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Distributions of load stresses and residual stresses at notches

Abstract

The fatigue strengh reduction factor K, can be mitigated or eliminated by suitable surface treatments. Analysis of these affects requires the knowledge of the distributions of load stresses and of residual stresses below the surface of notches. This paper describes a simple, approximate formula to determine load stress distributions and residual stress distributions at notches. The load stress distributions by the present approach were compared with finite element analysis under tension, bending and torsion loading. Residual stress distributions by the simple formula were compared with measured date by shot peening. An example of optimization in surface treatments by such analysis is shown.

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Abbreviations

a, b, c :

Constants in the load stress distribution

d :

Total depth to which the compressive residual stress extends (mm)

D :

Diameter, Large diameter of filleted shaft (mm)

K f :

Fatigue strength reduction factor, fatigue notch factor

K t :

Stress concentration factor

n :

Exponent in the load stress distribution

N f :

Number of cycles to failure

r :

Radius of fillet or semi-circular notch (mm)

R :

Radius of shaft (mm)

x :

Distance from notch root (mm)

w :

Half width of fillet or notch in their narrow section (mm)

η:

Distance from surface to the point where stress gradient at the surface meets the x-axis (mm)

σa :

Alternating stress (MPa)

σeq :

Equivalent stress (MPa)

σf :

Fatigue strength coefficient (MPa)

σF :

Fatigue strength (MPa)

σL :

Load stress at point x (MPa)

σm :

Mean stress (MPa)

σN :

Net stress (MPa)

σo :

Nominal stress (MPa)

σR :

Residual stress (MPa)

σR,P :

Maximum compressives residual stress or peak compressive stress (MPa)

ε:

Half width of the notch in plates or the radius at the narrow section of shafts (mm)

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Correspondence to Soon-Bok Lee.

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Lee, S. Distributions of load stresses and residual stresses at notches. KSME Journal 6, 132–139 (1992). https://doi.org/10.1007/BF02953081

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Key Words

  • Load Stress
  • Residual Stress
  • Fatigue Notch Factor
  • Shot Peening
  • Notch