Effect of Internal Microstructure Distribution on Quasi-Static Compression Behavior and Energy Absorption of Hollow Truss Struct

materials

Article Eﬀect of Internal Microstructure Distribution on Quasi-Static Compression Behavior and Energy Absorption of Hollow Truss Structures

Huilan Ren, Haiting Shen and Jianguo Ning *

School of Mechatronical Engineering, Beijing Institute of Technology, Beijing 100081, China; [email protected] (H.R.); [email protected] (H.S.) * Correspondence: [email protected]

Received: 17 October 2020; Accepted: 9 November 2020; Published: 12 November 2020

Abstract: In this work, hollow truss structures with different internal microstructure distributions, i.e., basic hollow truss structure (specimen HT), hollow truss structure with internal microstructure at joints (specimen HTSJ), and hollow truss structure with internal microstructure on tube walls (specimen HTSW), were designed and manufactured using a selective laser melting technique. The effect of internal microstructure distribution on quasi-static compressive behavior and energy absorption was investigated by experimental tests and numerical simulations. The experimental results show that compressive strength and specific compressive strength of specimen HTSW increase by nearly 50% and 14% compared to specimen HT, and its energy absorption per volume and mass also increase by 52% and 15% at a strain of 0.5, respectively. However, the parameters of specimen HTSJ exhibit limited improvement or even a decrease in different degrees in comparison to specimen HT. The numerical simulation indicates that internal microstructures change the bearing capacity and structural weaknesses of the cells, resulting in the different mechanical properties and energy absorptions of the specimens. Based on the internal microstructure design in this study, adding microstructures into the internal weaknesses of the cells parallel to the loading direction is an effective way to improve the compressive properties, energy absorption and compressive stability of hollow truss structures.

Keywords: hollow truss structure; internal microstructure distribution; compressive behavior; energy absorption capacity

1. Introduction Compared with solid structures, porous structures have a significant advantage in terms of specific stiffness/strength and specific surface area resulting in excellent energy absorption capacity, thermal management and acoustic insulation. Thus, they are widely used in many engineering applications as energy absorbers, lightweight structural components, thermal transfer/shields and biological bone grafts [1–4]. Although matrix material and relative density are important factors to determine the properties of porous structures, diverse cellular structures are the main reason why porous structures become integrated structure-function engineering materials. Hence, it is necessary to investigate the effect of porous structure on properties. Conventional porous structures contain a large number of randomly distributed pores, and the shape, size and distribution of the pores are usually irregular. For example, Tane et al. [5] produced porous iron using the continuous-zone-melting method in a pressurized nitrogen and hydrogen atmosphere, and the pore size and location of the corresponding specimen were stochastic. Xia et al. [6] manufactured closed-cell aluminum foams using the melt foam method,

Materials 2020, 13, 5094; doi:10.3390/ma13225094 www.mdpi.com/journal/materials Materials 2020, 13, 5094 2 of 14 and the cross-section of the cell shape was a polygon with uncertain sides. Previous research has shown that stochastic pores are not conducive to obtaining high compressive properties for porous structures due to higher stress concentration and earlier local failures, while ordered porous structures exhibit relatively uniform stress distribution and excellent mechanical properties in the family of porous structures [7,8]. Hence, more and more researchers are focusing on the study of ordered porous structures. In recent years, a variety of ordered porous structures can be fabricated with the advent and development of the additive manufacturing (AM) technique, especially the rapid development of selective laser melting (SLM). SLM technology, which is one of the advanced AM processes, is widely used in manufacturing metal porous structures due to its short process cycle and wide molding range [9]. The ordered porous structures with different cells, such as rhombic dodecahedron [10], octahedral [11], diamond [12] cubic [12], body-centered cubic [13], crystal-line lattice [14], and honeycomb [15], have been developed and widely concerned in previous work. These studies mainly focus on the effect of cellular structures on mechanical performance. With AM technology maturing, in addition to the various structural design and mechanical properties, more works starts to investigate how to obtain an ideal structure with excellent compressive properties and energy absorption when they are used as lightweight structure components and energy absorption devices [16–18]. At present, most of the porous structure designs that are widely concerned are solid strut structures. However, only a small number of people pay attention to the hollow strut structures, and some studies have shown that hollow strut structures can achieve better compression performance compared to foam and solid strut structures of a similar relative density [19]. For example, Douglas et al. [20] compared hollow and solid truss pyramidal sandwich structures with the same relative density of 2.8%, and results indicated that the peak stress of the hollow truss structures was approximately twice than that of the solid. Evans et al. [21] theoretically studied the energy absorption characteristics of hollow tube microlattice structures and demonstrated that the hollow tube microlattice structures presented promising performance indices due to the higher second area moments of hollow struts. Additionally, Liu et al. [22] further found that the dynamic energy absorption of hollow microlattice structures was significantly higher than the quasi-static. Zhao et al. [23] concluded that the energy absorption of the hollow structures can be significantly enhanced by inertial stabilization, a shock wave effect and strain rate hardening effect under dynamic loading. Although hollow strut structures present a significant advantage of compression performance in the porous structure family, how to further promote the energy absorption potential of hollow strut structures is still a challenging task. Liu et al. [24] designed the hollow microlattice structures and proposed several strategies to improve the energy absorption indices: (1) tube wall with gradient thickness can generate plastic buckling from top to bottom during compression, thereby avoiding a sudden collapse of hollow struts and improving energy absorption capacity; (2) using tube with gradient variation of radius makes the plastic deformation propagate progressively and raises the energy absorption density by over 40%; (3) hollow microlattice with water filler strengthens the microlattice via circumference expansion and suppression local wrinkles increases the volume energy absorption density by more than 100%. In this work, an innovative design method was introduced to improve the compressive properties and energy absorption of hollow strut structures. Namely, the interior of hollow struts was redesigned through adding a series of tubular internal microstructures to strengthen resistance to external load, which was expected to obtain an effective way to improve compression performance from within the hollow struts. Thereafter, a series of hollow truss structures with different internal structures were designed and manufactured using the selective laser melting technique. Quasi-static compression experiments were carried out so as to investigate how the mechanical behavior and energy absorption of the hollow truss structures change with the different internal microstructures. This study was expected to demonstrate that a reasonable addition of internal microstructures was conducive to improving the compressive properties and energy absorption capability for hollow truss structures. Materials 2020, 13, x 3 of 14 Materials 2020, 13, 5094 3 of 14

