Issue 77

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

inability to describe three-stage dependencies. Various applications of the simple power law model for the degradation of residual mechanical properties are known in the literature, as summarized in Tab. 3.

No

Authors

Year

Model

Additional remarks

Residual stiffness models

S

Wang S. S., Chim E. S. M.

1983 [31] 1986 [16]

, AN B b b B

+ 2

= − = 1 R

= + + 1 max 0

σ σ b

D

...

1

short-fiber glass composite, cyclic tension

S

2 max

S

10

− − F F F F 0

F 0 is the initial fatigue modulus that assumed to be the same as elastic modulus E 0 (F 0 ≈ E 0 ) S 0 is the initial stiffness measured at a loading rate of 4 Hz; A, B are the random variables that depend on the applied stress level; C is a random variable; A 1 , A 2 , A 3 are the parameters independent of applied stress level; fiber dominated composite (graphite/epoxy laminates) [90/+45/– 45/0] s , cyclic tension, 10 Hz, R = 0.1 F 1 is the initial fatigue modulus at the first cycle; matrix dominated composite (graphite/epoxy laminates [±45] 2s ), cyclic tension, 10 Hz, R = 0.1 A, B are the constant parameters fitted to stiffness measurements taken during fatigue testing σ S is the average damage threshold stress until which there is no relative loss of stiffness; N S is the number of cycles until which there is no evolution of the relative loss of stiffness; sheet molding compound composite, cyclic tension, R = 0.1, 10 Hz A = 1 linear strength degradation; A >> 1 “sudden death” behavior; A < 1 rapid initial loss in strength; cross-ply glass/epoxy laminates, cyclic tension A, B are the constants dependent on the material type and load conditions; R is a stress ratio; GFRP, polyester/ polyurethane resin, four-point bending fatigue, 0,8–2 Hz, R = 0,1, 0,3, 0,5, 0,7 Additional remarks –

Hwang W., Han K. S.

B

*

=

=

D

n

R

2

F

f

0

S

S

Yang J. N., Jones D. L., Yang S. H., Meskini A.

, AN D B

B

= − 1

= − = 1 R

AN

R

1990 [39]

S

S

S

3

0

0

= + , A A A B B A C = +

σ

1

2

3

max

F

F

Yang J. N., Lee L. J., Sheu D. Y.

, AN D B

B

= − 1

= − = 1 R

AN

R

1992 [40]

F

F

F

4

1

1

= + , A A A B B A C = +

σ

1

2

3

max

No

Authors

Year

Model

Passipoularidis V. A. Philippidis T. P. Brondsted P. Laribi M.A. Tamboura S. Fitoussi J. Tié Bi R. Tcharkhtchi A. Ben Dali H.

2011 described in [41]

S

S

1 (1 ) , B

B

= − −

= − = − 1 R

A n D

A n

(1 )

R

5

S

E

E

0

0

B

]   −     ) S N N

S

[

σ σ max S

= +

1 ( A

,

R

E

2018 [42]

0

6

B

]   −     ) S N N

S

[

σ σ max S

= − = − + 1 R

D

1 1 ( A

S

E

0

Residual strength models

1986 described in [43]

Stinchcomb W. W., Reifsnider K. L.

7

σ σ σ σ σ σ = − −   = − =  −    max max ( ) , 1 1 A R U U A R U U n n σ σ σ

,

D

Shaff J. R., Davidson B. D.

1997 [44, 45]

8

A

D'Amore A., Carpino G., Stupak P., Zhou J., Nicolais L. D’Amore A., Giorgio M., Grassia L.

−

B

1

σ σ R U

= −

σ

− (1 )(

−

R N

1),

max

−

B

1

1996 [46]

9

σ

σ σ

A

−

B

1

= − = 1 R

− (1 )(

−

D

R N

1)

max

σ

− (1 ) B

σ

U

U

A

− R N N − 1 B

−

B

1

σ σ

= + − = − = max 1 1 R

σ

− (1 )(

),

R

f

max

B

2015 [47]

,

10

–

σ

σ σ

A

−

B

1

− (1 )(

−

D

R N

1)

max

σ

− (1 ) B

σ

U

U

146