Design and Fabrication of Random Metal Foam Structures for Laser Powder Bed Fusion - MDPI

 
Design and Fabrication of Random Metal Foam Structures for Laser Powder Bed Fusion - MDPI
materials
Article
Design and Fabrication of Random Metal Foam
Structures for Laser Powder Bed Fusion
Nicola Contuzzi 1 , Sabina Luisa Campanelli 1 , Fabrizia Caiazzo 2, *             and Vittorio Alfieri 2
 1   Dip. di Meccanica, Matematica e Management—Politecnico di Bari, Viale Japigia 182, 70126 Bari (BA), Italy;
     nicola.contuzzi@poliba.it (N.C.); sabinaluisa.campanelli@poliba.it (S.L.C.)
 2   Dip. di Ingegneria Industriale—Università degli Studi di Salerno, Via Giovanni Paolo II 132,
     84084 Fisciano (SA), Italy; valfieri@unisa.it
 *   Correspondence: f.caiazzo@unisa.it
                                                                                                      
 Received: 12 March 2019; Accepted: 17 April 2019; Published: 20 April 2019                           

 Abstract: With the development of additive manufacturing, the building of new categories of
 lightweight structures such as random foams have been offered. Nevertheless, given the complexity
 of the required parts, macroscopic defects may result or the process may even fail. Therefore,
 proper actions must be taken at the design stage. In this paper, a method of design for additive
 manufacturing (DfAM) to build metal random foam structures is proposed. Namely, a procedure is
 suggested to generate a structure that has interconnected porosity. This procedure is based on the
 aimed fractional density and several technical requirements, and then the geometry is optimized
 and meshed. To validate the algorithm, a test article consisting of a metal cylinder with spherical
 random pores ranging from 1 to 6 mm in diameter with a resulting fractional density of 40 ± 2% has
 been conceived and manufactured by means of laser powder bed fusion (LPBF). On the basis of the
 outcome of the manufacturing process, crucial information has been gathered to update the algorithm.

 Keywords: additive manufacturing; design for manufacturing; random foam structures

1. Introduction
     Lightweight metal structures are widely used in aeronautics, automotive, biomedical [1], energy,
and bionics [2] fields. Namely, high strength-to-weight ratio, thermal and acoustic insulation, good
properties of energy absorption, and even electromagnetic shielding [3] benefit when metal cellular
materials are considered [4].
     For the purpose of designing and building, many different approaches have been discussed in
the literature. Interestingly, the concept has been significantly addressed in the field of additive
manufacturing (AM), as state-of-the-art and flexible processes have been developed that offer
new opportunities in terms of shapes, sizes, geometric mesostructures, material compositions,
and microstructures, and therefore improve both performance and life-cycle. Design for additive
manufacturing (DfAM) has been introduced for the purpose of exploiting all the opportunities in
AM [5,6]. By considering this, the production of freeform complex structures using potentially a wide
range of materials, including high-performance metals, has been allowed [7,8].
     Periodic structures are the most common cellular materials, given their capability to provide
variations in the structural properties and benefit controllable deformation. With respect to this
subject, several methods for designing lattice structures with controlled anisotropy are reported [9].
As a matter of fact, lattice-truss structures are affected by anisotropy resulting in weaker directions
depending on the arrangement of the trusses [10]. Nevertheless, since the direction of loading is not
known in advance of the specific applications (e.g., aerospace or medical), a lightweight structure is
required to exhibit a similar homogeneous mechanical behavior, hence the foams, i.e., samples with

Materials 2019, 12, 1301; doi:10.3390/ma12081301                                www.mdpi.com/journal/materials
Design and Fabrication of Random Metal Foam Structures for Laser Powder Bed Fusion - MDPI
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random pore distribution [11], represent a valid alternative to lattice-truss structures. On the other
hand, the conventional production of foams is currently limited to low-melting-point metals, such as
aluminum or copper. Consequently, other materials with higher strength must be investigated, and
therefore AM processes represent a valid alternative and are worth investigating for this purpose.
      In general, foam samples are designed using the reconstruction methods of either statistical or
stochastic, for example, a three-dimensional porous media is created from two-dimensional (2D) images
or a three-dimensional (3D) cloud of data points [12]. In this context, scanning electron microscopy [13],
computed tomography, and X-rays scanning have been considered [14] to generate the models. Then,
different fabrication techniques can be compared. In the literature, the methods of bubbling gas or
injecting a foaming agent in the molten alloy are referred to as conventional approaches [3], and
in the latter, expanding hydrogen is released, and therefore used to create pores [15]. Reviews of
other consolidated technologies such as the space-holder method [16] or the continuous zone melting
technique [17] are available in the literature. When moving to more recent methods, AM is certainly
suitable due to its advantages. For example, with specific reference to the building of metal random
foam structures, the advantage of control over size, density, and local distribution of the designed
porosity is documented [3]. In particular, layer-by-layer AM building (i.e., two-stage processing)
is expected to provide higher accuracy as compared with directed deposition AM (i.e., one-stage
processing) [18]. The feasibility of manufacturing similar-to-foam steel components with spherical
porosity adopting laser powder bed fusion (LPBF) has been explored [4], but limited research has been
devoted to the manufacturing of metal random foam structures, which have some issues that must
be addressed. First, interconnected porosity is mandatory in order to allow the extraction of loose
powder from cavities. Moreover, a proper size of pores is required to comply with the manufacturing
capability of the building machine to prevent inner supporting structures [19], which otherwise should
be removed in post-processing.
      To address this lack of knowledge, porous structures with random spherical pores and controlled
fractional density are designed and manufactured in this article. A DfAM approach is proposed
and the main issues are discussed. Namely, a three-dimensional porous structure is conceived with
given porosity, then the geometry is converted to optimized points and eventually meshed. Possible
errors, in terms of shapes and poor contours, are corrected. Prior to manufacturing, the structure
is checked layer-by-layer to assess its effective manufacturability. During manufacturing via LPBF,
several post-processing checks are conducted, and then crucial findings are drawn to update the
algorithm for random foam generation.

2. Materials and Methods

2.1. Design of a Random Foam
     Due to their random distribution of pores, foams have a complex internal structure and indeed
thin walls and a large empty volume of up to 90% could be required. Consequently, building via AM
techniques is challenging and there is a high probability of faulty parts. Therefore, a proper strategy at
the design stage should be adopted. For this purpose, three rules were proposed when LPBF is used:

•     Interconnection of inner pores is mandatory.
•     A minimum solid fraction preventing the collapse of the structure must be offered at any layer.
•     The wall thickness must be larger with respect to the effective melting diameter.

