PSI - Issue 39

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

757

10

Table 2. The computed values of the Williams series expansion, Mixed Mode loading,

e M =

0.66

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

53.00832

53.00914

-30.6011

-30.60482

1

1/2

2

1/2

1 , a MPa m ⋅

1 , a MPa m ⋅

-12.4999

-12.5000

0.00034

0

1 2 , a MPa

2 2 , a MPa

13.26144

13.26422

-7.65790

-7.65810

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

-1.64955

-1.65921

0.957402

0.958127

3/2

3/2

0.40912

0.41525

-0.23942

-0.23975

5/2

5/2

-0.12843

-0.12988

0.07466

0.074988

7/2

7/2

0.04299

0.04550

-0.02472

-0.026271

9/2

9/2

-0.00934

-0.01707

0.00798

0.00985

11/2

11/2

0.00549

0.00671

-0.00201

-0.00387

13/2

13/2

Table 3. The computed values of the Williams series expansion, Mixed Mode loading,

e M =

0.5

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

-35.33940

35.33942

-35.3388

-35.33942

1

1/2

2

1/2

1 , a MPa m ⋅

1 , a MPa m ⋅

0

0

0

0

1 2 , a MPa

2 2 , a MPa

8.84276

8.84281

-8.84356

-8.84281

2 3 , a MPa m 5 , a MPa m 7 , a MPa m 9 , a MPa m 11 , a MPa m − ⋅ − ⋅ − ⋅ − ⋅ − ⋅ 2 2 2 2 -0.01138 2 13 , a MPa m − ⋅ 15 , a MPa m − ⋅ 2

1/2

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 − ⋅ − ⋅ − ⋅ 1 1 − ⋅ − ⋅ 1 1 1

1/2

-1.10222

-1.10634

1.10390

1.10634

3/2

3/2

0.27589

0.27683

-0.27532

-0.27683

5/2

5/2

-0.08512

-0.08658

0.08499

0.08658

7/2

7/2

0.02967

0.03033

-0.02944

-0.03033

9/2

9/2

-0.01022

-0.01138

0.00923

0.01138

11/2

11/2

0.00356

0.00447

-0.00354

-0.00447

1 15 , a MPa m − ⋅

13/2

13/2