PSI - Issue 19

22 L.C. Araujo et al. / Procedia Structural Integrity 19 (2019) 19–26 L.C. Araújo et al. / Structural Integrity Procedia 00 (2019) 000 – 000 3. Fatigue limt from √ parameter The estimated value of the uniaxial fatigue limit, , with loading ratio R of -1 can be found from the relation of Murakami (2002), which is expressed by Eq. 12. = 1.41( + 120) (√ ) 1 6 (12) Yanase and Endo (2014) proposed that the torsional fatigue limit, , also with R of -1, is obtained from Eq.13. = 1.19( + 120) (√ ) 1 6 (13) where in Eq. 12 and 13, is the Vickers hardness of the material. The √ parameter corresponds to the square root of the projected area of a micro defect in the cross-section perpendicular to the maximum principal stress for the uniaxial and torsion cases. Considering the non-metallic inclusions of naturally defective materials, the value of √ can be obtained through a sample analysis and with a method of statistics of extreme value that are described in detail on Murakami (1994). With this statistical method it is possible to predict which is the largest √ that one expects to find from an internal inclusion. The √ is a function of the volume of material, which may be of the test specimen or of an entire mechanical component. The maximum estimated value of √ is renamed √ and this value that will be applied in Eq. 12 and 13. 4. Adapting the models of multiaxial fatigue to consider the small defects The purpose of this work is to combine the classical models of multiaxial fatigue with the fatigue limits estimated from the √ parameter, obtained for internally defective materials, considering the non-metallic inclusions of the material. For this, instead of calibrating the multiaxial models with data obtained from fatigue tests, it is suggested the use of the estimated limits, and , in the calibration of the models. So, in determining the material constants of each model the following relationships must be assumed: 0 = (14) 0 = (15) The great advantage in the use of the constants obtained from the estimated limits is that these limits are obtained relatively easily, quickly and at a reduced cost when compared to the experimental methods of lifting the fatigue limits. Another, is that with the use of the theory of the statistics of extreme value it is possible to consider the effect of size on the design of mechanical components, which is not feasible experimentally since tests would have to be made with components in real scale. 5. Material and experimental procedures The material used in the manufacture of the specimens is the DIN 42CrMo6 (AISI 4140) steel oil quenched and tempered at 600 °C, taken from crankshafts of generator sets, whose the mechanical properties are shown in Table 1. The specimens are smooth and round with diameter of 10 mm in the test section and have been designed according to international standard ASTM E466-15 (2015). 4

Table 1. Mechanical properties of analysed DIN 42CrMo6 steel. Yield Strength (MPa) Tensile Strength (MPa)

Elongation (%)

Vickers hardness

710

900

20

320