PSI - Issue 41

Yu.G Matvienko et al. / Procedia Structural Integrity 41 (2022) 192–198 Author name / Structural Integrity Procedia 00 (2019) 000–000

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Fig. 2. Typical interferograms obtained at the 521st cycle for remote stress increment from 38 to 79 MPa (a) and at the 1418th cycle for remote stress increment from 146 MPa to 178 MPa (b).

Numerical differentiation of discrete sets of the initial experimental data, which is necessary for a determination of circumferential strain values according to formula (1), employs an approximation of displacement components u and v by trigonometric series: � � ∑ � ��s � � � ∑ � sin � ��� � ��� , (2) where coefficients � and � follow from the least square method. The above-mentioned range of measurement uncertainty sets the lower limit on � and � values from series (2), which are involved for strain calculation. Normal strain increment ∆ � is defined as: ∆ � � ����� � � � � ∆ � . (3) A term �� � � � � in formula (3) represents experimentally measured relative value of the displacement component which is the normal to the surface of the specimen; µ is the Poisson’s ratio, t is thickness of the specimen, ∆ � � ∆� � / . Typical distributions of the relative circumferential strain ∆ � /∆ � and normal strain �∆ � / � increment along the hole edge can be found in the book of Shchepinov et al. (1996). Practical realization of the proposed non-destructive method for damage accumulation quantifying due to low cycle fatigue needs an availability of reliable information concerning circumferential and normal strain values at all investigated stages of low-cycle fatigue. Essential condition for reaching this goal resides in recording and reconstruction of high-quality reflection holographic interferograms at each loading step. This condition has been met in the course of present study. Interference fringe patterns (Fig. 2a) are related to the stage of local adoptability of the material under an influence of sign-changed local elastic-plastic deformation due to low-cycle fatigue or corresponds to the stable stage of local cyclic deformation process. A common special feature of all above mentioned images is that the interference fringes are either continuous between two specimen lateral faces or have its end at the hole edge. An opposite case occurs in Fig. 2b, where interruptions of interference fringes are clearly seen near the root of the notch (critical point A ). This fact evidences fatigue crack appearance on the external surface of the specimen. The crack can be observed at the 1418th cycle for all load increments corresponding to the positive remote stress range. When the remote stress level reaches negative values, the fatigue crack is closed and does not result in interruptions of the interference fringes.