PSI - Issue 39

Camilla Ronchei et al. / Procedia Structural Integrity 39 (2022) 460–465 Author name / Structural Integrity Procedia 00 (2021) 000–000

463

4

being i ϕ the angle of the i-th non-proportional strain path with respect to the material principal axis and i Φ the coefficient of non-proportionality of the i-th non-proportional strain path. Note that the material principal axis corresponds to the direction of the proportional strain path where the maximum value of the strain standard definition, ASME ε ∆ , is realised and the longest lifetime is attained. The parameters * k and * α of Eq. (3) are given by the following relationships:

2 ( ε ϕ ε  

)

N

   

1

M ∑

a exp

1

(4)

k

=

−

*

45

sen

° −  ∆



1

i

=

, ASME i

i

2 (

)

a exp N ε

  

   

1

N ∑

1

(5)

* α

=

−

Φ  ∆

ε

1

i

=

, ASME i

i

where M is the test number under proportional loading (by excluding those characterised by a strain path along 45°-direction) and N is the test number under non-proportional loading. Moreover, ( ) a exp N ε is computed through the tensile Manson-Coffin equation of the material by considering the experimental fatigue life, exp N . According to the above equations, * k is representative of differences in cyclic properties in comparison to proportional strain path, and * α is a material constant related to additional cyclic hardening. Readers may find more details about the computation of the above parameters in Borodii (2001) and Vantadori (2021). 4. Results and discussion In order to assess the RED criterion accuracy in estimating fatigue life of metallic components under non proportional loading, the biaxial fatigue tests described in Section 2 are simulated herein. In particular, Fig. 1 shows the experimental fatigue life exp N plotted against the refined equivalent deformation amplitude RED,a ε (see Eq. (2)); the red solid curve is related to the experimental tensile Manson-Coffin equation. A good agreement between experimental and theoretical data is in general observed since the theoretical results lie very close to the experimental curves, and this hold true independent of the loading condition being examined (that is, biaxial proportional and non proportional fatigue). As a matter of fact, only 22% of the theoretical results fall outside the scatter band 3x (see the red dashed lines in Fig. 1).

0.030

Proportional Non-prop. β =45° Non-prop. β =90°

0.010

ε RED,a

0.003

10 2 10 2

10 3

10 4

10 5

2 N exp , [cycles]

Fig. 1 Experimental fatigue life plotted in terms of refined equivalent deformation amplitude.