Crystallization modeling of two semi-crystalline polyamides during material extrusion additive manufacturing | Scientific Reports

Scientific Reports volume 14, Article number: 26297 (2024) Cite this article

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In this work, a heat transfer model is developed for thermally-driven material extrusion additive manufacturing of semicrystalline polymers that considers the heat generated during crystallization by coupling crystallization kinetics with heat transfer. The materials used in this work are Technomelt PA 6910, a semicrystalline hot melt adhesive with sub-ambient glass transition temperature (Tg) and slow crystallization, and PA 6/66, a traditional semicrystalline polyamide with a higher Tg and fast crystallization. The coupled model shows that the released heat during crystallization depends on material selection, with Technomelt PA 6910 and PA 6/66’s temperatures increased by less than 1 °C and up to 6.3 °C, respectively, due to enthalpy of crystallization. Increasing the layer time decreases the layer temperature as well as the initial crystallinity. However, its effect on final crystallinity in Technomelt PA 6910 is negligible due to continued crystallization of the material after printing. Experimental validation shows good agreement for Technomelt PA 6910, but consistently underpredicts PA 6/66 crystallinity. Increasing modeled environmental temperature leads to better agreement with experimental results for PA 6/66, suggesting that higher temperatures may have been experienced. Shear-induced crystallization may also be contributing to crystallinity in this material. The results from this model highlight the importance of and interrelationships between material and processing parameter selection and can aid in achieving quality prints from semicrystalline thermoplastics.

Fused filament fabrication (FFF) is a desktop scale, thermally-driven form of material extrusion additive manufacturing. In FFF, the final weld strength and residual stresses are a function of temperature during the built process. Experimental temperature measurements are the best direct determination of printed structure temperature; however, experimental temperature measurements have limitations. Thermocouple embedding requires print interruption, which adds extra cooling time to the printed layers and a thermocouple can provide information only for a single point1,2. IR thermography is limited to surface temperature measurements but without any print interruption3,4. Temperatures can be determined from thermocouples in the hot end, but this requires specific design of the hot end and provides information about the material prior to deposition5,6. The temperature profile within the part and between layers is of great importance in assessing the weld strength between deposited layers, which motivates continued research in predictive models.

To simulate heat transfer in FFF, achieving the exact solution to the overall heat transfer equation through analytical solving is prohibitively difficult due to the high complexity of the system, which encourages use of numerical solutions. Finite element analysis (FEA) is commonly used for complex engineering problems with specified boundary conditions. FEA divides the analyzed region into many finite elements called meshes, and then numerically solves a system of equations describing the system in nodal points of meshes. Interpolation functions are used between nodes in each mesh to describe the variation of the temperature as a function of the global coordinates. The size and shape of the meshes need to be defined in a way that the model can provide high accuracy without increasing the computational time and costs significantly. Many 2D and 3D FEA-based models of FFF have been reported that simulate heat transfer7,8,9,10,11.

Modeling of FFF for semicrystalline polymers is complicated by the crystallization process. Crystallization rates are temperature-dependent, so the amount of crystallization that occurs in a rapidly cooling process such as FFF is highly material- and process parameter-dependent. Crystallization may be induced by flow12,13. Furthermore, crystallization generates heat, which can change the thermal profile significantly14. These phenomena may also lead to variations in crystallinity within a printed structure, which affects physical and mechanical properties. Most FEA of semicrystalline polymer FFF has focused on how crystallization affects residual stresses and warpage15,16,17. Other work developed models for predicting interlayer fracture toughness18.

In this work, we present a FEA model of crystallization evolution during FFF that couples crystallization kinetics with a heat transfer model accounting for heat generated during crystallization. Two semicrystalline polyamides are considered: a hot melt adhesive with slow crystallization kinetics at relatively low temperatures and a polyamide 6/66 blend with fast crystallization kinetics at higher temperatures. The effects of layer time, which is the time required to print a single layer, and material selection on crystallization are predicted and compared to previous experimental work19. Additionally, time and location of formation of crystallites within the built structure is predicted. To our knowledge, this is the first report focused on the coupled relationship between crystallization and heat transfer in FFF. By comparing two semicrystalline materials with different crystallization behaviors, insights can be drawn for future material and process development.

Technomelt PA 6910, a semicrystalline polyamide-based hot melt adhesive, was kindly provided by Henkel. PA 6/66 is a blend of PA 6 and PA 66, which is a natural-colored Nylon 6/66 copolymer filament that is sold by KODAK as their Nylon 6 filament. Material-specific values used for modeling are summarized in Table 1. Density values were experimentally determined using a density kit and a laboratory scale (both from Mettler Toledo). The other properties in Table 1 were determined via differential scanning calorimetry (DSC) using a Mettler-Toledo DSC 3 + system.

