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.