PSI - Issue 28

Y. Matvienko et al. / Procedia Structural Integrity 28 (2020) 584–590 Author name / Structural Integrity Procedia 00 (2019) 000–000

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where m N  is number of loading cycles between two neighbouring points of SIF ( , ) 1 i m I K R N determination. It should be specially mentioned that employing relative SIF values, which are experimentally obtained at different stage of low-cycle fatigue, represents the key point that is essential for deriving relationship (5). This approach to quantifying damage accumulation process is implemented for the first time. The coefficient D S for given geometrical dimensions of specimens is defined by mechanical properties and deformation parameters of the material. The value D S is derived by normalizing Equation (5) in respect that total sum in the right-hand side must be equal to one. This follows from the definition of limiting value of damage accumulation function (3). A validity of this way is established by the fact that squares of areas lying under all three curves in Fig. 2, calculated by linear stepwise approximation, are equal within 6.7% ( ( ) 1 S R = 0.7290 Conventional Units (CU), ( ) 2 S R = 0.7810 CU and ( ) 3 S R =0.7425 CU). This good coincidence is the confirmation of reliability of the approach for damage accumulation quantifying through the use of relationship (5). The uncertainty between ( ) 1 S R and ( ) 3 S R equals to 1.8%. That is why the normalization has been performed by applying the closest parameters ( ) 1 S R and ( ) 3 S R . This procedure gives D S = 1.36. Thus, Formula (5) opens the remarkable capability of quantitative describing the effect of the stress ratio on fatigue damage accumulation process. Figure 4a demonstrates the graphical representation of Formula (5).

a b Fig. 4. Damage accumulation function for different stress ratio (a) and stress range (b) values.

5. Damage accumulation function in the case of stress range variation

In the case of constant stress ratio R = –0.33 MPa, explicit form of function  from equations (1) and (2) has the following form:

   K N N S K N N 1 1 ( ) ( 0) , ) (       i m I D

N N

   m F m 0

  , ) ( 

m D N

m

,

(6)

N

I

F

i

where D S =1.36 is the constant that has been derived from the experimental data obtained for three sets of coupons with given geometrical parameters, which have been tested for different stress range i   ( 1   =333.3 MPa and 2   =233.3 MPa). The value of ( ) 1 i I K   is a set of experimental SIF values obtained after m N cycles for different i   . The value of ) ( i F N   means number of cycles corresponding to fracture for different stress ranges i   . The value of D S is obtained by normalizing relationship (5). In this case, square of areas lying under two plots in Fig. 3 must be calculated. Required values are the following: ( ) 1   S = ( ) 1 S R =0.7290 UE and ) ( 2   S =0.7020 UE. The difference in ( ) 1 S R and ( ) 3 S R is equal to 3.7%. This suggests that earlier obtained result D S = 1.36 can be