2. Materials and Methods 2. Materials and Methods 2.1. Design of Hollow Truss Structures 2.1. Design of Hollow Truss Structures Hollow truss structures were modeled by the Solidworks software (2014sp 1.0, Dassault aircraft company,Hollow Par trussis, France) structures in this were work. modeled Axisymmetric by the Solidworks semi-unit software cells and (2014sp full-size 1.0, Dassaultspecimens aircraft were exhibitedcompany, in Paris, Figure France) 1 to clearly in this show work. the Axisymmetric structural characte semi-unitristics. cells Each and cell full-size was repeated specimens along were the normalexhibited coordinate in Figure axis,1 to clearlyand three show-unit the cells structural in each characteristics.axis were patterned Each to cell obtain was repeateda full-size along truss structure.the normal It coordinate can be observed axis, and that three-unit the truss cells structures in each were axis generated were patterned using to the obtain network a full-size struts. Meanwhile,truss structure. the It joint can be regions observed were that strengthened the truss structures by chamfers were generated to avoid using easy breakagethe network in struts. these positions.Meanwhile, the joint regions were strengthened by chamfers to avoid easy breakage in these positions.

Figure 1. SemiSemi-cellular-cellular models models and and corresponding design specimens: ( (aa)) semi semi-cellular-cellular model model of hollow truss, ( b)) basic hollow truss structure (specimen HT), ( c) semi-cellularsemi-cellular model with tubular microstructures at joint, ( d) hollow truss structure with internal microstructures at joints (specimen HTSJ), ((ee))semi-cellular semi-cellular model model with with tubular tubular microstructures microstructures on tube on walls, tube andwalls, (f) andhollow (f) truss hollow structure truss structurewith internal with microstructures internal microstr onuctures tube walls on tube (specimen walls (specimen HTSW). HTSW).

The ﬁrst group of truss structures was composed using hollow struts as shown in Figure1a,b, The first group of truss structures was composed using hollow struts as shown in Figure 1a,b, and the second group of truss structures was constructed by hollow struts with orthogonal tubular and the second group of truss structures was constructed by hollow struts with orthogonal tubular microstructures at the joints, which are displayed in Figure1c,d. The third group of truss structures microstructures at the joints, which are displayed in Figure 1c,d. The third group of truss structures was strengthened by tubular microstructures on the tube walls of hollow struts, and the corresponding was strengthened by tubular microstructures on the tube walls of hollow struts, and the structural characteristics are presented in Figure1e,f. Herein, it should be pointed out that the tubular corresponding structural characteristics are presented in Figure 1e,f. Herein, it should be pointed out microstructure positions of the second and third groups of specimens were completely complementary. that the tubular microstructure positions of the second and third groups of specimens were For the convenient record, the three groups of specimens (basic hollow truss structure, hollow truss completely complementary. For the convenient record, the three groups of specimens (basic hollow trussstructure structure, with internal hollow microstructure truss structure at joints, with and internal hollow microstructure truss structure at with joints, internal and microstructure hollow truss on tube walls) were named in sequence: specimen HT, specimen HTSJ and specimen HTSW, structure with internal microstructure on tube walls) were named in sequence: specimen HT, which are exhibited in Figure1b,d,f, respectively. The dimension of unit cells was 5 5 5 mm3 specimen HTSJ and specimen HTSW, which are exhibited in Figure 1b,d,f, respectively.× × The = = = dimension(L W of unitH cells5 mm was), 5 and× 5 radius× 5 mmRof (L the= W chamfer= H = is5 mm 1.3), mm. and Atradius the sameR of the time, chamfer the internal is 1.3 mm.geometrical At the same parameters time, the of theinternal cells geometrical are listed in Tableparameters1. of the cells are listed in Table 1.

Table 1. Details of design parameters of the specimens.

Specimen () () () () (mm) HT 2.4 1.6 - - -

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Table 1. Details of design parameters of the specimens.

Specimen D (mm) d1 (mm) d2 (mm) H1 (mm) L1(mm) HT 2.4 1.6 - - - HTSJ 2.4 1.6 0.8 2.5 2.5 HTSW 2.4 1.6 0.8 2.5 2.5

Note: structural parameters (D, d1, d2,H1,L1) were marked in Figure1a,c,e.

2.2. Fabrication and Tests The designed hollow truss structures were fabricated using Ti-6Al-4V powder in the present study. The Ti-6Al-4V powder was grade 23 with spherical particle sizes of 20–63 µm. The manufacturing process was carried out by using selective laser melting (FS121M, Farsoon High-technology company, Changsha, China). The approach most utilized for describing the manufacturing process is though the volumetric energy density (E), which is expressed as follows:

P E = (1) v h t · · where P, v, h, and t represent laser power, scanning speed, hatch spacing, and layer thickness, respectively. The detailed processing parameters applied to the present manufacturing process are listed in Table2. Three duplicates were prepared for the design of each group. Table3 lists the measured parameters (ρ) of the printed specimens. The measured densities of the specimens were calculated by dividing the volume of hollow truss structures with the mass of measured specimens. In general, the relative density (ρ) was determined as follow [13]:

ρ = ρ/ρ 100% (2) 0 × 3 Here ρ0 is the density of the matrix Ti-6Al-4V material (4.35 g/cm ).

Table 2. The process parameters used for manufacturing hollow truss structures.

