PSI - Issue 13

Mor Mega et al. / Procedia Structural Integrity 13 (2018) 123–130

127

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

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Table 3: Dimensions of each Brazilian disk specimen tested and the results obtained from the mechanical analyses.

( f ) 1

( f ) 2

( f ) III

specimen

B

2 R

2 a c

P c

K

K

K

ω

(mm) (kN) (MPa √ mm(mm) i ε ) (MPa √ mm)

( ◦ )

number (mm) (mm)

sp182 7.9 40.2 -2.2 14.3 11.78 33.00 33.93 sp181 8.0 40.2 -2.5 15.7 10.80 34.60 39.76 sp122 8.4 40.5 -4.4 15.6 10.83 27.02 57.66 sp112 8.4 40.8 -4.9 14.9 10.49 25.73 63.13 sp132 8.3 40.5 -9.9 15.5 7.46 10.16 70.83 sp142 8.4 40.6 -10.1 15.3 8.48 10.22 69.07 sp172 8.3 40.6 -12.9 15.2 7.84 5.28 78.17 sp1132 7.9 40.2 -12.9 16.0 7.12 5.58 76.15

0.20 0.19 0.39 0.37 0.74 0.73 0.85 0.72

and upper parts of the specimen, were averaged. These measurements were carried out with an Olympus Confocal Microscope (model number OLS4100; Tokyo, Japan) using its optical mode with a resolution of 0 . 16 (pixel / µ m) 2 . The critical load at fracture P c , for each specimen, was obtained from the Instron. Three-dimensional FE analyses were carried out in conjunction with the DE method and the mechanical M -integral to obtain the stress intensity factors K ( f ) 1 , K ( f ) 2 and K ( f ) III , resulting from the load at fracture. The values obtained at the specimen mid-thickness using the mechanical M -integral in the fourth, fifth and sixth domains were averaged and are presented in Table 3. From the results, it may be observed that for smaller loading angles, generally, the fracture load increased. In addition, as the loading angle increases K ( f ) 2 becomes dominant. In Table 4, the critical delamination length at fracture 2 a c for each specimen and the temperature di ff erence ∆ ϑ between the highest temperature measured during curing (85 ◦ C) and the temperature measured during the test are shown. These values were used in a three-dimensional FE thermal analysis of each specimen. In the same manner used for the mechanical case, stress intensity factors resulting from the residual thermal curing stresses K ( r ) 1 , K ( r ) 2 and K ( r ) III were obtained using the DE method and the thermal M -integral. In Table 4, the averaged residual stress intensity factors from the fourth, fifth and sixth domains are presented. The mechanical and residual stress intensity factors were superposed, namely K ( T ) m = K ( f ) m + K ( r ) m (1) where m = 1 , 2 , III and the superscripts T , f and r represent the total, mechanical and residual stress intensity factors, respectively. It may be observed from Table 4 that the residual stress intensity factors make only a small contribution to the total stress intensity factors. Using the total stress intensity factors, the critical interface energy release rate of

Table 4: Critical delamination length at fracture, temperature change and the residual thermal stress intensity factors obtained from the thermal analyses.

( r ) 1

( r ) 2

( r ) 3

specimen 2 a c number (mm)

K

K

K

ϑ

◦ C (MPa √ mm(mm) i ε ) (MPa √ mm)

sp182 14.3 -61.7 0.10 sp181 15.7 -61.6 0.18 sp122 15.6 -58.7 0.29 sp112 14.9 -61.0 0.18 sp132 15.5 -59.4 0.13 sp142 15.3 -58.8 0.29 sp172 15.2 -61.6 0.35 sp1132 16.0 -62.1 0.13

-0.12 0.00 -0.08 -0.13 -0.09 0.02 0.00 0.01

-0.02 -0.04 -0.02 -0.01 -0.02 -0.04 -0.04 -0.04