Issue 25

E. Maggiolini et alii, Frattura ed Integrità Strutturale, 25 (2013) 117-123; DOI: 10.3221/IGF-ESIS.25.17

The σ sum from the Ansys structural analysis is not so far from the Comsol integration for each opening angle taken into consideration (Fig. 5), it is never higher than 4% as a maximum error (Tab. 2).

σ eff,IG [MPa]

σ eff,int

σ eff,sum [MPa]

Error

2α [°]

[MPa]

[%]

0

9.47 9.37 9.74 9.37 7.67 6.26 4.61 1.00

7.47 7.58 7.97 7.82 6.64 5.56 4.23 1.00

7.22 7.65 8.01 7.84 6.70 5.61 4.23 1.00

-3.36 0.91 0.52 0.26 0.90 0.85 -0.13 0.00

30 60 90

120 135 150 180

Table 2: Value of σ eff,IG

, σ eff,int

and σ eff,sum

at any tested angle.

σ eff,IG [MPa]

σ eff,int [MPa]

Difference σ eff,sum

Error [%] 0.26 -0.60 -0.03 0.01 -0.05 0.00 0.00 0.00 0.04

ρ/c

[%]

[MPa]

9.37 9.42 9.47 9.52 9.54 9.55 9.32 8.99 8.31

7.82 7.84 7.87 7.91 7.94 8.06 8.18 8.16 7.84

-16.5% 7.84

0

0.125 0.25

-16.8% -16.9% -16.9% -16.8% -15.6% -12.2%

7.79 7.87 7.91 7.94 8.06 8.18

0.4 0.5

1 2 3 5

-9.2% 8.16

-5.6%

7.84

Table 3: Value of σ eff,IG

, σ eff,int

and σ eff,sum

at any tested ratio.

C HANGING THE FILLED RADIUS

B

y modifying the ratio of the filled radius over c; it is possible to compute effective stress in rounded geometries as well. Results related to the opening-angle equal to 90° are given in Tab. 3 and Fig. 6. The scatter between the Implicit Gradient effective stress and the integral value decreases by increasing the notch tip radius. In any case, the error between the integral value and its numerical approximation is very low. Hence, we can argue that the integral value of eq. (4) can be evaluated by means of generic FE software. The problem is the general relationship between the Implicit Gradient σ eff,IG and Integral value σ eff,int by combining different values of the opening angle and notch tip radius. The ratio between σ eff,IG and σ eff,int is given in Fig. 7.

0 2 4 6 8 10

σ eff,IG σ eff,int σ eff,sum

σ /σ nom

0

0.2

0.4

0.6

0.8

1

ρ/c

Figure 6: Trend of σ eff,IG

Vs σ eff,int

Vs σ eff,sum

on the filled radius.

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