PSI - Issue 83

Victor Rizov et al. / Procedia Structural Integrity 83 (2026) 85–94

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MatLab). The SERR is extracted by inserting * U in Eq. (18). The SERR is verified by the method of J integral (Broek (1986)). By making use of the contour, D , the solution of J is

3 2 1 D D D J J J J    ,

(29)

3 D J are found by integrating with the MatLab along parts, 1 D , 2 D and 3 D , of the contour

1 D J ,

2 D J and

where

(Fig. 1). The integral J confirms the correctness of the solution of SERR. 3. Change of SERR with time

Here, we evaluate effects of the acceleration of the beam structure on the SERR under creep conditions by applying the foregoing analysis. The influence of the beam geometry on the SERR is also studied. Graphs, illustrating how the SERR changes with time are shown. The analysis is applied to the case in which 1.4   , 0.5   , 0.7   , 0.9   , 3   , 0.6   , 1.4   , 0.010  b m, 0.013  h m, 0.006 1  h m, 0.150  a m and 0.600  l m.

Fig. 2. Change of SERR with time at 1.4   (graph 3). In order to evaluate the effect of the angular velocity of the beam on the SERR under creep conditions, the change of the SERR with time is shown in Fig. 2 at three values of parameter,  . As expected, SERR grows continuously with time (this is a result of creep). The SERR for these three values of  show relatively little difference, as can be seen from Fig. 2. Another observation is that SERR increases when the value of  rises (Fig. 1). Next, it is studied how the change in SERR with time is affected by the acceleration of the beam at its motion upward along axis, s . In this regard, Figure 3 shows change in SERR with time at three values of parameter,  , which coincide with the vales of  used in Fig. 2 (  is chosen equal to  in order to determine whose effect is stronger). The shapes of the graphs in Fig. 3 are similar to those of the graphs shown in Fig. 2. However, increase of 0.6   (graph 1), 1.0   (graph 2) and