Article
Effect of Internal Structure in the Compression Behavior of Casted Al/LECA Composite Foams H. Puga 1, * , Vitor H. Carneiro 2 and Joaquim Barbosa 1 1 2
*
CMEMS-UMinho, University of Minho, Campus Azurem, 4800-058 Guimaraes, Portugal;
[email protected] MEtRiCS-UMinho, University of Minho, Campus Azurem, 4800-058 Guimaraes, Portugal;
[email protected] Correspondence:
[email protected]; Tel.: +351-253-510-220
Received: 4 September 2018; Accepted: 23 October 2018; Published: 1 November 2018
Abstract: In this paper, low-cost, aluminum-based composite metal foams are produced by the gravity die casting technique using lightweight expanded clay (LECA) as space holders. The influence of the voids generated by LECA particles on the syntactic composite samples density and mechanical behavior is characterized by quasi-static uniaxial compression. It is shown that smaller particles generate higher relative densities and a reduction in the value of densification strain. The use of larger particle diameter promotes an increase in yield strength and a more stable plateau region of the stress–strain curve, leading to higher values of crushing energy absorption. The influence of the internal structure on these experimental results is correlated with elasto-plastic numerical simulations, and it is suggested that a small mismatch in LECA particle diameter is advantageous for enhancing mechanical properties. Keywords: syntactic foam; aluminum alloy; lightweight expanded clay (LECA) particles; casting
1. Introduction Composite metal foams (CMF) were invented in the late 1920s (e.g., Reference [1]). Since then, they have been the focus of many studies and developments, although it is only recently that they have found relevant industrial application. In fact, metallic foams show an interesting combination of physical and mechanical properties that make them extremely versatile and suitable for applications in areas where high stiffness/specific weight ratio is required [2]. Moreover, the presence of porosities/cavities and the essential inhomogeneity make it possible for them to efficiently absorb impact loads [3], besides revealing excellent acoustic/thermal insulation properties [4] and vibration damping [5]. These properties are attractive in many applications, especially railway, aeronautic, aerospace, and automotive industries, due to their direct influence on energy consumption [6]. Examples of current applications include ultralight panels, energy absorbing structures, heat dissipation media, electrodes for electric batteries, ultrasound deflectors, medical prosthesis, and heat exchangers. Given that innovation in the design and characterization of these composite materials is still possible, there are no boundaries for their industrial application [7]. However, due to the importance of cell morphology and density (even through the same specimen), modeling approaches may not be able to fully explain the variations in terms of mechanical properties. It is possible that cell volume distribution, changes in rib thickness, and internal void superficial areas need to be considered in terms of structural analysis to understand the deformation behavior in these syntactic foams. Traditionally, metallic foams are produced using mainly aluminum and magnesium-based alloys. Despite the variety of production methods, there are only two different routes to generate porosity/cavities [8]: self-formation or predesign. In the first case, the porosity forms in a self-evolution J. Compos. Sci. 2018, 2, 64; doi:10.3390/jcs2040064
www.mdpi.com/journal/jcs
J. Compos. Sci. 2018, 2, x FOR PEER REVIEW
2 of 11
J. Compos. Sci. 2018, 2, 64
2 of 11
porosity/cavities [8]: self-formation or predesign. In the first case, the porosity forms in a selfevolution process according to physical principles, and the cell structure is difficult to predict and process to physical andgas the into cell structure is difficult and control as they control according as they are obtainedprinciples, by injecting a melt. In the casetoofpredict predesign, the resulting are obtained by injecting gas into a melt. In the case of predesign, the resulting structure is determined structure is determined by a cell-forming mold, and the foam is obtained by powder metallurgy, by a cell-forming mold, and the foam obtained bymethod powdercovers metallurgy, sputtering, or investment sputtering, or investment casting. Eachisproduction a characteristic range of density, casting. Each production method covers a characteristic range of density, cell size, and cell topology. cell size, and cell topology. In casting, the use of soluble space holders like salt [9] or carbamide [10], In casting, the use of soluble space holders like salt [9] or carbamide [10], which are later removed which are later removed by immersion in water [11], is necessary. However, there is a recent trend to by in water [11], isspheres necessary. therespace is a recent trend to use low-density, useimmersion low-density, hollow as However, permanent holders. These allow veryhollow easy spheres as permanent space holders. These allow very easy control/manipulation of density and pore control/manipulation of density and pore size/shape, which have a crucial role in the