Process Parameters Values Laser power (W) 190 Scanning speed (mm/s) 900 Hatch spacing (µm) 100 Layer thickness (µm) 30 Volumetric energy density (J mm 3) 70 · −

Table 3. Measured parameters of the printed specimens.

Specimen Volume (mm3) Mass (g) Density ρ(g/cm3) Relative Density ρ(%) HT 15.12 15.07 15.08 4.03 0.16 1.19 0.04 28.26 0.66 × × ± ± ± HTSJ 15.10 15.18 15.06 4.85 0.23 1.43 0.07 34.07 0.81 × × ± ± ± HTSW 15.19 15.15 15.07 5.31 0.31 1.57 0.03 37.16 0.78 × × ± ± ±

The structures of specimen HT, which was selected as the representative of all printed specimens, were observed by a Scanning Electron Microscope (SEM, S-4800, Hitachi Limited, Tokyo, Japan). It can be found that the morphologies of the local surface were slightly different, as shown in Figure2. Melted powder adhesion was clearly observed in the structural outer surface, and, especially, the adhesion of powder particles on the side surfaces was more serious than the top surface and the bottom surface. In fact, the adhesion of powder affects the dimensional accuracy of fabricated structures [25]. In this work, to minimize the effect of adhesion particles on mechanical responses, all specimens were loaded along the top surface and bottom surface, which was also the printing Materials 2020, 13, 5094 5 of 14 orientation of the specimens. The electron universal testing machine (WDW-300, Changchun Kexin Company, Changchun, China) was employed to perform the compression tests at a strain rate of 3 1 10− s− . Moreover, a high definition digital camera (i-SPEED 3, Olympus corporation, Tokyo, Japan) wasMaterials utilized 2020, 1 to3, x record the deformation behavior of the specimens during the compression. 5 of 14

FigureFigure 2.2. Macro-Macro- and micro micro-observations:-observations: ( (aa)) printed printed specimen specimen HT, HT, (b (b) )top top local local surface, surface, (c ()c )bottom bottom locallocal surface,surface, andand ((dd,,ee)) sideside locallocal surfaces.surfaces.

TheThe followingfollowing compressivecompressive propertiesproperties ofof hollowhollow trusstruss structuresstructures werewere determineddetermined accordingaccording toto ISO13314-2011:ISO13314-2011: quasi-elasticquasi-elastic gradient gradient (E), (E), yield yield strength strength (σ y(),σ first), first maximum maximum compressive compressive strength strength (σc) and(σ) plateauand plateau stress stress (σp). ( Theσ). quasi-elasticThe quasi-elastic gradient gradient is the is gradient the gradient of the of straight the straight line in line the linear-elasticin the linear- stage.elastic The stage. yield The strength yield strength is the 0.2% is the off set 0.2% yield offset stress. yield The stress. first The maximum first maximum compressive compressive strength isstrength defined is from defined the initial from peak the initial stress peak in the stress stress–strain in the stress curve.–strain The plateau curve. stress The pla isteau calculated stress as is thecalculated mean stress as the between mean stress 20% andbetween 40% compressive20% and 40% strain. compressive strain.

3.3. Results CompressionCompression teststests werewere performedperformed toto investigateinvestigate thethe compressivecompressive propertiesproperties andand deformationdeformation behaviorbehavior ofof thethe hollowhollow trusstruss structures.structures. TheThe engineeringengineering stress–strainstress–strain curvescurves andand thethe correspondingcorresponding deformationdeformation process process are are exhibited exhibited in Figure in Figure3. In 3. terms In terms of specimen of specimen HT, the HT, stress–strain the stress curve–strain exhibits curve typicalexhibits three-stage typical three characteristics.-stage characteristics. The first The stage first is the stage linear-elastic is the linear stage-elastic where stage the where stress increasesthe stress almostincreases linearly almost with linea increasingrly with increasing strain, and strain, the specimen and the specimenis initially is deformed initially deformed by elastic by buckling elastic ofbu verticalckling of struts vertical (Figure struts3 (a-A)).(Figure Then,3a-A). theThen, curve the curve reaches reaches yield yield strength strength and slowlyand slowly increases increases to theto the first first maximum maximum compressive compressive strength. strength. At At the the same same time, time, plastic plastic yield yield occurs occurs in thein the vertical vertical struts struts of theof the specimen specimen (Figure (Figure3(a-B)). 3a Afterwards,-B). Afterwards, the second the second stage is stage initiated is initiated following following a post-yield a postsoftening-yield upsoftening to the onset up to of the densification, onset of densification, and this stage and known this as stage the plateau known stage as the and plateau is accompanied stage and by is significantaccompanied stress by fluctuations. significant stress In this flu stage,ctuations. each stress In this drop stage, corresponds each stress to dropthe collapse corresponds of a random to the porecollapse layer. of Fora random example, pore when layer. the For compressive example, strainwhen is the 13% compressive (Figure3(a-C)), strain specimen is 13% HT(Figure exhibits 3a-C), a brittlespecimen fracture HT exhibits in the corresponding a brittle fracture pore in layers.the corresponding Subsequently, pore the layers. rest of Subsequently, the structure supportsthe rest o loadf the untilstructure the strain supports approaches load until 20% the (Figure strain 3approaches(a-D)), and 20% the next(Figure collapse 3a-D), layer and isthe crushed. next collapse The collapse layer is modecrushed. is seen The as collapse the failure mode mode is of seen layer-by-layer as the failure manner. mode At of last, layer the-by compressive-layer manner. curve At enters last, into the thecompressive densification curve stage enters where into thethe stressdensification starts to stage increase where exponentially. the stress starts Meanwhile, to increase the exponentially. specimen is graduallyMeanwhile, forced the specimen into self-contact is gradually resulting forced in theinto porous self-contact structure resulting being in squeezed the porous into structure bulk solids. being squeezed into bulk solids. Similar compressive characteristics are presented in the loading process of specimens HTSJ and HTSW. However, there are still some differences between the specimens. (i) Specimen HTSW exhibits a remarkably higher yield strength and first maximum compressive strength (Figure 3c). Meanwhile, the plateau stress of specimen HTSW shows relatively stable fluctuations compared to specimens HT and HTSJ. (ii) The collapse positions of specimen HT and HTSJ are located in the middle of struts (Figure 3a-C and Figure 3b-C), but specimen HTSW is collapsed in joint regions of truss structures (Figure 3c-B). (iii) The fracture surfaces of the collapsed struts for specimens HT and HTSJ show an angle of 45° from the loading direction. In contrast, the fracture of specimen HTSW is nearly parallel to the loading direction. (iv) The collapse layers of specimen HT and HTSJ occur in horizontal relative movement during the collapse, and the inclinations of the deformed specimens are 25° and 27° at a strain of 0.4 (Figure 3a-E and Figure 3b-E), respectively. Nevertheless, the collapse layers of specimen

