Issue 77

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

B < 1 < C or

C < 1 < B

A e B + 2 B > 1 A e B + 2 B ≤ 1

B (1 – AC ) + B (1 – AC ) + B (1 – AC ) +

A < 1, B < 1 A > 1, B < 1 A < 1, B > 1

0 < A < 1

+ A > 1

–

–

–

–

–

–

–

–

–

+

+

+

+

+

+

B < 1,

+*

+*

3-stage

B ≤ 1, C ≤ 1 B ≥ 1, C ≥ 1

or B < 1, A < 0

B < 0 or B > 1 +

A = 1, B < 1 A = 1, B > 1

2-stage, D ′′ ≤ 0 2-stage, D ′′ ≥ 0

B > 1, A > 0,

+ A < 1

A < 0

A > 0

–

–

B < 1

B > 0

+

+

+

+

+

+

+

+

+

+

+

+

B < 1,

+*

+*

Descriptive capability

B > 1, A < 0,

0 < B < 1

+ A > 1

or B < 1,

A > 0

A > 0

A < 0

–

–

–

–

–

B > 1

B < 0

+

+

+

+

+

+

+

+

+

B > 1,

+:

+*

+*

– / +

– / +

– / +

– / +

– / +

– / +

– / +

– / +

+ / +

+ / +

+ / +

+ / +

+ / +

+ / +

+ / +

+ / +

+ / +

normalized damage

Damage /

– / +

– / +

– / +

– / +

– / +

– / +

– / +

– / +

– / +

+ / –

of cycles + / +

+ / +

+ / +

+ / +

+ / +

+ / +

+ / +

number

/relative

Absolute

A < 1, A ≠ 0, B > 0, B ≠ 1,

A > 0, A ≠ 1, B > 0, B ≠ 1

A ≠ 0, A ≠ 1, B > 0, B ≠ 1,

–0.5 B < A ≤ 1 – B ,

B ln(1 – A ) ≤ 1, AB < 0

A ≠ 0, A < 1, B ≠ 0,

AB e – B + C > 0 if B < 0

A ≠ 0, B ≠ 0, C ≠ 0,

0 < A < 1/ln( N f )

A (1– e – B ) + C ≤ 1,

A ( B – 1) > –1 if B < 1, A < 1 if B > 1

C ≠ 0, C ≠ 1, AC > 0

C > 0, B ≠ C , V > 0

A > 0, B > 0, C > 0

AB + C > 0 if B > 0,

A > 0, B ≠ 0, B < e

A < 1, A ≠ 0,

B > 0, B ≠ 1

0 < A < 1, B > 0,

0 < A < 1, B > 0,

C > 0, B ≠ C

A ≠ 0, 0 < B < 2

Constraints for parameters 0 < B ≤ 1

0 < A ≤ 1,

B ≠ 1, AB > 0

A > 0, B > 0

A < 0, B > 0,

B (1 – e A ) < 1

A > 0

parameters 1

2

2

2

2

3

2

3

4

3

2

2

3

2

1

2

2

Number of

Damage function Model name Linear

Table 10: Classification of the phenomenological models of residual mechanical properties

Simple power law Hahn H.T., Kim R.Y.

Quadratic

Mu P.G., Wan X.P., Zhao M.Y.

Wang Z., Song L., Lei J., Xu S.,

Wu F., Yao W.X. Pasternak H.

Adam T., Dickson R.F., Jones C.J., Reiter H., Harris B. and Kassapoglou C.

Philippidis T.P.,

Zong J., Yao W.

Qui Y., Shen W.

Mao H., Mahadevan S. Lian W., Yao W.

Yang J.N., Du S.

Engh B., Buene L.

Echtermeyer A.T.,

Tang H.C., Nguyen T., Chuang T., Chin J.,

Passipoularidis V.A.

Lesko J., Wu H.F.**

Post N.L., Bausano J., Case S.W., Lesko J.J.

Tate J.S., Kelkar A.D.

and Stojković N., Folić R.,

Polynomial models

Power law models

Exponential models

Logarithmic models

Model class

1

2

3

4

5

6

7

8

9

17

10

11

12

13

14

15

16

No.

166