Mater. Res. Soc. Symp. Proc. Vol. 1662 © 2014 Materials Research SocietyDOI: 1 557/op 010.1 l.2 . 4

THE RANDOM POROUS STRUCTURE AND MECHANICAL RESPONSE OF LIGHTWEIGHT ALUMINUM FOAMS

Max Larner1, John Acker2 and Lilian P. Dávila1,*

1 Materials Science and Engineering 2 Computer Science and Engineering

School of Engineering University of California Merced, 5200 N. Lake Road, Merced, CA 95343, U.S.A

ABSTRACT Lightweight porous foams have been of particular interest in recent years, since they have a very unique set of properties which can be significantly different from their solid parent materials. These properties arise from their random porous structure which is generated through specialized processing techniques. Their unique structure gives these materials interesting properties which allow them to be used in diverse applications. In particular, highly porous Al foams have been used in aircraft components and sound insulation; however due to the difficulty in processing and the random nature of the foams, they are not well understood and thus have not yet been utilized to their full potential. The objective of this study was to integrate experiments and simulations to determine whether a relationship exists between the relative density (porous density/bulk density) and the mechanical properties of open-cell Al foams. Compression experiments were performed using an Instron Universal Testing Machine (IUTM) on ERG Duocel open-cell Al foams with 5.8% relative density, with compressive loads ranging from 0-6 MPa. Foam models were generated using a combination of an open source code, Voro++, and MATLAB. A Finite Element Method (FEM)-based software, COMSOL Multiphysics 4.3, was used to simulate the mechanical behavior of Al foam structures under compressive loads ranging from 0-2 MPa. From these simulated structures, the maximum von Mises stress, volumetric strain, and other properties were calculated. These simulation results were compared against data from compression experiments. CES EduPack software, a materials design program, was also used to estimate the mechanical properties of open-cell foams for values not available experimentally, and for comparison purposes. This program allowed for accurate prediction of the mechanical properties for a given percent density foam, and also provided a baseline for the Al foam samples tested via the IUTM method. Predicted results from CES EduPack indicate that a 5.8% relative density foam will have a Young’s Modulus of 0.02-0.92 GPa while its compressive strength will be 0.34-3.37 MPa. Overall results revealed a relationship between pores per inch and selected mechanical properties of Al foams. The methods developed in this study can be used to efficiently generate open-cell foam models, and to combine experiments and simulations to calculate structure-property relationships and predict yielding and failure, which may help in the pursuit of simulation-based design of metallic foams. This study can help to improve the current methods of characterizing foams and porous materials, and enhance knowledge about their properties for novel applications. * Corresponding Author: ldavila@ucmerced.edu

4 26

H = 2.00 in

W = 1.25 in W = 1.25 in

INTRODUCTION Porous metallic materials are relatively novel alloys that contain air cavities to lower their overall densities [1-7]. These bulk materials usually have 2-25% density of their parent metallic alloy and have significantly different properties than their solid counterparts [1]. Typically porous materials have pore sizes defined as microporous (< 2 nm), mesoporous (2-50 nm) and macroporous (> 50 nm) [2]. Porous metallic materials fall within the macroporous length scale with pore sizes varying from the µm to mm range, depending on processing and applications [2]. Aluminum foams (Figure 1) are a type of porous metallic material typically created from an Al powder or melt and foaming agent mixture [1]. Common Al alloys used include 6101 and 6061; however others can also be used in the creation of foams [1, 3]. This metallic foam can also be produced using compressed air within a bath of molten Al, leading to its porous and random structure [1]. The foams can be heat treated to various temperatures in order to fine-tune their final properties [4]. The foams can be open- or closed-cell with a consistent cell size across the bulk material. Generally these foams have a high strength to weight ratio and high-energy absorption potential due to their porous nature. In addition, their porous structure allows them to be excellent acoustic insulators. Their high conductivity and surface area make them well suited for many thermal, chemical and filtration applications [1, 3-4]. These materials are processed by a number of techniques, the most common of which involves a molten aluminum bath and a foaming agent under a carefully controlled temperature-pressure environment [1]. Other methods include casting and burnout with a template, 3D-printing and injecting CO2 into a molten Al bath [1, 3]. The resulting open structure allows Al foams to have a much lower relative density than their parent material, typically 50%-90% less. Figure 1. ERG Duocel Al foams (commercially available) were tested under compressive loads [4]. Relative density of these foams was 5.8%, with (left) 20 PPI, and (right) 40 PPI. Dimensions H and W denote sample height and sample width respectively. The foam retains many of the parent mechanical properties but has several significant differences. Rather than concentrating stress at a load point, the foam transmits the stress multi-axially throughout the structure, decreasing the points of high stress concentrations [2]. In addition, Al foams have a very large densification strain as the structure fails [1-2]. Al foams typically have 5 to 10 times more damping ability than the parent material [1], hence their

