PSI - Issue 71

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

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stress to von-Mises equivalent stress.

Fig. 5, depicts the variation of stress triaxiality corresponding to maximum and minimum load at RT and 300 °C. For each crack size it is observed that the stress triaxiality is minimum at the crack tip which increases to a maximum little ahead of the crac k tip. As the stress σ 11 is 0 at the crack tip, the stress triaxiality is minimum, which result in large strains and blunting at the crack tip. Under large stress (σ 22 ) normal to the crack plane, the material just ahead of crack tip tries to contract in the 11 and 33 (out of plane) directions but is constrained by the surrounding material and this induces a triaxial state of stress near the crack-tip. Hence triaxiality is maximum at some distance away from the crack tip as shown in Fig. 5(a) and 5(b). After attaining the maximum value, triaxiality starts decreasing because the effect of amplification of stress decreases as the distance from the crack tip increases. It can be observed that with increase in crack size the stress triaxiality increases. The distance at which maximum triaxiality occurs increases marginally as the crack size increases. Further the distance of maximum triaxiality point is higher for RT than for 300 °C for a same crack size. 6. Ratcheting strain with in the CPZ The progressive increase of plastic strain with every cycle during fatigue loading is called ratcheting. Due to the asymmetric variation of stress i.e., the magnitude of stress at maximum load point is more than that at the minimum load point inside the CPZ, the  -  hysteresis loop shifts in the increasing direction of plastic strain. The material sees a stress cycles having a mean tensile stress which causes ratchet strain accumulation. Ratchet strain (ϵ rt ) for a particular cycle is defined as ½ (ϵ max + ϵ min) . Ratcheting strain accumulation during 50 cycle is Δϵ rt50 = ϵ rt50th - ϵ rt1st. For a crack size of 23.02 mm, variation of plastic strain in loading direction with number of cycles is shown in Fig. 6 (a). The ratcheting strain accumulation at the centre of the CPZ after 50 cycles is 0.00398 mm/mm and 0.020 mm/mm at RT and 300 °C, respectively. Similarly, at the maximum triaxiality location, the ratcheting strain accumulation at RT and 300 °C are 0.0046 mm/mm and 0.0024 mm/mm respectively. The ratchet strain accumulation is not the same at each location inside the CPZ. The location near the crack tip, experiences larger ratchet strain accumulation [Suresh (1998)]. Fig. 6 (b) depicts the variation of stress-strain hysteresis at different locations and temperatures inside the CPZ. At the maximum triaxiality location and 300 °C lower ratcheting rate has been observed with respect to the other cases as shown in Fig. 6(b). (b) Fig. 5. Stress triaxiality variation with distance from crack tip for different crack size at RT and 300 °C corresponding to (a) maximum load and (b) minimum load (a)