PSI - Issue 26

Sabrina Vantadori et al. / Procedia Structural Integrity 26 (2020) 106–112 Vantadori et al. / Structural Integrity Procedia 00 (2019) 000 – 000

107

2

Nomenclature a C

amplitude of the shear stress component

m

slope of S-N curve under fully reversed normal stress

m 

slope of S-N curve under fully reversed shear stress , a m N N amplitude and mean value of the normal stress component cal N calculated number of loading cycles to failure exp N experimental number of loading cycles to failure , eq a N equivalent normal stress amplitude 0 N number of loading cycles corresponding to both , 1 af  − and

, 1 af  − stress level

, 1 af  −

fully-reversed normal stress fatigue strength

u 

ultimate tensile strength

, 1 af  −

fully-reversed shear stress fatigue strength

Among such criteria, those based on the critical plane approach seem to be the most promising since they represent a satisfactory tool to evaluate fatigue life and to estimate the cracking direction (Ref. by Socie and Marquis, 2000). They can be sorted as (i) stress-based, (ii) strain-based, and (iii) energy-based criteria. The Carpinteri et al. criterion herein applied (Refs by Carpinteri et al. 2011, 2014, 2015, 2017, 2019, and Araujo et al., 2014) is a stress-based critical-plane method since the damage parameter adopted is an equivalent uniaxial stress defined as a combination of the stress vector components related to the critical plane. The criterion has been widely employed to simulate many experimental multiaxial fatigue tests, for both infinite life (Refs by Carpinteri et al. 2011, 2014, and Araujo et al., 2014) and finite life (Refs by Carpinteri et al. 2015, 2017, 2019). In the present paper, loading conditions involving axial loading and inner pressure are analysed by using the above criterion and the experimental load-controlled fatigue tests (Refs by Morishita et al., 2018, and Cruces et al., 2019), carried out at room temperature through a triaxial testing machine designed by some of the present authors (Ref. by Morishita et al., 2016). 2. Critical plane criterion and experimental tests The criterion by Carpinteri et al. proposes to transform the actual multiaxial stress state into an equivalent uniaxial one, with amplitude given by (Refs by Carpinteri et al. 2011, 2014, 2015, 2017, 2019; Araujo et al., 2014):

2

  

   



af

, 1 −

2

2

N

C

=

+ 



(1)

, eq a

, eq a

a



af

, 1 −

where

, 1 −   = +     m u N  

N N

(2)

, eq a a af

is the equivalent normal stress amplitude, and u  is the ultimate tensile strength of the material. Eq.(2) is based on the Gooodman linear interaction between the normal stress amplitude a N and the normal stress mean value m N . As is well-known, a N and m N can readily be computed since the direction of N is fixed with respect to time,