Three methods of quantifying part density were considered; pycnometry, Archimedes method and micrographic density. Archimedes and micrographic are the two most frequently cited methods for measuring density of SLM parts, with comparisons made in literature, it is known that they can give very different results [285]. In this thesis, the Archimedes method was used for measuring the density of all samples, with micrographic density only used for a selection of the highest densities from each build and the reasoning is presented here.
Alternative methods for measuring part density are available and one of these, pycnometry was considered. The principles of pycnometry are very similar to that used in the Archimedes method, as will be discussed below, but has the potential for higher accuracy. A comparison between sample density measurements made with the different methods was performed to contribute to the selection of the methodology and are presented here. The advantages and disadvantages of each method are discussed.
Archimedes
The Archimedes method for measuring gravimetric density was performed in accordance with ASTM B311 β 17 (Density of Powder Metallurgy (PM) Materials Containing Less Than Two Percent Porosity). The method is based on the principle that a body suspended in liquid experiences a reactionary force equal to the weight of liquid displaced. When the body is completely submerged then the volume of liquid displaced is equal to the volume of the body. The difference between the weight of the body in air and suspended in liquid is called the buoyancy force and equals the weight of the displaced liquid (Equation 9). This derives the equation which is used to calculate the density of the body.
ππ€ππ‘ππ = πππ’ππ¦ππππ¦ = πππππ¦ β ππ π’ππππππ
Equation 9
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πππππ¦= ππ€ππ‘ππβ πππππ¦ πππππ¦β ππ π’ππππππ
Equation 10
Where Mwater and Οwater are the mass and density of the displaced water, Mbody and Οbody are the mass and density of the specimen being measured and Msubmerged is the weight of the specimen while submerged in water.
The apparatus was set up in accordance with ASTM B311-17, as see in Figure 108.
Distilled water was used as the reference liquid. An analytical balance was used, with precision of 0.0001 g. A nichrome wire, with diameter of 0.1 mm, was used to hold the specimens. The specimens were 8 mm x 8 mm blocks with 17 mm height, however, builds often did not reach this height and were stopped early. This is reflected in the errors calculated for each specimen. The blocks were built with a support structure comprising four trapezoidal feet for ease of building and removal from the build plate. Before measuring the sample density, the samples were cleaned to remove all loose surface powder using ultrasonic baths, run at room temperature for 60 minutes.
Figure 108 Analytical balance measuring the weight of a sample in water
To calculate the error of the density, the error from the readings were recorded and the propagation of errors for Equation 10 was calculated in Equation 19. The derivation of this equation was based on equations for error propagation from NIST/SEMATECH [286]. The propagation of error from an equation in the form of Equation 11 is shown in Equation 12, and the error for Equation 13 is shown in
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Equation 14, where B and C are theoretical inputs to calculate A and αΊB, αΊC and αΊA are the errors associated with these values.
π΄ = π΅ + πΆ
The equation to calculate the Archimedes density from the mass of a body in water and in air is shown in Equation 10. This equation can be written in the form of Equation 15 to simplify the error propagation to Equation 16, with factors altered to the form of Equation 17. The error of these factors can be calculated as in Equation 18 which combine to form Equation 19.
110 density of samples built through SLM and is the most time and resource efficient way of obtaining sample densities that was considered for this project.
The Archimedes method is considered highly accurate and has been compared favourably in literature to micrographic density [287]. Even with light samples, of 1 g, the contribution of errors generated from the scales is very low. The readings can be wrong where surface roughness prevents wetting the surfaces of the samples or where the water can infiltrate the surfaces. This can be indicated by the appearance of bubbles on the surface as the sample is submerged or where bubbles grow as air leaves cavities of the sample. With the former issue, shaking the submerged samples releases the surface bubbles allowing the wetting of the sample to improve. The latter problem highlights a failure in the methodology. A similar standard, ASTM B962 β 17, exists for PM parts with greater porosity which requires immersing the samples in oil to prevent water infiltrating the samples, this was not considered necessary as pores are less likely to appear near the surface of SLM samples as was empirically evident during the project, except where samples had very high levels of porosity (>10%).
Where very high levels of porosity occur, there is also a risk of internal trapped but loose powder, which should not contribute to the density of the sample.
Water has high surface tension, which causes meniscus to appear at the beaker and at the wire, which causes a small error. To avoid this, many researchers use ethanol or acetone as the reference fluid.
The density of water is another source of error in the experiments, as it varies with temperature. In this work the temperature of the room is recorded but not the temperature of the water. It can be expected that water temperature is stable during recording the results of each set of experiments but variations in temperature are more extreme with seasonal changes, which has potential implications in direct comparison of results. If the density of the water is recorded incorrectly, it will introduce a bias error, which compromises absolute results but does not affect the observed trends.
With the aim of minimising porosity, the important measure is not absolute density but relative density. This can only be done with the Archimedes method where the ideal density is known. This value is known for AA6061 and AlSi10Mg but not for the blended material. An attempt was made to measure the ideal density by measuring
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the density of the powder but the Archimedes density of the blended material SLM samples regularly recorded values higher than this.
For the reasons highlighted with errors from water density measurements and knowing the ideal density of the materials, the Archimedes method was used to measure the trend of densities from each build, while micrographic densities were used to evaluate the relative densities, which is only required of the highest density samples.