Issue 77

A. Sivtseva et alii, Fracture and Structural Integrity, 77 (2026) 138-172; DOI: 10.3221/IGF-ESIS.77.10

Tate J. S., Kelkar A. D. [69]

Adam T., Dickson R.F., Jones C.J., Reiter H., Harris B. [65]

1

1

A = 1.1, B = 1.1

A = 0.5, B = 1.5

A = 0.5, B = 1.5

3

7

D

D

D′

D′

A = 1.1, B = 1.1

0

0

N f

0

1

0

1

0

1

N f

0

1

N

N

n

n

Wang C., Zhang J [70]

1

C ≥ 2

1< C < 2

1< C < 2

4

D

D′

C ≥ 2

0

0

1

0

1

n

n

Table 7: The typical dependencies D(n) and D′(n) of logarithmic models. Adam T., Dickson R.F., Jones C.J., Reiter H. and Harris B. model. The authors [65] proposed using a model of the type:

1

1

   

   

   

   

A

A

B

B

   

   

   

   

σ σ − U R

− log log0.5 N

− log log0.5 N

*

σ σ σ σ = + − (

−

=

= − − 1 1

D

) 1

,

,

(49)

σ

R

U

max

max

σ σ −

−

−

N

N

log

log0.5

log

log0.5

f

U

f

max

where A and B are parameters determined based on test results, and the number of cycles N varies from 0.5 (corresponding to static failure) to N f . Rewriting this expression yields: − −               ′ = − − = −                           1 1 ln2 ln2 ln2 1 1 1 , 1 . ln2 ln2 ln2 ln2 B B A A A f f f f N N N D D AB N N N N N (50) This model can only be represented as a function of the absolute number of cycles and only with “normalized damage”. The constraints on the function’s range of values imply that A > 0 and B > 0. The first derivative of the damage function is positive for positive values of the model parameters. The conditions determining the existence of zeros of the second derivative of the damage function over the considered range of cycles cannot be expressed analytically. Therefore, by selecting parameters, it was demonstrated (Tab. 7) that the model is capable of describing two-stage dependencies with decelerated damage accumulation, as well as both types of three-stage dependencies. Shokrieh M. M., Lessard L. B. [75, 76] proposed to take the equivalent number of fatigue cycles equal to 0.25, since static loading is a quarter of a cycle, and the model takes the form:

   

   

A B

   

   

− log log 0.25 N

(

)

σ

σ σ σ − + max U

= − 1

,

R

max

−

N

log

log0.25

f

(51)

   

   

A B

   

   

− log log 0.25 N

(

)

= − 1

− + E E E

E

,

R

f

f

0

−

N

log

log0.25

f

159