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
Static Load
Stress
F and P are applied and remain constant
Stress Ratio, R = 1.0
Time
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?
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!
Types of Cyclic Stress:
1. Repeated and Reversed (i.e. RR Moore,
rotating shafts, etc.) – mean stress = 0.
2. Fluctuating stress (mean stress not zero):
a. Tensile mean stress (can cycle between
tension and compression or all tension)
b. Compressive mean stress (can cycle
between tension and compression or all
compression)
c. Repeated, one-direction stress
Definitions:
  max   min
a 

2
2
m 
 max   min
 min
R
 max
= Alternating stress
= Mean stress
2
= R value:
R = 0, repeated and one direction, i.e.
stress cycles from 0 to max value.
R =-1, Fully reversed (R-R Moore)
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
1.Repeated and Reversed Stress
 min
R
 1
 max
The average or mean stress is zero.
Cyclic loading. (a) Very low amplitude acoustic vibration. (b) High-cycle fatigue: cycling well
below general yield, y. (c) Low cycle fatigue: cycling abovegeneral yield (but below the tensile strength ts).
All stresses above are repeated and reversed (R = -1)
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/rotating_beam_fatigue.aspx
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
Test Data
Stress,  (ksi)
Fatigue Testing
Number of Cycles to Failure, N
Data from R. B. Englund, 2/5/93
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.
Representative Endurance Strengths
Estimated endurance strength of steel is about 0.50 * Su
2. Fluctuating Stress
• When an element experiences alternating
stress, but the mean stress is NOT zero.
Load varies between P and Q over time
2.Fluctuating Stress Example
• Bending of Rocker Arm
Valve Spring Force
Valve Open
Valve
Closed
• Tension in Valve Stem
Valve
Closed
RBE
2/1/91
Valve Spring Force
Valve
Open
Adapted from R. B. Englund
Types of Fluctuating Stress:
Tensile Stress w/ Tensile Mean
• Case 1:
max  min
a 
2
max  min
m 
2
Partially Reversed w/ Tensile Mean
• Case 2:
max  min
a 
2
max  min
m 
2
max is tensile and min is compressive
Partially Reversed w/ Compressive Mean
• Case 3:
max  min
a 
2
max  min
m 
2
max is tensile and min is compressive
Compressive Stress w/ Compressive Mean
• Case 4:
max  min
a 
2
max  min
m 
2
max and min are both compressive
Repeated – One Direction Stress
• Case 5:
Example of the Effect of Stress Ratio
on Endurance Strength of a Material
Mott, Fig. 5-11, Pg. 180
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).
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!!!!!!!!!!
B
Instantaneuos
Fast Fracture!
A
Crack
nucleation
and Growth
The endurance limit plotted against the tensile strength. Almost all materials
fail in fatigue at stresses well below the tensile strength.
Design Factor
• Analysis
Failure Strength
Factor of Saf ety 
Applied Stress
Sy
Example :
N

• Design
Failure Strength
Allowable Stress 
Design Factor
Sy
Example :
 ALLOW 
N
Factors Effecting Design Factor
•
•
•
•
•
•
Application
Environment
Loads
Types of Stresses
Material
Confidence
Factors Effecting Design Factor
• Application
• How many will be produced?
•
•
•
•
•
• What manufacturing methods will be
used?
Environment
Loads
Types of Stresses
Material
Confidence
• What are the consequences of
failure?
•Danger to people
•Cost
• Size and weight important?
• What is the life of the component?
• Justify design expense?
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
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
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
Factors Effecting Design Factor
•
•
•
•
Application
Environment
Loads
Types of Stresses
• Material
• Confidence
• Material properties
• Ultimate strength, yield strength,
endurance strength,
• Ductility
•Ductile:
•Brittle:
%E  5%
%E < 5%
• Ductile materials are preferred for
fatigue, shock or impact loads.
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?
Recommended Design Factors
Confidence in material
properties, analysis,
loads, the environment,
etc.
See Mott,
pages 185 - 186
Design Factor