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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/rotating_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 isthe 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. 2. Fluctuating Stress • When an element experiences alternating stress, but the mean stress is NOT zero. Load varies between P and Q over time

16. 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

17. Types of Fluctuating Stress:

18. Tensile Stress w/ Tensile Mean • Case 1:

19. Partially Reversed w/ Tensile Mean • Case 2: smax is tensile and smin is compressive

20. Partially Reversed w/ Compressive Mean • Case 3: smax is tensile and smin is compressive

21. Compressive Stress w/ Compressive Mean • Case 4: smax and smin are both compressive

22. Repeated – One Direction Stress • Case 5:

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

24. 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).

25. 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!!!!!!!!!!

26. B Instantaneuos Fast Fracture! A Crack nucleation and Growth

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

28. Design Factor • Analysis • Design

29. Factors Effecting Design Factor • Application • Environment • Loads • Types of Stresses • Material • Confidence

30. 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?

31. 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

32. 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

33. 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

34. 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.

35. 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?

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

37. Design Factor