Chapter 5

1
Chapter 5 Design for Different Types of Loading

• Part 1 Types of stress and loading, stress
  ratio, endurance strength, design factors
• Part 2 Failure theories

• E. R. Evans, Jr./ R. Michael
• MET 210W

2
Static Load
F and P are applied and remain constant
Stress
Stress Ratio, R 1.0
Time
3
Dynamic Stress

• Loads that vary during normal service of the
  product produce dynamic stress.
• Dynamic stress can be cyclic or random.
• High cycle fatigue part subject to millions of
  stress cycles.
• Examples Parts subject to dynamic stress?

4
Cyclic loads produce cyclic stress which can lead
to mechanical fatigue failure
Mechanical Fatigue The progressive and
localized structural damage that occurs when a
material is subjected to cyclic loading. The
cyclic stress is well below tensile, Su and
yield, Sy , strengths!
5
Types of Cyclic Stress

• Repeated and Reversed (i.e. RR Moore, rotating
  shafts, etc.) mean stress 0.
• Fluctuating stress (mean stress not zero)
• Tensile mean stress (can cycle between tension
  and compression or all tension)
• Compressive mean stress (can cycle between
  tension and compression or all compression)
• Repeated, one-direction stress

6
Definitions
Alternating stress
Mean stress
R value R 0, repeated and one direction,
i.e. stress cycles from 0 to max value. R -1,
Fully reversed (R-R Moore)
7
1.Repeated Reversed Stress

• an element subjected to a repeated and
  alternating tensile and compressive stresses.

Continuous total load reversal over time
Demo Switch to Excel
8
1.Repeated and Reversed Stress

• The average or mean stress is zero.

9

• Cyclic loading. (a) Very low amplitude acoustic
  vibration. (b) High-cycle fatigue cycling well
• below general yield, sy. (c) Low cycle fatigue
  cycling abovegeneral yield (but below the tensile
  strength sts).

All stresses above are repeated and reversed (R
-1)
10
Fatigue Testing

• Bending tests
• R-R More Spinning bending elements most
  common.
• Fast, cost effective, pure bending stress
• See http//www.instron.co.uk/wa/solutions/rotatin
  g_beam_fatigue.aspx

11
Fatigue Testing

• Bending tests
• Sontag Constant stress cantilever beams
• Good for flat stock (sheets)
• Get shear stress in addition to bending stress.

Top View
Specimen
12
Fatigue Testing
Test Data
Stress, s (ksi)
Number of Cycles to Failure, N
Data from R. B. Englund, 2/5/93
13
Endurance

• Endurance strength is the stress level that a
  material can survive for a given number of load
  cycles.
• Endurance limit is the stress level that a
  material can survive for an infinite number of
  load cycles.
• Estimate for Wrought Steel
• Endurance Strength 0.50(Su)
• Most nonferrous metals (aluminum) do not have an
  endurance limit.

14
Representative Endurance Strengths
Estimated endurance strength of steel is about
0.50 Su
15
(No Transcript)
16
2. Fluctuating Stress

• When an element experiences alternating stress,
  but the mean stress is NOT zero.

Load varies between P and Q over time
17
2.Fluctuating Stress Example

• Bending of Rocker Arm

Valve Spring Force
Valve Open
Valve Closed

• Tension in Valve Stem

Valve Closed
Valve Spring Force
Valve Open
RBE 2/1/91
Adapted from R. B. Englund
18
Types of Fluctuating Stress
19
Tensile Stress w/ Tensile Mean

• Case 1

20
Partially Reversed w/ Tensile Mean

• Case 2

smax is tensile and smin is compressive
21
Partially Reversed w/ Compressive Mean

• Case 3

smax is tensile and smin is compressive
22
Compressive Stress w/ Compressive Mean

• Case 4

smax and smin are both compressive
23
Repeated One Direction Stress

• Case 5

24
Example of the Effect of Stress Ratio on
Endurance Strength of a Material
Mott, Fig. 5-11, Pg. 180
25
Stages of Fatigue

1. Micro structural changes nucleation of
   permanent damage (mm)
2. Creation of microscopic cracks (mm)
3. Growth and coalescence of cracks into dominant
   crack (striations).
4. Stable crack growth (Beach marks)
5. Instability and rapid failure (area goes down,
   stress goes up eventually exceeding tensile
   strength).

26
Stages of Fatigue

1. Micro structural changes nucleation of
   permanent damage (mm)
2. Creation of microscopic cracks (mm)

These two steps crack initiation 99 of the
total life!!!!!!!!!!!!!!!!!!! Key prevent cracks
from forming at surface!!!!!!!!!!
27
B
Instantaneuos Fast Fracture!
A
Crack nucleation and Growth
28

• The endurance limit plotted against the tensile
  strength. Almost all materials
• fail in fatigue at stresses well below the
  tensile strength.

29
Design Factor

• Analysis
• Design

30
Factors Effecting Design Factor

• Application
• Environment
• Loads
• Types of Stresses
• Material
• Confidence

31
Factors Effecting Design Factor

• Application
• Environment
• Loads
• Types of Stresses
• Material
• Confidence

• How many will be produced?
• What manufacturing methods will be used?
• What are the consequences of failure?
• Danger to people
• Cost
• Size and weight important?
• What is the life of the component?
• Justify design expense?

32
Factors Effecting Design Factor

• Application
• Environment
• Loads
• Types of Stresses
• Material
• Confidence

• Temperature range.
• Exposure to electrical voltage or current.
• Susceptible to corrosion
• Is noise control important?
• Is vibration control important?
• Will the component be protected?
• Guard
• Housing

33
Factors Effecting Design Factor

• Application
• Environment
• Loads
• Types of Stresses
• Material
• Confidence

• Nature of the load considering all modes of
  operation
• Startup, shutdown, normal operation, any
  foreseeable overloads
• Load characteristic
• Static, repeated reversed, fluctuating, shock
  or impact
• Variations of loads over time.
• Magnitudes
• Maximum, minimum, mean

34
Factors Effecting Design Factor

• Application
• Environment
• Loads
• Types of Stresses
• Material
• Confidence

• What kind of stress?
• Direct tension or compression
• Direct shear
• Bending
• Torsional shear
• Application
• Uniaxial
• Biaxial
• Triaxial

35
Factors Effecting Design Factor

• Application
• Environment
• Loads
• Types of Stresses
• Material
• Confidence

• Material properties
• Ultimate strength, yield strength, endurance
  strength,
• Ductility
• Ductile E ? 5
• Brittle E lt 5
• Ductile materials are preferred for fatigue,
  shock or impact loads.

36
Factors Effecting Design Factor

• Application
• Environment
• Loads
• Types of Stresses
• Material
• Confidence

• Reliability of data for
• Loads
• Material properties
• Stress calculations
• How good is manufacturing quality control
• Will subsequent handling, use and environmental
  conditions affect the safety or life of the
  component?

37
Recommended Design Factors
Confidence in material properties, analysis,
loads, the environment, etc.
See Mott, pages 185 - 186
38
Design Factor