Issue 62

Yu. G. Matvienko et alii, Frattura ed Integrità Strutturale, 62 (2022) 541-560; DOI: 10.3221/IGF-ESIS.62.37

MPa and then, through an intermediate zero point, to the minimum value  0 MIN = –120 MPa, and then again back to zero. Each loading step, at which specific reflection holographic interferogram is recorded, is defined by remote stress increment        1 0 0 0 i i i . In addition, the interferogram sets have been recorded on the 2900th, 3128th, 3931st, and 4133rd cycles for each zero to positive peak half cycle to obtain a detailed quantitative description of the fatigue crack initiation and further growth. Typical interference fringe patterns obtained at the first (  0 from 135 to 162 MPa) and 1316th (  0 from 143 to 174 MPa) cycles at almost equivalent remote stress increments are shown in Fig. 2a and 2b, respectively. Horizontal and vertical diameters in Fig. 2 correspond to coordinate axis x and y shown in Fig. 1, respectively. It should be noted that interference fringes in these images do not have interruptions between the hole boundary and the lateral edges of the specimen. Revealed fringe configuration evidences an absence of detectable defect of short crack type on the specimen surface. Such fringe behaviour is representative characteristic of the initial and stable stage of the local elastic-plastic deformation process. This means that accumulation of the material subsurface damages occurs during these stages only. The above-mentioned process exerts a very week influence on the material surface layers and cannot be discovered by means of holographic interferometry. Typical distributions of the in-plane displacement components u (curves 1, 3) and v (curves 2, 4) in the Cartesian coordinate system along the line of contact interaction in the specimen with push fit (no clearance and interference between the hole boundary and the cylindrical steel inclusion) are presented in Fig. 3. These experimental dependencies correspond to the fringe patterns shown in Fig. 2.

Figure 3: Distributions of in-plane displacement components (1, 3) an (2, 4) obtained at the 1st (remote stress increase from 135 to 162 MPa) and 1316th (remote stress increase from 143 to 174 MPa) loading cycle. The distribution of the circumferential strain   along a circular hole boundary of 0 r radius, when the input data are expressed through displacement components u and v in the Cartesian coordinate system, has the following form:

  

  

 1 cos v



u

 









sin

(1)









r

0

where polar angle ϕ is counted from tension-compression direction ( x -axis) anti-clockwise (see Fig. 1a). Numerical differentiation of discrete sets of 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 values by trigonometric series:

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