Fatigue Crack Paths 2003

Table 4: Errors δ % at different distances from the notch tip

P E N (eccentric load)

P E N(three point bending)

No. 0.1ρ 0.3ρ 0.7ρ ρ 2ρ 10ρ 20ρ 0.1ρ 0.3ρ 0.7ρ ρ 2ρ 10ρ 20ρ

1 1.8 -0.1 -1.3 -0.2

1.9 -0.9 -1.8 -0.1

2 0.6 0.1 -0.7 -0.8 0.2

1.6 0.6 -2.1 -2.9 -3.7

3 0.6 -0.2 -1.6 -1.9 -1.1 0.3 0.6 0.8 -0.0 -1.8 -2.5 -3.6 -4.1 7.4

4 1.3 1.2 0.2 -0.1 -0.2 -0.2 0.1 1.8 1.9 0.9 0.4 -0.7 -1.2 0.5

5 0.9 0.4 -0.5 -0.7 -0.3 -0.0 0.1 1.4 1.3 0.3 -0.1 -0.8 -1.0 0.6

6 0.4 -0.2 -1.0 -0.9 -0.3 0.0 0.2 0.8 0.5 -0.2 -0.3 -0.2 -0.2 2.4

7 1.0 0.8 0.0 -0.3 -0.4

1.7 1.6 -0.8 -2.0 -1.4

8 -0.0 -0.6 -0.9 -0.7 0.3

1.1 0.6 -1.4 -2.3 -0.9

9 1.8 1.8 0.7 0.3 -0.0 -0.3 -0.0 2.1 2.4 1.2 0.7 -0.5 -1.3 0.4

10 1.4 1.2 0.1 -0.1 -0.1 -0.2 0.0 1.8 1.9 0.8 0.3 -0.7 -1.2 0.5

11 0.9 0.5 -0.3 -0.4 -0.1 -0.1 0.1 1.4 1.2 0.2 -0.2 -1.0 -1.1 0.7

12 1.5 1.5 0.4 -0.2 -0.6

2.2 2.1 -0.6 -1.9 -1.5

13 0.6 0.1 -0.4 -0.6 0.0

1.6 1.2 -1.2 -2.3 -1.0

14 2.7 2.7 1.2 0.7 0.1 -0.5 -0.1 3.0 3.1 1.6 1.0 -0.4 -1.4 0.4

15 2.5 2.3 0.8 0.3 -0.1 -0.3 -0.1 2.9 2.9 1.3 0.7 -0.6 -1.4 0.5

16 2.2 1.9 0.4 0.1 -0.2 -0.2 0.1 2.6 2.4 0.9 0.3 -1.0 -1.2 0.7

17 2.8 2.8 0.9 -0.0 -1.1

3.3 3.1 -0.2 -1.9 -1.8

18 2.1 1.7 0.2 -0.4 -0.5

3.0 2.5 -0.7 -2.2 -1.5

19 2.3 1.1 -0.0 -0.1 -0.0 -0.2 -0.0 2.5 1.3 0.2 0.0 -0.5 -1.5 0.5

20 2.2 0.8 -0.3 -0.5 -0.4 -0.1 0.2 2.5 1.3 0.3 -0.0 -0.5 -1.5 0.5

21 2.1 0.6 -0.6 -0.8 -0.6 0.0 0.3 2.4 1.2 -0.0 -0.2 -0.9 -1.4 0.8

22 2.7 1.7 0.4 -0.1 -0.8

3.0 1.8 -0.7 -1.8 -1.7

23 2.3 1.1 -0.1 -0.4 -0.4

3.0 1.7 -0.8 -1.9 -1.6

C O N C L U S I O N S

Some equations suitable for describing the distribution of the maximumprincipal stress

along the entire ligament width of finite size plates and bars subjected to bending are

presented. The equations are obtained by combining a recent formulation suitable for

describing the stress distributions in the vicinity of U and V–shaped notches and some

suggestions due to Glinka and Newport. The method involves global equilibrium

conditions and it does not require additional coefficients determined by a best fitting of

numerical data.

Validation of the method has been performed on the basis of about 90 different FE

models. The agreement between theoretical distributions and numerical data was seen to

be very satisfactory.