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HTSW extend around the loading direction (Figure 3c-E) and the inclination of specimen HTSW is nearly 13° (nearly half the inclination of the deformed specimens HT and HTSJ), which exhibits the relativelyMaterials 2020 superior, 13, 5094 structural stability of specimen HTSW during the compression. 6 of 14

Figure 3. The stress–strain curves and deformation characteristics of the different specimens (a) specimen HT, (b) specimen HTSJ and (c) specimen HTSW. Figure 3. The stress–strain curves and deformation characteristics of the different specimens (a) specimen HT, (b) specimen HTSJ and (c) specimen HTSW. Similar compressive characteristics are presented in the loading process of specimens HTSJ and HTSW. However, there are still some differences between the specimens. (i) Specimen HTSW 4. Discussion exhibits a remarkably higher yield strength and first maximum compressive strength (Figure3c). 4.1.Meanwhile, Effect of Internal the plateau Microstructures stress of specimen on Mechanical HTSW Properties shows relatively stable fluctuations compared to specimens HT and HTSJ. (ii) The collapse positions of specimen HT and HTSJ are located in the middle of strutsThe mechanical (Figure3(a-C,b-C)), parameters but of specimen different HTSW specimens is collapsed determined in joint according regions to of ISO13314 truss structures-2011 are compared(Figure3(c-B)). in Table (iii) The4. Herein, fracture specific surfaces parameters of the collapsed are applied struts forby dividing specimens the HT measured and HTSJ density show anof truss structures with corresponding mechanical parameters of the specimens to highlight the effect angle of 45◦ from the loading direction. In contrast, the fracture of specimen HTSW is nearly parallel ofto the internal loading microstructures. direction. (iv) The Meanwhile, collapse layers a dimensionless of specimen HT parameter and HTSJ is occur called in horizontal the stress relative drop movement during the collapse, and the inclinations of the deformed specimens are 25 and 27 at a ◦ ◦ strain of 0.4 (Figure3(a-E) and Figure3(b-E)), respectively. Nevertheless, the collapse layers of specimen HTSW extend around the loading direction (Figure3(c-E)) and the inclination of specimen HTSW Materials 2020, 13, 5094 7 of 14

is nearly 13◦ (nearly half the inclination of the deformed specimens HT and HTSJ), which exhibits the relatively superior structural stability of specimen HTSW during the compression.

4. Discussion

4.1. Effect of Internal Microstructures on Mechanical Properties The mechanical parameters of different specimens determined according to ISO13314-2011 are compared in Table4. Herein, specific parameters are applied by dividing the measured density of truss structures with corresponding mechanical parameters of the specimens to highlight the effect of internal microstructures. Meanwhile, a dimensionless parameter is called the stress drop coefficient (θ), expressed as θ = ∆σ/σc to characterize the stability of plateau stress [26]. Here, ∆σ is the difference value between the first maximum compressive strength and the adjacent valley stress.

Table 4. Mechanical parameters of the diﬀerent specimens.

Specimen E E/ρ σy σy/ρ σc σc/ρ σp σp/ρ θ HT-1# 2137.25 1789.99 128.10 107.29 162.57 136.16 124.35 104.15 0.82 HT-2# 2233.46 1870.57 131.02 109.73 167.52 140.30 113.45 95.02 0.76 HT-3# 2330.63 1951.95 135.18 113.22 163.68 137.09 107.15 89.74 0.83 Average 2237.50 1873.95 131.72 110.31 163.59 137.00 112.88 94.51 0.78 Stand. dev. 93.13 78.00 3.46 2.91 3.93 3.30 5.73 9.64 0.05 HTSJ-1# 2569.43 1788.05 145.85 101.50 170.00 118.30 161.45 112.35 0.79 HTSJ-2# 2507.29 1751.77 151.08 105.14 176.09 122.54 160.95 112.00 0.91 Average 2518.60 1745.02 149.21 103.83 173.11 120.47 161.31 112.25 0.82 Stand. dev. 51.37 43.03 3.36 1.31 2.98 2.07 0.36 0.25 0.09 HTSW-1# 2830.74 1799.58 199.33 126.72 242.37 154.08 161.95 102.96 0.54 HTSW-2# 2643.13 1680.31 193.29 122.88 244.38 155.36 171.00 108.71 0.44 HTSW-3# 2641.07 1679.00 193.02 122.71 247.12 157.10 180.00 114.43 0.50 Average 2701.02 1717.11 197.57 125.60 244.61 155.51 169.87 107.99 0.47 Stand. dev. 129.72 82.47 4.55 2.89 2.51 1.59 10.13 6.44 0.07 − Note: the units of parameters and speciﬁc parameters are MPa and MPa g 1 cm3, respectively. · − ·

