Issue 77

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

A

− − − + (1 )(1 (1 ) ), B R N 1

σ σ R U − = − =− 1 1 R = +

σ

max

B

Ganesan C., Joanna P.S.

2018 [48]

woven

GFRP,

cyclic

tension,

11

σ

σ σ

A

R = 0.5, 3 Hz

− − − + (1 )(1 (1 ) ) B R N 1

D

max

σ

−

σ

B

1

U

U

f is the frequency; θ is the smallest ply angle of the laminate to the loading direction; A, B are the material parameters; B = R (stress ratio) for – ∞≤ R ≤1, B = 1/ R for 1< R ≤∞

− 0.6 sin B

θ

  

  

σ

A

 

 

(

)

− 1.6 sin B

θ

C

σ σ U R

σ

− =

−

−

B

N

1

(

1),

max

2003, 2005 [49, 50]

max

C

σ

f

Epaarachchi J.A., Clausen P.D.

U

12

− 1.6 sin B

θ

  

  

σ

σ σ

A

(

)

C

= − = 1 R

−

−

D

B

N

1

(

1)

max

σ

C

σ

f

U

U

Table 3: Power law models of degradation of residual mechanical properties

Power law models of Hahn H. T. and Kim R. Y. type. Hahn H. T. and Kim R. Y. [51] proposed using the following expression to determine the residual strength:

σ σ = − A A R U

ABN ,

(10)

where A is the constant, B is the parameter, which depends on the characteristics of fatigue loading (considering a single stress level, B is treated as a constant). This expression can be considered an analogue of the linear model if the residual mechanical characteristic is considered to be σ A R . However, it can be shown that this model can be reduced to the following form: (11) where A , B are the model parameters dependent on loading conditions. The model can be represented as a function of both the absolute and relative number of cycles, and it is possible to take into account the residual value of the mechanical characteristic before fatigue failure. The constraints on the range of the function imply that A < 1, with A ≠ 0. When B = 1, this model is linear. The constraints on the positivity of the first derivative of the damage function imply that AB > 0. Various options for using this power law model for the degradation of residual mechanical properties are presented in Tab. 4. Depending on the value of parameter B , the following situations are possible (Fig. 5): ‒ when 0 < B < 1, then D ′′ > 0, which corresponds to a two-stage dependence with accelerated damage accumulation; ‒ when B < 0 or B > 1, then D ′′ < 0, which corresponds to a two-stage dependence with decelerated damage accumulation. ( 1 1 ) ( ) ( )( − − 1 1 ) σ σ σ − − ′ ′′ D A B B = − = − − 1 R = − 1 D AB An =− 1 2 2 , , , B B B U D An An

No

Authors

Year

Model

Additional remarks

Residual strength models

A is a constant; B is a parameter, which depends on the characteristics of fatigue loading A, B, C are the experimental fitting parameters; Β is a parameter of the statistical distribution of initial strength data; graphite/epoxy laminate [0/90/±45] S , 20 Hz, R = 0.1 σ R , σ U , σ max are the characteristics normalized by β; V is a parameter determining the rate of strength degradation; A, B are the parameters of the S-N curve for the characteristic fatigue life

1

 

  

σ σ

AB

Hahn H. T., Kim R. Y.

1975 [51]

A

1

A A

σ σ

= −

= − = −  − 1 1 1 R

, ABN D

N

σ

R

U

A

σ

U

U

σ σ β σ = − С С C B

max A N A

,

R

U

Yang J. N., Liu M. D.

1977 [52]

1

2

 

  

C B

β σ

σ σ

С

= − = −  − 1 1 1 R

D

N

max

σ

С

σ

U

U

σ σ σ σ − − V U C

V

σ σ V V

σ A N B range

= −

,

max

R

U

C

U

max

Yang J. N., Sun C. T.

1980 [53]

3

1

  

   

σ σ σ σ σ σ − − B V range U V C U U

V V

σ σ

= − = − − 1 1 1 R

D

A

N

max

σ

C

U

max

147