overall size/shape, have [12]. a crucial role in thesteel overall mechanical [12]. Commonly, steelthis hollow mechanical which properties Commonly, hollow spheresproperties are employed to accomplish task spheres are employed to accomplish this task due to their inherent structural strength, capability due to their inherent structural strength, capability of being densely packed, and regular shape [13]. of densely packed, regular shape spheres [13]. Anisalternative route toexpanded the use of steel hollow Anbeing alternative route to the and use of steel hollow using lightweight clay (LECA) as spheres is using (LECA) as permanent spacepossess holderslow [6].density Due to and its high permanent spacelightweight holders [6].expanded Due to itsclay high porosity, LECA particles can porosity, LECA particles possess low density can be obtained at low cost.and Additionally, they are be obtained at low cost. Additionally, they areand characterized by good thermal acoustic insulation characterized by good thermal and acoustic insulation [14], are chemically inert, and have been proven [14], are chemically inert, and have been proven to be an excellent filler in concrete composites [15]. to be an excellent fillerinformation in concrete composites However, detailed information concerning their However, detailed concerning[15]. their mechanical characterization and possible mechanical applicationscharacterization is still limited. and possible applications is still limited. In In this this work, work, LECA LECA was was used used as as aa permanent permanent space space holder holder to to produce produce cast cast aluminum aluminum alloy alloy composite foams. Cylindrical-shaped foam samples were produced using different LECA particle composite foams. Cylindrical-shaped foam samples were produced using different LECA particle dimensions/densities submitted to compressive testing dimensions/densities and and submitted to compressive testing to to determine determine the the influence influence of of these these factors factors in in the the overall overall static static mechanical mechanical behavior behavior of of the the foam. foam. 2. 2. Experimental Experimental Methodology Methodology 2.1. Materials 2.1. Materials LECA has a solid clay composition that is filled and expanded with gas bubbles. Its generic clay LECA has a solid clay composition that is filled and expanded with gas bubbles. Its generic clay composition is described in Table 1. composition is described in Table 1. Table 1. Lightweight expanded clay (LECA) chemical composition. Table 1. Lightweight expanded clay (LECA) chemical composition. Elements
Elements w (%) w (%)
SiO2
SiO2 61.95 61.95
Al2 O3
Al2O3 17.91 17.91
Fe2 O3
Fe2O3 8.18 8.18
K2 O
K2O 3.90 3.90
CaCO3
MgO
S
Other
CaCO3 MgO S Other 5.39 5.39 1.381.38 0.570.57 Balance Balance
With the the objective objective of of determining determining the the role role of of particle particle diameter diameter and and sample sample density density in in the the static static With mechanical behavior behavior of of this this kind kind of of composite, composite, three three sizes sizes of of LECA LECA particles particles with with a nominal diameter diameter mechanical of 2.02, 2.02, 3.49, 3.49, and and 5.86 5.86 mm mm were were selected selected(Figure (Figure1). 1). of
Figure Figure 1. 1. Normal distribution of of lightweight lightweight expanded expanded clay clay (LECA) (LECA) particles. particles.
J. Compos. Sci. 2018, 2, 64 J. Compos. Sci. 2018, 2, x FOR PEER REVIEW
3 of 11 3 of 11
Table 2 presents the composition of the commercially available AlSi7Mg alloy used in this work Table 2 presents the composition of the commercially available AlSi7Mg alloy used in this work as evaluated by optical emission spectrometry. as evaluated by optical emission spectrometry. Table 2. Aluminum alloy chemical composition. Table 2. Aluminum alloy chemical composition.
Alloy
Alloy
AlSi7Mg
AlSi7Mg
Si 7.44
Si
7.44
Chemical Composition (wt %) Chemical Composition (wt %) Fe Mg Cu Mn Zn Ti Al Res. Fe Mg Cu Mn Zn Ti Al Res. 0.13 0.58 0.07 0.07 0.05 0.11 Bal. 0.12
0.13
0.58
0.07
0.07
0.05
0.11
Bal.
0.12
2.2. Experimental Procedure 2.2. Experimental Procedure Figure 2 shows the experimental set-up used in the present work. The AlSi7Mg was melted and Figurethe 2 shows theatexperimental in the present The work. The AlSi7Mg and held inside crucible 700 °C for 30set-up min forused homogenization. molten alloy waswas thenmelted degassed ◦ C for 30 min for homogenization. The molten alloy was then degassed held inside the crucible at 700 by ultrasound for 5 min and refined by addition of 0.2% of master alloy (Al5Ti1B). Melt temperature by ultrasound 5 min refinedofby 0.2% of the master temperature was controlled for within anand accuracy ±2addition °C. Afterof20 min, alloyalloy was(Al5Ti1B). poured inMelt the steel die (40 was diameter) controlled filled withinwith an accuracy of ± 2 ◦ C. After 20 min, the°C. alloy poured in the conditions, steel die (40 five mm mm expanded clay preheated to 350 Forwas all experimental ◦ C. For all experimental conditions, five samples diameter) filled with expanded clay preheated to 350 samples were poured by gravity casting. were poured by gravity casting.
