Understanding softening of amorphous materials for FFF applications

Appendix A Material properties

The material properties used for the analytical and numerical modeling are shown in Table 9.

Appendix B COMSOL multiphysics

B.0.1 Simulation setup

To simulate the pressure-induced melt removal process, it is necessary to simulate the material and air interface interaction. The physics that allowed the simulation are laminar flow, level set, and heat transfer in fluids within COMSOL Multiphysics. A time-dependent study with phase initialization was employed for the simulation, required for the level set physics.

In the global definition section, variables were created. In particular, the heater temperature and the viscosity model parameters for each material were defined. The viscosity model used for the numerical simulations was the fitted model shown in Eq. (23). The model calculates the viscosity as a function of temperature. For each material, the respective fitting parameters were used. Later, a step function was created for the application of the force.

The geometry was modeled axisymmetric in a 2D plane. Here, a rod (polymer) with a radius of 3.175 mm and a length of 15 mm was used. Next to the rod, an air region with a height of 7 mm and a width of 5 mm was created. Since the melt film is created next to the heated region (area of interest), only this area was modeled. Later, the regions were assigned with the respective material. Figure 11 shows the geometry.

Figure 11:

COMSOL geometry where (A) is the entire geometry and (B) is a region were material was removed.

Figure 12 shows a schematic of the sections where the boundary conditions were applied. From herein, the boundary condition section will be referred according to the section letter. Here, the shaded area in yellow corresponds to the polymer material, while the red shaded area corresponds to the air. A region was removed (0.01 mm by 1 mm) at the upper region of the material and air interface. The region was removed to approximate the simulation setup to the experimental setup as there is no wall at the end of the guider. The shape of the removed region can be seen between sections B and C.

Figure 12:

Schematic of section where boundary conditions were applied.

Each material property was assigned according to the respective material. In the laminar flow physic, two-fluid properties and material regions were created. As the materials have high viscosity, the inertial terms were neglected. Section A corresponds to the inlet. A pressure inlet was applied to this section, assigning the applied force to the material. The pressure was set together with the step function, which helps the numerical simulation at the first steps. A slip wall boundary condition (from (3.175, 6) to (3.175, 15)) corresponding to section B was assigned, simulating the guider used in the experimental setup. Section E corresponds to a wall with a no-slip condition, and it is the surface where the melted material flow. Section D corresponds to an outlet.

In the level set physic, the reinitialization parameter was set to 14 × 10⁻⁵ m/s. A good estimation of the reinitialization parameter is the maximum expected velocity magnitude (“Two-Phase Flow Modeling Guidelines” n.d.). At the same time, the initial values of both materials were specified, and the initial interface was defined. Section A corresponds to the inlet of fluid #2, and D is assigned as an outlet. Finally, a cubic discretization was selected to increase the resolution of the material and air interface.

In the heat transfer in fluids physic, two liquids were assigned. A thermal insulation boundary condition was assigned to Sections A–C. Section E is a temperature boundary condition corresponding to the plate temperature. An outflow boundary condition in section D was also defined to allow heat flow out of the geometry. Moreover, the Phase Change Material feature for the material was enabled, which tracks the position of the melting/softening region within the simulation. Here the melting/softening temperature and the heat of fusion of the material were specified. Notice that the heat of fusion was given only for PA6 and PP as these are semi-crystalline materials and have a defined melting temperature. For the Amorphous materials, the heat of fusion had a zero value, and the glass transition temperature, assumed as the softening temperature, was used as the melting temperature.

Two multiphysics were enabled for the simulation. These are two-phase flow and nonisothermal flow. In the two-phase flow physic, each material was assigned. Material #1 corresponds to air while material #2 corresponds to the polymer material. In the nonisothermal flow physic, the viscous dissipation option was disabled. Also, the surface tension between the materials was disabled.

A fine free triangular mesh was used for the majority of the geometry. An extra-fine mesh was used to increase the resolution of the area of interest using fluid dynamics physics. The rest of the geometry was meshed using a regular mesh as shown in Figure 13. Meshing consisted of 11,866 domain elements and 530 boundary elements. A mesh sensitivity analysis was not performed in this work. However, it is suggested for future work to study the effect of mesh size on the simulationresults.

Figure 13:

Schematic of the mesh resolution for the simulation geometry.

A simulation time of 35 s was implemented to compare the experimental data, including starting and removing the sample from the heated surface. Finally, the results were processed and compared with both the experimental data and the analytical solution.

Appendix C DSC analysis

DSC results for two heating ramps are shown in Figure 14. The results are averaged from three runs, all at the same conditions.

Figure 14:

DSC results for (A) PA6, (B) PP, (C) PC, and (D) PVC.

Figure 14A shows the DSC result for the PA6 material. At a temperature ramp of 10 K/min, an exothermic region can be observed around a temperature of 443 K. To discard the presence of water, the PA6 was dried at a temperature of 85 °C for 12 h. As observed in the figure, the exotherm can be observed even for the dry material. This transition is not observed for a 2 K/min temperature ramp due to the sensitivity decrease. For a high heating rate, the resolution is decreased while the sensitivity increased. The opposite happens when the heating rate is decreased (Saeed et al. 2016). The exothermic region is due in part to the recrystallization of the PA6 molecules at the respective temperature (Ma et al. 2016; Rwei et al. 2016).

Figure 14C and D show the results for the PC and PVC respectively. As shown in the figure for PC, the glass transition can be observed for both heating rates. Artifacts at the end of the data can be seen for the 10 K/min heating rate. These artifacts are also present for PVC for both heating rates. Artifacts are thermal events that do not directly relate to changes in the physical properties of the sample “Unusual Sample Properties as an Origin of Artifacts” (n.d.).

For the PVC material, the first transition occurs at 65.15 °C and represents the glass transition temperature. The first endothermic region represents the softening of the partially gelled crystallites or the level of gelation present in the first area. The second endotherm means the softening of crystallites that did not gel during the heating of the sample (Gramann et al. n.d.). With this information, the degree of gelation can be determined. To calculate the degree of gelation, two endothermic areas, H _a and H _b , are needed (Fujiyama and Kondou 2003). The degree of gelation can be calculated using Eq. (25).

Endotherm A and B are 4998 and 626 J/kg for a 10 K/min heating rate. The degree of relation results in 88.87%. The higher the degree of gelation, the better the mechanical properties of the material will be (Zajchowski 2005).