PSI - Issue 13

Ramdane Boukellif et al. / Procedia Structural Integrity 13 (2018) 85–90

89

5

Boukellif et al. / Structural Integrity Procedia 00 (2018) 000–000

¯ σ xy

¯ σ yy

(30;30)

(5)

¯ σ xx

(4)

(3)

(2)

2 a

α

(1)

( x a , y a )

y

x

Fig. 3: Inclined center crack ( x a ; y a ) = (15; 15) mm, 2 a = 2 mm , α = 60 xx = 30 MPa, ¯ σ yy = 90MPa , ¯ σ xy = 20MPa. Di ff erent locations of strain gauges: square (1) : 6 mm x 6 mm; square (2) : 12 mm x 12 mm; square (3) : 18 mm x 18 mm; square (4) : 24 mm x 24 mm; square (5) : 28 mm x 28 mm. ◦ in finite plate 30 mm x 30 mm under boundary loads ¯ σ

Table 8: Results of parameter identification depending on locations of strain gauges, see Fig. 3.

parameters

given

identified square (3)

square (1)

square (2)

square (4)

square (5)

¯ σ xx [MPa] ¯ σ yy [MPa] ¯ σ xy [MPa]

30 90 20 60 15 15 1

29 , 94

30 , 0 90 , 0

29 , 99 89 , 99

29 , 99 89 , 99

29 , 99

89 , 973

90 , 0 20 , 0 0 , 99 60 , 0 15 , 0 15 . 0

20 , 0

19 , 99 0 , 999

20 , 0

20 , 0

a [mm]

1 , 006

1 , 0

0 , 999

α [ ◦ ]

60 , 0

59 , 986

59 , 986

66 , 337

x 0 [mm] y 0 [mm]

5 , 59

14 , 99 14 , 99

15 , 0 15 , 0

15 , 0

11 , 87

14 , 99

3.2.3. Parameter identification depending on the size of the plate and related gauge positions To determine the maximum size ( x c , y c ) of the plate at which a small crack is detected accurately, di ff erent plate sizes have been examined, where the strain gauges are always close to the edges. Hereby a center crack length of 2 a = 2 mm was assumed, see Fig. 2(c). Tab. 9 shows the given problems and results of parameter identification depending on the dimensions of the plate. It is very interesting to see that the small crack and all parameters could be identified on large plates up to 60 mm x 60 mm.

Table 9: Results of parameter identification depending on the size of the plate and gauge positions.

parameters

given identified given identified given identified given identified given identified given identified

( x c , y c ) [mm]

(20; 20)

(30; 30)

(40; 40)

(50; 50)

(60; 60)

(70; 70)

¯ σ xx [MPa] ¯ σ yy [MPa] ¯ σ xy [MPa]

30 90 20 60

29 , 99 89 , 99

30 90 20 60

29 , 99

30 90 20 60

29 , 99 89 , 99 20 , 00 59 , 99 0 , 999 19 , 99 19 , 99

30 90 20 60

29 , 99 89 , 99 19 , 99 60 , 35 1 , 000 24 , 99 25 , 00

30 90 20 60

30 , 00 90 , 00 20 , 00 59 , 92 0 , 999 29 , 98 29 , 99

30 90 20 60

90 , 0 20 , 0 60 , 0 0 , 99

20 , 0 60 , 0

α [ ◦ ]

1

1

1

1

1

a [mm] x 0 [mm] y 0 [mm]

1

1 , 0

10 10

10 , 0 10 , 0

15 15

15 , 00 15 . 00

20 20

25 25

30 30

35 35

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