PSI - Issue 34

Camilla Ronchei et al. / Procedia Structural Integrity 34 (2021) 166–171 C. Ronchei, S. Vantadori, D. Scorza, A. Zanichelli, A. Carpinteri / Structural Integrity Procedia 00 (2021) 000 – 000

169

4

where eff  is the effective Poisson ratio, and a  and a  are defined by the well-known tensile and torsional Manson-Coffin equations, respectively. Then, the fatigue lifetime is assessed by means of an equivalent strain amplitude, eq ,a  , together with a unique material reference curve, i.e. the tensile Manson-Coffin curve. More precisely, the above equivalent strain amplitude (also named fatigue damage parameter) is expressed by a combination of the amplitudes of the normal, N ,a  , and tangential, C ,a  , displacement vectors acting on the critical plane:



  2 

  2    a a



2







(2)

eq ,a

N , a

C , a

It should be highlighted that the value of N ,a  can be readily evaluated, since the direction of the normal vector N  is time-invariant, while the direction of the tangential vector C  changes during a loading cycle, and the definition of the corresponding amplitude is not unique. In the present paper, for computing C ,a  , the maximum rectangular hull method proposed by Araújo et al. (2011) is implemented in the criterion formulation. Finally, by equating Eq. (2) with the tensile Manson-Coffin equation, the number f N of loading cycles to failure can be worked out through an iterative procedure. 4. Criterion validation: results and discussion To assess the Carpinteri et al. criterion accuracy in estimating fatigue life of AM metals, the fatigue tests described in Section 2 are simulated herein. The values of the material parameters of the Manson-Coffin curves, required for the application of the criterion, are reported in Table 1. The effective Poisson ratio, eff  , is assumed to be equal to the elastic one, e  , since the Poisson ratio for plastic strain is not reported in the original work by Molaei et al. (2018). Figs 1(a) and 1(b) show the experimental fatigue life exp N plotted against the equivalent strain amplitude eq ,a  (see Eq. (2)) for vertical and diagonal AM specimens, respectively. The red solid curves are related to the experimental tensile Manson-Coffin equations. 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 specimen build direction, in accordance with the experimental outcomes. As a matter of fact, only 12% and 18% of the theoretical results related to vertical and diagonal AM specimens, respectively, fall outside the scatter band 3x (see the red dashed lines in Figs 1(a) and 1(b)).

0.030

(b)

Tension Torsion B. in phase

(a)

Tension Torsion B. in phase B. out-of-phase

10 7 DAMAGE PARAMETER,  eq,a 10 2 10 3 10 2

EQUIVALENT STRAIN AMPLITUDE,  eq,a 0.010

0.003

10 4

10 5

10 6

10 7

10 2 10 2

10 3

10 4

10 6

10 5

2 N exp , [cycles]

2 N exp , [cycles]

Fig. 1 Experimental fatigue life plotted in terms of equivalent normal strain amplitude: (a) vertical and (b) diagonal AM Ti-6Al-4V specimens.