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).