PSI - Issue 39

Larisa Stepanova et al. / Procedia Structural Integrity 39 (2022) 748–760 Author name / Structural Integrity Procedia 00 (2019) 000–000

758

11

Table 4. The computed values of the Williams series expansion, Mixed Mode loading,

e M =

0.33

Coefficients of the Williams power expansion, Mode I

Coefficients, MD method

Coefficients, Analytical Solutions

Coefficients of the Williams power expansion, Mode II

Coefficients, MD method

Coefficients, Analytical Solutions

17.66901

17.66971

-30.60482

-30.60484

1

1/2

2

1/2

1 , a MPa m ⋅

1 , a MPa m ⋅

12.4999

12.5000

0.00013

0

1 2 , a MPa

2 2 , a MPa

4.41973

4.42140

-7.65749

-7.65810

1

1/2

2

1/2

− ⋅

− ⋅

3 , a MPa m

3 , a MPa m

-0.55218

-0.55317

0.95389

0.95812

1

3/2

2

3/2

− ⋅

− ⋅

5 , a MPa m

5 , a MPa m

0.12978

0.13841

-0.23753

-0.23974

1

5/2

2

5/2

− ⋅

− ⋅

7 , a MPa m

7 , a MPa m

-0.04292

-0.04329

0.06811

0.07498

1

7/2

2

7/2

− ⋅

− ⋅

9 , a MPa m

9 , a MPa m

0.01437

0.01516

-0.02363

-0.02624

2 11 , a MPa m − ⋅ 13 , a MPa m − ⋅ 15 , a MPa m − ⋅ 2 2

9/2

1 11 , a MPa m − ⋅ 13 , a MPa m − ⋅ 15 , a MPa m − ⋅ 1 1

9/2

-0.00412

-0.00569

0.00711

0.00985

11/2

11/2

0.00192

0.00223

-0.02566

-0.00387

13/2

13/2

Table 5. The computed values of the Williams series expansion, Mixed Mode loading,

e M =

0.16

Coefficients of the Williams power expansion, Mode I

Coefficients, MD method

Coefficients, Analytical Solutions

Coefficients of the Williams power expansion, Mode II

Coefficients, MD method

Coefficients, Analytical Solutions

4.73458

4.73458

-17.6680

-17.66971

1

1/2

2

1/2

1 , a MPa m ⋅

1 , a MPa m ⋅

21.6503

21.65063

0.00102

0

1 2 , a MPa

2 2 , a MPa

1.18470

1.18471

-4.42152

-4.42140

1 3 , a MPa m 5 , a MPa m 7 , a MPa m 9 , a MPa m 11 , a MPa m − ⋅ 13 , a MPa m − ⋅ 15 , a MPa m − ⋅ − ⋅ − ⋅ 1 1 − ⋅ − ⋅ 1 1 1 1

1/2

2 3 , a MPa m 5 , a MPa m 7 , a MPa m 9 , a MPa m 11 , a MPa m − ⋅ 13 , a MPa m − ⋅ 15 , a MPa m − ⋅ − ⋅ − ⋅ − ⋅ − ⋅ 2 2 2 2 2 2

1/2

-0.14821

-0.14822

0.53245

0.55317

3/2

3/2

0.036485

0.037088

-0.12901

-0.13841

5/2

5/2

-0.01054

-0.01160

0.042911

0.04329

7/2

7/2

0.00359

0.00406

-0.01482

-0.01516

9/2

9/2

-0.00134

-0.00152

0.00439

0.00569

11/2

11/2

0.00045

0.00059

-0.00135

-0.00223

13/2

13/2