La opinión de la población peruana y los impactos de la migración

From the results obtained for the JOSH.OUT sequence, the pattern is for high crack propagation rates at the start of the sequence. The simulated sequence contains high stress

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ranges at the beginning and these become smaller towards the end. This can be observed by looking at the plot of the sequence in Figure 4.21. This distribution represents long term loading conditions commencing from more severe loading representing stormy conditions. This is one o f the reasons why there is a high crack growth rate at the beginning o f each repetition followed by almost constant growth rate and subsequent fall. This illustrates the potential significance of sequence effects under typical multi sea-state loading conditions and the mechanisms of crack growth acceleration and retardation involved under these conditions need to be modelled for adequate fracture mechanics analysis under variable loading conditions.

An example o f a typical crack growth in T-butt welded plate is shown in Figure 4.22 for specimen T09. The crack seems to have initiated quite quickly and propagated at a steady rate. At around 130,000 cycles, the crack growth seems to have changed and become more rapid, the slope becoming steeper until failure. In addition, if one looked at the point where the sequence started again, that is the point where the crack growth increased as indicated by the red lines in Figure 4.23. This can be seen in all the crack growth curves under the JOSH.OUT sequence, that when it reaches this repetition of cycles, the crack growth rate increases.

The comparison work between the air curve and the seawater curve is not straight forward as tests carried out under seawater with CP in general have shorter fatigue. Some o f the specimen with overprotection did not get through the whole loading sequence and if the sequence has not reached stationary point, the equivalent stress range might be different. However, from what was observed from the crack growth study. Figure 4.23 demonstrates a couple o f interesting points. The first is that the crack initiated quicker under higher stress range. The employment of CP also encourages early initiation and has a more aggressive crack growth rate. The interesting point is that the crack growth curve for air become less steep from initiation until the sequence is repeated then the crack depth increases rapidly. For the tests conducted with CP protection, the slope is in a straight line, suggesting a constant crack growth rate. Another point o f observation is that if the crack growth is below 2mm when the sequence is repeated, the specimen will usually

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survive until the next repetition of the cycles. Anything above 2mm will result in a correspondingly high growth rate resulting in failure.

The test conducted at the lower stress level of 104 MPa reveals more interesting crack growth information (Figure 4.24). The fatigue life of TC02 was sufficiently long that it experiences many repetitions of the service loading. The distinctive increase of crack growth at a repetition point o f the sequence is also lessened, showing a much smoother growth curve. The crack also did not seem to initiate until about a third of its fatigue life. Unlike all the other tests at high stress levels, there seems to be an initiation period. More tests conducted at lower stress range under CP would be very useful, especially for studying the effect of CP has on the initiation period and it is closer to service condition. Also longer period o f crack growth can encourage the formation o f calcareous deposits, which can affect the crack growth mechanism.

4.4.1 Calcula tion o f Crack growth Ra te

The crack propagation data for T-butt welded plates were obtained using ACPD technique. The crack growth rates were obtained from the crack growth for the study of fatigue behaviour under variable amplitude loading. Figure 4.24 showed the crack growth rate for TCOl, TC02 and TMOl plotted against the number o f cycles. The figure shows that there is an increase in growth rate after every repetition of the sequence. The usual representation of the crack growth rate would be to plot the crack growth rate against the stress intensity factor ranges, but since the tests were conducted under variable loading conditions, the difficulties arise in calculating the corresponding stress ranges. Under variable loading, the stress ranges vary constantly. Also by using the intensity factor ranges in the plot, it does not show the variation o f crack growth rate with time.

The three main values that were needed to plot the crack growth rate curves are the crack growth rate (da/dN), the stress intensity factor range (Ak) and the stress intensity correction factor, Y. The value of Y o f T-butt welded plates were calculated using parametric equations from a study by Brennan [4.10]. The crack growth rates were

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obtained using the incremental polynomial method from the ASTM E 647-88 [4.11], where seven data points were used for the curve fitting o f second order polynomial trend line. This method is sufficient for constant amplitude loading, but there was no mention for its use with variable amplitude loading, where the growth is not consistent. However as there was no alternative method, this method was employed for the calculation. As for the calculation for stress intensity factor range, variable amplitude loading also raises problems. In order to calculate the corresponding stress ranges, the loading sequence has to be divided into smaller blocks with its own equivalent stress ranges. Thus, the crack depth measured at a particular point was matched to the particular block with specific stress range. This method uses the idea of equivalent stress concept ignore the effect of prior stress ranges that might affect the crack growth. This assumption does not include any o f the load or sequence interaction affect, but there was no simple method available for such calculation.

4.4.2 Discussion o f Crack Growth Rate

Figure 4.20 shows the plots o f stress intensity factors against crack growth plot for different T-butt plates. Figure 4.26 is the crack growth rate plot containing all the results for air tests and Figure 4.27 is for tests conducted under seawater with CP. The points in the presented figures have large scatters as this was calculated for variable amplitude loading. The stress intensity factor against crack growth rate plots for each individual plate can be seen from Figure 4.28 to Figure 4.35. The plots show quite a wide scatter overall especially for the lower stress range region. The explanation o f the scatter at lower stress range region could be that tests experienced most o f the stress under lower region. The other explanation is that lower stress region was more prone to calculation errors. The calculation errors could derive from the method used to obtain the crack growth rate, as mentioned earlier, where the likely points to be affected are at the starts and the ends of the sequence. The points in question can be demonstrated schematically in Figure 4.36, where the crack growth rate is compared directly to the crack growth. The perpendicular lines in Figure 4.36 represent the repetition of the sequence. It was noted for the crack growth plot that the depth increase dramatically at each starting o f the sequence. The crack growth rate plot below represents this change also. On closer inspection, the peak

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and trough o f the crack growth rate does not coincide with the beginning and end of the sequence. The differences in the da/dN are quite high and this could be seen in most of the plots for AK against da/dN. Thus, this could lead to errors in the calculation.

Figure 4.28 to Figure 4.35 are crack growth rate plots for each individual tests. They are represented in term for each repetition o f the JOSH.OUT sequence by the different markers. From studying these plots, the first sequence is usually at a lower growth rate level than the follow on repetitive sequence, because the crack is still relatively shallow. For the air data, as the stress intensity range increase, so does the crack growth rate. These normally flatten out as the crack size increases. These plots show that for a certain value o f AK, there are several values of da/dN. This may suggest that there are load interaction effects, but the values are low so these could just be scatters in the data. The likely load interaction mechanisms are crack retardation and acceleration. For this particular sequence, the retardation is likely to occur at the middle of the sequence, as the load is smaller, when compared to the prior loading. There should be a drop in the value of da/dN As for the crack acceleration, this is expected at the start sequence, when the low load is followed by high load. These mechanisms though cannot be seen clearly in these plots and other explanations are needed.

For the tests conducted under seawater with CP, the plots suggest a constant crack growth rate for all the values of AK Figure 4.33 and Figure 4.35. The fatigue lives for CP tests are very short and some did not complete the whole sequence, thus the equivalent stress ranges employed in the calculation could be wrong. The behaviour though does fit in with the crack growth under CP for constant amplitude loading, where there is a plateau.

From the crack growth rate study, there is a need for a clearer way o f analysing the crack propagation under variable amplitude loading. The erratic crack growth affects the way in which the crack growth rate was calculated. It was also noted by Etube [4.5] for tests under JOSH generated sequence that that the crack growth was not steady under variable amplitude. This could be due to the way JOSH generated the sequence. This problem of the JOSH generated sequence is taken up in more detail in Chapter 5.

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4.5

Discussion on Weided Joint Ciassification for T-butt Weided