potential usefulness for energy damping applications (e.g. crash protection). This causes Al foams to be very lightweight materials with distinctive mechanical properties and many potential applications where high strength and low weight are critical (e.g. the aerospace and automotive industries). These materials have also been used for impact absorption for military vehicles, catalytic environments for chemical reactions, baffles and structural supports for liquid tanks, and acoustic insulation in high noise areas [1, 4]. In the literature, metallic foams have been studied in detail for their potential properties for different applications [1-8]. A design guide published by M. Ashby [1] provides an excellent overview of these materials including properties, processing and applications. In addition, Ashby presents several theoretical models for approximating foam properties based on its relative density. Previous work by Oliveira et al. [5] provides a basis for simplifying the foam structure for simulation purposes. An investigation by Veale [6] covers modeling and simulation of the foams through a series of methods with some experimental validation. Another study by Cooke [7] uses a different mathematical model, regular Kelvin cells, to approximate foam characteristics under compressive loading. In addition, Kraynik and Reinelt [8] reported that random Voronoi cells may be used to accurately model a foam for computer simulations. In order to further advance these materials, more work needs to be done in characterizing the foam structure-property relationships. Since these materials can be difficult to produce or obtain experimentally, a theoretical approach may greatly enhance understanding and pursuit of porous metallic materials for specific applications. It is possible and necessary to enhance understanding of these materials through an integrated experimental-simulation approach in order to fully explore their mechanical properties. The objective of this study was to combine experiments and simulations to determine whether a relationship exists between the relative density (porous density/bulk density) and the mechanical properties of Al foams. The general approach for this work involved: (1) conducting compression experiments using the Instron Universal Testing Machine (IUTM) on Al foam specimens and analyzing key mechanical properties, (2) independently creating random porous models using an open-source software (Voro++) [9], (3) performing FEM simulations via COMSOL software on 3D CAD models of Al foams under compressive loads, (4) comparing simulation results against experimental data and adding properties not readily measurable in the laboratory (e.g. maximum von Mises stress), and (5) using a material design program (CES EduPack) to estimate the mechanical properties of Al foams for values not available experimentally, and for further comparisons. PROCEDURE Experimental Component Various 6061-T6 Duocel Al foam samples were obtained from ERG Aerospace [4]. Samples had a fixed dimension of 1.25 in x 1.25 in x 2.00 in (Table 1). Additionally, these samples had a 5.8% relative density and pore distributions of 20 and 40 pores per inch (PPI). All of the samples were compressed using an Instron Universal Testing Machine at standard temperature and pressure, and at a compression rate of 1 mm/min (Figure 2a). The foam was continuously compressed to a maximum stress of 6 MPa in order to gain a representative curve for a foamed material (Figure 2b). The Al foam samples were also subjected to a cyclic load/unload condition

with an extensometer to obtain accurate measurements for Young’s Modulus (E) calculations. Specifically, the experimental procedure involved: a) obtaining an Al foam sample, inspecting its quality and setting it up in the IUTM, b) performing uniaxial cyclical compression tests on the Al foam sample until failure, and c) analyzing the resulting stress-strain curve to calculate its mechanical properties and compare these to ERG specifications and simulations. Table 1. Dimensions for Al foam specimens.

