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Cyclic Loading

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The following graphs illustrate some variations of cyclic loading. Note the stress fluctuation with respect to the vertical axis.

Sinusoidal Fluctuating Stress


Repeated Stress (zero to max)
R = 0  and  A = 1


Zero to Min (opposite of zero to max)
R = ∞  and  A = -1


Completely (or Fully) Reversed Sinusoidal Stress
R = -1  and  A = ∞

For the above cyclic loading plots, the positive stress region is tension and the negative region is compression. The more negative the value, the greater the compression.

Nomenclature

symbol	description
σmax	maximum stress
σmin	minimum stress
σm	mean stress
σa	amplitude stress
σr or Δσ	stress range
R	stress ratio
A	amplitude ratio

Equations

The equations of the stresses for cyclic loading are as follows:

σm =	σmax + σmin 2

σa =	σmax – σmin 2

σ_r = σ_max – σ_min

σ_max = σ_m + σ_a
σ_min = σ_m - σ_a

ratios:

R  =

σmin σmax

A  =

σa σm

As the mean stress increases, the stress amplitude must decrease in order for the material to withstand the applied stresses. This condition can be summarized by the Goodman relationship.

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Related
▪ L - Modified Goodman Diagram