PSI - Issue 13

Roberta Amorim Gonçalves et al. / Procedia Structural Integrity 13 (2018) 1256–1260 Author name / Structural Integrity Procedia 00 (2018) 000 – 000

1259

4

(11)

for the C&S model (Carpinteri and Spagnoli, 2001), and by:

(12)

for the L&M model (Liu and Mahadevan, 2005).

4. Results and discussion

The fracture plane orientation , which is determined by the applied stress amplitudes, is in fact unique for all the models. More specifically, the higher the ratio , the lower the angle , consistent with the fact that tends to zero for uniaxial normal stress and to 45° for pure shear loading. On the other hand, the critical plane orientation, , corresponding to a given loading condition, varies appreciably from one model to another. For a given model, depends on the applied stress amplitudes as well as on the fatigue properties of the material. The error index, I , associated with the application of any of the six models, refers to the relative difference between the two sides of the inequality. I can thus be expressed as: (13) The values of I corresponding to the different loading conditions are listed in Table 2, for the variety of materials involved. Except for a few cases, the vast majority of the I values are situated within the range -10% to 10%, indicating a good predictive capability of the criteria in question. This is also demonstrated by Fig. 2, where the overall average values of I are also shown. One can thus conclude that, except for the McDiarmid model, the others are moderately conservative, with the C&S, L&M and P models exhibiting the lowest error compared to other three. Table 2. Error index, corresponding to the multiaxial fatigue criteria, for the different loading conditions. Index Error - I (%) σ a (MPa) τ a (MPa) Ma Mc F C&S L&M P Material: Hard steel: f -1 = 313.9 MPa; t -1 = 196.2 MPa; σ u = 704.1 MPa 327.7 0.0 4.4 -4.8 4.4 1.8 4.3 4.4 308.0 63.9 4.6 -4.1 4.6 1.2 3.3 3.8 255.1 127.5 8.2 1.0 8.2 3.1 5.3 5.5 141.9 171.3 3.6 -0.4 3.5 -1.5 0.3 0.2 0.0 201.1 2.5 2.5 2.5 1.9 2.3 2.5 Material: Hard steel: f -1 = 313.9 MPa; t -1 = 196.2 MPa; σ u = 680.0 MPa 138.1 167.1 1.0 -2.8 0.9 -3.9 -2.8 -2.3 245.3 122.65 4.0 -2.6 4.0 -0.8 1.3 1.4 299.1 62.8 1.7 -6.3 1.7 -1.5 0.3 0.9 Material: 42CrMo4: f -1 = 398.0 MPa; t -1 = 260.0 MPa; σ u = 1025.0 MPa 328.0 157.0 6.8 -4.7 6.7 0.7 4.5 4.2 233.0 224.0 10.9 2.8 10.8 4.1 6.6 7.3 Material: 34Cr4: f -1 = 410.0 MPa; t -1 = 256.0 MPa; σ u = 795.0 MPa 314.0 157.0 2.0 -3.4 2.0 -2.8 -0.8 -0.5 Material: 30NCD16: f -1 = 660.0 MPa; t -1 = 410.0 MPa; σ u = 1880.0 MPa 485.0 280.0 4.7 -3.2 4.7 -0.3 1.1 1.8 Material: Mild steel: f -1 = 235.4 MPa; t -1 = 137.3 MPa; σ u = 518.8 MPa 245.3 0.0 4.2 1.1 4.2 3.9 4.0 4.1 235.6 48.9 7.2 4.3 7.2 5.9 6.0 6.3 187.3 93.6 7.8 5.5 7.8 4.7 5.0 5.0 101.3 122.3 2.6 1.3 2.5 -1.0 -1.0 -0.8 0.0 142.3 3.6 3.6 3.6 3.6 4.0 3.6 Material: Cast iron: f -1 = 96,1 MPa; t -1 = 91,2 MPa; σ u = 230.0 MPa 93.2 0.0 -3.0 -38.7 -3.0 -3.6 -13.9 -3.0 95.2 19.7 3.4 -33.1 3.4 2.5 -26.3 2.8 83.4 41.6 5.6 -26.3 5.6 4.0 4.8 3.8 56.3 68.0 8.5 -13.2 8.4 5.4 6.8 5.9 0.0 94.2 3.3 3.3 3.3 -1.7 2.7 3.3