It can be seen from Table4 that specimen HTSW exhibits superior compressive properties. For instance, the yield strength, first maximum compressive strength and plateau stress of specimen HTSW increase by nearly 50% in comparison to specimen HT. At the same time, the increase ratios of specific yield strength, specific first maximum compressive strength and specific plateau stress of specimen HTSW are 14% compared to the corresponding parameters of specimen HT. However, the yield strength and first maximum compressive strength of specimen HTSJ only experience a close to 10% increase compared to specimen HT. Meanwhile, the specific yield strength and specific first maximum compressive strength of specimen HTSJ are even lower than those of specimen HT. This indicates that adding microstructures into tube walls of the hollow truss structure (such as specimen HTSW) is more conducive to improving the compressive properties. Additionally, the stress drop coefficients of the different specimens are compared, and the coefficient of specimen HTSW is significantly lower than the other two sets of specimens. A lower coefficient of stress drop means a better compression stability to some extent. Apparently, specimen HTSW presents a relatively excellent compression stability during the collapse. In order to reveal the reason for the differences in compressive properties of the specimens, LS-DYNA was employed to describe the compressive behavior [27]. Finite element models of unit cells for specimens HT, HTSJ, and HTSW were established, and the elastic-plastic material model was applied to describe the behavior of matrix material. The parameters are as follows: density ρ = 4.35 g/cm3, elastic modulus E = 110 GPa, yield strength σy = 1080 MPa, and Poisson’s ratio µ = 0.3. The cells 3 1 were loaded from the top surface to bottom surface at a fixed strain rate of 10− s− . Figure4 shows Materials 2020, 13, 5094 8 of 14 the stress distribution of cells and sectional views. It can be seen that the stress concentration of the cells for specimens HT and the HTSJ mainly occurs in the struts along the loading direction, while the stress concentration of the cell for specimen HTSW appears at the joint region. The sectional views clearly show the internal geometry of the different cells and the stress concentration regions are very close to structural weaknesses parallel to the loading direction, as shown in Figure4b,d,f. It should be noted that the internal microstructures of specimen HTSW reinforce the structural weakness of hollow struts, while the internal microstructures of specimen HTSJ strengthen the non-weak regions of hollow struts. Stress-strain curves of the different cells were extracted from the numerical simulation as shown in Figure5, and the results show that the compressive stresses were all increased with the addition of microstructures inside the cells. Thus, it can be concluded that adding different internal microstructures changes the structural weaknesses of the original cells and leads to the different bearing capacities of the cells. Moreover, compared to the cell of specimen HTSJ, the compressive MaterialsstressMaterials of 2020 the2020,, 1 cell133,, xx for specimen HTSW is higher. This indicates that strengthening the internal weakness88 ofof 1414 of the cells parallel to the loading direction is a more effective way to improve the mechanical mechanicalproperties.mechanical Therefore,properties.properties. specimen ThereTherefore,fore, HTSW specimenspecimen presents HTSWHTSW superior presentspresents mechanical superiorsuperior properties mechanicalmechanical in all propertiesproperties specimens inin due allall specimenstospecimens strengthening duedue toto the strengtheningstrengthening internal weaknesses thethe internalinternal of the weaknessesweaknesses cells. ofof thethe cells.cells.

FigureFigure 4.4. StressStress distributiondistribution andand sectionalsectionalsectional view viewview ABCD ABCDABCD at atat the thethe strain strainstrain of ofof 3%: 3%:3%: ( a ((,aab,,b)b) the) thethe cell cellcell of ofof specimen specimenspecimen HT, HT,(HT,c,d) (( thecc,,dd)) cell thethe of cecell specimenll ofof specimenspecimen HTSJ, HTSJ,HTSJ, and (andande,f) ( the(ee,,ff)) cell thethe of cellcell specimen ofof specimenspecimen HTSW. HTSW.HTSW.

FigureFigure 5. 5. StressStress-strainStress--strainstrain curves curves of of the the different didifferentﬀerent cells cells obtained obtained by by numerical numerical simulation.simulation.

4.2.4.2. EffectEffect ofof InternalInternal MicrostructuresMicrostructures onon DeformationDeformation FailureFailure AAlthoughlthough the the specimens specimens exhibit exhibit the the same same failurefailure mode mode in in a a layer layer--byby--layerlayer manner manner during during compression,compression, therethere areare stillstill somesome differencesdifferences affectedaffected byby internalinternal microstructuresmicrostructures suchsuch asas collapsecollapse position,position, fracture fracture surface, surface, etc.etc. InIn order order to to visually visually reveal reveal the the effect effect ofof internalinternal microstructuresmicrostructures on on deformdeformationation failure, failure, a a numerical numerical simulation simulation is is used used to to describe describe the the collapse collapse process. process. Herein, Herein, maximummaximum shearshear strainstrain failurefailure criterioncriterion isis applied,applied, whichwhich isis setset toto 0.150.15 totaltotal shearshear strain.strain. TheThe collcollapseapse processprocess ofof locallocal cellscells isis onlyonly simulated,simulated, whichwhich isis enoughenough toto rerevealveal thethe failurefailure characteristicscharacteristics ofof hollowhollow trusstruss structures.structures. FigureFigure 66 exhibitsexhibits thethe stressstress distributiondistribution andand deformationdeformation statestate ofof thethe locallocal cellscells forfor specimensspecimens HTHT andand HTSJHTSJ toto revealreveal thethe effecteffect ofof internalinternal microstructuresmicrostructures onon collapsecollapse positions.positions. ItIt cancan bebe vivivividlydly seenseen thatthat thethe hollowhollow strutsstruts parallelparallel toto thethe loadingloading directiondirection areare thethe mainmain bearingbearing microstructuresmicrostructures basedbased toto thethe stressstress distribution,distribution, whichwhich cancan bebe clearlyclearly observedobserved atat thethe strainstrain ofof 0.02.0.02. Then,Then, thethe hollowhollow strutsstruts betweenbetween thethe upperupper andand lowerlower cellscells collapsecollapsedd inin thethe middlemiddle ofof strutsstruts asas thethe strainstrain increasedincreased toto 0.12.0.12. InIn orderorder toto fullyfully revealreveal thethe failurefailure characteristics,characteristics, aa sectionalsectional viewview ABCDABCD ofof thethe locallocal cellscells waswas extrextracted.acted. ItIt cancan bebe observedobserved thatthat thethe stressstress concentrationconcentration ofof specimenspecimen HTHT isis obviousobvious inin thethe holloholloww strutsstruts parallelparallel toto the the loading loading direction. direction. The The stress stress concentration concentration regions regions also also correspond correspond to to the the structural structural