     The first rule is a technical requirement for the extraction of the residual metal powder. The second
and third rules are conceived to allow effective, rather than ineffective, manufacturing of the parts.
For example, a sensible balancing between solid fraction and connected pores (Figure 1) is required
to prevent collapse of the structure under its own weight where inner supporting structures must be
avoided. Moreover, a minimum size of bulky material must be allowed between adjacent pores to offer
local strength to effectively support the next building layers.
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            Figure1.1. Cross-section
            Figure     Cross-section of
                                     ofaasample
                                          samplewith
                                                withreduced
                                                     reducedsolid
                                                             solidfraction
                                                                   fractiondue
                                                                            dueto
                                                                                toconnected
                                                                                   connectedpores.
                                                                                             pores.

     With respect to the third rule, the effective melting diameter of the laser beam must be evaluated
      With respect to the third rule, the effective melting diameter of the laser beam must be evaluated
in advance via preliminary quality job [6] in order to assess the actual resolution of the process, walls
 in advance via preliminary quality job [6] in order to assess the actual resolution of the process, walls
thinner than the actual size of a single scanning line are not possible. Further investigation resulting in
 thinner than the actual size of a single scanning line are not possible. Further investigation resulting
additional precautions and guidelines for design are reported in the relevant section of this article.
 in additional precautions and guidelines for design are reported in the relevant section of this article.
2.1.1. Generating the Solid Model
 2.1.1. Generating the Solid Model
      At first, to design a random foam, a flowchart was proposed (Figure 2). The algorithm was
       At first, to design a random foam, a flowchart was proposed (Figure 2). The algorithm was fed
fed with crucial input data, i.e., a range for the pore size, and the aimed fractional density of the
 with crucial input data, i.e., a range for the pore size, and the aimed fractional density of the foam
foam and the wall thickness depending on the accuracy and the resolution of the printing machine.
 and the wall thickness depending on the accuracy and the resolution of the printing machine. The
The driving idea was to build the CAD model by means of piling up N modelling layers, which were
 driving idea was to build the CAD model by means of piling up N modelling layers, which were
required to comply with the referred building rules and the aimed fractional density. The number
 required to comply with the referred building rules and the aimed fractional density. The number of
of modelling layers was based on the height of the structure being designed, as well as the available
 modelling layers was based on the height of the structure being designed, as well as the available
computing power. Calculations were performed using a developed macro software (Excel, 2016,
 computing power. Calculations were performed using a developed macro software (Excel, 2016,
Microsoft, Redmond, WA, USA), where the range of the pore diameter was given and a cloud of
 Microsoft, Redmond, WA, USA), where the range of the pore diameter was given and a cloud of
random pore centers was generated (Figure 3) in a cylindrical coordinate system within each the layers,
 random pore centers was generated (Figure 3) in a cylindrical coordinate system within each the
from layer 1 to N. Spherical pores of random size were provided (see Figure 4), in compliance with
 layers, from layer 1 to N. Spherical pores of random size were provided (see Figure 4), in compliance
both the constraints of fractional density and the wall thickness. If the condition of interconnection
 with both the constraints of fractional density and the wall thickness. If the condition of
was matched, the next modelling layer was generated, otherwise, the current layer was deleted and
 interconnection was matched, the next modelling layer was generated, otherwise, the current layer
regenerated. The process was repeated up to the actual size of the sample. Then, a final check on the
 was deleted and regenerated. The process was repeated up to the actual size of the sample. Then, a
interconnection was conducted. Eventually, the solid CAD model was generated.
 final check on the interconnection was conducted. Eventually, the solid CAD model was generated.
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                                                             THICKNESS
                FULL PART               calculate N        of the modelling
                                                              THICKNESS
                                                                 layer
                FULL PART               calculate N         of the modelling
                                                                  layer

                                        initialize
                                    the layer   id x=0
                                         initialize
                                     the layer id x=0

                                           x+1
                                           x+1

                                                                 model         y
                                           x
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        Figure 4. Generation of spherical pores for the current modelling layer, with resulting porous
        structure.
       Figure  4. Generation of spherical pores for the current modelling layer, with resulting porous
       structure.
        Figure 4.4.Generation
                    Generationofof spherical
                                spherical    pores
                                          pores      forcurrent
                                                for the  the current modelling
                                                                modelling         layer,
                                                                          layer, with    with resulting
                                                                                      resulting           porous
                                                                                                porous structure.
 2.1.2.structure.
         Generating the STL File
 2.1.2.  Generatingthe
2.1.2. Generating          theSTLSTLFileFile
       A number of steps must be addressed to effectively build the part via AM, irrespective of the
 2.1.2.A
       AGenerating
           number of
 manufacturing
          number        ofthe    STL
                             steps
                        technology.
                            steps       File
                                       must
                                      must      be addressed
                                             Indeed,
                                               be    addressed
                                                         a proper   tomesh
                                                                   to   effectively       build the
                                                                                was required
                                                                       effectively       build    theandpart
                                                                                                       part was viaprovided
                                                                                                               via   AM, irrespective
                                                                                                                     AM,     irrespective      of the
                                                                                                                                  to the printing
                                                                                                                                              of   the
 manufacturing
 machine
manufacturing
       A number         technology.
              via antechnology.
                         STL
                         of  steps(standard
                                       must  Indeed,
                                            Indeed,     aaproper
                                                betriangle proper
                                                     addressed        mesh
                                                              language)
                                                                    tomesh      was[20].
                                                                               file
                                                                               was
                                                                        effectively     required
                                                                                       required
                                                                                          build      and
                                                                                             Therefore,
                                                                                                    and
                                                                                                  the   partwas
                                                                                                              atvia
                                                                                                            was    provided
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                                                                                                                     AM,          to the
                                                                                                                                      the
                                                                                                                         theirrespective
                                                                                                                   provided    solid
                                                                                                                                 to    modelprinting
                                                                                                                                               ofwas
                                                                                                                                           printingthe
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 converted
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             viain  an
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                                                                                    points
                                                                                     [20].   Therefore,
                                                                                              located
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 manufacturing technology. Indeed, a proper mesh was required and was provided to the printing            on  at
                                                                                                             atthefirst  the
                                                                                                                    outside
                                                                                                                 first  the    solid
                                                                                                                                skin
                                                                                                                              solid    model
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 CAD
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                                                                                                                         the solid whenof
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 this
 were
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 CAD   method
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                                                   to the overall
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                                                              along        5), many
                                                                       precision.
                                                                          5),    many
                                                                       high-curvature      points
                                                                                        Therefore,
                                                                                          points    were
                                                                                                   were      generated
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                                                                                                surfaces.    general          and most
                                                                                                                         method
                                                                                                              Nevertheless, and     most
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                                                                                                                                               them
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 were
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         time consuming
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                                                                (Figuregenerating
                                                                           5), many     Therefore,
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                                                                                       Therefore,      the
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 were redundant and ineffective to the overall precision. Therefore, the general method was deemed  in
                                                                                                   With
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 inverted  the        of Pauly
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                                                                 referred simplification,
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                                                                                           implemented.             simulation
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                                                                                                                                           reduced.
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 decreased (Figure 6), the geometry was not affected and the occurrence of noise points was reduced.

