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 Stress Stress Ratio, R = 1.0
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. All stresses above are repeated and reversed (R = -1)
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:

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 Strength = 0.50(Su)
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

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
Reversed is the worst case and is the case used to determine the endurance strength of materials (RR Moore, etc)
Fluctuating stress has less effect on endurance strength than reversed
Mott, Fig. 5-11, Pg. 180

25. Stages of Fatigue:
Micro structural changes – nucleation of permanent damage (mm)
Creation of microscopic cracks (mm)
Growth and coalescence of cracks into dominant crack (striations).
Stable crack growth (Beach marks)
Instability and rapid failure (area goes down, stress goes up eventually exceeding tensile strength).

26. Stages of Fatigue:
Micro structural changes – nucleation of permanent damage (mm)
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. fail in fatigue at stresses well below the tensile strength.
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 < 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

38. Design Factor