PSI - Issue 5

J. V. Araújo dos Santos et al. / Procedia Structural Integrity 5 (2017) 1198–1204 J.V. Araújo dos Santos et al. / Structural Integrity Procedia 00 (2017) 000 – 000

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3.2. Quantitative analysis of the results

Table 2 lists the relative difference between the peak values of DCD and MCD, defined according to       ( ) max ( ) ( ) max max DCD x MCD x DCD x RD r s r   As expected, the differences for a specific shearing amount and distinct damages do not change significantly, since we are taking the relative difference. On the other hand, the differences change abruptly from shearing amount to shearing amount. (11)

Table 2. Relative difference between the peak values of DCD and MCD. Relative difference, RD [%]

Shearing amount x  [mm]

Damage case 1

Damage case 2

Damage case 3

Damage case 4

2 5

0.96 3.32

0.96 3.32

0.96 3.31

0.96 3.31

10 20 30

51.63 76.22 84.37

51.63 76.22 84.37

51.63 76.22 84.37

51.63 76.22 84.38

Table 3. Area below the peak values of DCD and MCD.

Damage case 1

Damage case 2

Damage case 3

Damage case 4

Shearing amount x  [mm]

Area below peak of r DCD ( x )

Area below peak of s MCD ( x )

Area below peak of r DCD ( x )

Area below peak of s MCD ( x )

Area below peak of r DCD ( x )

Area below peak of s MCD ( x )

Area below peak of r DCD ( x )

Area below peak of s MCD ( x )

0.2339 0.2339 0.2339 0.2339 0.2339

0.2329 0.2315 0.2290 0.2242 0.2194

0.5255 0.5255 0.5255 0.5255 0.5255

0.5230 0.5201 0.5146 0.5038 0.4929

0.8991 0.8991 0.8991 0.8991 0.8991

0.8951 0.8899 0.8805 0.8620 0.8433

1.3952 1.3952 1.3952 1.3952 1.3952

1.3888 1.3807 1.3662 1.3374 1.3082

2 5

10 20 30

As can be seen in Table 3, the values of the area below the peak values of DCD are constant for each damage case, whereas a small decrease with the shearing amount is observed for a certain damage case in the area below the peak values of MCD. This is due to the numerical natural of the approximation used, since we are applying finite differences. Anyway, these changes are very small, since, for instance, all the relative differences between the respective values of DCD and MCD are below 7%, as reported in Table 4.

Table 4. Relative difference between the areas below the peak values of DCD and MCD. Relative difference [%]

Shearing amount x  [mm]

Damage case 1

Damage case 2

Damage case 3

Damage case 4

0.45 1.03 2.07 4.12 6.20

0.45 1.03 2.07 4.11 6.20

0.45 1.03 2.07 4.12 6.21

0.45 1.03 2.08 4.14 6.23

2 5

10 20 30