Figure Figure 2. 2. Composite Compositeproduction productionset-up. set-up. (1) (1)Metallic Metallicmould; mould;(2) (2)aluminum aluminumalloy alloymelt; melt; (3) (3) LECA LECA particles; particles;(4) (4)steel steelnet. net.
2.3.Samples SamplesCharacterization Characterization 2.3. As-cast specimens specimenswere weremachined machinedinindry drycondition conditionusing usingaaEFI EFIDU DU25 25Lathe Lathemachine machine(Trofa, (Trofa, As-cast Portugal),as aspresented presentedininFigure Figure3a, 3a,ininorder ordertotoobtain obtaina cylindrical a cylindrical geometry (D30 × (mm)). 40 (mm)). Portugal), geometry (D30 × 40 A A carbide uncoated (H10) insert was selected for roughing and finishing operations using the depths carbide uncoated (H10) insert was selected for roughing and finishing operations using the depths of of cut feed shown in Table The interrupted cuts highmetal metalremoval removalrates ratesand andthe thematerial materialof of cut andand feed shown in Table 3. 3. The interrupted cuts atathigh thespecimens specimenswere were also also relevant relevant factors factors in in the the choice choice of of the the insert. insert. the
J. Compos. Sci. 2018, 2, 64 J. Compos. Sci. 2018, 2, x FOR PEER REVIEW
4 of 11 4 of 11
Table Table3.3.Sample Samplemachining machiningdetails. details.
Specification Specification Insert Insert Rotational speed,speed, N (rpm) Rotational N (rpm) Depth ap (mm) Depth of cut,of apcut, (mm) v (m/min) CuttingCutting speed,speed, v (m/min) Feed, fa (mm/rev) Feed, fa (mm/rev)
Value Value Carbide (Uncoated Carbide (Uncoated H10) H10) 1200 1200 0.50 0.50 60.00 60.00 0.10 0.10
Densitiesof ofthe theproduced producedcomposites compositeswere weredetermined determinedby bythe theratio ratiobetween betweenvolume volume(evaluated (evaluated Densities by the measurement of the samples with a Mitutoyo Digimatic 500-170 caliper (Mitutoyo Corporation, by the measurement of the samples with a Mitutoyo Digimatic 500-170 caliper (Mitutoyo Kawasaki, Kanagawa accuracy 0.01 accuracy mm) and0.01 mass (evaluated on (evaluated a VIBRA AJ-620 Corporation, Kawasaki,Prefecture, KanagawaJapan), Prefecture, Japan), mm) and mass on a CE digital scale, Tokyo,scale, Japan, accuracy 0.001 g). Five static uniaxial tests for tests each VIBRA AJ-620 CE digital Tokyo, Japan, accuracy 0.001 g). Five staticcompression uniaxial compression specimen type were carried out on an AMTEK LR50K Plus universal testing machine (Meerbusch, for each specimen type were carried out on an AMTEK LR50K Plus universal testing machine Germany) with a crosshead of 1 mm/min using 50 N prestress and kN (Meerbusch, Germany) withspeed a crosshead speed of 1 mm/min using 50 N stopped prestressafter andreaching stopped 50 after load. During testing, displacements and loads were recorded to calculate the instant values of sample reaching 50 kN load. During testing, displacements and loads were recorded to calculate the instant strain and stress.strain and stress. values of sample Resultsand andDiscussion Discussion 3.3.Results Figure3b 3bshows showsthe themachining machiningof ofthe thesamples samplesto toaafinal finalcylindrical cylindricalshape. shape.The Thealuminum aluminumalloy alloy Figure fraction revealed a smooth surface finishing, while the LECA fraction displayed rough cavities fraction revealed a smooth surface finishing, while the LECA fraction displayed rough cavities due due to fragile their fragile collapse both and casting and the machining process. aAlthough a was steel to their collapse during during both casting the machining process. Although steel mesh mesh was placed during the filling process to coerce the particles (see Figure 2), their low density placed during the filling process to coerce the particles (see Figure 2), their low density 3 )—when compared with liquid aluminum alloy (2.40 g/cm3 )—and the overall (0.27–0.55 g/cm g/cm 3)—when (0.27–0.55 compared with liquid aluminum alloy (2.40 g/cm3)—and the overall turbulence during casting generatedaamixed mixed open/closed open/closedcellular cellularstructure. structure.InInFigure Figure3b,c 3b,cititcan canbe be turbulence during casting generated observed that particles and surface tension promoted an open cell structure, while the ones apart made observed that particles and surface tension promoted an open cell structure, while the ones apart a closed cell. In fact, pouring, the LECA particles were were in contact, thus promoting an open made a closed cell. In before fact, before pouring, the LECA particles in contact, thus promoting an cell structure. However, due to turbulence and density mismatch, some of them could move and open cell structure. However, due to turbulence and density mismatch, some of them could move individualize. If theIfcompaction loadsloads were not able compensate these effects, was a tendency and individualize. the compaction were nottoable to compensate these there effects, there was a to form closed cell cellular tendency to form closed cellstructures. cellular structures.
