Design and Fabrication of Random Metal Foam Structures for Laser Powder Bed Fusion - MDPI
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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; email@example.com (N.C.); firstname.lastname@example.org (S.L.C.) 2 Dip. di Ingegneria Industriale—Università degli Studi di Salerno, Via Giovanni Paolo II 132, 84084 Fisciano (SA), Italy; email@example.com * Correspondence: firstname.lastname@example.org 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 , energy, and bionics  fields. Namely, high strength-to-weight ratio, thermal and acoustic insulation, good properties of energy absorption, and even electromagnetic shielding  benefit when metal cellular materials are considered . 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 . As a matter of fact, lattice-truss structures are affected by anisotropy resulting in weaker directions depending on the arrangement of the trusses . 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
Materials 2019, 12, 1301 2 of 13 random pore distribution , 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 . In this context, scanning electron microscopy , computed tomography, and X-rays scanning have been considered  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 , and in the latter, expanding hydrogen is released, and therefore used to create pores . Reviews of other consolidated technologies such as the space-holder method  or the continuous zone melting technique  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 . 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) . The feasibility of manufacturing similar-to-foam steel components with spherical porosity adopting laser powder bed fusion (LPBF) has been explored , 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 , 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.
Materials 2019, 12, 1301 3 of 13 Materials 2019, 12, x FOR PEER REVIEW 3 of 13 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  in order to assess the actual resolution of the process, walls in advance via preliminary quality job  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.
Materials 2019, Materials 12, x1301 2019, 12, FOR PEER REVIEW 44 of of 13 13 Materials 2019, 12, x FOR PEER REVIEW 4 of 13 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
Materials 2019, 12, x FOR PEER REVIEW 5 of 13 Materials Materials2019, 2019,12, 12,x1301 FOR PEER REVIEW 55of of13 13 Materials 2019, 12, x FOR PEER REVIEW 5 of 13 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. file was effectively required required build and Therefore, and the partwas atvia was provided first AM, to the the theirrespective provided solid to modelprinting ofwas printingthe machine converted machine via viain an ana STL point STL (standard cloud (standard to be triangle meshed triangle language) at next language) file step, file . points . Therefore, located Therefore, 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 of the model was solid was converted CAD converted machine model inaand in via aanpoint point STL cloud strategically cloud to be to (standard be meshedalong gathered meshed triangle at next at next language) step, step, points high-curvature filepoints located surfaces. . located Therefore, on the on thefirst at outside Nevertheless, outside skin skin the solid whenof of the the model solid shifting solid was CAD this CAD model method model converted and to inand strategically a strategically random a point cloudfoam gathered structure gathered to be along meshedalong at high-curvature (Figure 5), many high-curvature next step, points surfaces. points were surfaces. located Nevertheless, generated onNevertheless, the outside and when skinmost when of theshifting of them shifting solid this were this CAD method redundant method modelto to and aa random random and strategically foamgathered ineffective foam structure structure (Figure to the overall (Figure along 5), many precision. 5), many high-curvature points Therefore, points were were generated the generated surfaces. general and most method Nevertheless, and most was of when of them deemed them shifting were to were redundant thisbemethod time consuming redundant and to aand ineffective andfoam ineffective random to to the the probabilityoverall the overall structure precision. ofprecision. (Figuregenerating 5), many Therefore, defects points in Therefore, the the were general thegeneral mesh and generated method method was specific and deemed was errors most deemed of them of to to be inverted be time time consuming normal consuming vectors and and or the bad the probability edges probabilitywas of of generating expected generating to bedefects high. defects were redundant and ineffective to the overall precision. Therefore, the general method was deemed in With in the the a mesh goal mesh and of and specific optimized specific errors cloud errors of of inverted points, inverted to be time normal the vectors approach consumingvectors of or or and bad theedges Pauly bad  was edges was was probability expected referred expected totobe of generating toandhigh. WithWith bedefects high. a goal implemented. in the of optimized Using a goal mesh ofand cloud cloud thisspecific method optimized of points, which errors of of the approach considers points, inverted the of Pauly incremental approach normal vectors  ofandor was Pauly referred hierarchical badedgeswaswasto and implemented. clustering, referred expectedtoiterative and Using With this simplification, to beimplemented. high. method Using a goal and ofthis which particle method optimized considers simulation which cloud of incremental algorithms considers points, the andcreate to incrementalhierarchical approach andPauly of clustering, approximations hierarchical  was iterative of clustering, referred simplification, point-based models, iterative to and and the particle number simplification, implemented. simulation of points and Using particle algorithms significantly this method simulation whichto create decreased algorithmsapproximations (Figure to create considers incremental 6), theof point-based geometry approximations and hierarchical models, wasofnot the point-based clustering, number affected iterative and of points the occurrence models, significantly the number simplification, of noise decreased of points and particlewas (Figure reduced. significantly simulation 6), the geometry decreased algorithms towas (Figure notthe 6), create affected geometry and was approximations the occurrence affectedofand notpoint-based of noise thepoints models, wasnumber occurrence the reduced. of noise of points pointswas reduced. significantly 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.