                                     Figure 5. Point cloud for a cubic random foam structure.
                                    Figure5.
                                    Figure     Pointcloud
                                            5.Point  cloudfor
                                                           foraacubic
                                                                 cubicrandom
                                                                       randomfoam
                                                                              foamstructure.
                                                                                   structure.

                                     Figure 5. Point cloud for a cubic random foam structure.

                              Figure 6.
                              Figure    Processing aa cloud
                                     6. Processing    cloud of
                                                            of points
                                                               points using
                                                                      using the
                                                                            the approach
                                                                                approach of
                                                                                         of Pauly.
                                                                                            Pauly.
                             Figure 6. Processing a cloud of points using the approach of Pauly.
                              Figure 6. Processing a cloud of points using the approach of Pauly.
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     The second main step was meshing the cloud of points. The constrained Delaunay triangulations
(CDT)The  second
        [14]      main as
             was used    step a was  meshing
                                reference   andthe    cloudconveniently
                                                   it was    of points. The  constrained
                                                                           adjusted     to meetDelaunay     triangulations
                                                                                                    the requirements      of
(CDT)   [14] was  used   as  a  reference  and    it  was  conveniently    adjusted     to  meet
building using a foam structure, where distortion of triangles may result around the pores. As      the  requirements     of
building
expected,using  a foam structure,
           a mismatch    was foundwhere      distortion
                                       between             of triangles
                                                    the theoretical      may result
                                                                     original         around
                                                                               spherical         the pores.
                                                                                            surface    in the As  expected,
                                                                                                               solid model
a
and its approximation upon triangularization, i.e., a chordal error resulted on each pore and and
  mismatch    was  found    between    the theoretical    original   spherical   surface    in the   solid  model    had its
                                                                                                                          to
approximation   upon triangularization,
be reduced to improve       the quality of thei.e., mesh.
                                                    a chordal
                                                            To error  resulted on
                                                                this purpose,   new each  pore and
                                                                                       vertices         had to
                                                                                                   needed    to be
                                                                                                                 bereduced
                                                                                                                    created
to improve
when         the quality
       the chordal   error of   the mesh.
                             exceeded        To thisthreshold.
                                         a certain      purpose, However,
                                                                    new vertices
                                                                               theneeded
                                                                                     elementtosize be created
                                                                                                       used to when
                                                                                                                  achievethea
chordal  error exceeded     a  certain threshold.      However,    the element    size used
given limit chordal error may have been very small, and therefore refining the mesh would have to  achieve   a  given  limit
chordal
resulted error  may have
          in increased        been very small,
                           unmanageable              and therefore
                                               geometrical     data. refining
                                                                       One may   theassume
                                                                                      mesh would         have resulted
                                                                                                the chordal      error wasin
increased  unmanageable       geometrical   data.    One  may    assume  the chordal    error
accepted when the order of magnitude of the accuracy of the printing process was matched.       was   accepted    when   the
orderAdditionally,
      of magnitudegeneral
                       of the accuracy    of the
                                errors such         printing outpointing
                                               as inverted    process was normal
                                                                            matched.   vectors and poor connections
     Additionally,   general    errors such   as  inverted   outpointing    normal
of edges had to be addressed, which involved regenerating the triangle and stitching  vectors     and poorthe  connections
                                                                                                                  vertexes,
of edges  had  to be  addressed,     which   involved     regenerating    the  triangle    and
respectively. In general, for foam structures there was no need for specific guidance in additionstitching    the  vertexes,
                                                                                                                          to
respectively. In general,   for  foam  structures     there was   no need  for  specific
the common rules for smoothing [22]. The STL file was then sliced before processing.      guidance      in addition   to the
common rules for smoothing [22]. The STL file was then sliced before processing.
2.1.3. Slicing the Model
2.1.3. Slicing the Model
      Once the building direction had been set for the building layers, the solid 3D part was converted
      Once the building direction had been set for the building layers, the solid 3D part was converted to
to 2D slices. The total number of slices depended on the overall height of the structure and the
2D slices. The total number of slices depended on the overall height of the structure and the thickness
thickness of the building layer, which was different from the thickness of the modelling layer. In
of the building layer, which was different from the thickness of the modelling layer. In LPBF, the latter
LPBF, the latter was a compromise between the penetration depth of the laser beam and the mean
was a compromise between the penetration depth of the laser beam and the mean particle size of the
particle size of the metal powder to lay [23].
metal powder to lay [23].
      Thin lines in each slice could result in manufacturing defects when the laser beam was scanned
      Thin lines in each slice could result in manufacturing defects when the laser beam was scanned
along it, and therefore additional actions were taken for the purpose of manufacturability. For each
along it, and therefore additional actions were taken for the purpose of manufacturability. For each
layer, the wall thickness, i.e., the gap between adjacent pores, was considered and compared to the
layer, the wall thickness, i.e., the gap between adjacent pores, was considered and compared to the
actual resolution of the building process, which depended on the effective melting diameter. When
actual resolution of the building process, which depended on the effective melting diameter. When
the threshold had not been matched, the radius of the adjacent pores was reduced (Figure 7) to allow
the threshold had not been matched, the radius of the adjacent pores was reduced (Figure 7) to allow
effective building of a solid gap. Upon correction, any change to the fractional density was negligible.
effective building of a solid gap. Upon correction, any change to the fractional density was negligible.

