Issue56

S. I. Eleonsky et alii, Frattura ed Integrità Strutturale, 56 (2021) 171-186; DOI: 10.3221/IGF-ESIS.56.14

where E is the elasticity modulus of the material; Δ n a is the notch length increment. Two parameters in relationship (2), notch mouth opening displacement at point n -1 denoted as 1 Δ n v  and notch opening displacement at point n -0.5 denoted as 0.5 Δ n v  , must be obtained from experimental data. These points are shown in Fig. 7.

Figure 7: Typical interference fringe pattern obtained in terms of in-plane displacement component v as the result of narrow notch prolongation, Δ ௩ = 29.0. Measurement procedure includes a determination of notch opening displacements in two points n -1 and n -0.5 with co- ordinates ( Δ , n r a     ) and ( Δ / 2, n r a     ), respectively (see Fig. 6 and 7). The point n -1 can be reliably identified in any interference fringe pattern of type shown in Fig. 7 as the interface between the dark and bright parts of the crack line. The point n -0.5 is located in the middle of the bright segment of the notch line. The value of the notch opening at points n-1, denoted as 1 1 1 Δ n n n v v v        , can be derived in the following way. First, the absolute fringe orders in the upper and the lower notch borders, which correspond to displacement components 1 n v   and 1 n v   , respectively, must be calculated starting from zero order fringe. After this displacement component values 1 n v   and 1 n v   , are derived by formula (1):   are the absolute fringe orders related to the upper and the lower crack borders, respectively;  is the wavelength of laser illumination;  = π /4 is the sensitivity angle (Fig. 5). We should keep in mind that 1 n v   and 1 n v   as well as 1 v n N   and 1 v n N   have opposite physical signs (Fig. 6). The notch mouth opening displacement (NMOD) in the point n - 1 follows from (3):   1 1 1 1 1 1 Δ Δ 2sin Ψ 2sin Ψ v v v n n n n n n v v v N N N                  , (4) where 1 Δ v n N  is the fringe order difference referred to the point n -1. This value is counted over the single fringe pattern, as it is shown in Fig. 7, between two points, belonging to the upper and the lower crack borders. Interference images of large scale are used for this purpose. The value of the notch opening displacement (NOD) at the point n -0.5 (Fig. 6), denoted as     , can be determined in the same way. Thus, two experimentally measured parameters, namely NMOD v v    1 1 2sin Ψ v n n v N       , 1 1 2sin Ψ v n n v N       , (3) 1   and v n N 1 v n N

Δ n v

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0.5

0.5

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