13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- Hertzian hypotheses are satisfied which implies elastic stress conditions, smooth surfaces, plain strain hypothesis and thick enough specimen to satisfy the semi infinite contact configuration. The low surface roughness of specimens, the large lateral width of cylinder pads and the 10 mm specimen thicknesses support such hypothesis. Besides, a posteriori stress analysis shows that all the crack nucleation conditions correspond to elastic stress conditions ( y VM σ σ < 1). A major interest of this analytical stress description is the very fast computation of the cyclic stress path which allows an extensive non local multiaxial fatigue stress analysis. 4.2. Crossland’s Multiaxial Fretting criterion The stress loadings operating below the surface are multiaxial and therefore a multixial fatigue analysis is required. The Crossland’s multiaxial fatigue approach [12], well adapted to describe the fatigue response of the studied alloy, is considered. The crack risk is expressed as a linear combination of the maximum amplitude of the second invariant of the stress deviator 2,a J , and the maximum value of the hydrostatic pressure ( h,max σ ) (Fig. 5a). ( ) ( ) [ ] ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ − − = ∈ ∈ 1/2 0 0 t T t T max S(t) S(t ) : S(t) S(t ) D max 0 (t) Σ Deviatoric space 'Φ Φ D 2 D 2 1 J2,a = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ Σ σ = ∈ ( (t)) trace 3 1 max t T h,max Stress loading path Stress deviator ( (t)).1I trace 3 1 S(t) (t) Σ =Σ − Hydostactic stress 2,a C h,max C eq. . J σ = +α σ Equivalent Crosslandstress with 3 3 d d d C σ τ −σ α = cracking if: d C eq. σ ≥τ maximum at the trailing contact border(hot spot) sliding zones sticked zone very sharp gradients C eq._max C eq. σ σ d C eq._max 476 MPa >>τ = σ (a) (b) Figure 5. a) Illustration of the Crossland criterion – b) Crossland distribution of the FF2 condition (local stress analysis) (Table 2) The crack nucleation condition is verify if the equivalent Crossland fatigue stress is becoming larger than the shear fatigue limit : d 2,a C h,max C eq. . J σ = +α σ ≥τ with for the studied alloy 0.28 Cα = (1) Figure 5b shows the distribution of Crossland criterion computed for a representative Fretting Fatigue crack nucleation condition (i.e. FF2 test, Table 2) applying a local stress analysis. Confirming the experimental results, the maximum risk value is localized at the trailing contact border. The distribution shows very sharp gradients and a dissymmetry of the profile induced by stick zone offset generate by the fatigue mismatching strain deformation within the interface.
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