             Figure 7. Gap between adjacent pores, before and after correction of the wall thickness.
             Figure 7. Gap between adjacent pores, before and after correction of the wall thickness.
2.2. Manufacturing of the Foams
2.2. Manufacturing
     An EOSINT M270of the laser
                           Foamssintering system (EOS, Krailling, Germany) with Yb-fibre laser source
was used   to manufacture
     An EOSINT              the sintering
                   M270 laser    test article. A prealloyed,
                                            system               argon-atomized
                                                      (EOS, Krailling,   Germany)  virgin
                                                                                     with commercial   EOS
                                                                                           Yb-fibre laser     GP1
                                                                                                           source
stainless
was usedsteel   powder, 36the
           to manufacture         mean
                             µmtest       grain
                                      article. A size,  corresponding
                                                  prealloyed,             to standard
                                                                 argon-atomized         UNS
                                                                                   virgin    S17400 chromium
                                                                                          commercial   EOS GP1
copper  precipitation  hardening    steel in  terms  of  nominal   chemical   composition
stainless steel powder, 36 μm mean grain size, corresponding to standard UNS S17400         was  usedchromium
                                                                                                       [6]. High
strength,  good corrosion   resistance,                                                                  ◦ C, and
copper precipitation   hardening    steelgood    mechanical
                                          in terms    of nominalproperties
                                                                    chemicalat composition
                                                                               temperatureswasup used
                                                                                                 to 316[6]. High
good  toughness   were  offered.  Indeed,   this  material   is generally used  in chemical  and
strength, good corrosion resistance, good mechanical properties at temperatures up to 316 °C, andpetrochemical
industry, as well were
good toughness    as in aerospace   and marine,
                        offered. Indeed,            food processing
                                            this material              and
                                                             is generally   power
                                                                          used      plants [24].
                                                                                in chemical  and petrochemical
industry, as well as in aerospace and marine, food processing and power plants [24]. trials aimed to
     Processing  parameters   (Table  1) and  scanning    strategies were  based  on preliminary
optimize  the process
     Processing       for the purpose
                 parameters    (Table 1)ofand
                                            a full dense structure.
                                                scanning   strategiesAn
                                                                      wereaccuracy  of 0.02
                                                                             based on       mm and trials
                                                                                       preliminary   a minimum
                                                                                                           aimed
to optimize the process for the purpose of a full dense structure. An accuracy of 0.02 mm and a
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minimum     size ofdiameter
size of building    buildingofdiameter
                                0.190 mmof 0.190
                                            were mm    wereand
                                                  checked   checked
                                                                theseand
                                                                      werethese
                                                                             usedwere  used tothe
                                                                                  to address    address
                                                                                                   issuesthe
                                                                                                          of
issues
chordaloferror
           chordal
                and error  and wall thickness,
                     wall thickness,             respectively,
                                     respectively,             although
                                                    although the          the mechanical
                                                                  mechanical               stability
                                                                               stability during      during
                                                                                                 building  is
building  is highly dependent   on  geometry   and  must be discussed   on
highly dependent on geometry and must be discussed on a case-by-case basis.a case-by-case  basis.
     To
     To prevent
         prevent oxidation
                   oxidation during
                               duringthe
                                       theprocess,
                                            process,a controlled nitrogen
                                                      a controlled         atmosphere
                                                                    nitrogen   atmospherewaswas
                                                                                             arranged,   the
                                                                                                  arranged,
oxygen  content
the oxygen        being
             content    taken
                      being    below
                            taken     0.8%.
                                   below  0.8%.

      Table 1.
      Table 1. Processing parameters in
               Processing parameters in laser
                                        laser powder
                                              powder bed
                                                     bed fusion
                                                         fusion (LPBF)
                                                                (LPBF) of
                                                                       of EOS
                                                                          EOS GP1
                                                                              GP1 stainless
                                                                                  stainless steel
                                                                                            steel powder.
                                                                                                  powder.

                                                  Factor
                                               Factor                   Value
                                                                           Value
                                             Laser
                                          Laser     power
                                                 power                  195
                                                                          195WW
                                           Scanning   speed
                                         Scanning speed                0.75 m/s
                                                                         0.75 m/s
                                            Hatch
                                          Hatch    spacing
                                                spacing                100  μm
                                                                          100 µm
                                           Scan length
                                             Scan  length               2020
                                                                           mmmm
                                         Layer thickness
                                            Layer thickness             2020
                                                                           μmµm

3. Results
3. Results and
           and discussion
               discussion

3.1. Modelling
3.1. Modelling of
               of aa Cylindrical
                     Cylindrical Random
                                 Random Pore
                                        Pore Foam
                                             Foam
      To test
      To  test the
                the algorithm
                      algorithm and     and find
                                            find any
                                                  any possible
                                                        possible strategy
                                                                  strategy toto fix
                                                                                fix the
                                                                                    the procedure,
                                                                                         procedure, aa metal
                                                                                                         metal cylindrical
                                                                                                                 cylindrical
random     pore   foam    has  been       considered.   A   nominal   diameter   of 20
random pore foam has been considered. A nominal diameter of 20 mm and height of 50 mm,  mm   and  height   of 50  mm, for
                                                                                                                       for aa
total volume                        3
total volume of  of 15700
                     15700 mmmm3,, have  have been
                                              been set.
                                                     set. Then,
                                                          Then, spherical
                                                                 spherical random
                                                                            random pores
                                                                                       pores have
                                                                                             have been
                                                                                                   been generated
                                                                                                          generated inin the
                                                                                                                         the
solid  volume,     the  pore  diameter        has been   conveniently    set to range   between
solid volume, the pore diameter has been conveniently set to range between 1 and 6 mm to prevent 1 and   6 mm    to prevent
supporting in
supporting         LPBF, the
               in LPBF,    the minimum
                                minimum allowed allowed diameter
                                                           diameter being
                                                                     being 88 mm.    The centers
                                                                               mm. The    centers of
                                                                                                  of the
                                                                                                      the pores
                                                                                                          pores have
                                                                                                                  have been
                                                                                                                       been
generated    in  a cylindrical      coordinate     system   aiming  to a fractional  density
generated in a cylindrical coordinate system aiming to a fractional density of 40 ± 2%.       of 40 ±   2%.
      For the
      For  the purpose
                purpose of  of generating
                                generating the   the solid
                                                      solid model,
                                                             model, 20
                                                                     20 modelling     layers has
                                                                         modelling layers    has been
                                                                                                  been chosen,     each one
                                                                                                         chosen, each   one
being   2.5 mm    thick.   Three       complete   iteration  cycles of the  algorithm    have been
being 2.5 mm thick. Three complete iteration cycles of the algorithm have been required to generate  required   to generate
the structure
the structure to to be
                     be built.
                         built. ItIt isisworth
                                          worthnoting
                                                 notingthat
                                                          thatseveral
                                                               severalpores
                                                                       poresintersecting
                                                                               intersectingthe outer
                                                                                             the outer skin areare
                                                                                                         skin   required  in
                                                                                                                   required
order
in     to to
   order   allow
              allow powder
                      powder   ejection
                                   ejectionduring
                                              duringbuilding,
                                                       building,moreover,
                                                                  moreover,as  asrequired,
                                                                                  required,interconnection
                                                                                             interconnection among
                                                                                                                 among the
                                                                                                                         the
pores  is mandatory       (Figure
pores is mandatory (Figure 8).          8).

