4. B modeling#

4.1. Characteristics of modeling#

The entire test piece is meshed into quadrangular elements with 8 knots or triangular elements with 6 knots.

It has 2416 nodes, 625 quadrangles, 185 triangles, and 264 segments.

4.2. Characteristics of the mesh#

_images/100000000000015C0000014F50B6C4E10275F342.png _images/100000000000019F00000133ED4158D091129F49.png

4.3. Tested sizes and results#

The energy return rate \(G\) is calculated by the \(\mathrm{THETA}\) method for the following 5 crowns:

  • Crown 0: \({R}_{\mathrm{inf}}=\mathrm{0,02}\mathrm{mm}\) \({R}_{\text{sup}}=\mathrm{0,18}\mathrm{mm}\)

  • Crown 1: \({R}_{\mathrm{inf}}=\mathrm{0,2}\mathrm{mm}\) \({R}_{\text{sup}}=1\mathrm{mm}\)

  • Crown 2: \({R}_{\mathrm{inf}}=1\mathrm{mm}\) \({R}_{\text{sup}}=2\mathrm{mm}\)

  • Crown 3: \({R}_{\mathrm{inf}}=2\mathrm{mm}\) \({R}_{\text{sup}}=3\mathrm{mm}\)

  • Crown 4: \({R}_{\mathrm{inf}}=3\mathrm{mm}\) \({R}_{\text{sup}}=5\mathrm{mm}\)

Identification

Reference \({J}_{\mathrm{ASTM}}\)

Aster

\(\text{\%}\) difference

G (N/mm) Crown No. 0 UY=0.2 mm

5.8

6.2

6.9

G (N/mm) Crown No. 0 UY=0.4 mm

22.6

23.1

2.1

G (N/mm) Crown No. 0 UY=0.6 mm

47.2

47.2

0.2

G (N/mm) Crown No. 0 UY=0.8 mm

74.7

72.8

2.5

G (N/mm) Crown No. 0 UY=1.0 mm

103.7

98.2

4.3

G (N/mm) Crown #1 UY=0.2mm

5.8

5.3

8.7

G (N/mm) Crown #1 UY=0.4 mm

22.6

20.7

8.3

G (N/mm) Crown #1 UY=0.6 mm

47.2

43.8

7.3

G (N/mm) Crown #1 UY=0.8mm

74.7

68.6

8.2

G (N/mm) Crown #1 UY=1.0 mm

103.7

94.2

9.2

G (N/mm) Crown #2 UY=0.2 mm

5.8

5.4

7.4

G (N/mm) Crown #2 UY=0.4 mm

22.6

21.1

6.8

G (N/mm) Crown #2 UY=0.6 mm

47.2

44.2

6.4

G (N/mm) Crown #2 UY=0.8mm

74.7

69.1

7.5

G (N/mm) Crown #2 UY=1.0 mm

103.7

94.7

8.8

Identification

Reference J ASTM

Aster

\(\text{\%}\) difference

G (N/mm) Crown #3 UY=0.2 mm

5.8

5.3

9.5

G (N/mm) Crown #3 UY=0.4 mm

22.6

20.2

10.6

G (N/mm) Crown #3 UY=0.6 mm

47.2

42.6

9.8

G (N/mm) Crown #3 UY=0.8 mm

74.7

67.2

10.1

G (N/mm) Crown #3 UY=1.0 mm

103.7

92.6

10.7

G (N/mm) Crown No. 4 UY=0.2 mm

5.8

5.4

7.9

G (N/mm) Crown #4 UY=0.4 mm

22.6

20.8

8.0

G (N/mm) Crown No. 4 UY=0.6 mm

47.2

43.7

7.5

G (N/mm) Crown #4 UY=0.8mm

74.7

68.4

8.4

G (N/mm) Crown #4 UY=1.0 mm

103.7

93.8

9.5

Stability of \(G\) with the choice of crowns

Identification

Crown 2

Crown 3

Crown 4

\(\text{\%}\) Maximum variance

G (N/mm) UY=0.2mm

5.4

5.4

5.3

5.4

2.2

G (N/mm) UY=0.4mm

21.1

21.1

20.2

20.8

4.2

G (N/mm) UY=0.6 mm

44.2

42.2

42.6

43.7

3.7

G (N/mm) UY=0.8mm

69.1

69.1

67.2

68.4

2.8

G (N/mm) UY=1.0mm

94.7

94.7

92.6

93.8

2.1

4.4. notes#

The value of \(G\) in the Aster model is lower than the value in the reference.

The difference is around \(\text{10\%}\) for all crowns. The stability between the crowns is satisfactory.