PSI - Issue 39

Daniela Scorza et al. / Procedia Structural Integrity 39 (2022) 503–508 Author name / Structural Integrity Procedia 00 (2019) 000–000

507

5

The number

f N of loading cycles to failure can be obtained from the solution of the following expression:

(

)

(

) ( 2

) ( 2 m

)

(

)

2

2

m*

m

(6)

N

N N N N C

N N

1 af , σ τ −

σ

+

=

2

' eq ,a

1

0

0

1

0

af ,

f

f

a

af ,

f

−

−

(

) ( m

)

being the equivalent normal stress amplitude at finite life defined as . Since the aim of the present work is to couple the above multiaxial criterion with the area -parameter model, the fatigue strengths 1 af , σ − and 1 af , τ − of Eqs (3-6) are replaced with the values of wl σ and wl τ listed in Table 1. In such a way, the criterion can be used to estimate the fatigue lifetime of naturally defective high strength steels under multiaxial loading. 5. Results and discussion The accuracy of the fatigue lifetime estimation is evaluated by means of the root mean square error method (Walat and Łagoda, 2014). In particular, the value of mean square error RMS T is computed as follows: 1 0 ' eq ,a N N a af , f m u N N N σ σ − = +

n

(

)

10 E RMS

= ∑

with

E

2 log N N n = f ,exp f ,cal

RMS T =

(7)

RMS

1

i

where n is the total number of data, f ,cal N is the theoretical one. Figure 2 shows the mean square error of the fatigue life values estimated by employing the Carpinteri et al. criterion and the fatigue strength values listed in Table 1. It can be observed that, by using the fatigue limits obtained for the control volume 3 1 2400 V mm = , the best fatigue life estimations are provided, being the RMS T slightly greater than 2. On the contrary, mean square error values significantly greater may be computed by employing the fatigue strengths related to the crankshaft volume and those experimentally evaluated. f ,exp N is the experimental multiaxial fatigue life, and

8.0

T MRS =7.65

6.0

V 1 =2400 mm 3 V cr. =7.9E+09 mm 3 Exp. fatigue strengths

T MRS =5.70

2.0 MEAN SQUARE ERROR, T RMS 4.0

T MRS =2.31

0.0

Fig. 2. Mean square error related to AISI 4140 determined by employing the fatigue limits of Table 1. In Figure 3, the comparison between experimental data and theoretical estimations in terms of fatigue life is reported by considering the fatigue strengths listed in Table 1. The solid line indicates f ,cal f ,exp N N = , the dashed lines correspond to f ,cal f ,exp N N equal to 0.50 and 2 (scatter band 2), and the dot-dashed lines correspond to f ,cal f ,exp N N equal to 0.33 and 3 (scatter band 3). Figure 3 confirms that the use of a control volume equal to that of the specimen gauge region provides the best results, since 62% of the estimated fatigue lives fall within the scatter band 2, whereas 77% falls within the scatter band 3 (Fig. 3(a)). On the contrary, the fatigue lives estimated by considering the control volume equal to the whole crankshaft volume are too conservative (Fig. 3(b)), whereas the use of the fatigue strengths experimentally obtained is too non conservative being almost all the points out of the scatter band 3 on the right-hand side of the graph (Fig. 3(c)).