                                            (a)                              (b)
                                                 (a) solid
                     Figure 8. Random pore foam: (a) solid fraction,
                                                           fraction, (b) distribution of pores.

     A total
     A total of
             of 192
                192 pores
                    pores has
                            has been
                                 been generated
                                       generated (Figure
                                                  (Figure 9)
                                                           9) and
                                                              and the
                                                                  the highest
                                                                      highest frequencies
                                                                              frequencies of
                                                                                          of occurrence
                                                                                             occurrence have
                                                                                                         have
been found
been found for
             for the
                  the groups
                      groups with
                                with pore
                                      pore size
                                            size between
                                                 between 1.51.5 and
                                                                and 2.5
                                                                    2.5 mm.   On the
                                                                         mm. On   the other
                                                                                      other hand,
                                                                                            hand, the
                                                                                                   the lowest
                                                                                                       lowest
frequency  resulted  for the groups   with  pores ranging  between   3.5 and 6.0 mm.  Indeed, larger
frequency resulted for the groups with pores ranging between 3.5 and 6.0 mm. Indeed, larger pores    pores are
unfavorable  as  they would    result in reduced  local strength, and  therefore they would  not comply
are unfavorable as they would result in reduced local strength, and therefore they would not comply      with
the basic
with      rules rules
     the basic  of theofalgorithm.
                          the algorithm.
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                               60
                               60
                   60 50
                      50
                       pores
                    of pores
                   50 40
                      40
         Number of pores

                   40 30
           Number of

                      30
           Number

                   30 20
                      20
                   20 10
                      10
                   10 0
                       0
                    0                   1.0 -- 1.5
                                       1.0     1.5     1.5 -- 2.0
                                                      1.5     2.0     2.0 -- 2.5
                                                                     2.0     2.5      2.5 -- 3.0
                                                                                      2.5    3.0     3.0 -- 3.5
                                                                                                    3.0     3.5     3.5 -- 4.0
                                                                                                                   3.5     4.0     4.0 -- 4.5
                                                                                                                                  4.0     4.5
                                    1.0 - 1.5      1.5 - 2.0      2.0 - 2.5       Pore
                                                                                  2.5
                                                                                  Pore  size [mm]
                                                                                      - 3.0
                                                                                        size   [mm]
                                                                                                 3.0 - 3.5      3.5 - 4.0      4.0 - 4.5
                                                                               Pore size [mm]

                                           Figure 9.
                                           Figure  9. Pore
                                                      Pore size
                                                           size distribution
                                                                distribution in
                                                                              in the
                                                                                  the model
                                                                                      model of
                                                                                            of the
                                                                                                the random
                                                                                                    random foam.
                                                                                                            foam.
                                           Figure 9. Pore size distribution in the model of the random foam.
                                        Figure 9. Pore size distribution in the model of the random foam.
        AA bulky
            bulky 6579.06
                    6579.06 mmmm33 volume
                                    volume resulted,
                                             resulted, thus
                                                        thus yielding
                                                              yielding aa fractional
                                                                             fractional density
                                                                                         density of
                                                                                                  of 41.88%.
                                                                                                      41.88%.
        A bulky 6579.06 mm3 3volume resulted, thus yielding a fractional density of 41.88%. Interconnection
   Interconnection
     A bulky 6579.06
   Interconnection   of the
                    of  themm
                            poresvolume
                            pores can be
                                  can be checked
                                         checked   bythus
                                          resulted,by means
                                                      means  of virtual
                                                                virtual
                                                           yielding
                                                             of          longitudinal
                                                                      a longitudinal   sectionsof
                                                                          fractional density
                                                                                      sections  (Figure 10) at
                                                                                                   41.88%.
                                                                                               (Figure  10) at
   of the pores can be checked by means of virtual longitudinal sections (Figure 10) at 25%, 50%, and 75%
   25%,  50%, and
Interconnection    75%
   25%, 50%, andof75%    volume
                    the volume   cut.
                         pores can be checked by means of virtual longitudinal sections (Figure 10) at
                                 cut.
   volume cut.
25%, 50%, and 75% volume cut.

        Figure 10.
        Figure  10. Virtual
                     Virtual  longitudinal sections
                     Virtual longitudinal
                             longitudinal  sections at
                                           sections at 25% (A-A
                                                    at 25%
                                                       25%  (A-A view),
                                                           (A-A  view), 50%
                                                                 view), 50% (B-B
                                                                        50%  (B-B view)
                                                                            (B-B  view) and
                                                                                  view) and 75%
                                                                                        and 75% (C-C
                                                                                            75%  (C-C view)
                                                                                                      view)
        volume
     Figure      cut.
            10. cut.
        volume  Virtual longitudinal sections at 25% (A-A view), 50% (B-B view) and 75% (C-C view)
     volume cut.
            Further checks
           Further            must be
                      checks must    be  conducted
                                      beconducted
                                         conductedonon  transverse
                                                     ontransverse   cross-sections,
                                                         transversecross-sections,
                                                                     cross-sections,asasas
                                                                                         anan
                                                                                         an  example,
                                                                                                 example,
                                                                                             example,      virtual cuts
                                                                                                             virtual
                                                                                                           virtual       at 10
                                                                                                                      cuts
                                                                                                                   cuts at  10
                                                                                                                            at
   10mm
    mm   mm and
       Further
           and 2525
               and 25mmmm
                  checks  height
                            height
                          must be
                     mm height    are
                                    areconsidered
                                         considered
                                  areconducted
                                       considered  (Figure
                                                     (Figure
                                                 on(Figure   11)
                                                    transverse11)when:
                                                                  when: the
                                                                          thesolid
                                                                              solid
                                                                 cross-sections,
                                                             11) when:  the solidasfraction
                                                                                    fraction   is
                                                                                     an example,
                                                                                   fraction     is effective
                                                                                                   effective
                                                                                                       virtual
                                                                                              is effective    to support
                                                                                                                 support
                                                                                                             to cuts at 10
                                                                                                                 support   the
                                                                                                                          the
mm   next
    next     layers,
       andlayers,
              25 mm
            layers,  the
                    the  wallsize
                         wall
                       height
                     the wall  sizeconsidered
                              are
                              size   exceedsaaaminimum
                                   exceeds
                                    exceeds     minimum
                                                (Figure 11)
                                               minimum      threshold
                                                           threshold
                                                              when: the
                                                            threshold  of190
                                                                     ofof  190µm,
                                                                         solid
                                                                           190 μm,   and
                                                                                   and
                                                                                fraction
                                                                               μm,   andthethe
                                                                                          is     maximum
                                                                                             maximum
                                                                                             effective
                                                                                           the   maximum       chordal
                                                                                                          tochordal
                                                                                                             support    error
                                                                                                                     error
                                                                                                               chordal the
                                                                                                                        erroris
next is layers,
    0.15
    is   0.15
           mm.
        0.15   mm.
                 the wall size exceeds a minimum threshold of 190 μm, and the maximum chordal error
               mm.
is 0.15 mm.