Figure 3. Composite sample representation: (a) machining process; (b) composite sample representation; Figure 3. Composite sample representation: (a) machining process; (b) composite sample (c) particle interaction schematics. representation; (c) particle interaction schematics.
J. Compos. Sci. 2018, 2, x FOR PEER REVIEW
5 of 11
The final specimen dimensions, weight, and calculated densities are presented in Figures 4 and 5 ofthe 11 depended on the diameter of the LECA particles, with J. Compos. Sci. 2018, 2, 64 5 of 11 lower diameters leading to higher samples density. The final specimen dimensions, weight, and calculated densities are presented in Figures 4 and 5. It can be observed that sample density depended on the diameter of the LECA particles, with the Thediameters final specimen dimensions, weight, and calculated densities are presented in Figures 4 and 5. lower leading to higher samples density. It can be observed that sample density depended on the diameter of the LECA particles, with the lower diameters leading to higher samples density. J. 2, x FOR PEER REVIEW 5.Compos. It can Sci. be 2018, observed that sample density
Figure 4. Produced sample dimensions. Figure 4. Produced sample dimensions. Figure 4. Produced sample dimensions.
Figure 5. Produced sample densities. Figure 5. Produced sample densities.
An initial theoretical stacking proposal of the LECA particles is suggested in Figure 6a, where the An initial stackingmay proposal of the LECA particlestriangle. is suggested in Figure 6a, where fundamental areatheoretical between particles be described by an isosceles However, this principle Figure 5.may Produced sample densities. the fundamental area between particles be described by an isosceles triangle. However, this was changed to a real stacking of LECA particles after the aluminum infiltration by cutting the principlesamples was changed to a real stacking of LECA the aluminum by cutting produced and calculating the areas of theparticles scalene after triangles formed byinfiltration adjacent particles. An initialsamples theoretical stacking proposal of the LECA particles is suggested inadjacent Figure 6a, where the produced and calculating the areas of the scalene triangles formed by particles. From this analysis, the relationship between triangle areas and average side lengths was evaluated, the fundamental area between particles may be described by an isosceles triangle. However, this this relationship triangleareas areasand and average side lengths was there evaluated, asFrom shown in analysis, Figure 6b.the Given the higherbetween ratios between lengths in smaller particles, was principle was changed to a real stacking of LECA particles after the aluminum infiltration by cutting a slightly higher concentration of aluminum alloy in the particle–particle boundaries, increasing the the produced samples and calculating the areas of the scalene triangles formed by adjacent particles. wall thickness, which increased the density of the samples. Additionally, the higher standard deviation From this analysis, the relationship between triangle areas and average side lengths was evaluated,
J. Compos. Sci. 2018, 2, x FOR PEER REVIEW
6 of 11
as shown in Figure 6b. Given the higher ratios between areas and lengths in smaller particles, there J. Compos. Sci. 2018, 2, 64 6 of 11 was a slightly higher concentration of aluminum alloy in the particle–particle boundaries, increasing the wall thickness, which increased the density of the samples. Additionally, the higher standard deviation inwith samples higher was the correlated with diameter the higher sample diameter in samples higherwith diameters wasdiameters correlated with higher sample mismatch, as shown in Figure as 1. shown in Figure 1. mismatch,
Figure LECAstacking stackinganalysis: analysis:(a) (a)Theoretical Theoretical and ratio results. Figure 6.6. LECA and real realarea areacalculation; calculation;(b) (b)dimension dimension ratio results.