Al Foam Sample

Width (mm)

Height (mm)

Depth (mm)

PPI Relative Density (%)

Young’s Modulus (MPa)

Experimental 31.8 50.8 31.8 20 5.8 238 Experimental 31.8 50.8 31.8 40 5.8 160

Figure 2. Al foams used in the laboratory: a) testing setup for uniaxial compression of a foam sample in an Instron Universal Testing Machine, and b) typical foam stress-strain curve upon compression. Courtesy of M. Ashby (2000). Simulations and Design-based Predictions Component Modeling the Al foam and simulating a compressive load applied to the porous material were pursued next. For the modeling portion, random Voronoi structures representing Al foams were created (Figure 3) using Voro++ [9], an open-source computer program. Voro++ was used to calculate Voronoi cells within a given volume of a foam model. The Voro++ code was subsequently modified to allow for a specific number of cells in the given volume. The Voro++ software calculated vertex points of the cells and connections between the vertices. This information was then imported into MATLAB for processing before generating the desired foam models for FEM simulations. In particular, the modeling and simulation setup involved: a) utilizing the Voro++ code to export spatial coordinates of Voronoi cell vertices (Figure 3a), b) importing Voro++ data into MATLAB [11] to construct and apply model parameters for an Al 6061-T6 foam model, c) importing the resulting foam model into COMSOL Multiphysics 4.3 using a LiveLink for MATLAB interface (Figure 3b), d) setting boundary conditions and compressive loads (0-2 MPa) using compression plates (Figure 3c) for simulation purposes (Figure 3d), e) simulating and analyzing mechanical properties such as von Mises stress, displacement and strain energy data, and f) comparing simulation results against experimental measurements.

a) b)

Figure 3. Workflow process illustrating the creation of foam models and simulation setup. Each snapshot shows: a) cell vertices created in desired volume using Voro++, with each vertex represented by a sphere, b) cell edges represented by solid cylinders form a foam model, c) an Al 6061-T6 foam model prior to FEM simulations. High strength steel plates were added to the top and bottom of the foam model to perform uniform compression simulations, and d) roller constraints (bars) were added to the compression plates to prevent shifting of the model during simulations. A compressive load was defined on the top plate (red arrows) and a fixed constraint on the bottom plate (triangles) to simulate IUTM compression conditions. CES EduPack [12] was used to approximate the mechanical properties of ERG Duocel Al foam for a range of percent density values. In particular, the CES Synthesizer module was used to calculate a range of predictive compressive strength values for several foam density values. Al 6061-T6 was selected as the material of interest and was defined as an open-cell foam in the software. Density was selected to vary from 1-50% relative density. With these values as input, the CES Synthesizer module was used to calculate a range of low and high values for compressive strength per foam density, which were later used to compare with experimental and simulation values. RESULTS Experimental Component Stress-strain curves were obtained upon compression tests via the IUTM setup in order to analyze the mechanical properties of the Al foam samples investigated. A total of four experimental samples were tested, each of the same relative density (5.8%), with two samples each of 20 and 40 PPI. Figure 4 shows characteristic stress-strain plots after compression of two foam samples (Table 1) with different PPI values yet the same relative density (5.8%). In this study, the compressive strength of an Al foam is defined as the shoulder value prior to yielding strain in the compressive stress-strain plot, as shown with a dashed arrow in Figure 4. Al foam samples have a characteristic plateau near the peak value in the stress-strain plot, where stress remains constant for large strains as previously reported by Ashby [1]. The resultant Young’s moduli (E) from compression experiments are summarized in Table 1.

Figure 4. Stress vs. strain curves after uniaxial compression for selected 5.8% relative density ERG Duocel Al foams. The 20 PPI foam was found to be stronger than the 40 PPI foam, as predicted by Ashby [1]. Simulations and Design-based Predictions Component Several compression simulations of Al foam models with varied relative densities were pursued to determine the largest number of cells and volume possible to most accurately model a foam’s behavior within a practical amount of time. Upon compression simulations of each Al foam model as depicted in Figure 5, several key mechanical properties were evaluated via COMSOL Multiphysics 4.3. Particularly, the von Mises stress was thoroughly analyzed, as it represents the total stress at a particular point in the structure, and is a standard criterion for yielding in metals. As described previously [13], the significance of the von Mises stress is that if its value in a particular location is greater than the material’s yield strength, then that location in the model is likely to begin to yield and deform plastically. Figure 5 shows: a) a representative 3D Al foam model, and b) von Mises stress distributions and deformations after a 0.4 MPa compressive load. These distributions show that the stress is maximum around the cell vertices (Figure 5c), which is consistent with independent findings by Cooke [7] and Jang et al. [14].

