l9 fatigue v1c

ME366 Spring 2015 Professor Nathan Salowitz1

ME 366: Design of Machine Elements

Lecture 9: Introduction to Fatigue


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


Agenda

Review of Static Failure

Introduction to Fatigue Analysis


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 +


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


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


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


Case: Aloha Airlines Flight 243

Undetected multiple site fatigue cracking


Case Southwest Flight 812


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


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)


Fatigue Promoters

Residual Stresses

Elevated temperatures

Temperature cycling

Corrosive environment

Frequency


Analyzing Fatigue

a


Analyzing Failure

Where did fatigue start?

Identify Beach marks?

Final region of failure?

Ductile or brittle material?

Anything else unique?

Q&A


Analyzing Failure






Q&A


Examples in Text

z


Text table of Schematics


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)


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


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


Loading

Alternating load centered at 0

0

x

t


Resulting Information

S-N curve

Fatigue strength Sf (Mpa or psi)

Endurance limit


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


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


Strain Life Model

Best explains the nature of fatigue

Requires idealizations that lead to uncertainties

Not useful for design


Hysteresis

Strain softening material


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


Strain Life Equations

2=

2+

2

2= 2

2=

2

2=

2 +

2

2N reversals / cycle


Issues With Strain Life

How do you determine the total strain at concentration point/crack tip?

Material data is not readily available


Coming Up

More Fatigue


Exam Notes

Combined loading

Pressure vessels

Beam bending

Buckling

Static failure

Fatigue


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)

NO LATE ASSIGNMENTS

l9 fatigue v1c

Documents