Figure7 shows 7 shows average stress–strain behavior under uniaxial compression samples Figure thethe average stress–strain behavior under uniaxial compression of of samples with with different LECA particle diameters. It suggests that the particle diameter and, by consequence, different LECA particle diameters. It suggests that the particle diameter and, by consequence, the the density of the samples, had a primary role in the mechanical performance of this cellular material. density of the samples, had a primary role in the mechanical performance of this cellular material. Nevertheless, every tested configuration was able to replicate a typical three-stage curve of a foam Nevertheless, every tested configuration was able to replicate a typical three-stage curve of a foam structure under compression, with pronounced linear elastic, plateau, and densification regions. structure under compression, with pronounced linear elastic, plateau, and densification regions.
J. Compos. Sci. 2018, 2, x FOR PEER REVIEW J. Compos. Sci. 2018, 2, 64 J. Compos. Sci. 2018, 2, x FOR PEER REVIEW
7 of 11 7 of 11 7 of 11
Figure 7. Compressive stress–strain behavior for different particle diameters.
On an initial stage, the samplestress–strain was constrained byfor a different preload (Figure 8a), which was negligible Figure Compressive stress–strain behavior for different particle particle diameters. diameters. Figure 7.7.Compressive behavior and corresponded to point (a) in Figure 7. As the loads imposed on the samples increased, there was On an an initial initial stage, the sample sample wasvalues constrained by aa preload preload (Figure 8a), which was7), negligible a proportional linear increase in stress until yielding occurred (point (b)which in Figure as shown On stage, the was constrained by (Figure 8a), was negligible and corresponded to point pointincrease (a) in in Figure Figure 7. As As theloads loads imposed onthe thesamples samples increased, there was wasto in corresponded Figure 8b. A to further in the loading ledimposed to the internal cellularincreased, structure there starting and (a) 7. the on a proportional linear increase in stress values until yielding occurred (point (b) in Figure 7), as shown in progressively collapse in a plateau region. As the strain increased, the internal aluminum walls a proportional linear increase in stress values until yielding occurred (point (b) in Figure 7), as shown Figure 8b. A further increase in the loading led to the internal cellular structure starting to progressively collapsed due to the combined complex loading states (point (c) of Figures 7 and 8) and, although the in Figure 8b. A further increase in the loading led to the internal cellular structure starting to collapse instrain a plateau As the the internal aluminum walls collapsed due to values of wereregion. increased, the strain stress increased, was linear. During this thealuminum internal structure progressively collapse in a plateau region. As fairly the strain increased, theperiod, internal walls the combined complex loading states (point (c) of Figures 7 and 8) and, although the values of strain of the LECA particles was crushed by severe aluminum plastic wall deformation. By this phase, the collapsed due to the combined complex loading states (point (c) of Figures 7 and 8) and, although the were increased, the stress was fairly linear. During this period, the internal structure ofThe the LECA metallic foam were completely compromised their initiallinear. spherical cell stable configuration. increase values of strain increased, the stress was fairly During this period, the internal structure particles wasparticles crushed by severe aluminum plastic wall deformation. By thisinternal phase,By the metallic foam inthe theLECA referred compression strain implied that the original cellular LECA structure was lost of was crushed by severe aluminum plastic wall deformation. this phase, the completely compromised their initial spherical cell stable configuration. The increase in the referred and that the remaining clay densified as the aluminum cells tended to close (Figures 7 and 8d). metallic foam completely compromised their initial spherical cell stable configuration. The increase compression impliedstrain that the original LECAcellular internal structure wasstructure lost andwas thatlost the in the referredstrain compression implied thatcellular the original LECA internal remaining clay densified as the aluminum cells tended to close (Figures 7 and 8d). and that the remaining clay densified as the aluminum cells tended to close (Figures 7 and 8d).
Figure 8. Example of sample behavior during uniaxial compression test: (a) pre-stress; (b) plastic collapse; (c) deformation during plateau stress; and (d) densification.
Figure 8. Example of sample behavior during uniaxial compression test: (a) pre-stress; (b) plastic
From Figures 7 and 8, it is possible to understand the static mechanical behavior of this kind of collapse; (c) deformation during plateau stress; and (d) densification. metallic foam. Figure 9 suggests that an increase in particle diameter generated an elevation in yield Figure 8. Example sample absolute behavior during uniaxial compression test: (a) pre-stress; plastic strength, although the of samples’ and relative densities decreased (see Figures 5(b)and 6). From Figures 7 and 8, it is possible to understand the static mechanical behavior of this kind of collapse; (c) deformation during plateau stress; and (d) densification. metallic foam. Figure 9 suggests that an increase in particle diameter generated an elevation in yield strength, although7 the absolute relative densities Figuresof5this andkind 6). of From Figures andsamples’ 8, it is possible to and understand the static decreased mechanical(see behavior
metallic foam. Figure 9 suggests that an increase in particle diameter generated an elevation in yield strength, although the samples’ absolute and relative densities decreased (see Figures 5 and 6).
