The Computational Experiments: B. Effects of variation, Length scale, relative pore size and distribution

Given that the importance of modelling both the surface profile and the sub-surface porosity is established, the next step is to examine the effect of variations and length scales in the models.
Examining the results presented above, we see that the von Mises stress (S, Mises) and equivalent plastic strain (PEEQ) results show similar features. The PEEQ information is perhaps more useful as it indicates accumulated strain. This means that the magnitude of the results increase with increasing numbers of half cycles. For the von Mises stress results, the effect of plastic strain is to unload the stress raising features, so the magnitude of difference these results to the nominal stress gets smaller with increasing numbers of half cycles, and local regions where plasticity has occurred can show as having lower stress after multiple cycles than the yield stress. On that basis, results from hereon are presented as PEEQ, at the 5thhalf cycle.

Results from models with varying maximum pore diameter

The results presented in Figure 7 show the results from the 12 computational models for which the spacing factor was set to be 3. For each row, the first three images show equivalent plastic strain (PEEQ) results after the 5th half cycle of loading. The pattern of pore distribution is self-evident, but it should be noted that the models are arranged in order from left to right in order of increasing pore void area. Because the mesh for these models is so fine in the regions local to the pores and surface features, the mesh lines have been suppressed, but results have been displayed using the“Quilt” option, so that elements are shown as a single colour, rather than as an interpolation. This makes the larger elements visible at the edges of the PEEQ zones.

Results from models with varying spacing between pores (fully dense)

The results presented in Figure 8 show the results from the 12 computational models for which the maximum pore diameter was set to be 50 μm. Notice that the models shown in row (b) are repeated from Figure 7, but shown here for their position in the context of varying the spacing factor.

Assessment of the statistical distribution“porosity volume fraction”

The images shown in the right hand columns of Figures 7 and 8 are statistical distribution measures of the “porosity volume fraction” , as defined in Section 4.5. In addition to the mean and standard deviation data for “porosity volume fraction” the mean and standard deviation for the number of pores is also given. These were obtained based on data calculated from 50,000 model geometry creations for each combination of maximum pore diameter and spacing factor. The white dashed lines represent the approximate position in the distribution of the three models shown to the left, for which the FEA analysis was carried out. The porosity distributions can be seen to be sensibly similar to Gaussian for most cases except for the larger maximum pore diameter, Figure 7(d).