Experimental Mechanics

, Volume 22, Issue 5, pp 180–187 | Cite as

Cumulative damage with interaction effect due to fatigue under torsion loading

An analysis of the interaction effect on the basis of a continuous-damage concept is made using published test results obtained from two-step fatigue tests at room temperature
  • Thang Bui-Quoc


The cumulative-fatigue damage concept previously developed by means of the test results obtained under axial loading is adapted for the cyclic-torsion case. The development allows one to establish the fatigue diagram (shear strain versus cycles at failure) and to calculate the remaining life under several level straining. As the damage function is strain dependent, the predictions are different from those given by the linear-damage rule.

An interaction effect between strain levels is considered to explain the strong deviation of the sums of cycle-ratios from unity. Empirical relations have been established for taking into account this effect. Essentially, this approach gives a theoretical sum of cycle-ratios greater than unity for two increasing strains; this sum is smaller than unity for the opposite case. The correlation between estimates and some published test results (torsion and axial straining) is then discussed.


Fatigue Mechanical Engineer Interaction Effect Fluid Dynamics Shear Strain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of Symbols

K, c, d, m

material constants




number of applied cycles


number of cycles at failure


number of cycles at failure corresponding to σ*

\(\overline N \)

revised value ofN due to interaction-effect consideration


stress amplitude


characteristic stress amplitude


cycle-ratio (=n/N)


total shear-strain range


reference shear-strain range


fatigue strength associated with Δγ r


shear strain corresponding to static failure under a torsion test


1 +ℓn(Δγ/Δγ r )


1 +ℓn(2γ f /Δγ r )


1 +ℓn(Δγ e /Δγ r )


λ f m/(m-1)


(λ/λ f ) m



$$\left\{ {_{\lambda _1 - 1 for decreasing strains}^{\lambda _f ^* - \lambda _1 for increasing strains} } \right.$$

associated with first strain level


associated with second strain level


original value


final value

associated with interaction-effect consideration


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Copyright information

© Society for Experimental Mechanics, Inc. 1982

Authors and Affiliations

  • Thang Bui-Quoc
    • 1
  1. 1.Ecole PolytechniqueMontrealCanada

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