Figure 5. Models of an Al foam showing its open structure: a) before compression simulations, b) after a 0.4 MPa compressive load, and c) after the same compression simulation as b) with another view of von Mises stress concentrations located at cell vertices. The likelihood of failure is therefore highest around the cell vertices, consistent with prior findings [7, 14].

a) b) c)

Compressive Strength

Onset of Densification

Young’s Modulus from Cyclical Compressions

Results from CES EduPack analysis are shown in Figure 6, which represent predictive data of the mechanical properties of varying density Al foams. Compressive strength vs. relative density shows an exponential relationship, and a range of compressive strength values is associated with each density value (Figure 6). Equations 1 and 2 describe the fundamental scaling equations [1] used in CES EduPack as relevant in this study. Other related predictions are shown in Table 2.

Figure 6. Scaling equation graph showing compressive strength vs. relative density for various Al foams (6061-T6). The red box highlights the Al samples investigated in this study. Courtesy of Granta Design (2013). Eqn. 1

Eqn. 2

where σc, σc,s, ρ and ρs denote foam compressive strength, solid compressive strength, foam density and solid density respectively in Equation 1, and E, Es, ρ and ρs represent foam Young’s modulus, solid Young’s modulus, foam density and solid density respectively in Equation 2 [1]. Table 2. Al foam (5.8% relative density) results from experiments and simulations.

Al Foam Specimen

Experimental Compressive

Strength (MPa)

COMSOL Compressive Yield

(5.8% Density, 50 PPI) (MPa)

CES Synthesizer Scaling

Compressive Strength (MPa)

20 PPI 1.2 0.4 0.34-3.37 40 PPI 0.6 0.4 0.34-3.37

Results from the simulations and experiments were compared with equivalent data obtained from CES EduPack, as shown in Table 2. The material design software provided ranges of compressive strength based on scaling equations, which were used as expected values for the simulation and experimental results. In the experimental case (Table 2), the 20 and 40 PPI aluminum foams at 5.8% relative density failed within the CES range values. In all simulation cases in Table 3 (except for 11.52% relative density), the von Mises stress yield criterion indicated that the foam would begin to fail within the CES specified ranges. A goal of the simulations was to determine the appropriate foam model (i.e. size, number of cells) needed to replicate experimental results as closely as possible using the compressive yield values.

Table 3. Foam models subjected to compressive simulations and respective properties. Relative Density

(%)

Pores per Inch

(PPI)

Number of Cells

CES Synthesizer Compressive Strength

(MPa)

COMSOL Compressive Load

(MPa) 1.41 41.04 10 0.04-0.42 0.1 3.03 41.04 10 0.13-1.32 0.3 5.74 50.80 8 0.34-3.37 0.4 7.51 24.29 7 0.51-5.15 0.5 9.51 24.29 7 0.73-7.33 1.0 11.52 27.36 10 0.98-9.78 0.9

DISCUSSION AND CONCLUSIONS The experimental tests provided good baseline values for compressive strength for the Al foams studied. When combined with scaling equation results, the two datasets provided an expected value range for compressive strength when performing simulations. The 8-cell foam model (Table 3) representing a 5.8% density (50 PPI) showed yielding at a 0.4 MPa load, in good agreement with the experimental data for the 40 PPI foam sample (Table 2). The importance of these findings is that a relatively simple way of creating a random foam model was devised, and that the resulting models can be used to determine the mechanical properties of a given percent density and PPI foam relatively precisely and easily, without resorting to expensive experimentation or overly simplified models. The experimental foams failed as previously reported independently by Ashby et al. [1], with the lower PPI foam failing at higher load values. In addition, the 40 PPI experimental foam failed at similar load values to the 50 PPI simulated foam with equivalent relative density. Modeling via Voro++ is a useful method for approximating open-cell porous structures. Careful control of parameters must be taken into account when designing a foam model with a particular relative density and PPI. In order for the modeling scheme to function properly, the foam model must be large enough to ensure real foam behavior. If the model is too small, compression simulations will not be able to accurately predict the foam failure load. On the other hand, if the model is too large, the simulation will require vast computational resources which render the simulation impossible. Foam models allow exploration of potential advanced materials by fine-tuning their structure-properties relationships. Modeling of Al foams will allow for distinct models to be created with relative ease, and their density and PPI parameters can be adjusted accurately. This provides the opportunity to investigate controlled conditions and structures in a unique way, not experimentally feasible. Given the number of experimental samples and simulations studied, the potential factors for variation include sample quality, testing conditions, and volume and number of cells within a model. Trends indicate that a few compression tests are needed per sample for reliable experimental measurements, and that simulations require several iterations to determine accurate models, providing a confidence level for future efforts. Most significantly, a relationship between pores per inch and the mechanical properties of Al foams was determined. From experiments, Al foams with the same relative density (5.8%) yet different PPI values revealed remarkably distinct mechanical properties. The trend seems to indicate that as PPI decreases, the overall mechanical properties increase. This result is reasonable because as the PPI decreases, with the relative density remaining constant, the cell

