PSI - Issue 28

Sabrina Vantadori et al. / Procedia Structural Integrity 28 (2020) 1055–1061 Author name / Structural Integrity Procedia 00 (2019) 000–000

1059

5

respect to time. On the other hand, the definition of the amplitude a C is not unique, since the shear stress vector ( ) t C describes a closed path  on the critical plane. The present criterion implements the a C computation by means of the Maximum Rectangular Hull (MRH) method proposed by Araujo et al. (2011). The mechanical aspects which motivate the measure of the shear stress amplitude on the basis of the MRH method are hereafter explained. A convex hull is the smallest convex region that contains a set of points. In the framework of a critical-plane-based multiaxial model, a convex hull is hence the smallest region (in a material plane) which contains the shear stress path  . The mechanical basis behind such an assumption is that not all the ( ) t C states belonging to  contribute to fatigue damage. As a matter of fact, it seems reasonable to assume that only the shear stresses on the convex hull boundary threaten the material integrity in the setting of endurance under high-cycle fatigue regime. Therefore, the convex hull itself (and its geometrical characteristics) may appropriately characterize the severity of the shear loading, eventually leading to fatigue failure. According to the Carpinteri et al. criterion, the number of loading cycles to failure, cal N , can be obtained from the iterative solution of the following equation:

2

2

1

2







   

     



m      

  

  

  

N

N

N

*

m

m





2

, 1 

af

2

N

C

0







cal

cal

(6)

, eq a

, 1 

a

af

N N

N





, 1 

0

0

af

cal

, 1 af   and

, 1 af   (generally referred

Equation (6) is determined from Equation (4) by replacing the fatigue strengths 6 2(10) loading cycles) with the fatigue strengths at fatigue finite life

to 0 N =

cal N , exploiting the Basquin expression

1/

m

, 1       af af

, 1 0 ( /

)

cal N N

for fully reversed normal stress (

) and the expression for fully reversed shear stress (

1/

m



 are the slopes of the SN curve for fully reversed normal stress

af 

, 1 0 ( / 

)

cal N N







). In Eq.(6), m and m

, 1 

af

m N C  

m N C   

(

) and fully reversed shear stress (

).





3. Experimental campaign examined The criterion is here applied to some medium/high-cycle fatigue tests available in the literature, performed on smooth specimens made of ductile cast iron EN-GJS-400-18 and alternatively subjected to constant amplitude uniaxial and biaxial loading (Tovo et al. (2014)). More precisely, the microstructural properties of the examined ductile cast iron are shown in Tab. 1, whereas the specimens geometry and sizes (expressed in mm) are shown in Fig.3. As can be remarked from Tab. 1, the quality of the ductile cast iron can be considered sufficiently good, as is proved by the high ratio of the graphite nodularity. However, the microstructure is rather coarse, as is proved by the low nodule count and relatively high average nodule size. Specimens were produced by coring the real component in a potential critical zone, consisting in a large crossbar, having a length of 2.5m, of a hydraulic press for ceramic tiles.

Table 1. Microstructural properties of the ductile cast iron EN-GJS-400-18 (Tovo et al. (2014)). Properties Nodule count [nod. No/mm 2 ]  50 (X100) Nodularity [%]  80-85 Average nodule size [µm]  50 Ferrite [%]  90