**7.2 Material Properties**

**7.2.1 Density**

The bulk density of stainless steel 316L is 8000kg/m^{3} ^{[188]}. Since the built
part’s density in SLM process have been shown to reach a maximum of
99.93%, the value used for the FE model was 7994kg/m^{3}.

The powder bed density during the SLM process has been measured by the
method described in section 3.4.3, and the result shown in section 6.3
presented that the stainless steel 316L powder supplied by LPW Technology
formed a powder bed density of 4880kg/m^{3}.

**7.2.2 Thermal conductivity **

Stainless steel 316L is a temperature dependent material where its thermal properties vary at different temperatures. The thermal conductivity of fully solid stainless steel 316L is 16.2W/m·K at 100°C, and 21.5W/m·K at 500°C

[188]

. Therefore, Equation (3.2) is converted to Equation (7.1) for calculating the thermal conductivity kS (S for solid) at different temperatures for the bulk stainless steel.

(7.1)

The parts generated by the SLM process have a maximum density of 99.93%. The gas in the pores also has temperature dependent conductivity, making it complicated to calculate the combined thermal properties. Since

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the density of built part is close to the bulk material, the conductivity of the
gas in the pores is ignored due to its minimal effect, 0.02622W/m·K at 25°C,
0.0457W/m·K at 325°C and only being 0.07% in the part ^{[110]}. Therefore the
values for full solid stainless steel 316L were used in the heat transfer
modelling.

To measure the powder bed thermal conductivity, containers shown in Figure
3-15 were built with 1mm thick top and bottom lid, and a series of sidewall
thickness 1mm, 1.5mm, 2mm, 2.5mm and 3mm. Due to the accuracy and
limitations of the thermal conductivity apparatus^{[172]}, three measuring
temperatures 100°C, 200°C and 300°C were selected. Each measurement
was repeated twice to obtain a reliable range of the readings, and the results
were shown in Figure 7-1.

**Figure 7-1 Powder bed thermal conductivity based on different sidewall ****thickness **

In Figure 7-1, the sidewall thickness shows a linear effect on the measurement results, and the powder bed thermal conductivity was obtained when the sidewall thickness was zero. The results show the LPW powder bed has thermal conductivity of 0.5W/m·K at 100°C, 1.2W/m·K at 200°C and

y = 1.9711x + 0.4834

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1.9W/m·K at 300°C. These values were inputted into Equation (3.2) to calculating the thermal conductivity kp (P for powder) at different temperatures for the powder bed, shown in Equation (7.2).

(7.2)

**7.2.3 Specific heat capacity **

The specific heat capacity of solid stainless steel 316L is 500J/kg·K at the
temperature 0-100°C ^{[188]}. The parts generated by the SLM process have a
maximum density of 99.93%, and only 0.07% porosity. The remaining 0.07%

of air has specific heat capacity 1005J/kg·K in the temperature range ^{[189]},
and its specific heat capacity is also temperature dependent ^{[190]}. The
influence rate of the air on the built part specific heat capacity is calculated
below:

As discussed in section 7.2.2, due to the small influence rate of the air and the complex calculation for the combining properties, the specific heat capacity of the gas in the pores is ignored, and the values for fully solid stainless steel 316L were used in the heat transfer modelling.

Based on the temperature dependent specific heat capacity values obtained
from the metal handbook ^{[188]}, the Equation (3.4) is converted to Equation
(7.3) for calculating the specific heat capacity CpS (S for solid) at different
temperatures for the bulk stainless steel.

^{ } (7.3)

A Shimadzu DSC-60 with temperature range -150 to 600°C, heat flow range

±40mW was used for measuring the specific heat capacity thermal curves of
the stainless steel 316L powder provided by LPW Technology ^{[191]}. The heat

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flow as a function of temperature is shown in Figure 7-2. The measurement was repeated to reduce any reading or operating errors, and the results are shown in Figure 7-3.

**Figure 7-2 Specific heat thermal curve for stainless steel 316L powder **

* Figure 7-3 Calculated specific heat capacity of powder bed *
-4

-2 0 2 4 6 8

0 100 200 300 400 500 600

**Sp****e****ci****fi****c ****h****e****at ****cap****ac****ity ****(J****/g****K****) **

**Temperature (°C) **

First test Second test

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The calculated specific heat capacity of stainless steel 316L powder bed is between 0-654J/kg·K at the temperature 0-550°C with temperature dependent property. Measurement errors between temperature range 0-180°C resulted in negative values. These errors appear in the range when the heat flow increased gradually in Figure 7-2 at the beginning of the measurement, where this increase rate did not repeat when the samples were cooled down at the end of the measurement.

Due to the large measuring error by the experiment above, another estimation method for the specific heat value at typical room temperature conditions was developed. The powder bed can be defined as a mixture of powder and air, and the specific heat capacity of the powder bed may be calculated by two main medium values – solid stainless steel 316L and air.

The measured powder bed density is 4880kg/m^{3}, which is 61% of solid full
density 8000kg/m^{3} with specific heat capacity 500J/kg·K; the remaining 39%

of air has specific heat capacity 1005J/kg·K^{[192]}. So the estimated specific
heat capacity value can be calculated by the equation below:

⁄

Considering the temperature dependence, the estimation solution used above is converted to Equation (7.4) to calculate the specific heat capacity CpP (P for powder) for the powder bed at a given temperature T.

( ) _{ }( ) _{ }( ) (7.4)

Where CpA (A for air) is the specific heat capacity for the air, and it has the
same relationship with the temperature described in the Equation (3.4) ^{[193]}.
Based on the temperature dependent specific heat capacity values obtained
from the reference ^{[190]}, the Equation (3.4) is converted to Equation (7.5) for
calculating the specific heat capacity CpA (A for air) at different temperatures
for air.

^{ } (7.5)