Non-stochastic Ti–6Al–4V foam structures with negative Poisson’s ratio Li Yang a , Denis Cormier b,n , Harvey West a , Ola Harrysson a , Kyle Knowlson a a Edward P. Fitts Department of Industrial & Systems Engineering, North Carolina State University, 400 Daniels Hall, 111 Lampe Drive, Raleigh, NC 27695, USA b Department of Industrial Systems Engineering, Rochester Institute of Technology, 81 Lomb Memorial Drive, Rochester, NY 14623-5603, USA article info Article history: Received 19 March 2012 Received in revised form 13 August 2012 Accepted 13 August 2012 Available online 19 August 2012 Keywords: Cellular materials Porous materials Titanium alloys Failure abstract This paper details the design, fabrication, and testing of non-stochastic auxetic lattice lattice structures. All Ti–6Al–4V samples were created via the Electron Beam Melting (EBM) additive manufacturing process. It was found that the Poisson’s ratio values significantly influence the mechanical properties of the structures. The bending properties of the auxetic samples were significantly higher than those of currently commercialized metal foams. The compressive strength was moderately higher than available metal foams. These results suggest that metallic auxetic structures have considerable promise for use in a variety of applications in which tradeoffs between mass and mechanical properties are crucial. & 2012 Elsevier B.V. All rights reserved. 1. Introduction For a specimen subjected to uniaxial stress in the elastic region, Poisson’s ratio is defined as the negative ratio of the transverse strain to the axial strain, and can theoretically range from  1.0 to 0.5 for isotropic structures and materials. Although materials with negative Poisson’s ratios are not commonplace, the emergence of additive manufacturing processes with few geo- metric limitations has generated considerable interest in this class of materials. Materials with negative Poisson’s ratios (auxetic materials) were first reported by Lakes in 1987 [1]. He described a straight- forward method to produce polymer foam structures with nega- tive Poisson’s ratios. The technique involves first compressing a regular foam structure in three orthogonal directions and then holding it there at an elevated temperature for a period of time. After allowing it to cool to room temperature, it is then decom- pressed. The technique typically starts with a low relative density foam in order to accommodate the volume of materials com- pressed [2], and it is primarily used with polymer materials. A number of researchers have successfully employed this process to produce structures with negative Poisson’s ratio [3–5]. According to the theory of elasticity for isotropic materials, the shear modulus G and bulk moduli K can be determined by Eqs. (1) and (2): G ¼ E 2ð1 þ nÞ ð1Þ K ¼ E 3ð12nÞ ð2Þ where n is the Poisson’s ratio of the material. From Eqs. (1) and (2), it is clear that when Poisson’s ratio is negative, the material will have G*K which indicates significantly higher shear modulus than bulk modulus. Materials that possess superior shear modulus are expected to possess high indentation resistivity [6], high torsional rigidity [7], high bending stiffness; shear resistance [8], and high energy absorption efficiency [4]. Furthermore, auxetic materials are also appealing candidates for use as cores in sandwich panels [9]. During the bending of a sandwich panel, the inner half of the bending section is subjected to compressive stress while the outer half is subjected to tensile stress. For regular materials with a positive Poisson’s ratio, the compressed section’s cross sectional area tends to expand while the elongated section’s area tends to shrink. This produces internal shear stress and buckling of the cellular structure. For auxetic materials, the compressed section exhibits transverse shrinkage, therefore these parts are expected to have better overall mechanical properties during bending. Although there have been theoretical analyses of auxetic structures, challenges with manufacturing these geometries have limited their use in practical applications until very recently [10]. Furthermore, the majority of research dealing with auxetic materials has been focused on polymer materials. As new techniques for synthesis of these materials became available, Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/msea Materials Science & Engineering A 0921-5093/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.msea.2012.08.053 n Corresponding author. Tel./fax: þ1 585 475 2713. E-mail addresses: lyang5@ncsu.edu (L. Yang), drceie@rit.edu (D. Cormier), hawest@ncsu.edu (H. West), harrysson@ncsu.edu (O. Harrysson), kyle.knowlson@gmail.com (K. Knowlson). Materials Science & Engineering A 558 (2012) 579–585