CHAPTER 2. LITERATURE REVIEW
2.2 Additive manufacturing (AM) and applications
2.3.3 Melting viscosity, surface tension and particle size
The other important parameters in the SLS process are melting viscosity, surface tension and particle size. The relationships among these parameters for viscous sintering was firstly established by Frenkel in 1945 [Ajoku et al, 2006b], whose formula states that the energy generated during viscous flow is equal to the energy
Chapter 2. Literature Review Page 26
gained by the reduction in the surface area. Frenkel then used an equation to explain the neck formed in a combination of two adjacent particles, n, as shown in equation 2.2 and Figure 2-12. o r t r x 2 3 2 ... (2.2) where: x = half the thickness of the neck, r = radius of a sphere, = surface tension of the material, t = time needed for sintering and 0 = melting viscosity.
Figure 2-12 Frenkel‟s sintering model [Ajoku et al, 2006b]
Frenkel analysed the initial stages of the sintering process in crystalline particles and stated that, when high temperature is applied this could serve as a catalyst which will change the crystal form of the structures. Increasing the temperature of the particle resulted in an increase in surface contact area between adjacent particles, and the volume of viscous flow between the particles can cause or eliminate pores. It can be assumed that the sintering that occurs between two particles is formed completely when x/r = 0.5 [Rosenzweig and Narkis, 1981].
From this theory, using equation 2.2, Frenkel illustrated the role of temperature during the sintering process and confirmed that using higher temperatures cause an increase in necking radius between sintered particles. Greater bonding between the particles occurs and pores are reduced when the necking radius increases.
Figure 2-13 Cross-section of particle-particle bonding in x, y and z axes (Dx > Dy > Dz)
Chapter 2. Literature Review Page 27
In addition, Ajoku et al [2006b] investigated the bonding between particles in each different fabrication orientation. This phenomenon was observed when they investigated the effect of build orientation and end-of-vector (EOV) effect on the mechanical properties of laser-sintered components. A 3D Systems Vanguard SI laser sintering machine was used and a laser scanning strategy in the x scan vector only was applied.
They illustrated the cross-section of particle-particle bonding in the x, y and z axes fabrication orientations, and the findings showed that the diameter of the neck in thex axis (Dx) is greater than the diameter of the neck in the y axis (Dy), and then (Dx)
and (Dy) are greater than the diameter of the neck in the z axis (Dz), as illustrated in
Figure 2-13.
Polymer powder melts when an infrared laser sinters the component, where the particles bond together. The laser scans as a vector on a layer to build up the first layer of component in the x direction and forms a neck with diameter Dx, as shown in Figure 2-13(a). After finishing the first vector in this direction, the laser switches off automatically and an increment occurs in the y direction that allows the laser to scan the next vector. The bonding in the previous vector is shown in Figure 2-13(a), and the bonding between particles in the x direction is quite similar. But particles in the previous vector in the y direction will have cooled and, therefore the bonding between these particles will be less than between those in the x direction, with a smaller necking diameter Dy (Figure 2-13(b)). After this layer is completely sintered, then a new layer of powder is applied. The particle bond in the previous layer will have cooled to the point where the bonding between particles in different layers is less than the bonding between particles in different vectors with an even smaller neck diameter,
Dz (Figure 2-13 (c)).
From their work, Ajoku et al [2006b] summarised that the mechanical properties from different fabrication orientations are different (anisotropy). The highest tensile and compression strength results from an x axis-fabricated part and the lowest results from the z axis fabrication orientation. This agrees with the results of previous work by Gibson and Shi [1997], in which the best tensile strength of a laser-sintered part results from the test component built in the x axis orientation and the lowest value is obtained from the z axis. However, for flexural strength, the highest value is obtained
Chapter 2. Literature Review Page 28
from the y axis-fabricated component, followed by that in the x axis and the lowest value for the z axis.
These findings also showed that the degrees of bonding between particles and the subsequent bonding between layers are different in each direction of fabrication. Bonding is also affected by the scanning strategy applied in each layer for different fabrication orientations.
In selective laser sintering, the laser scans across the whole two-dimensional area, which consists of parts being built. Greater time is taken for the laser to restart scanning on a subsequent layer if the two-dimensional scan area is larger.
a. Melting viscosity (0)
The melt flow ratio or melt flow index (MFI) can be used to determine the melt viscosity of a material. For polymer materials, the standard test of melt flow ratio can be applied to measure its melt flow properties [ASTM D1238, 2004].
The MFI has units of gram/10min, determined from the mass of polymer extruded during 10 minute of steady flow.
For instance, Kim and Creasy (2004) investigated the melt flow characteristics of PA6 and PA6/clay nanocomposite, as shown in Figure 2.14. They found that the melt flow of PA6 was 1.68 times greater than that of the PA6 nanocomposite.
Figure 2-14 Melt flow response of polyamide with and without nanoclay reinforcement (Kim and Creasy, 2004)
For most polymers, the temperature dependence of viscosity is modeled with an Arrhenius relationship as follows (Nelson et al., 1993):
Chapter 2. Literature Review Page 29 RT E A m exp ……….………. (2.3)
where Eis the activation energy for viscous flow and A is the frequency factor, R is the gas constant and T is the absolute temperature (K).
The melt viscosity,
m
, of polymers follows an Arrhenius relationship with temperature (T), typically decreasing by a factor of 2 for every 25oC increase in temperature at low shear rates (Nelson et al., 1993).Equation 2.3 also suggests that, to consistently produce parts with uniform quality, the size of powder particles and their distribution must be uniform to ensure a uniformity of polymer molecule weight since melting viscosity is influenced by average molecular weight (Mw).
The melting viscosity and molecular weight of polymer material follow the relationship given by Shi et al [2004] as shown in equation 2.4:
0 = k(Mw)n ... (2.4)
where 0 is the melting viscosity, Mw is molecular weight, k is a constant, and n is
another constant value that depends on the critical molecular weight value MC. When
the molecular weight is less than MC, n = 1, if it is or greater than MC, n = 3.4.
Equation 2.4 indicates that melting viscosity varies with change in molecular weight. So the quality of the SLS product is affected by the molecular weight via the melting viscosity [Shi et al, 2004]. More discussion of this relationship is given in section 2.3.4
b. Surface tension ()
“Surface tension is the driving force for sintering, where the viscous forces must be overcome in order to allow powder sintering” [Ajoku et al, 2006b]. An interaction between molten and non-molten particles occurs during the sintering process, where the molten particle flow freely to attract non-molten powder particles. The powder melts as large amounts of energy go through the surface of the powder bed. The molten particles flow freely to minimise surface energy within the powder particles. As necks form between particles, surface tension causes the material from the two particles to flow together [Nelson, 1993]. The surface tension of polymer powder is about 0.02-0.03 N/m [Shi et al, 2004].
Chapter 2. Literature Review Page 30
c. Particle size
The particle size of the powder material is a factor that must be considered in achieving the required surface smoothness and feature definition of the product. The precision and density of SLS parts is also affected by particle size, which may be different when different methods are used in producing the powder. For polymer material, particle sizes between 75-100µm are suitable, where a larger size of particle can cause a bigger step/layer thickness effect but a smaller size is difficult to spread [Shi et al, 2004].