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:
- Use the same surface profile for each model
- Vary the maximum Pore Diameter, for fixed Spacing Factor
- Vary the Spacing Factor, for fixed maximum Pore Diameter
- Create three models for each trial, for full FEA analysis
- Create 50,000 geometries for each trial, for statistical assessment