J. Compos. Sci. 2018, 2, x FOR PEER REVIEW
8 of 11
J. Compos. Sci. 2018, 2, 64
8 of 11
J. Compos. Sci. 2018, 2, x FOR PEER REVIEW
8 of 11
Figure 9. Detailed results of the uniaxial compression testing. testing. Figure 9. Detailed resultsstrength of the uniaxial compression In order to justify this increase in yield when the overall density was increased, three fundamental two-dimensional unitary cells representing the aluminum/LECA foam were modeled In order order to to justifythis thisincrease increase yield strength when the overall density was increased, In in in yield strength when theLECA overall density was increased, (Figure 10a). Thesejustify fundamental models were composed of particles with 3.5 mm three diameter. three fundamental two-dimensional unitary cells representing the aluminum/LECA foam were fundamental two-dimensional unitary cells representing the aluminum/LECA foam were modeled Themodeled regular rib model represented the fundamental situation in which stacking promotes regular (Figure 10a). These fundamental models were composed of LECA particles with 3.5 a mm (Figure 10a). These fundamental models were composed of LECA particles with 3.5 mm diameter. areadiameter. where particles are regularly spaced andthe may be correlated with the lowerstacking particle diameters, as The model represented fundamental situation in which The regular ribregular model rib represented the fundamental situation in which stacking promotes promotes a regular shown in Figure 1. Both “thin” and “thick” rib models represented variations in the periodicity a regular area where particles are regularly spaced and may be correlated with the lower particle area where particles are regularly spaced and may be correlated with the lower particle diameters, asof the fundamental two-dimensional cells, being associated with the standard deviations in higher particle diameters, as shown in Figure 1. Both “thin” and “thick” rib models represented variations in the shown in Figure 1. Both “thin” and “thick” rib models represented variations in the periodicity of the periodicity oftwo-dimensional theinfundamental two-dimensional cells, being associated with theastandard deviations diameters shown Figure 1. cells, Thesebeing referred models were subjected to uniaxial compression fundamental associated with the standard deviations in higher particle in higher particle diameters shown in Figure 1. These referred models were subjected to a uniaxial simulation using finite element (FEA)models (Figurewere 10b);subjected the details which compression are presented in diameters shown in Figure 1. analysis These referred to aofuniaxial compression simulation using element analysis 10b); details of which are simulation using finite element analysis (FEA) (Figure(FEA) 10b); the details of the which presented in and Table 4. Fundamentally, thesefinite simulations allowed the (Figure determination of are reaction loads presented in Table 4. Fundamentally, these simulations allowed the determination of reaction loads Table 4. Fundamentally, allowed the the determination of reaction andin the deformations in the modelsthese that simulations were used to calculate apparent stresses andloads strains and deformations in the models that were used to calculate theapparent apparentstresses stressesand andstrains strains in in the the deformations in the models that were used to calculate the referred models.
referred models. referred models.
Figure 10. Representation of the simulation (a) models and (b) boundary conditions. Figure Representationof of the the simulation simulation (a) and (b)(b) boundary conditions. Figure 10.10. Representation (a)models models and boundary conditions.
Table 4. Finite element analysis (FEA) inputs details.
Table 4. Finite element analysis (FEA) inputs details. Model Static Structural—Nonlinear Isotropic Young’s Modulus (GPa) Material Model Static Structural—Nonlinear70 Isotropic (CastMaterial Aluminum Alloy) Young’s Poisson’s Ratio (-) 0.33 Modulus (GPa) 70
(Cast Aluminum Alloy)
Poisson’s Ratio (-)
0.33
J. Compos. Sci. 2018, 2, 64
9 of 11
Table 4. Finite element analysis (FEA) inputs details. Model
Static Structural—Nonlinear Isotropic
J. Compos. Sci. 2018, 2, xAluminum FOR PEER REVIEW Material (Cast Alloy)
Young’s Modulus (GPa)
70
Poisson’s Ratio (-)
0.33
Tangent Modulus (GPa)
0.5
9 of 11
Tangent Modulus (GPa) 0.5 Yield Strength (MPa) 197 Yield Strength (MPa) 197 Element Type PLANE183 Meshing ElementDescription Type PLANE183 Quadratic—High order 2d—8 noded Meshing Description Quadratic—High order 2d—8 noded Solver Sparse Direct Equation Solver Solver Sparse Direct Equation Solver Simulation Outputs Vertical loads and displacement Simulation Outputs Vertical loads and displacement From these simulations, simulations, it was possible to determine determine the apparent stress–strain stress–strain curves curves of the Based on on these these curves, curves, the the apparent apparent yield yield strength strength (Figure (Figure 11b) 11b) of the referred models (Figure 11a). Based models could be determined by observing the deviation from the numerical results from the initial models could determined observing the deviation from numerical results elastic proportional plot.