                                                            (a)
                                                            (a)                                (b)
                                                                                              (b)
                                    Figure 11.
                                    Figure     Virtual (a)
                                           11. Virtual  transverse cross-sections
                                                       transverse  cross-sections at
                                                                                  at (a)   (b)mm
                                                                                      (a) 10
                                                                                          10  mm and
                                                                                                   and(b)
                                                                                                       (b)25
                                                                                                          25mm
                                                                                                             mmheight.
                                                                                                               height.
                                  Figure 11. Virtual transverse cross-sections at (a) 10 mm and (b) 25 mm height.
                               Figure 11. Virtual transverse cross-sections at (a) 10 mm and (b) 25 mm height.
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 3.2.
3.2.  Buildingofof
 3.2.Building
      Building ofaaaCylindrical
                     CylindricalRandom
                    Cylindrical  RandomPore
                                Random  Pore Foam
                                        PoreFoam
                                             Foam
      The
      The  optimized
       Theoptimized
           optimizedSTL  STL  source
                         STLsource    file
                              sourcefile   has
                                      filehas   been
                                           hasbeen    used
                                                beenused
                                                      usedto to  manufactureeight
                                                             tomanufacture
                                                                 manufacture    eight  samples
                                                                                eightsamples    (Figure
                                                                                       samples(Figure
                                                                                                (Figure12)12) by
                                                                                                          12)by   means
                                                                                                              bymeans
                                                                                                                  means
 of
of  LPBF,
 ofLPBF,   for
    LPBF,for    which
            forwhich    a natural
                 whichaanatural    direction
                           naturaldirection
                                   directionof  of growth
                                                ofgrowth
                                                    growthhashas   been
                                                             hasbeen     considered
                                                                   beenconsidered
                                                                         consideredwithwith the
                                                                                       withthe   axis
                                                                                            theaxis   of
                                                                                                 axisof   the
                                                                                                       ofthe  cylinders
                                                                                                          thecylinders
                                                                                                               cylinders
 being
being   orthogonal
        orthogonaltotothe
 beingorthogonal          thebuilding
                         the  buildingplate,
                             building    plate,thus
                                          plate, thuspreventing
                                                  thus preventing
                                                        preventing  supporting
                                                                      supporting
                                                                       supportingstructures. The
                                                                                    structures.
                                                                                     structures.Thenominal
                                                                                                  The nominalmodel
                                                                                                       nominal       has
                                                                                                                 model
                                                                                                                  model
 been
has    compared
     been  compared with   the
                        with   built
                              the    foam
                                  built     (Figure
                                         foam   (Figure13), in
                                                          13), terms
                                                                in termsof pore
                                                                           of    size
                                                                              pore    and
                                                                                    size   wall
                                                                                         and wallthickness,
 has been compared with the built foam (Figure 13), in terms of pore size and wall thickness, aimingthickness,aiming
                                                                                                                aimingto
 check
to
 tocheckthe
    checkthe reliability
           thereliabilityof the
                reliabilityof   building
                            ofthe
                               thebuilding process
                                   buildingprocess   and
                                              processand  possibly
                                                         andpossibly  update
                                                              possiblyupdate   the
                                                                          updatethe design algorithm.
                                                                                   thedesign
                                                                                       designalgorithm.
                                                                                              algorithm.

                        Figure
                         Figure12.
                                12.Cylindrical
                                    Cylindricalrandom
                                                randomfoams
                                                       foamsmanufactured
                                                            manufacturedby
                                                                         bymeans
                                                                           meansof
                                                                                 ofLPBF.
                                                                                    LPBF.
                                                                                    LPBF.

                                         (a)
                                          (a)                                           (b)
                                                                                         (b)
       Figure13.
      Figure  13. Comparing
                  Comparingthe
              13.Comparing  thenominal
                                nominalsolid
                               nominal  solidmodel
                                         solidmodeltoto
                                               model  the built
                                                      tothe
                                                         the    foam,
                                                            built
                                                             built     (a) (a)
                                                                   foam,
                                                                    foam,  and  (b) are
                                                                            (a)and
                                                                                and  (b)views
                                                                                    (b) are   of opposite
                                                                                         areviews
                                                                                             views of     sides.
                                                                                                    ofopposite
                                                                                                       opposite
      sides.
       sides.
         Transverse cross-cuts of the samples have been made at a given height (Figure 14). Since the
  direction    of building
       Transverse
         Transverse             is parallel
                       cross-cuts
                        cross-cuts      of  thetosamples
                                         ofthe     the longitudinal
                                                  samples   have
                                                              havebeen
                                                                     beenaxis
                                                                          madeof aatat
                                                                           made      sample,
                                                                                        aagiven
                                                                                           giventhese
                                                                                                 heightcuts
                                                                                                  height     are made
                                                                                                         (Figure
                                                                                                          (Figure    14).in
                                                                                                                    14).      a plane
                                                                                                                          Since
                                                                                                                           Since  the
                                                                                                                                   the
 which
direction
  directionis of
              parallel
               ofbuildingto the
                   building        building
                              isisparallel
                                    parallelto  layer.
                                               to the   The resulting
                                                   thelongitudinal
                                                       longitudinal       circular
                                                                        axis
                                                                         axisof        cross-sections
                                                                              ofaasample,
                                                                                     sample,   these    have
                                                                                                thesecuts
                                                                                                       cuts arebeen
                                                                                                             aremade
                                                                                                                 made compared
                                                                                                                         in
                                                                                                                          inaaplane to
                                                                                                                                plane
  their
which     counterpart
  whichisisparallel
              parallelto  in
                         tothethe    nominal
                             thebuilding
                                    buildinglayer.model
                                                 layer.Theat   the
                                                        Theresultingsame  height
                                                                resultingcircular   (Figure   15).
                                                                           circularcross-sections   To  be
                                                                                       cross-sectionshave   specific,
                                                                                                        havebeen       the
                                                                                                               beencompared  average
                                                                                                                      comparedto    to
  diameter
their         of each circle
  theircounterpart
          counterpart    in
                          inthe
                              the (i.e., each section
                                    nominal
                                     nominal      modelof
                                                model    atatathe
                                                                pore)
                                                               the    hasheight
                                                                   same
                                                                    same   been measured
                                                                          height   (Figure
                                                                                    (Figure15). by To
                                                                                               15). optical
                                                                                                    Tobe     microscopy
                                                                                                        bespecific,
                                                                                                            specific, the   (Table
                                                                                                                        theaverage
                                                                                                                             average 2)
  and
diameterthe percentage
  diameter    of
               ofeach       absolute
                   eachcircle
                         circle  (i.e.,   mismatch
                                   (i.e.,each
                                          each section has
                                                 section  ofbeen
                                                         of         evaluated.
                                                              aapore)
                                                                 pore) has
                                                                        hasbeen
                                                                             beenItmeasured
                                                                                     is worth noting
                                                                                    measured     by     that microscopy
                                                                                                  byoptical
                                                                                                     optical  although
                                                                                                               microscopy  a range
                                                                                                                              (Table
                                                                                                                               (Tableis
2)set for
  2)and
     andthethe  pore   size
           thepercentage    in   the
                percentageabsolute     design
                                absolutemismatch algorithm,
                                             mismatchhas        diameters
                                                          hasbeen           below
                                                                 beenevaluated.       the  lower
                                                                       evaluated.ItItisisworth    limit
                                                                                            worthnoting may
                                                                                                   notingthat be  found
                                                                                                           thatalthough    when
                                                                                                                 althoughaarange   the
                                                                                                                                range
iscut isfor
  isset
     set  close
          for thetopore
             the     the size
                    pore pole
                          sizein of  the
                                 inthe     spherical
                                      thedesign       pore. diameters
                                           designalgorithm,
                                                    algorithm,     diametersbelow
                                                                                belowthe  thelower
                                                                                              lowerlimit
                                                                                                      limitmay
                                                                                                             maybe befound
                                                                                                                       foundwhenwhen
the
 thecut
     cutisisclose
             closeto
                   tothe
                      thepole
                          poleof
                               ofthe
                                  thespherical
                                      sphericalpore.
                                                pore.
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                           Figure  14.Example
                            Figure14.  Exampleofofaacross-cut
                                                     cross-cutsection
                                                               sectionofofthe
                                                                           thesample
                                                                               samplefoam.
                                                                                      foam.