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4.2. Effect of Internal Microstructures on Deformation Failure Although the specimens exhibit the same failure mode in a layer-by-layer manner during compression, there are still some differences affected by internal microstructures such as collapse position, fracture surface, etc. In order to visually reveal the effect of internal microstructures on deformation failure, a numerical simulation is used to describe the collapse process. Herein, maximum shear strain failure criterion is applied, which is set to 0.15 total shear strain. The collapse process of local cells is only simulated, which is enough to reveal the failure characteristics of hollow truss structures. Figure6 exhibits the stress distribution and deformation state of the local cells for specimens HT and HTSJ to reveal the effect of internal microstructures on collapse positions. It can be vividly seen that the hollow struts parallel to the loading direction are the main bearing microstructures based to the stress distribution, which can be clearly observed at the strain of 0.02. Then, the hollow struts between the upper and lower cells collapsed in the middle of struts as the strain increased to 0.12. In order to fully reveal the failure characteristics, a sectional view ABCD of the local cells was extracted. It can be observed that the stress concentration of specimen HT is obvious in the hollow struts parallel to theMaterials loading 2020 direction., 13, x The stress concentration regions also correspond to the structural weaknesses9 of 14 of the cells, which are marked by the black arrow in Figure6a. Afterwards, the collapse position weaknesses of the cells, which are marked by the black arrow in Figure 6a. Afterwards, the collapse appears in the structural weaknesses. The internal microstructures of specimen HTSJ reinforce the joint position appears in the structural weaknesses. The internal microstructures of specimen HTSJ regions (non-weak regions of the cell), and the stress concentration also occurs in the hollow struts reinforce the joint regions (non-weak regions of the cell), and the stress concentration also occurs in as shownthe hollow in Figure struts6b. as Fromshown the in Figure failure 6b. mechanism From the failure of specimens mechanism HT of and specimens HTSJ, itHT can and be HTSJ, concluded it that thecan structuralbe concluded weaknesses that the structural (the middle weaknesses of hollow (the middle struts) of parallel hollow struts) to the parallel loading to directionthe loading cause the stressdirection concentration cause the stress and lead concentration to the collapse and lead of tohollow the collapse struts. of Actually, hollow struts.the collapse Actually, position the is largelycollapse determined position by is thelargely structural determined weakness by the structural in the loading weakn direction.ess in the loading direction.

FigureFigure 6. Stress 6. Stress distribution distribution and and deformation deformation state predicated predicated by by numerical numerical simulation: simulation: (a) the (a local) the local cells ofcells specimen of specimen HT HT and and (b) (b the) the local local cells cells of of specimen specimen HTSJ. HTSJ.

Figure 7 displays the deformation evolution of the unit cell for specimen HTSW. It intuitively shows that the stress concentration mainly occurs at the joint region of the cell, which can be clearly observed at the strain of 0.04. Compared to the hollow struts of specimen HT, the hollow struts of specimen HTSW are strengthened by internal microstructures. The joint region of specimen HTSW becomes the structural weakness, and the stress concentration mainly occurs in the region marked by the black arrow in Figure 7. With the compressive strain increasing, the joint region gradually collapses. Then, the hollow strut inserts into the abdomen of the joint region, and the collapsed cell extends around the loading direction. Therefore, it can be summarized that the failure mechanism of hollow truss structures is closely related to the structural weaknesses parallel to the loading direction. Different internal microstructures change the structural weaknesses inside the cells, cause the different stress concentrations and affect the collapse position of truss structures. In fact, the collapse of the cell around the loading direction is conducive to obtaining better compressive stability of the specimens during the collapse, which can be confirmed by the aforementioned stress drop coefficient. Moreover, the internal microstructures affect the characteristics of the fracture surfaces of the specimens. The fracture surfaces of the struts for specimens HT and HTSJ show the angle of 45° from

Materials 2020, 13, 5094 10 of 14

Materialsspecimen 2020 HTSW, 13, x are strengthened by internal microstructures. The joint region of specimen10 HTSW of 14 becomes the structural weakness, and the stress concentration mainly occurs in the region marked theby theloading black direction, arrow in while Figure the7. fracture With the surface compressive of specimen strain HTSW increasing, is almost the jointparallel region to the gradually loading direction.collapses. The Then, fracture the hollow surface strut with inserts a 45° intoangle the of abdomeninclination of can the be joint attributed region, to and the the development collapsed cell of maximumextends around shear thestress, loading which direction. is oriented Therefore, diagonally it can to bethe summarized direction of compression that the failure [28]. mechanism The failure of mechanismhollow truss can structures be revealed is closely from related the pla tostic the deformation structural weaknesses of larger grains. parallel The to thelarger loading grains direction. within theDiff materialerent internal deform microstructures with a rotation change that gives the structural rise to localized weaknesses softening inside and the is cells, propagated cause the along different the diagonalstress concentrations surface [28,29]. and aItff shouldect the collapsebe pointed position out that of truss the structures.fracture surface In fact, of the the collapse simulated of the struts cell shownaround in the Figure loading 6 is direction a failure isto conducive describe the to obtaining45° shear betterangle compressivedue to grid interference, stability of the but specimens this does notduring affect the revealing collapse, the which failure can characteristics be confirmed byof the cells. aforementioned stress drop coefficient.

FigureFigure 7. 7. StressStress distribution distribution and and deformation deformation evolution evolution of of unit unit cell cell for for specime specimenn HTSW. HTSW.

