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INPUT   DATA

♥ EXAMPLE Of Input/Output

Title

Mean stress applied, σm
Stress amplitude applied, σa
Ultimate tensile strength, Sut
Endurance limit, S'e
Surface finish factor, ka
Size factor, kb
Load type factor, kc
Temperature factor, kd
Miscellaneous effects factor, ke

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OUTPUT   VARIABLES   &   GRAPHS

FACTOR-OF-SAFETY	n
♦ Goodman criterion		Graphs:  Dynamic design diagram
♦ Gerber criterion

Safety Factors In Dynamic Design

Fatigue refers to the response of a material to repeated application of stress or strain. It occurs when a material ruptures when subjected to numerous repetitions of a stress, even though a single application of that stress is not great enough to cause rupture. The most commonly employed models for demarcating the safe stress region and estimating the safety of a material under cyclic-fatigue loading are: Goodman criterion and Gerber criterion. The equations for computing the corresponding factor-of-safety are:

where
     n = factor of safety
     σ_a = stress amplitude
     σ_m = mean stress
     S_ut = ultimate tensile strength of material
     S'_e = endurance limit obtained from standard fatigue test
     S_e = endurance limit for component under investigation
     k_a = surface finish factor
     k_b = size factor
     k_c = load type factor
     k_d = temperature factor
     k_e = miscellaneous factor

All stress and yield values are given here in the same units.

These criteria are usually represented graphically by plotting the mean stress along the horizontal axis and the alternating stress along the vertical axis. The closed area defined by the Goodman straight (or Gerber parabolic) line and the axes are considered safe (i.e. n >= 1).The Goodman line usually matches data for many brittle metallic alloys, and the Gerber parabola for more ductile materials.

Tips

    ◊ Use link EXAMPLE Of Input/Output  to demo data entry expectations and results; you may edit & use it as starting point
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BIBLIOGRAPHY

• Brown TH; Marks' Calculations for Machine Design; McGraw Hill, New York, 2005, Chapter 7.
• Young WC & Budynas RG; Roark's Formulas for Stress and Strain; 7th Edition, McGraw Hill, New York, 2002.