PSI - Issue 19

L.C. Araujo et al. / Procedia Structural Integrity 19 (2019) 19–26 L.C. Araújo et al./ Structural Integrity Procedia 00 (2019) 000 – 000

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for nucleation of a crack is the shear stress and that the propagation is strongly influenced by the normal stress. Findley (1959) was the first researcher to use the concept of critical plane with his model, which makes a linear relationship between the shear stress amplitude, , and the maximum normal stress, , . It considers the critical plane as the one with maximum combination of these two parameters. The Findley model for fatigue strength is expressed by Eq. 4. ( , ) ( + , ) = (4) where the critical plan ( , ) is defined by the maximum value of the term in brackets found from all plans ( , ) that pass through a material point of a component submitted to a stress history. The and are parameters of the material and can be calculated from Eq. 4, with the fatigue limit obtained from simple uniaxial tests ( 0 ) and simple torsional tests ( 0 ), both with loading ratio R of -1, as shown below: = 1 √ − − 0.5 1 (5) and = 0 2√ − 1 (6) where = 0 / 0 . Susmel and Lazzarin (2002) proposed the Modified Wöhler Curves Method (MWCM). In this model the critical plane is one of the planes that experience the maximum amplitude of the shear stress and among those the one with the highest normal stress. In the condition of the fatigue strength the MWCM is represented as follows: ( , ) + ( , ) = (7) as in the Findley ’s model and are parameters of the material and can be obtained from Eq. 7, with the fatigue limit obtained from simple uniaxial tests ( 0 ) and simple torsional tests ( 0 ), both with loading ratio R of -1 and are defined as in Eq. 8 and 9. = 0 − 0 2 (8) = 0 (9) Susmel, Tovo and Lazzarin (2005) also defined the variable of Eq. 7, which represents the influence of normal stress on fatigue strength, limiting the use of the model, which applies up to a limit value, , above which it has no meaning and therefore the MWCM cannot be applied. The values of and are obtained as follows: = , (10) = 0 2 0 − 0 (11) There are several known ways of finding the values of , for the Crossland model, and of finding the values of , which is applied in both the Findley model and the MWCM. Therefore in this work, the Maximum Rectangular Hull (MRH) method proposed by Araújo et al. (2011) were used, which in addition to being easy to implement considers the effect of non-proportionality of stress histories. This method considers as the amplitude value the diagonal of the largest rectangle capable of enveloping the shear stress history.