A 2D heat transfer model was created using COMSOL Multiphysics 5.4 to simulate heat transfer within hollow single road boxes with different wall lengths of 25 mm, 40 mm, and 60 mm. Technomelt PA 6910 and PA 6/66 were modeled. We previously compared the crystallization kinetics of these two polyamides20. Conduction and natural convection are considered in the model, but radiation is neglected because it does not significantly affect heat transfer on the FFF scale given the relatively low temperature and small thermal masses10,11,21. A printer fan was not used in the experimental setup, so forced convection was not considered. The model also includes a measurement of relative crystallinity. These equations are described in greater detail below.

In FFF, material is deposited layer-by-layer to achieve the final part. The deposited layers cool down rapidly to maintain their shape. Therefore, the model simulates material deposition and its thermal effects on previously deposited layers. To model heat transfer within a FFF build during printing, several simplifications were made. The road shape is assumed to have a rectangular cross-section with full contact between roads. Generally, road cross-sections in single road width parts can be described geometrically as rectangular bonded sections with semi-circular non-bonded sections22. Since the bonded portion of these materials is much larger than the non-bonded portion19, approximating the road geometry as rectangular is reasonable. To further simplify the model, material flow was not simulated directly. Instead, a uniform change in height across the part at a specified time was considered, and the initial temperature of each layer was specified as the extrusion temperature (220 °C for Technomelt PA 6910, 250 °C for PA 6/66). The temperature-dependence of material properties was neglected to simplify calculations.

The governing differential heat transfer equation is given by Eq. 1:

where ρ is the density of the material, Cp is the heat capacity and k is the thermal conductivity. Q describes the external sinks or internal heat sources, which can result from chemical reactions or crystallization. Therefore, Q will be used to couple the heat transfer model with crystallization kinetics analysis.

The crystallization kinetics of the material (either Technomelt PA 6910 or PA 6/66) was coupled with the heat transfer model to investigate the amount and location of development of crystallites during FFF. Additionally, the coupled model accounts for the released heat during crystallization. The model for crystallization kinetics needs to account for the non-isothermal characteristic of FFF. Avrami developed an isothermal model for the kinetics of crystallization23, which was extended by Ozawa to constant cooing rate conditions24, and further extended by Nakamura to non-isothermal conditions at any cooling rate25.

n is the Avrami exponent and α is relative crystallinity calculated by the partial area method, which is the area under the crystallization peak at time t divided by the total area. KNak is the Nakamura kinetics crystallization function, which is related to the Avrami coefficient (KAv) and Ozawa constant (KOz) by:

Nakamura’s model provides information about the relative crystallinity as a function of thermal history independent from the cooling rate, which makes it well-suited to analysis of FFF due to the different cooling rates under non-isothermal conditions3. Note that relative crystallinity is defined as the fraction of total crystallinity at a specified time.

Nakamura’s theory was simplified by Patel and Spruiell into a differential form (Eqs. 2),26 which is useful for coupling with thermal models27.

A modified form of the Avrami coefficient is used in this work that accounts for non-isothermal crystallization28. Therefore, KAv and Koz are dependent on the nucleation, growth, and cooling rates. KAv and KOz were determined in previous work via DSC and fast scanning calorimetry (FSC)20. KNak was calculated according to Eq. 3 and the logarithm of KNak was fit to a second order polynomial to describe KNak as a function of T. For Technomelt PA, 6910, the relationship between KNak and T is

For PA 6/66, the relationship between KNak and T is

The fits for both polynomial regressions are very good (R2 = 0.9876 for Eq. 5, R2 = 0.9678 for Eq. 6). Since the data were collected using FSC, values for Knak were determined across broad temperature ranges (15–70 °C for Technomelt PA 6910, 70–170 °C for PA 6/66)20.

Nakamura’s non-isothermal crystallization kinetics model can be coupled to the heat transfer model in COMSOL using Distributed ODE interfaces for numerical analysis. The generated heat Q in Eq. 1 is defined as Eq. 7 and completes the set of equations required for this modeling:

Hf is the heat of fusion, which is 25 J/g for Technomelt PA 6910 and 35 J/g for PA 6/66, and ρ is 985 kg/m3 for Technomelt PA 6910 and 1,140 kg/m3 for PA 6/66.

A schematic of a hollow box and its cross-section used in modeling is shown in Fig. 1. Heat transfer was simplified into a 2D model by neglecting the heat diffusion within the road length. The initial temperature for each layer was set to the extruder temperature of 220 °C for Technomelt PA 6910 and 250 °C for PA 6/66. To account for heat conduction between the build plate and deposited layers, the bottom of the first road was set to the bed temperature of 60 °C. Convective cooling of the layers before deposition of the next layer is modeled by external natural convection, which considers air as the cooling fluid with an absolute pressure of 1 atm and a constant ambient temperature of 26 °C based on experimental measurements. Based on a constant print speed of 10 mm/s, layers times of 10 s, 16 s, and 24 s are calculated for boxes with wall lengths of 25 mm, 40 mm, and 60 mm, respectively. A layer height of 0.15 mm and a layer width of 0.4 mm is used in the model. These values were chosen because they match a previous experimental study19. 8 layers are considered for this model.

Schematic of the hollow cube geometry for the heat transfer model.