         Figure
          Figure15.
         Figure  15.Example
                15.  Exampleof
                    Example  ofthe
                            of  thenominal
                               the  nominalcross-section
                                   nominal  cross-sectioncorresponding
                                           cross-section               totothe
                                                          correspondingto
                                                         corresponding     the actual
                                                                            theactual cross-cut
                                                                                actualcross-cut section.
                                                                                       cross-cutsection.
                                                                                                 section.

     Table 2.
     Table     Nominal vs
                       vs average actual
                                  actual circle diameter
                                                diameter (ordered by size) and corresponding mismatches.
      Table2.2.Nominal
                Nominal vsaverage
                           average actualcircle
                                          circle diameter(ordered
                                                          (orderedby
                                                                   bysize)
                                                                      size)and
                                                                            andcorresponding
                                                                                correspondingmismatches.
                                                                                              mismatches.
                         Nominal (mm)(mm)
                            Nominal
                            Nominal   (mm)  Actual
                                             Actual(mm)
                                            Actual  (mm)
                                                     (mm) MismatchMismatch
                                                              Mismatch    (%)(%)
                                                                         (%)
                         0.46 0.46
                               0.46              0.51
                                                0.51
                                                  0.51             8.9
                                                                    8.9 8.9
                         1.81 1.81
                               1.81             1.97
                                                 1.97
                                                  1.97              8.8 8.8
                                                                   8.8
                         2.62                   2.71                    3.2
                              2.62
                               2.62              2.71
                                                  2.71             3.2
                                                                    3.2 1.4
                         2.87                   2.91
                         2.88 2.87
                               2.87              2.91
                                                  2.91
                                                2.98               1.4
                                                                    1.4 3.6
                         2.91 2.88
                               2.88              2.98
                                                  2.98
                                                3.07               3.6
                                                                    3.6 5.3
                         3.51 2.91
                               2.91             3.79
                                                 3.07
                                                  3.07              5.3 8.1
                                                                   5.3
                         4.13 3.51
                               3.51             4.12
                                                 3.79
                                                  3.79              8.1 0.0
                                                                   8.1
                         4.37                   4.45                    1.8
                              4.13
                               4.13              4.12
                                                  4.12             0.0
                                                                    0.0 1.4
                         4.38                   4.32
                         4.81 4.37
                               4.37              4.45
                                                  4.45
                                                4.92               1.8
                                                                    1.8 2.2
                         6.00 4.38
                               4.38              4.32
                                                  4.32
                                                6.17               1.4
                                                                    1.4 2.8
                              4.81
                               4.81              4.92
                                                  4.92             2.2
                                                                    2.2
                              6.00               6.17
                               6.00of 4.0% resulted,
                                                  6.17             2.8
     An average absolute mismatch                    and two reasons2.8
                                                                     can be inferred for conditions of
mismatch above 5%. At first, the resolution of the printing machine is a factor in the roundness error
      An average  absolute    mismatch ofof4.0%       resulted,  and two    reasons    can bebeinferred  for
                                                                                                           forconditions
when An   average
       small       absolute
             circles, (i.e., at mismatch
                                the poles of a4.0%     resulted,
                                                  sphere,   for a and
                                                                  circletwo   reasons
                                                                          of 0.46   mmcannominalinferred
                                                                                                   diameter)   conditions
                                                                                                                must be
ofofmismatch
    mismatch  above
               above  5%.
                       5%.  At
                             At first,
                                  first, the
                                          theresolution
                                              resolution  of
                                                           ofthe
                                                              the printing
                                                                   printing  machine
                                                                               machine   is
                                                                                          isaafactor
                                                                                               factorin
                                                                                                      inthe
                                                                                                          the roundness
                                                                                                               roundness
drawn (Figure 16). Moreover, high percentage mismatch could result as a consequence of wall collapse,
error
 errorwhen
       whensmall
             smallcircles,
                    circles,(i.e.,
                              (i.e.,atatthe
                                         thepoles
                                             polesofofaasphere,
                                                         sphere,for
                                                                  foraacircle
                                                                         circleofof0.46
                                                                                    0.46mm
                                                                                         mmnominal
                                                                                               nominaldiameter)
                                                                                                        diameter)must
                                                                                                                    must
be
 bedrawn
     drawn(Figure
            (Figure16).
                      16).Moreover,
                            Moreover,high  highpercentage
                                                 percentagemismatch
                                                               mismatchcould couldresult
                                                                                     resultasasaaconsequence
                                                                                                  consequenceofofwallwall
Materials 2019, 12, 1301                                                                                  11 of 13
Materials
Materials 2019,
          2019, 12,
                12, xx FOR
                       FOR PEER
                           PEER REVIEW
                                REVIEW                                                                    11
                                                                                                          11 of
                                                                                                             of 13
                                                                                                                13

