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 ), meso (between ) and macro (larger than ) 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.
Compressive properties
The most frequently reported mechanical property of titanium foams is compressive strength. It was generally accepted that the compressive properties of metal foams depended on the properties of the cell wall rather than on pore size. However, more recent research has indicated that smaller pore sizes equate to higher compressive strength. As pore sizes reach nano-dimensions, the relationship is even more clear due to changes in deformation mechanism.
Tuncer & Arslan fabricated titanium foams via the space-holder method using various shaped space-holders to elucidate the effect of cell morphology on mechanical properties. They found that foams created with needle-like urea space-holders exhibited a decrease in elastic modulus and yield strength when compared to spherical pores.
Processing methods
Many metal foam manufacturing techniques are accomplished by the introduction of a gaseous phase into a precursor matrix, which can occur in either molten metal or a powdered metal form. Due to titanium's high melting point () and high chemical affinity with oxygen, nitrogen, carbon and hydrogen (which dissolve rapidly either in liquid or solid titanium at a temperature above ), solid-state processes based on powder densification are the preferred method of fabrication.
Processing methods must also be designed to avoid exposure to air or moisture; vacuum or inert gas sintering processes are usually sufficient for preventing contamination.
Loose-powder (gravity) sintering
Utilizing powder metallurgy routes for titanium foam fabrication allows for production at lower temperatures than those required through a melt process and reduces overall risks for contamination. In loose-powder sintering (also known as gravity sintering), pores are created through diffusion bonding arising from the voids existing between packed powder particles. Axial compaction followed by sintering follows the same procedure as above, but pressure is applied for compaction of the precursor material. For both compaction methods, the resulting pore morphology is dependent upon the morphology of the metallic powder, making it difficult to control the size, shape, and distribution of the pores. Another disadvantage includes the relatively high probability of pore collapse and limited achievable porosity levels.
Expansion of pressurized bubbles
To produce titanium foams via expansion of pressurized gas, the titanium precursor mixture is placed within a gas-tight metal can, which is evacuated after filling. The metal can is pressurized with inert gas — most commonly argon — and is pressed isostatically. The gas-filled pores are contained within the compacted matrix, and upon exposure to elevated temperatures, these bubbles expand through creep of the surrounding metal matrix. Since processing titanium foams using hot isostatic pressing (HIP) eliminates the need for separate compaction and sintering processes, a wider variety of custom shapes and sizes are possible than via loose powder sintering techniques.
Disadvantages of this process include reduced pore connectivity, limited achievable porosity, and a complicated experimental set-up. However, a unique aspect of the HIP process with respect to titanium (and other polymorphic materials) is that transformation superplasticity can be enhanced through the HIP process by way of thermal cycling, or by cycling around the alpha/beta allotropic temperature boundaries of the metal.
Superplastic expansion Titanium undergoes allotropic transformation from its α-phase (hexagonal close-packed (hcp) structure at temperatures less than ) to its β-phase (body centered cubic, bcc) structure at temperatures above ). Alpha-phase titanium products typically exhibit medium to high strength with excellent creep strength, whereas beta-phase titanium products typically exhibit very high strength and low ductility. Foams created under thermal cycling conditions have been shown to exhibit increased porosity due to the density difference between allotropic phases. Davis et al. produced titanium foams with 41% porosity (as compared to 27% porosity through the normal HIP creep mechanism). Increases in overall ductility were also observed in foams created through thermal cycling. In a similar experiment, porosity of 44% was achieved and determined as the maximum achievable porosity under thermal cycling conditions.
A later study also utilized exploitation of transformation superplasticity conditions through HIP, but in this case, the titanium powder in the precursor matrix was replaced with titanium wires to create anisotropic pores. The resulting anisotropic pores showed closer correlation with natural bone in that the foams exhibited higher elastic moduli, yield strength and deformation when subjected to longitudinally loaded forces than when loads were applied transversely.
Space-holder technique The space-holder technique is the most commonly employed method for producing titanium foams. The space-holder technique allows for the fabrication of higher porosity foams () than other techniques, while also giving the engineer more control over pore fraction, shape and connectivity. Mechanical properties can be adjusted through the size, shape and quantity of space-holders employed. The space-holder technique was first demonstrated by Zhao and Sun for the fabrication of aluminum foams in a powder metallurgical method, which consisted of the incorporation of NaCl as a space-holder. The space-holder was mixed into the powder mixture and dissolved prior to sintering. The same method was used to create titanium foams for the first time when Wen et al. utilized ammonium hydrogen carbonate spacers.
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