PSI - Issue 71

Prakash Bharadwaj et al. / Procedia Structural Integrity 71 (2025) 26–33

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The estimation of plastic zone size is conducted based on the variation of back stress of maximum principal stress component during the applied loading and unloading cycle. In a fatigue loading cycle, the principal back stress fluctuates between maximum and minimum values. Contours of the principle back stress (X 22 ) corresponding to maximum and minimum load at 300 °C and R = 0.1 is shown in Fig. 2(a) and 2(b) respectively. The principle back stress at maximum and minimum load changed with the distance from the crack tip in a specific direction ahead of the crack tip. The distance from the crack tip to the intersection point of principal back stress at maximum and minimum loads delineates the limiting boundary of the CPZ in that direction. The shape of the CPZ is derived by integrating the limiting point in all directions ahead of the crack tip. The limiting boundary of the Monotonic Plastic Zone (MPZ) in front of the crack tip in all directions is defined as the point when the principal back stress reaches zero. The variation of the principal back stress relative to the distance from the crack tip within a crack plane for a crack size of 23.02 mm and a Stress Intensity Factor (K) range of 20.75 MPa- √m is illustrated in Fig. 3 (a). Fig. 3(b) also illustrates the typical contours of the MPZ and the CPZ at RT. The size of the CPZ is approximately 1/3 rd of the size of the MPZ at both the RT and 300 °C. 4. Effect of crack size, load ratios and temperature on CPZ Fig. 4 (a) shows CPZ variation with crack size. During the investigation of the effect of crack size on CPZ, the R and Pmax were 0.1 and 15kN, respectively. The range of the K was varied from 10 MPa- √m to 21 MPa - √m. The variation illustrates that increasing crack size raises the CPZ value. As the crack size enlarges, K, adjacent to the crack tip proportionately rises [ Anderson et al. (2025)]. The stress intensity near the crack tip is more significant for larger cracks, resulting in an increased region of plastic deformation. An elevated K value leads to a greater CPZ [Irwin et al. (1960)]. The results are consistent at both RT and 300 °C. The increase in CPZ at the threshold zone is less than that of the Paris regime's crack growth region. At 300 °C, the value of CPZ is less than at RT for the same crack size, R, and Pmax. This shows the material's hardening behaviour at 300 °C. Fig. 4 (b) illustrates the effect of R on CPZ for a specified crack size of 22.5 mm, subjected to a maximum load of 15 KN at both RT and 300 °C. CPZ is maximum at R = -1 and minimum at R = 0.5. This is attributed to maximum load range for R = -1 with same maximum load. The results are consistent with the literature [Paul et al. (2016)]. The material exhibits hardening behaviour at 300 °C, resulting in a reduced CPZ value for each R value compared to RT.

(a) (b) Fig. 4. CPZ variation with (a) Crack Size and (b) load ratio at RT and 300 °C, for P max = 15 KN

5. Stress triaxiality with in the CPZ State of strain and stress plays important role in materials deformation at the crack tip and further crack propagation. Fracture or failure, which processed due to void initiation, extension, coalescence and cleavage fracture are highly dependent on field constraint or triaxiality. Stress triaxiality gives the relative contribution of hydrostatic and equivalent stress in materials deformation. In present study, stress triaxiality is taken as the ratio of hydrostatic