Results of The Computational Experiments: A. Significance of
modelling both surface profile and sub-surface
porosity
There are two parts to this paper. The first part concerns the
significance of modelling both surface profile and sub-surface porosity.
The second part is concerned with the effects of relative pore sizes and
levels of porosity for a reasonably homogeneous porosity distribution:
this will be addressed in Section 6 and thereafter.
Description of the models
In this first part, three models were created: (a) a model with a rough
surface profile, (b) a model with sub-surface porosity, and (c) a model
which combined the rough surface profile and the sub-surface porosity.
For each model, equivalent boundary conditions and five half cycles of
fully reversed loading steps of ±270 MPa pressure were applied. The mesh
size in the neighbourhood of the surface profile and porosity features
was controlled to be similar in each case. In a similar previous study
[63] it was found that the basic stress and equivalent plastic
strain pattern was established after the first load, and the development
of those patterns became clear after only a few half cycles.
A further model with neither roughness nor porosity is unnecessary, as
the result is analytically obvious. In this case, the state of stress is
constant through the whole model, and equal to the applied pressure,
±270 MPa. Since the yield stress is never exceeded, there can be no
plastic strain even after multiple reverse loadings. An equivalent
nominal stress state is seen in each of the other models at Saint Venant
distances from the stress raising features.
Computational results
The results are shown in Figure 5 for equivalent plastic strain (PEEQ),
and in Figure 6 for von Mises stress. The model configuration is similar
to that illustrated in Figure 2(d), with the area shown just including
the roughness and sub-surface porosity region, i.e. an area of
0.55 by 1 mm. The results from left to right indicate the state of PEEQ
or stress following each of the five half cycles of loading.
As is self-evident, the top rows of both figures show the effect of
roughness only, the middle rows show the effect of porosity only, and
the bottom rows show results where both the roughness and the porosity
are modelled. The legends for these figures are given in Table 1. Figure
5 is plotted on a logarithmic scale, down to the grey region showing
equivalent plastic strain of less than 1×10-7. In the
case of Figure 6, the von Mises stress colour bands indicate the steps
in the material definition so that the boundary between dark and pale
blue is equivalent to the nominal state of stress, 270 MPa. As the
elements of the model are tiny, the mesh lines have been suppressed, but
an impression of the mesh size is given by allocating one colour per
element.
It is clear from the results that the combined effect of both surface
roughness and sub-surface porosity leads to a greater sub-surface
penetration of local plastic strain than is the case where either
surface roughness of sub-surface porosity is considered alone, see Table
4. Additionally, the level and extent of the plastic strain is also
significantly greater when both roughness and porosity are modelled. In
all three cases, the level of plastic strain increases with the number
of load cycles, but the extent is almost constant.
In Figure 6, the regions of the material for which the yield stress has
been exceeded are shown in green. Higher stress values are present in
localised regions, but the elements with those results are too tiny for
the other colour contour bands to be visible.
It is to be noted that the extent of yield stress region is highest
following the first half cycle, and reduces on subsequent cycles. Thus
it seems that the effect of load cycling is to redistribute the stress
field through the plastic deformation.