4.3. EffectMoreover, of Internal the Microstructures internal microstructures on Energy Absorption affect the characteristics of the fracture surfaces of the specimens. The fracture surfaces of the struts for specimens HT and HTSJ show the angle of 45◦ from the loadingThe effect direction, of internal while microstructures the fracture surface on the of energy specimen absorption HTSW is of almost a hollow parallel truss to structure the loading is investigated in this section. It is expected that a more ideal energy-absorbing structure will be direction. The fracture surface with a 45◦ angle of inclination can be attributed to the development of obtainedmaximum through shear stress, the internal which is design oriented of diagonally hollow truss to the structures. direction Here, of compression the energy [28 absorption]. The failure is determined as [23]: mechanism can be revealed from the plastic deformation of larger grains. The larger grains within the material deform with a rotation that gives rise to localized softening and is propagated along W = σ(ε)dε (3) the diagonal surface [28,29]. It should be pointed out that the fracture surface of the simulated struts shown in Figure6 is a failure to describe the 45 shear angle due to grid interference, but this does not ◦ ∫ σ(ε)dε affect revealing the failure characteristics ofW the= cells. (4) ρ 4.3. Effect of Internal Microstructures on Energy Absorption where W and W are the energy absorption capacity (energy absorption per unit volume) and specificThe energy effect absorption of internal (energy microstructures absorption on per the unit energy mass), absorption respectively. of a hollow ε is the truss specified structure strain is andinvestigated σ is the incompressive this section. stress. It is expected Besides, thatenergy a more absorption ideal energy-absorbing efficiency is also structure investigated will beto evaluate obtained thethrough energy the absorption internal design behavior of hollow which truss can structures. be expressed Here, as the[30]: energy absorption is determined as [23]: Z∫ σε(ε)dε (5) Wη = σ(ε)d ε (3) v σε 0 where σ is the maximum stress before the specified strain. Figure 8 presents the energy absorption capacity and specific energy absorption at different strains. Figure 8a shows that specimen HTSW has an excellent energy absorption capacity compared to specimens HT and HTSJ. For example, the energy absorption capacity of specimen HTSW increases that of specimen HT by 52% and that of specimen HTSJ by 30% at a strain of 0.5, respectively. The reason is that specimen HTSW strengthens the structural weaknesses of specimen HT, improves the compressive stability of plateau stress, and so significantly increases the energy absorption capacity.

Materials 2020, 13, x 11 of 14

This indicates that strengthening internal weaknesses of truss structures are conducive to improving energy absorption per unit volume. Deshpande [2] grouped the porous structures into two categories: stretch-dominated structures and bending-dominated structures. Here, for a comprehensive comparison, the W − ε curves of bending-dominated structures (diamond [12], rhombic dodecahedron [31]), stretching-dominated structures (cubic [12] and truncated cuboctahedron [12]) and titanium foam [32] were obtained to compare the energy absorption capacity of the hollow truss structures (stretch-dominated structure in this work). It is worth noting that the matrix material of bending-dominated and stretching- dominated structures is all Ti-6Al-4V, and their relative densities range from 24% to 37%. Although the relative density of the diamond structure, cubic structure, titanium foam, specimen HTSJ and HTSW are very close, specimen HTSW exhibits a stronger energy absorption capacity than the other specimens. In fact, this further verifies that strengthening the internal weaknesses of the hollow truss structures does help to improve the energy absorption capacity.

MaterialsConsidering2020, 13, the 5094 effect of specimen mass, the specific energy absorption W of all specimens11 of 14 is presented in Figure 8b. The W − ε curves show that specimen HTSW has the highest specific energy absorption during compression. For example,R ε the energy absorption per unit mass of σ(ε)dε specimen HTSW increases that of specimenW HT= by0 15%, and that of specimen HTSJ by 18%(4) at the m ρ strain of 0.5. Specimen HTSW reinforces the structural weaknesses of the hollow struts, improves the stabilitywhere ofW plateauv and W stress,m are the and energy increases absorption the energy capacity absorption (energy absorption capacity per per unit unit volume) mass. and This specific reveals energy absorption (energy absorption per unit mass), respectively. ε is the specified strain and σ is that strengthening the internal weaknesses of the hollow truss structure is also good for improving the compressive stress. Besides, energy absorption efficiency is also investigated to evaluate the energy energy absorption per unit mass. absorption behavior which can be expressed as [30]: Figure 9 presents the η − ε curve characteristics of the specimens including the rising stage, the R ε stable stage and the declining stage. In the rising stageσ(ε) dofε the curve, the energy absorption efficiency η = 0 (5) increases rapidly. Next, a relatively steady stage σofmax theε energy absorption efficiency within a wide strain range, which is related to the plateau stage of the compressive stress–strain curve, is found. At where σ is the maximum stress before the specified strain. the decliningmax stage, the energy absorption efficiency gradually decreases. Specimen HT has the most Figure8 presents the energy absorption capacity and specific energy absorption at di fferent superiorstrains. energy Figure absorption8a shows that efficiency specimen including HTSW has the an excellenthighest efficiency energy absorption peak and capacity later compareddecay behavior to , resultingspecimens from HT its and relatively HTSJ. For stableexample, plateau the energy stress absorption and wid capacitye strain of specimen range. HTSW Although increases the that energy absorptionof specimen efficiency HT by of 52% specimen and that HTSW of specimen takes HTSJ second by 30% place, at a its strain η − ofε 0.5, curve respectively. has minimal The reason fluctuation is over thatthe specimenentire strain HTSW range, strengthens which the shows structural that weaknesses specimen ofHTSW specimen presents HT, improves the best the stability compressive during compression.stability of This plateau shows stress, to and some so significantlyextent that increasesstrengthening the energy the absorptioninternal weaknesses capacity. This of indicates the hollow trussthat structure strengthening is beneficial internal to weaknesses improve compressive of truss structures stability are conducive in the energy to improving absorption energy process. absorption per unit volume.