Figure 11. 11. FEA FEA results: results: (a) (a) model model apparent apparent stress stress strain strain curves; curves; and (b) apparent yield strength. Figure
Based on on the the results results shown shown in in Figure Figure 11b, 11b, it it was was possible possible to to determine determine that that the the deviations deviations from from Based the theoretical theoretical isosceles isosceles triangles triangles between between particles particles might might generate generate aa variation variation in in the the values values of of yield yield the strength. However, However, as as shown, shown, this this deviation deviation of of the the isosceles isosceles model, model, which which is is typical typical of of the the higher higher strength. LECA diameters diameters due due to to particle particle diameter diameter mismatch mismatch (Figures (Figures 11 and and 4), 4), might might increase increase the the average LECA average values of of yield yield strength. strength. values The suggested suggested hypothesis hypothesis was was supported supported by by the the analysis analysis of of the the plateau plateau region. region. Given Given the the higher higher The average yield strength ability of these thick/thin ribs, the structure with higher particle diameter average yield strength ability of these thick/thin ribs, the structure with higher particle diameter provided aa near stress plateau plateau (Figure (Figure 9), 9), according according to to Equations Equations (1)–(3), (1)–(3), due due to to aa well well provided near constant constant stress distributed thru-height deformation. distributed thru-height deformation. 2 ∅ =∅ 2.0=𝑚𝑚 → 𝜎→ = 58.67𝜀 + 9.80 𝑅2 =R0.99 2.0 mm σ = 58.67ε + 9.80 = 0.99
(1) (1)
2 ∅ =∅ 3.5 → 𝜎→ = 15.06𝜀 + 17.54 𝑅2 = R 0.78 =𝑚𝑚 3.5 mm σ = 15.06ε + 17.54 = 0.78
(2) (2)
2
=𝑚𝑚 6.0 mm σ = 29.52ε + 21.01 = 0.81 ∅ =∅ 6.0 → 𝜎→ = 29.52𝜀 + 21.01 𝑅2 = R 0.81
(3)(3)
In samples with smaller particles diameter, a more localized deformation was promoted due to In samples with smaller particles diameter, a more localized deformation was promoted due to the lower yield strength, and the different cellular layers progressively collapsed, generating a gradual the lower yield strength, and the different cellular layers progressively collapsed, generating a gradual increase in sample stiffness that was proved by the high slope in the plateau equation of these samples. This steady densification generated a smooth collapse, as shown by the data concerning the standard deviation of Equations (1)–(3) relatively to the established experimental plateaus of Figure 7. In terms of densification, smaller particles promoted an increase in density and, as a consequence,
J. Compos. Sci. 2018, 2, 64
10 of 11
increase in sample stiffness that was proved by the high slope in the plateau equation of these samples. This steady densification generated a smooth collapse, as shown by the data concerning the standard deviation of Equations (1)–(3) relatively to the established experimental plateaus of Figure 7. In terms of densification, smaller particles promoted an increase in density and, as a consequence, the overall densification strain was reduced. Given that the cellular structure was only able to collapse until all LECA-filled cells were crushed, the relative amount of these structures decreased, as did the allowable admitted deformation for this process to occur. Finally, it was apparent that an increase in particle size was advantageous to elevate the crushing energy until the densification strain. The elevation of yield strength and a more linear plateau promoted a more efficient route to absorb crushing energy. 4. Conclusions In the present work, the role of LECA particle diameter in the overall Al composite density and mechanical behavior was studied. The main conclusions to be draw from the study are as follows: (1) (2)
(3)
(4)
Gravity casting can be a successful route to manufacture low-cost cellular structures. The different LECA particle diameters have a predominant role in the density and overall mechanical behavior of the final composites. Experimental results showed that smaller particles generated higher densities and consequently resulted in a reduction in the value of strain densification. The use of higher particle diameter generates an elevation in yield strength and a more constant stress value during the plateau region. Furthermore, the referred mechanical characteristics allow higher values of crushing energy absorption in more elevated particle diameters. The role of internal structure in the overall mechanical behavior of these composites was analyzed by an elasto-plastic numerical model. It is suggested that a small mismatch in LECA particle diameter is advantageous to enhance mechanical properties.
