PSI - Issue 33

Yu. Matvienko et al. / Procedia Structural Integrity 33 (2021) 491–497 Author name / Structural Integrity Procedia 00 (2019) 000–000

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specimen faces for the same through hole as proposed by Pisarev et al. (2018). The optical set-up includes two symmetrical illumination directions, lying in the same plane, and one observation direction coinciding with the normal to the plane surface of the object. Direct counting of fringe orders between two basic points in interference fringe patterns gives required values of the secondary hole diameter increments of Δ � � � and Δ � � � along principal stress directions: Δ � � � � � � ���Φ � � ⁄ ∆ �� , Δ � � � � � � ���Φ � � ⁄ ∆ �� �, (1) where λ denotes wavelength; Φ is the sensitivity angle between illumination and observation directions; Z = A and Z = B define two opposite external faces; values ∆ �� and ∆ �� represent differences in absolute fringe orders counted over the single fringe pattern between two basic points corresponding to directions of principal strains � and � , respectively. Two basic points at each fringe pattern are established as the points of intersection of the secondary hole diameter coinciding with the definite principal stress direction and drilled hole contour. These diameters coincide with horizontal and vertical lines in all individual images, as presented above, for in-plane displacement components u and v , respectively. Pisarev et al. (2018) established that required values of principal residual strain components, which are used below as current damage indicators, can be expressed as: � � Δ � � ��� � , � � Δ � � ��� � , (2) The essence of the developed approach resides in the fact that the evolution of principal residual strain components, which are referred to the secondary hole edge, can be effectively used for quantification of damage accumulation. A powerfulness of this methodology has earlier been demonstrated by Matvienko et al. (2021) proceeding from fracture mechanics parameters evolution for notches emanating from through-thickness open hole in plane specimens at different stages of low-cycle fatigue. It has been shown that the explicit form of the damage accumulation function � � � , �� , � � can be expressed as: � � � , �� , � � � ∑ � �� �� � ,���� �� �� � ,� � ��∆� � � �� �� � ,� � ����� � �� � � � � �� � � � �� , (3) where � is current number of loading cycles; � � � corresponds to failure of the specimen; � ( i = 1, 2) denotes stress ratio; values Z = A and Z = B define two opposite external faces; �� ( k = 1, 2) is principal residual strain components used for the analysis; �� � � , � � represents a set of experimental �� values after reaching � cycles for different � ; �� � � , � � is �� -value obtained for the specimen without preliminary low-cycle fatigue; � � � � means number of cycles before fracture for different stress ratios; �� � � , �� is normalizing coefficient that must be derived from the experimental data of type shown in Fig. 3 for each specific �� parameter and the stress ratio � ; Δ � � ��� � � denotes number of loading cycles between two neighboring points of �� � � , � � determination. where � is the secondary hole radius. 3. Damage accumulation functions