Figure 8. Energy absorbed at different strains: (a) energy absorption per unit volume and (b) energy absorption per unit mass. Figure 8. Energy absorbed at different strains: (a) energy absorption per unit volume and (b) energy absorptionDeshpande per unit [2] mass. grouped the porous structures into two categories: stretch-dominated structures and bending-dominated structures. Here, for a comprehensive comparison, the Wv ε curves of − bending-dominated structures (diamond [12], rhombic dodecahedron [31]), stretching-dominated structures (cubic [12] and truncated cuboctahedron [12]) and titanium foam [32] were obtained to compare the energy absorption capacity of the hollow truss structures (stretch-dominated structure in this work). It is worth noting that the matrix material of bending-dominated and stretching-dominated structures is all Ti-6Al-4V, and their relative densities range from 24% to 37%. Although the relative density of the diamond structure, cubic structure, titanium foam, specimen HTSJ and HTSW are very close, specimen HTSW exhibits a stronger energy absorption capacity than the other specimens. In fact, this further verifies that strengthening the internal weaknesses of the hollow truss structures does help to improve the energy absorption capacity. Considering the effect of specimen mass, the specific energy absorption Wm of all specimens is presented in Figure8b. The Wm ε curves show that specimen HTSW has the highest specific − energy absorption during compression. For example, the energy absorption per unit mass of specimen HTSW increases that of specimen HT by 15%, and that of specimen HTSJ by 18% at the strain of 0.5. Specimen HTSW reinforces the structural weaknesses of the hollow struts, improves the stability Materials 2020, 13, 5094 12 of 14 of plateau stress, and increases the energy absorption capacity per unit mass. This reveals that strengthening the internal weaknesses of the hollow truss structure is also good for improving energy absorption per unit mass. Figure9 presents the η ε curve characteristics of the specimens including the rising stage, − the stable stage and the declining stage. In the rising stage of the curve, the energy absorption efficiency increases rapidly. Next, a relatively steady stage of the energy absorption efficiency within a wide strain range, which is related to the plateau stage of the compressive stress–strain curve, is found. At the declining stage, the energy absorption efficiency gradually decreases. Specimen HT has the most superior energy absorption efficiency including the highest efficiency peak and later decay behavior, resulting from its relatively stable plateau stress and wide strain range. Although the energy absorption efficiency of specimen HTSW takes second place, its η ε curve has minimal fluctuation − over the entire strain range, which shows that specimen HTSW presents the best stability during compression. This shows to some extent that strengthening the internal weaknesses of the hollow truss

Materialsstructure 2020 is, beneﬁcial13, x to improve compressive stability in the energy absorption process. 12 of 14

Figure 9. TheThe energy energy absorption absorption efficiency efficiency of the specimens. 5. Conclusions 5. Conclusions In this work, hollow truss structures with different internal microstructure distributions were In this work, hollow truss structures with different internal microstructure distributions were successfully fabricated using the selective laser melting technique. The effect of internal microstructure successfully fabricated using the selective laser melting technique. The effect of internal distribution on compressive behavior and energy absorption was investigated. Conclusions were microstructure distribution on compressive behavior and energy absorption was investigated. drawn as follows: Conclusions were drawn as follows: (1).(1) WWhenhen the the internal internal microstructures microstructures are are distributed distributed in in the structural weaweaknessesknesses of the cells parallelparallel to to the the loading loading direction, direction, the the compressive compressive strength strength and and specific specific compressive strength of basicbasic hollow hollow truss truss structures structures can can be be increased increased by by nearly nearly 50% 50% and and 14%, 14%, respectively. respectively. However, However, whenwhen the the non-weak non-weak regions regions of the of cells the are cells reinforced are reinforced by internal by microstructures, internal microstructures, the compressive the compressiveproperties of properties the specimen of exhibit the specimen limited exhibit improvement limited or improvement even a decrease or in even diff erent a decrease degrees. in (2) differentBy analyzing degrees. the failure characteristics, it can be found that internal microstructures change (2). Bythe analyzing structural the weaknesses failure characteristics, inside the cells, it can cause be found the di thatfferent internal stress microstructures distributions andchange lead the to structuthe diffralerent weaknesses collapse positions inside the of hollowcells, cause truss the structures. different Besides, stress distributions the specimens and that lead collapse to the at differentjoint regions collapse exhibit positions more excellent of hollow compressive truss structures. stability Besides, during the collapse.specimens that collapse at (3) jointStrengthening regions exhibit the structuralmore excellent weaknesses compressive inside stability the cells during can improvethe collapse. the bearing capacity (3). Strengtheningand the compressive the structural stability weaknesses of hollow truss inside structures, the cells so can it is improve conducive the to bearing increasing capacity the energy and theabsorption compressive per unit stability volume of hollow and mass. truss structures, so it is conducive to increasing the energy (4) absorptionAdding microstructures per unit volume into and the mass. internal weaknesses of the cells parallel to loading direction (4). Addingis an eff ectivemicrostru wayctures to improve into the the internal compressive weaknesses properties, of the energycells parallel absorption to loading and compressive direction is anstability effective of hollowway to truss improve structures. the compressive properties, energy absorption and compressive stability of hollow truss structures.

Funding: This research was funded by the National Natural Science Foundation of China, grant number 11872124.

Acknowledgments: Thanks for the financial support from the National Natural Science Foundation of China. (No. 11872124).

Conflicts of Interest: The authors declare no conflict of interest.

References

Materials 2020, 13, 5094 13 of 14

Author Contributions: Conceptualization, H.S. and H.R.; Methodology, H.S.; Software, H.R.; Validation, J.N., and H.R.; Writing—original draft preparation, H.S.; Writing—review and editing, H.R.; Supervision, J.N.; project administration, J.N.; funding acquisition, H.R. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the National Natural Science Foundation of China, grant number 11872124. Acknowledgments: Thanks for the financial support from the National Natural Science Foundation of China. (No. 11872124). Conflicts of Interest: The authors declare no conflict of interest.

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