PSI - Issue 26

Marco Maurizi et al. / Procedia Structural Integrity 26 (2020) 336–347

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M. Maurizi and F. Berto / Structural Integrity Procedia 00 (2019) 000–000

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In light of the results of the present paper and the previous studies, a greater future e ff ort in developing new analytical and empirical solutions, and further experimental verifications is hence justified.

Appendix A.

The angular functions of Eq. 1a can be found in Lazzarin and Tovo (1998) as:

f rr ( θ, λ 1 , χ 1 ) = (3 − λ 1 ) cos [(1 − λ 1 ) θ ] − χ 1 (1 − λ 1 ) cos [(1 + λ 1 ) θ ] f θθ ( θ, λ 1 , χ 1 ) = (1 + λ 1 ) cos [(1 − λ 1 ) θ ] + χ 1 (1 − λ 1 ) cos [(1 + λ 1 ) θ ] .

(A.1) (A.2)

Since the integrals of Eq. A.1-A.2, appearing in Eq. 1b, can be trivially computed, they are not reported here for brevity. In Fig. A.9 the stress singularity 1 − λ 1 along the notch front for the angle 2 α = 60 ◦ is reported, including also the values for ν = 0 . 45.

Fig. A.9: Stress singularity 1 − λ 1 vs. z / h , notch opening angle 2 α = 60 ◦ , including the values for ν = 0 . 45. The displacement component u y along the V-notch flank, i.e. θ = γ ( γ in Fig. 2b), for both the opening angles is reported in Fig. A.10.