New Insights into Change Rate of Pore Volume – Taking Titanium Foam for Example

The space holder technique is widely used to fabricate metal foams, especially titanium foam. However, how to obtain the desired porosities is a big challenge for this technique, because they are not always equal to the expected ones. The results of the previous study (i.e., P = ax + b, where a = 1/(1 + δ), b = δ/(1 + δ)) give a very interesting conclusion that is the change rate of pore volume (δ) is an indefinite mathematical constant. Based on the research work, we obtains a new result by establishing a mathematical model, which can be expressed as equation δ = ϕ − 1. Here, ϕ is the length index product of the ratio between the actual length and the designed length of the sintered metal foam. It reveals that the length index product (ϕ) is also an indefinite mathematical constant and we can measure its value. Therefore, solving δ means both a and b are solved, so the porosity (P) of titanium foam can be predicted by the equation P = ax + b, depending on the spacer content (x). This indicates that in the absence of porosity measurements, the macroscopic dimensions of the sintered metal foam can be measured to obtain a controlling equation for porosity.