edges become thicker and require more stress to reach their yield point. The integration of experiments and simulations is a cost and time efficient approach to investigate advanced materials such as foams. In the future, additional foam models with wider variation of relative density and PPI can be investigated to further validate the methodology reported in this study, or to compare against independent experimental measurements. These varied models can be created with relative ease and flexibility using the modeling scheme described in this study. ACKNOWLEDGEMENTS The authors want to thank B. Doblack, M. Diaz Moreno, T. Allis and M. Dunlap at UC Merced for their technical assistance with this project. Also, Chris Rycroft at UC Berkeley for his assistance with the Voro++ random cell generator. An NSF-CAMP Student Research Funds award supported co-author (JA) for this work. In addition, NSF-COINS awards supported co-authors (JA and ML), providing funds for the summer portion of the work. This work was performed under the auspices of the NSF-funded COINS award under contract No. 0832819. REFERENCES 1. M.F. Ashby, A.G. Evans, N.A. Fleck, L.J. Gibson, J.W. Hutchinson and H.N.G. Wadley, in

Metal Foams: A Design Guide, edited by M.F. Ashby (Elsevier Science Publisher, Burlington, MA, 2000) pp. 6-52.

2. J. Luyten, S. Mullens and I. Thijs, KONA Powd. Part. J. 28, 131–142 (2010). 3. Handbook of Cellular Metals: Production, Processing, Applications, edited by H.P.

Degischer and B. Kriszt, (Wiley-VCH, Germany, 2002). 4. ERG Duocel® Aluminum Foam website. August 15, 2013 from

http://www.ergaerospace.com/Aluminum-properties.htm 5. B.F. Oliveira, L.A.B. da Cunda and G.J. Creus, Mechanics of Advanced Materials and

Structures, 16 (2), 110-119 (2009). 6. P.J. Veale, M.S. Thesis, University of Massachusetts Amherst, 2010. 7. R. Cooke, M.S. Thesis, Naval Postgraduate School, 2001. 8. A.M. Kraynik and D.A. Reinelt, Foam microrheology: From honeycombs to random foams

(online documentation: http://faculty.smu.edu/reinelt/foam_rheology.pdf). Engineering Sciences Center, Sandia National Laboratories, Albuquerque, NM, 1999.

9. Voro++ website. July 15, 2013 from http://math.lbl.gov/voro. 10. COMSOL Multiphysics 4.3. The COMSOL Group (2013) website. June 15, 2013 from

http://www.comsol.com. 11. MATLAB. MathWorks Group (2013) website. July 12, 2013 from

http://www.mathworks.com/products/matlab. 12. CES EduPack. Granta Material Intelligence (2013) website. August 10, 2013 from

http://www.grantadesign.com. 13. M. Larner and L.P. Dávila, The Mechanical Properties of Porous Aluminum using Finite

Element Method Simulations and Compression Experiments, Mater. Res. Soc. Symp. Proc. 1580, mrss13-1580-bbb09-05, doi:10.1557 / opl.2013.663 (2013).

14. W.-Y. Jang, S. Kyriakides and A.M. Kraynik, On the Compressive Strength of Open-Cell Metal Foams with Kelvin and Random Cell Structures, Int. J. Solids Struct. 47, 2872-2883 (2010).