13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- 5. Comparison between experiments and fatigue modeling 5.1. Local « hot spot » fatigue analysis The multaxial fatigue analysis is applied using a local stress description at the hot spot stress location (i.e. trailing contact border). The analysis is performed for each plain fretting and fretting fatigue crack nucleation conditions and reported in a 2,a J - h,max σ diagram (Fig. 6). 0 -a -c c a Z X P Q (t) stick zone sliding zones “hot spot” stress analysis (x=-a, z=0) 2,a C h,max C eq. J σ = +α ⋅σ 0 100 200 300 400 500 600 0 200 400 600 800 J (MPa) 2,a (MPa) h,max σ no crack nucleation cracking Plain Fretting Fretting Fatigue Figure 6. Local Crossland analysis at the “hot spot” trailing contact border. As expected, the experimental data are highly dispersed and systematically above the material boundary. This local Crossland fatigue approach does not integrate the severe stress gradients operating next to the ”hot spot” and therefore is not suitable to predict the fretting cracking risk. To quantify the stability of the prediction, the mean value and the square root variance of the equivalent Crossland stress obtained for the 16 test conditions are computed. ∑ = σ = σ N i 1 C. eq. C. eq. (i) N 1 , x100 %E d d C. eq. C. eq. ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ τ σ −τ σ = , ( ) N 1 (i) V N i 1 C. eq. C. eq. C. eq. − σ −σ σ = ∑ = , x100 V %V . Cross eq. C. eq. C. eq. ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ σ σ σ = (2) The C eq. %Eσ allows to estimate the global error of prediction versus the theoretical material prediction, whereas the C eq. %Vσ variable provides a relative estimation of the dispersion. For the given local fatigue description, we found C eq. %Eσ = +36 % and C eq. %Vσ = 16% which correspond to a critical overestimation and a high dispersion. 5.2. Non local « critical » distance fatigue approach The critical distance method which consists to define the stress state at a certain distance below the contact “hot spot” (Fig. 7a) is applied. Using the Taylors’s theory [13] which approximates the critical distance as the half value of the long crack propagation transition 0b , we deduced :
RkJQdWJsaXNoZXIy MjM0NDE=