Author Contributions: Conceptualization, H.P. and V.H.C.; Methodology, J.B.; Resources, H.P.; Data Curation, V.H.C.; Writing-Original Draft Preparation, H.P. and V.H.C.; Writing-Review & Editing, H.P., V.H.C. and J.B. Funding: This work is supported by the research doctoral grant PD/BD/114096/2015 and postdoctoral grant SFRH/BPD/76680/2011 through Portuguese National Funding Agency for Science (FCT). In addition, this work is supported by FCT with the reference project UID/EEA/04436/2013 and by FEDER funds through the COM-PETE 2020 with the reference project POCI-01-0145-FEDER-006941. Conflicts of Interest: The authors declare no conflicts of interest.
References 1. 2. 3. 4. 5. 6. 7. 8.
Meller, M.A. Produit Métallique Pour L’obtention D’objets Laminés, Moulés Ou Autres, Et Procédés Pour Sa Fabrication. French Patent 615147, 30 December 1926. Czekanski, A.; Elbestawi, M.A.; Meguid, S.A. On the FE modeling of closed-cell Aluminum Foam. Int. J. Mech. Mater. Des. 2005, 2, 23–34. [CrossRef] Chen, S.H.; Chan, K.C.; Wu, F.F.; Xia, L. Achieving high energy absorption capacity in cellular bulk metallic glasses. Sci. Rep. 2015, 5, 10302. [CrossRef] [PubMed] Dyga, R.; Witczak, S. Investigation of Effective Thermal Conductivity Aluminum Foam. Proc. Eng. 2012, 42, 1088–1099. [CrossRef] Lamanna, E.; Gupta, N.; Cappa, P.; Oliver, M.; Strbik, I.I.I.; Cho, K. Evaluation of the dynamic properties of an aluminum syntactic foam core sandwich. J. Alloys Compd. 2017, 695, 2987–2994. [CrossRef] Bonani, B.B.; Khabushan, J.K.; Kahani, R.; Raouf, A.H. Fabrication of metallic composite foam using ceramic porous spheres “Light Expanded Clay Aggregate” via casting process. Mater. Des. 2014, 64, 310–315. García-Moreno, F. Commercial Applications of Metal Foams: Their Properties and Production. Materials 2016, 9, 85. [CrossRef] [PubMed] Banhart, J. Light-Metal Foams—History of Innovation and Technological Challenges. Adv. Eng. Mater. 2013, 15, 82–111. [CrossRef]
J. Compos. Sci. 2018, 2, 64
9. 10. 11. 12. 13. 14. 15.
11 of 11
Vesenjak, M.; Sulong, M.A.; Opara, L.V.; Borovinsek, M.; Mathier, V.; Fiedler, T. Dynamic compression of aluminium foam derived from infiltration casting of salt dough. Mech. Mater. 2016, 93, 96–108. [CrossRef] Bafti, H.; Habibolahzadeh, A. Compressive properties of aluminum foam produced by powder-Carbamide spacer route. Mater. Des. 2013, 52, 404–411. [CrossRef] Soni, B.; Biswas, S. Development of Al Foams by a Low-cost Salt Replication Method for Industrial Applications. Mater. Today Proc. 2015, 2, 1886–1891. [CrossRef] Nayyeri, M.; Mirbagheri, M.; Fatmehsari, D. Numerical evaluation of the stacking effect of spheres on the mechanics of tailor-made aluminum foams. Comp. Struct. 2017, 159, 316–326. [CrossRef] Avila, M.G.; Rabiei, A. Effect of Sphere Properties on Microstructure and Mechanical Performance of Cast Composite Metal Foams. Metals 2015, 5, 822–835. [CrossRef] Ardakani, A.; Yazdani, M. The relation between particle density and static elastic moduli of lightweight expanded clay aggregates. Appl. Clay Sci. 2014, 93–94, 28–34. [CrossRef] Hubertová, M.; Hela, R. Durability of Lightweight Expanded Clay Aggregate Concrete. Proc. Eng. 2013, 65, 2–6. [CrossRef] © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