Materials 2019, 12, 1301 x FOR PEER REVIEW 6 of 13 The second main step was meshing the cloud of points. The constrained Delaunay triangulations (CDT)The second  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)  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 . The STL file was then sliced before processing. guidance in addition to the common rules for smoothing . 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 . metal powder to lay . 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 . High strength, good corrosion resistance, ◦ C, and copper precipitation hardening steelgood mechanical in terms of nominalproperties chemicalat composition temperatureswasup used to 316. 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 . in chemical and petrochemical industry, as well as in aerospace and marine, food processing and power plants . 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
Materials 2019, 12, 1301 7 of 13 Materials 2019, 12, x FOR PEER REVIEW 7 of 13 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.
Materials2019, Materials 2019,12, 12,1301 xx FOR FOR PEER PEER REVIEW REVIEW 88 of of 13 13 Materials 2019, 12, x FOR PEER REVIEW 8 of 13 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.
Materials 2019, 12, 1301 9 of 13 Materials Materials2019, 2019,12, 12,xxFOR FORPEER PEERREVIEW REVIEW 99ofof13 13 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.
Materials 2019, 12, 1301 10 of 13 Materials Materials2019, 2019,12, 12,xxFOR FORPEER PEERREVIEW REVIEW 10 10ofof13 13 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. References 1. Khoda, A.K.; Ozbolat, I.T.; Koc, B. Designing heterogeneous porous tissue scaffolds for additive manufacturing processes. Comput. Aided Des. 2013, 45, 1507–1523. [CrossRef] 2. Emmelmann, C.; Sander, P.; Kranz, J.; Wycisk, E. Laser additive manufacturing and bionics: Redefining lightweight design. Phys. Procedia 2011, 12, 364–368. [CrossRef] 3. Seo, J.; Lee, K.; Shim, D. Effects of process parameters on properties of porous foams formed by laser-assisted melting of steel powder (AISI P21)/foaming agent (ZrH2) mixture. Opt. Laser Technol. 2018, 98, 326–338. [CrossRef] 4. Caiazzo, F.; Campanelli, S.; Cardaropoli, F.; Contuzzi, N.; Sergi, V.; Ludovico, A. Manufacturing and characterization of similar to foam steel components processed through selective laser melting. Int. J. Adv. Manuf. Technol. 2017, 92, 2121–2130. [CrossRef] 5. Rosen, D. Computer-aided design for Additive Manufacturing of cellular structures. Comput. Aided Des. Appl. 2007, 4, 585–594. [CrossRef] 6. Usera, D.; Alfieri, V.; Caiazzo, F.; Argenio, P.; Corrado, G.; Ares, E. Redesign and manufacturing of a metal towing hook via laser additive manufacturing with powder bed. Procedia Manuf. 2017, 13, 825–832. [CrossRef] 7. Syam, W.; Jianwei, W.; Zhao, B.; Maskery, I.; Elmadih, W.; Leach, R. Design and analysis of strut-based lattice structures for vibration isolation. Precis. Eng. 2018, 52, 494–506. [CrossRef] 8. Caiazzo, F.; Cardaropoli, F.; Alfieri, V.; Sergi, V.; Cuccaro, L. Experimental analysis of Selective Laser Melting process for Ti-6Al-4V turbine blade manufacturing. In Proceedings of the XIX International Symposium on High-Power Laser Systems and Applications 2012, Istanbul, Turkey, 10–14 September 2012. 9. Xu, S.; Shen, J.; Zhou, S.; Huang, X.; Xie, Y. Design of lattice structures with controlled anisotropy. Mater. Des. 2016, 93, 443–447. [CrossRef] 10. Tan, P.; Tong, L.; Steven, G.P. Behaviour of 3D orthogonal woven CFRP composites, part II: FEA and analytical modeling approaches. Compos. Part A Appl. Sci. Manuf. 2000, 31, 273–281. [CrossRef] 11. Betts, C. Benefits of metal foams and developments in modelling techniques to assess their materials behaviour: A review. Mater. Sci. Technol. 2012, 28, 129–143. [CrossRef] 12. Chougrani, L.; Pernot, J.; Véron, P.; Abed, S. Lattice structure lightweight triangulation for Additive Manufacturing. Comput. Aided Des. 2017, 90, 95–104. [CrossRef]
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