered at 0
0
x
t
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ME366 Spring 2015 Professor Nathan Salowitz23
Resulting Information
S-N curve
Fatigue strength Sf (Mpa or psi)
Endurance limit
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ME366 Spring 2015 Professor Nathan Salowitz24
Example
What is the maximum allowable stress to survive 100,000 cycles?
How many cycles will a component with max= 35MPa survive?
What is the endurance limit for this material?
Class
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ME366 Spring 2015 Professor Nathan Salowitz25
Fatigue is Hard to Predict
Prediction is imprecise
Testing of components necessary for reasonable prediction
Stress life is the most common method
Simple
Adequate for high cycle fatigue
Least accurate for low cycle fatigue
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ME366 Spring 2015 Professor Nathan Salowitz26
Strain Life Model
Best explains the nature of fatigue
Requires idealizations that lead to uncertainties
Not useful for design
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ME366 Spring 2015 Professor Nathan Salowitz27
Hysteresis
Strain softening material
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ME366 Spring 2015 Professor Nathan Salowitz28
Strain Life Coefficents
Fatigue Ductility Coefficient: f': true strain corresponding to fracture
Fatigue Strength Coefficient: f': true stress corresponding to fracture
Fatigue Ductility Exponent: c
Fatigue Strength Exponent: b
2N reversals / cycle
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ME366 Spring 2015 Professor Nathan Salowitz29
Strain Life Equations
2=
2+
2
2= 2
2=
2
2=
2 +
2
2N reversals / cycle
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ME366 Spring 2015 Professor Nathan Salowitz30
Issues With Strain Life
How do you determine the total strain at concentration point/crack tip?
Material data is not readily available
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ME366 Spring 2015 Professor Nathan Salowitz31
Coming Up
More Fatigue
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ME366 Spring 2015 Professor Nathan Salowitz32
Exam Notes
Combined loading
Pressure vessels
Beam bending
Buckling
Static failure
Fatigue
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ME366 Spring 2015 Professor Nathan Salowitz33
Homework #5 Due 3/3/2015 in class
Reading
Chapter 5
Homework Assignment 5-3 a, b, & d (10 points)
5-11 (10 points)
5-19 a & e (10 points)
5-24 (10 points)
5-29 (10 points)
5-36 (10 points)
5-38 (see eq 3-42) (10 points)
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