The load applied was ±270 MPa, which for a perfect specimen without surface or porosity features would represent von Mises stress of 90% of yield. In other words, the strain would be completely elastic and fully reversible. The effect of the surface roughness or porosity features is to create localised stress raisers, which lift the local stress field into the plastic regime. Subsequent reverse loading and reloading cycles develop the local plasticity zones. As the purpose of this study is to consider how this repeated loading might contribute to our understanding of fatigue life, in the analyses presented here multiple loading steps were defined, to give five fully reversed half cycles.
The particular model information is presented in Table 2. This provides both particular dimensional information as well as indicative mesh size information.

Geometry creation

A heuristic geometry creation tool is described, that can generate multiple example geometries, “computational specimens” that can subsequently be modelled and analysed using finite element analysis.
The surface roughness was defined randomly at 12.5 μm intervals, in a range of ±50 μm from the nominal surface, using the same method as described in [63]. In the current paper, the profile is defined by a discrete set of points, through which a spline interpolation is fitted. In [63] it was established that the choice of interpolation scheme made little significant different to the stress and plastic strain distribution in the sub-surface region. This same surface profile was used for each model. The test of randomness and scale variation was addressed by introducing variation in the porosity configurations.
There are considerable geometry handling issues with the definition of porosity. The requirement that this paper sets out to address is the generation of geometry that has some reasonable similarity with the size of porosity and lack of fusion (LOF) regions observed in real additive manufactured products. It has to be admitted that a region of LOF is not the same as a perfectly circular void, but it is necessary to keep the model simple in the first instance. If one considers the effect on the load path, then the approximation may not be unreasonable. The generation of the circular pores is illustrated in Figure 3. The centres of the pores are placed randomly within a defined zone of the model, which is the 0.3 × 1 mm rectangle shown in dashed lines.
To satisfy Resolution 1 , the tool must be capable of generating similar geometries with similar porosity volume fractions, and to achieve this, the distribution of the pores was controlled by an exclusion method [56]. The coordinates of the pore centres were generated randomly, then as each consecutive pore was placed its distance from previously generated pores was checked. If that distance was too small then the pore would be rejected from the model, and the next coordinate pair would be assessed. In Figure 3, this is illustrated by the exclusion zone circles, and it can be seen that no such circles can intersect. One limitation of this method is that the computer program that embodies it must be finite: only a finite number of pore generation attempts can be made. For small numbers of large pores, it is readily possible to be assured that for any instance of a random distribution of pores, it would be impossible to add an additional valid one: i.e. this is “fully dense random packing” . For larger numbers of smaller pores this becomes increasingly difficult to be sure to achieve, even for very large numbers of pore placement attempts. The significance of achieving this “fully dense”packing is that the resulting porosity distribution is“homogeneous” [57-58]. It should also be noted that, because of the random nature of the pore placement process, it is possible for somewhat different levels of porosity and numbers of pores for different “computational specimens” produced using the same parameters.
The defined zone is set back by 0.1 mm from the nominal surface to avoid the possibility of a pore breaking through to the surface: this is a requirement of Resolution 2a . In reality, it is quite possible that such a pore break-through would then lead to the creation of a new surface profile feature: so while in the modelling world we can differentiate between pores and surface profile, in reality these would be inter-related.
In this model, to meet the requirement of Resolution 3a , the diameter of the pores has been set to be linearly proportional to the distance from the left hand edge of the defined zone. The remaining requirements of Resolutions 2a and 3b are achieved by varying the Maximum pore diameter variable, while the requirement ofResolution 4 is met by varying the Spacing factor.

Computational specimen test matrix

A test matrix was created, based on the geometry definition requirements, constraints, and variables identified by the scheme of Resolutions. For the purposes of this paper, the only variable parameters are the Maximum pore diameter and the Spacing factor. The heuristic tool can be used to create a number of “computational specimens” for each set of parameters: in this case three models were created for each parameter set for which a full FEA cyclic loading analysis was carried out. A further 50,000 geometries were computed for statistical assessment of porosity volume fraction and the number of pores count.
In summary, these studies: