PSI - Issue 13

H. Soares et al. / Procedia Structural Integrity 13 (2018) 1786–1791 Soares et al. / Structural Integrity Procedia 00 (2018) 000 – 000

1790

5

Figure 6 shows the SSF evolution for both materials and loading paths. It can be concluded that the damage scale varies according to the loading path, stress level and material, which confirms the literature results. This is shown by the lines ’ slope depicted in the graphs. Therefore, the transformation of normal and shear stresses for the same stress space using a constant is unsuitable to estimate fatigue strength under multiaxial loading conditions. Also, heat treatment has a strong influence on the stress scale factor, and therefore, on the damage scale. Other interesting result was observed in Case 3, the out-of-phase loading path has a downwards offset, i.e. the stress scale is generally lower in Case 3 comparatively to Case 2 in both materials. This demonstrates the loading path effect on the stress scale factor. Table 1 shows the estimates for the critical angle orientation using the critical plane model mentioned in Section 3.1. These estimates can be correlated with the experimental results depicted in Figure 7.

a) b) Fig. 6. SSF results in the normal stress space. a) Loading case 2, b) Loading case 3.

Table 1. Critical plane estimates. Case 2

Case 3

Findley

41

41

Brown-Miller

-37

-37

F-S

39

39

S-W-T Liu I Liu II

0 0

0 0

±45

±45

Figure 7 shows the experimental crack initiation results for Cases 2 and 3. The correlation between the critical plane estimates and the experimental results show an improved performance of the SWT and LIU I models. These models emphasize normal stresses/strains which may indicate a strong influence of normal stresses in crack initiation phase. Moreover, heat treatment does not have a significative influence on the crack initiation plane for non proportional loadings, on the other hand, for proportional loadings different crack initiation planes were obtained.

a)

b)

c)

d)

Fig. 7. Experimental crack initiation planes for Case 2 and Case 3.