PSI - Issue 28

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

1058

4

2



    

   

   



3 1 

, 1 

af

45









(3)

  

2



, 1 

af

, 1 af   and

, 1 af   are the fatigue strength (at a given number 0 N of loading

where  is expressed in degree, and

6 2(10) cycles) for fully reversed normal stress and that for fully reversed shear

cycles, generally assumed equal to

stress, respectively. At each time instant t , the stress vector w S related to the above critical plane orientation may be decomposed in two components: the normal stress vector N and the shear stress vector C , which are perpendicular to and lying on the critical plane, respectively (Fig. 2). Note that, during the period T , the direction of the normal stress vector is fixed with respect to time, whereas the shear stress vector describes a closed path  on the critical plane.

Z

N

S w

w

Critical plane

X

P

u

C

Y

v

Fig. 2. Puvw local frame at point P (where u -axis is the intersection between the critical plane and the plane defined by w and Z -axis) and components of the stress vector w S acting on the critical plane. The Carpinteri et al. criterion proposes to transform the actual multiaxial stress state into an equivalent uniaxial one, whose amplitude is computed as follows:

2

  

   



, 1 

af

2

2

(4)

N

C



 



, eq a

, eq a

a



, 1 

af

with

, 1          m u N  

N N

(5)

, eq a a af

where , eq a N is the equivalent normal stress amplitude, and u  is the ultimate tensile strength of the material. The above-mentioned , eq a N is based on the well-known linear interaction between the normal stress amplitude a N and the normal stress mean value m N , described by the diagram of Gooodman. Such an equivalent amplitude is introduced in order to take into account that a tensile mean stress, superimposed on an alternating normal stress, strongly reduces the fatigue strength of metals. As has previously been discussed, a N and m N can readily be computed since the direction of N is fixed with