collapse,  in fact,ofa major
in fact, a region      regiondefect
                               of major
                                     was defect
                                         found was    found
                                                 between    thebetween  theofinterfaces
                                                                interfaces    pores withofnominal
                                                                                           pores with   nominal
                                                                                                   diameters   of
diameters
1.81         of 1.81
      and 3.51        and 3.5117),
                mm (Figure      mm   (Figure
                                   where     17),
                                          wall     where wall
                                               thickness         thickness
                                                           of 0.283  mm wasof set
                                                                              0.283
                                                                                  in mm  was setOn
                                                                                     the model.   in the
                                                                                                     the basis
                                                                                                          model.
                                                                                                               of
On
this,the  basis
      it may  beofassumed
                    this, it may   be constraint
                             that the assumed that
                                                 giventhetoconstraint  given
                                                            wall thickness  into
                                                                               thewall thickness
                                                                                   design         in the
                                                                                           algorithm  of adesign
                                                                                                           metal
algorithm
foam, mustofbe  a metal
                  shiftedfoam,
                           from must
                                0.190 be
                                       mmshifted  from
                                           to 0.300  mm 0.190   mm to 0.300 mm at least.
                                                           at least.

                Figure
                Figure 16.
                       16. Detail
                           Detail of
                           Detail of roundness
                                  of roundness error
                                     roundness error for
                                                     for the
                                                         the circle
                                                             circle of
                                                                    of 0.46
                                                                       0.46 mm
                                                                            mm nominal
                                                                               nominal diameter.
                                                                                       diameter.
                                                                                       diameter.

        Figure
        Figure 17.
               17. Detail
                   Detail of
                          of collapse
                             collapse at
                                      at the
                                         the interface
                                             interface between
                                                       between pores,
                                                               pores, nominal
                                                                      nominal geometry
                                                                              geometry is
                                                                                       is superimposed.
                                                                                          superimposed.

      For
      For the
          the final
               final purpose
                     purpose ofof checking
                                  checking thethe fraction
                                                    fraction density,
                                                             density, weighing
                                                                      weighing has
                                                                                 has been
                                                                                      been performed
                                                                                            performed andand the
                                                                                                              the
density has been measured via the   the Archimede
                                         Archimede method.
                                                        method. An average weight of 52.786 g resulted; and
given a reference full
                    full density
                         density of
                                  of 7.9  g/cm333, an average volume
                                     7.9 g/cm                  volume of
                                                                       of 6681
                                                                          6681 mm
                                                                                    3
                                                                                mm33 resulted, thus yielding to
aa 1.5%
   1.5% error
        error with
               with respect
                     respect to
                             to the
                                 the nominal
                                      nominal model.       The mismatch
                                                  model. The   mismatch isis thought
                                                                             thought to
                                                                                      to be
                                                                                         be affected
                                                                                             affected by
                                                                                                      by aa small
                                                                                                            small
quantity of  trapped   powder   inside   the specimen     and
          of trapped powder inside the specimen and a minor   a minor geometric
                                                                      geometric   internal
                                                                                  internal error.
                                                                                            error.

 4. Conclusions
4.  Conclusions
      In this
      In this paper,
               paper, an
                      an approach
                         approach to to design
                                        design and
                                                and build
                                                      build random
                                                             random foam
                                                                      foam structures
                                                                              structures with
                                                                                          with interconnected
                                                                                                 interconnected
porosity   has  been presented.   The strategy  has  been  optimized   for  additive  manufacturing
porosity has been presented. The strategy has been optimized for additive manufacturing via             via laser
                                                                                                             laser
powder    bed  fusion. For  this purpose, several  rules have  been  proposed.    Namely,   at the
powder bed fusion. For this purpose, several rules have been proposed. Namely, at the design stage, design  stage,
aa general
   general algorithm
            algorithm has
                       has been
                           been developed
                                 developed and
                                             and tested
                                                  tested to
                                                         to model
                                                            model aa random
                                                                     random foamfoam structure
                                                                                      structure using
                                                                                                 using technical
                                                                                                        technical
 and manufacturing
and   manufacturing constraints
                       constraints such
                                    such as
                                         as the
                                            the range
                                                 range of
                                                        of the
                                                           the pore
                                                               pore size,
                                                                    size, the
                                                                           the wall
                                                                                wall thickness,   and the
                                                                                     thickness, and   the aimed
                                                                                                           aimed
 fractional density. The  latter depends  on  the specific application  of  the
fractional density. The latter depends on the specific application of the foam. foam.
      In this phase, a combination of constrained Delaunay triangulations and the approach of Pauly
has been implemented to reduce the number of modelling points, and therefore the total size of the
STL file has benefited.
Materials 2019, 12, 1301                                                                                         12 of 13

      In this phase, a combination of constrained Delaunay triangulations and the approach of Pauly
has been implemented to reduce the number of modelling points, and therefore the total size of the
STL file has benefited.
      To test the approach, a steel cylindrical random foam has been designed and built. Good agreement
with the nominal model source file has been achieved, with minor errors of approximately 4.0%,
on average, for circle diameter. Crucial findings have been drawn to update the algorithm for model
generation, nevertheless, the intended volume, hence the intended density, has been matched in
this research with an overall 1.5% mismatch. This approach of designing random pore distributions
within a given bulk volume can be used to model any complex structure where inner interconnected
porosity is required in the form of random foam for the purpose of lightening the structure. A check of
manufacturability is the preliminary step before developing a structured experimental plan to further
investigate the impact of pore distribution on the mechanical properties.

Author Contributions: Conceptualization, N.C., S.L.C., F.C. and V.A.; methodology, N.C. and S.L.C.; software,
N.C. and S.L.C.; validation, F.C. and V.A.; formal analysis, N.C., S.L.C., F.C., and V.A.; investigation, N.C.,
S.L.C., F.C., and V.A.; resources, F.C. and V.A.; data curation, N.C., S.L.C., F.C., and V.A.; writing—original draft
preparation, N.C. and V.A.; writing—review and editing, S.L.C. and F.C.; visualization, N.C., S.L.C., F.C., and V.A.;
supervision, S.L.C. and F.C.
Funding: This research received no external funding.
Acknowledgments: Authors are thankful to AITeM-PromozioneL@ser for supporting the research.
Conflicts of Interest: The authors declare no conflict of interest.

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