Titanium foams exhibit high specific strength, high energy absorption, excellent corrosion resistance and biocompatibility. These materials are ideally suited for applications within the aerospace industry. An inherent resistance to corrosion allows the foam to be a desirable candidate for various filtering applications. Further, titanium's physiological inertness makes its porous form a promising candidate for biomedical implantation devices. The largest advantage in fabricating titanium foams is that the mechanical and functional properties can be adjusted through manufacturing manipulations that vary porosity and cell morphology. The high appeal of titanium foams is directly correlated to a multi-industry demand for advancement in this technology.
Characterization Banhart describes two dominating perspectives in which cellular metals are characterized, referring to them as atomistic and macroscopic. The atomistic (or molecular) perspective holds that a cellular material is a construction of struts, membranes, and other elements which possess mechanical properties of their bulk metal counterpart. Indeed, the physical, mechanical, and thermal properties of titanium foams are commonly measured using the same methods as that of their solid counterparts. From a macroscopic perspective, the cellular structure is perceived as a homogeneous structure and characterized by considering the effective (or averaged) material parameters.
Microstructure Titanium foams are characterized structurally by their pore topology (relative percentage of open vs. closed pores), porosity (the multiplicative inverse of relative density), pore size and shape, and anisotropy. Microstructures may be examined by optical microscopy, scanning electron microscopy and X-ray tomography. Categorizing titanium foams in terms of pore structure (as either open- or close-celled) is the most basic form of differentiation. In close-celled foams, pores are composed of bubbles entrapped in the metallic solid. These foams consist of a continuous network of sealed pores wherein interconnections between the pores are virtually non-existent. Alternatively, in open-celled foams, the pores are interconnected and solid struts allow fluid to pass through. Most manufactured foams contain both types of pores, although in many cases the subtype is minimal. According to the IUPAC, pore sizes are classified into three categories: micro (less than 2 nm), meso (between 2 and 50 nm) and macro (larger than 50 nm) pores.
Mechanical properties As with other metal foams, the properties of titanium foams depend mostly on the properties of the starting material and the relative density of the resultant foam. Thermal properties in foams – such as melting point, specific heat and expansion coefficient – remain constant for both the foams and the metals from which they are composed. However, the mechanical properties of foams are greatly influenced by microstructure, which include the aforementioned properties as well as anisotropy and defects within the foam's structure.
Sensitivity to impurities The mechanical properties of titanium foams are sensitive to the presence of interstitial solutes, which present limitations to processing routes and utilization. Titanium has a high affinity for atmospheric gases. In foams, this is evidenced by the metal's tendency to trap oxides within cell edges. Micro-hardness of cell walls, elastic modulus, and yield strength increase as a result of interstitial solutes; ductility, which is a function of the quantity of interstitial impurities, is consequently reduced. Of the atmospheric gases, nitrogen has the most significant impact, followed by oxygen and carbon. These impurities are often present in the precursor mixture and also introduced during processing.
Theoretical models for predicting mechanical properties
Gibson & Ashby models Gibson & Ashby micromechanical models for porous materials provide mathematical equations for the prediction of mechanical parameters based on experimentally determined geometric constants. The constants of proportionality are determined by fitting experimental data to various mathematical models for structures consisting of cubes and solid struts and are dependent upon cell geometry. A limitation of the Gibson & Ashby model is that it is most accurate for foams exhibiting porosities higher than 70%, although experimental comparisons for lower porosity foams have shown agreement with this model. Ye & Dunand found reasonable agreement to the Gibson & Ashby model for titanium foams exhibiting 42% porosity. Ultrasonic measurements provided an average Young's modulus value of 39 GPa, which is in relatively good agreement with the Gibson & Ashby prediction of 35 GPa. The Gibson & Ashby models assume ideal structures; microstructural irregularities (e.g. inhomogeneous pore distribution; defects) are not considered. Additionally, experimental results from which the predetermined proportionality constants were based on experimental values that were obtained from simple compression tests. Consequently, they may not be applicable for multiaxial loads.
Minimum solid area (MSA) models Minimum solid area models assume that the load bearing area (cross-sectional area normal to the stress) is the logical basis for modeling mechanical behavior. MSA models assume pore interaction results in reduction of stress. Therefore, the minimum solid areas are the carriers of stress. As a result, predicted mechanical properties fluctuate based on the quantification of the solid area of the foam. For titanium foams consisting of partially sintered powders, the minimum solid area consists of the neck area between powders through the cross-section of cell walls between macropores. The mathematical relationships in MSA models are relatively consistent with the Gibson & Ashby model. However, the MSA models are designed to predict mechanical property parameters over a broader range of porosity levels. Like the Gibson & Ashby models, MSA models were derived assuming idealized (defect-free) structures containing uniform pore shapes, size and distribution.
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