PSI - Issue 33

Sabrina Vantadori et al. / Procedia Structural Integrity 33 (2021) 773–780 Author name / Structural Integrity Procedia 00 (2019) 000–000

775

3

2. Stress-based multiaxial fatigue criterion The criterion here employed is a stress-based multiaxial fatigue criterion (under high/medium-cycle fatigue regime) formulated for conventional metallic materials, which can be thought of as homogeneous and isotropic ones (Vantadori et al. (2020a)). Such a criterion, based on the so-called critical plane approach, allows us to estimate the fatigue strength (for both infinite and finite life tests) and the fatigue lifetime (for finite life tests) of metallic structural components under proportional and non-proportional constant amplitude cyclic loadings. An advantage of the above criterion is that it can be applied to: (i) different multiaxial loading conditions, i.e. constant and variable amplitude loading (Carpinteri et al. (2018) and Vantadori et al. (2018)), and (ii) different structural component configurations, i.e. plain and notched specimens (Ronchei and Vantadori (2021)). The main steps of the criterion are hereafter summarised. 2.1. Critical plane orientation Let us consider a generic material point P of a smooth component under multiaxial constant amplitude cyclic loading, and a fixed reference system XYZ . The principal stresses ( 1 2 3      ) and the corresponding principal stress directions (1,2 and 3) are, in general, time-varying. Therefore, averaged principal stress directions, named 1 2 ˆ , ˆ and 3 ˆ , are assumed to correspond to the instantaneous ones when 1  achieves its maximum value during the period. The above assumption makes the implementation of the criterion rather simple. The normal w to the critical plane is determined through a rotation  of the 1 ˆ direction, in the plane 13 ˆ ˆ . In particular, the off-angle  is given by the following empirical expression:   2 1 1 3 1 8 af , af ,               (1) respectively, at a given number of loading cycles (generally assumed equal to 2ꞏ10 6 cycles). 2.2. Fatigue strength and lifetime estimation At each time instant t , the stress vector w S , related to the local reference system uvw on the critical plane, may be decomposed in two components, that is: (1) a component N , normal to the critical plane, whose direction is fixed with respect to time; (2) a component C , lying on the critical plane, whose direction is time-varying. The criterion proposes to transform the actual multiaxial stress state into an equivalent uniaxial stress, whose amplitude eq,a  is computed by means of the following expression: where 1 af ,   and 1 af ,   are the fatigue strengths for fully reversed normal stress and for fully reversed shear stress,

 2



2

2

(2)

N

C







1     af , af ,



1

eq,a

eq ,a

a

with:





eq,a N N

N

(3)

 





1

a af ,

m u



where a N and m N are the amplitude and the mean value of N , respectively; a C is the amplitude of C and is determined by means of a min-max procedure available in the literature (Araújo et al. (2011)). Moreover, u  is the material ultimate tensile strength.