PSI - Issue 43

Stanislav Žák et al. / Procedia Structural Integrity 43 (2023) 23 – 28 Author name / Structural Integrity Procedia 00 (2022) 000 – 000

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the data can be analyzed assuming the condition λ = 0.2 (since usual values of λ are reported in range between 0.2 and 0.35, see e.g. work by (Aranda et al., 2022), and fitting results in Table 2 are close to the 0.2 value).

Table 2. Fitting parameters for the semi-empirical fracture criteria. ω = 52.1°

ω according to eq. (4)

Relative difference in %

Identifier

G I, c / J·m

0 / °

G I, c / J·m

0 / °

-2

-2

λ

Ψ

λ

Ψ

G I, c

λ

Ψ 0

Mo-Cu-glass material system (0.5 Pa pressure during the deposition)

H-S

186.4·10 -3 516.2·10 -3 729.9·10 -3 163.3·10 -3 890.9·10 -3 1412·10 -3 0.6 88·10 -3 3.815·10 -3 4.299·10 -3

0.190 0.187

- -

123.2·10 -3 498.8·10 -3 729.9·10 -3 80.46·10 -3 480.6·10 -3 701. 8·10 -3 19.41·10 -3 69.14·10 -3 105.7·10 -3

0.159 0.203

- -

51.30 19.88 -

C-H-S

3.46

7.79 -

BS-A-Ch

-

-20.1

-

-22.3

0.00 -

9.87

Mo-Cu-glass material system (1 Pa pressure during the deposition)

H-S

0.183 0.286

- -

0.129 0.203

- -

102.99 41.99 - 85.35 40.78 -

C-H-S

BS-A-Ch

-

-33.1

-

-22.3

101.19 -

48.43

Mo-PI material system

H-S

0.039 0.059

- -

0.198 0.241

- -

96.46 94.48 95.93

80.26 - 75.61 -

C-H-S

BS-A-Ch

-

-5.6

-

-27.2

-

79.41

Table 3. G I, c for the semi-empirical fracture criteria, assuming λ = 0.2. Identifier G I, c / J·m -2 ( ω = 52.1°) G I, c / J·m

-2 ( ω according to eq. (4))

Relative difference of G

I, c in %

Mo-Cu-glass material system (0.5 Pa pressure during the deposition)

H-S

203.4·10 -3 571.1·10 -3

186.9·10 -3 485.6·10 -3

8.84

C-H-S

17.60

Mo-Cu-glass material system (1 Pa pressure during the deposition)

H-S

186.7·10 -3 523.2·10 -3

165.6·10 -3 468.3·10 -3

12.78 11.74

C-H-S

Mo-PI material system

H-S

17.72·10 -3 42.54·10 -3

19.72·10 -3 49.26·10 -3

10.10 13.64

C-H-S

While even in case of fixed value of λ = 0.2 there are differences between the H-S and C-H-S methods (mainly due to the absence of wider range of Ψ ), the differences between G I, c -values with the change of ω are more consistent. Moreover, it is a common practice to evaluate the G I, c only from the buckling delamination measurements using suitable criterion and fixed value of λ . With this in mind, the data from Table 2 and Table 3 show significant influence of incorporating the correct phase angle ω . In case of Mo-Cu-glass system, the true ω equals to 49.95°, which is less than 3° lower than originally used value of 52.1°. However, such a small change in the phase angle leads to strong shift of the measured data into more shear loading regimen (see Fig. 2a) and, subsequently, the more realistic value of G I, c is smaller. Therefore, the assumption of ω = 52.1° leads to an overestimation of the interface strength, which can lead to unexpected failures and wrong designs. For the case of Mo-PI interface, the true ω equals to 69.77° , which is more than 17° higher than originally used value of 52.1°. This causes a shift of the measured and evaluated data from pure shear loading to mixed-mode loading (see Fig. 2b). This leads to underestimation of the interface strength according to original approach, effectively creating large safety reserve and inhibiting the true potential of the materials. However, it should be mentioned that in case of the Mo-PI dataset, the large scatter of the Γ ( Ψ ) values for ω = 52.1° and their almost pure shear behavior may have an influence on the fracture criteria fitting. While this may be an additional influential factor,