Single road boxes were printed on an Ultimaker 3 using the same print conditions as were input to the models. Specifically, the extruder temperature was set to 220 °C for Technomelt PA 6910 and 250 °C for PA 6/66. The bed temperature was set to 60 °C and the lab temperature was 22 ± 1 °C. The single road width boxes had wall lengths of 25 mm, 40 mm, and 60 mm and were printed at a layer height of 0.15 mm and layer width of 0.4 mm. A print speed of 10 mm/s was used throughout, so the 25 mm box had a layer time of 10 s, the 40 mm box had a layer time of 16 s, and the 60 mm box had a layer time of 24 s. Technomelt PA 6910 single road width boxes have been previously reported19, while PA 6/66 single road width boxes were printed at the three wall lengths. Figure 2 shows a representative single road width box.

Representative single road width box of PA 6/66 with a wall length of 40 mm.

Material properties given in Table 1 were determined via DSC. Tg and Tm were determined from the heating cycle at 10 K/min. Crystallinity in the PA 6/66 boxes was characterized using DSC at a heating rate of 10 K/min in the top (layer 8), middle (layers 4 and 5), and bottom (layer 1) of the box. The melt enthalpy in the first heating cycle was measured. For determination of relative crystallinity, complete crystallinity was defined based on the maximum enthalpy of melting that could be determined from each material, which was obtained from the heating cycle after cooling each material from the melt 10 K/min – this measurement gave Hf. Each condition was measured in triplicate.

Density was measured using an XPR-S density kit on a balance (Mettler Toledo). Filament specimens were used for both materials to ensure that specimens were void-free. Each specimen was weighed air and then again in a liquid (water for PA 6/66, ethanol for Technomelt PA 6910 due to its low density). The density (ρ) was then calculated using Eq. 8:

where wair is the weight in air, wliquid is the weight when immersed in the liquid, and ρliquid is the liquid’s density.

The time-temperature profiles from the coupled thermal model with crystallization kinetics for boxes of Technomelt PA 6910 with different wall lengths are shown in Fig. 3. The thermal profiles are probed at the top center of each layer to study the effect of layer time on the interfacial temperature for each layer, which is important to interlayer diffusion and evolution of mechanical strength at the interface. In all models, the first layer quickly cools from the extrusion temperature of 220 °C to the bed temperature of 60 °C due to heat conduction between the first layer and the print bed. The effect of print bed temperature on thermal profile decreases at subsequent layers and a steady state temperature profile is observed after layer 4. Therefore, layer 5, which captures a steady state temperature profile and experiences heat transfer from three layers above, is selected as the study target for the rest of the work.

Simulated time-temperature profile of printing the first eight layers of Technomelt PA 6910 for layer times of: (a) 10 s (box side length of 25 mm); (b) 16 s (40 mm); (c) 24 s (60 mm). Temperatures for a given layer are reported for the center of that layer’s top surface. The crystallization window is between the dashed lines and the fast crystallization window is shaded gray.

As can be seen in Fig. 3, layer 5’s minimum temperature during printing, which occurs just before deposition of layer 6, increases from 30 °C to 44 °C as the layer time decreases from 24 s to 10 s. The increased temperature gradient between layers with increased layer time has been previously reported for FFF11,29 and is consistent with the increased warpage in boxes with longer wall length in Pourali and Peterson19. The crystallization window for Technomelt PA 6910 was previously found to be between 15 °C and 70 °C20. Crystallization is favored in the temperature range of 35 °C to 45 °C, which will be referred to as the fast crystallization window. Since Technomelt PA 6910 has a low temperature range crystallization window that includes ambient temperature, parts spend a lot of time at temperatures where crystallization can occur.

Figure 4a compares the temperature profile for layer 5 of models with different layer times. Deposition of layer 6 results in a temperature spike in layer 5 due to incoming heat from the new layer. The interfacial temperature between layers 5 and 6 for samples with layer times of 10 s, 16 s, and 24 s peak at 128 °C, 124 °C, and 121 °C, respectively. All of these temperatures are all well above 85 °C, the melting temperature of Technomelt PA 6910. The high weld line temperature results in good welding between layers, which we have previously reported for single road width and multi-road width specimens19. Deposition of layer 7 increases the surface temperature of layer 5 above the crystallization window, which can aid in further diffusion of polymer chains across the weld interface for improved weld strength. However, the temperature spike associated with layer 8’s deposition for models with longer layer times is within the crystallization window due to their longer cooling time between layer depositions.

(a) Temperature profile and (b) relative crystallinity of layer 5 as a function of cooling time for Technomelt PA 6910 models with different layer times/box lengths. Temperatures are taken from the center of layer 5’s top surface, relative crystallization is taken from the center of layer 5’s cross-section. The crystallization window is between the dashed lines and the fast crystallization window is shaded gray.

The relative crystallinity of layer 5 as a function of time is shown in Fig. 4b. Steep slopes associated with faster crystallization are observed in the initial cooling times, followed by a gentle slope representing slower crystallization at longer cooling times. The rate of relative crystallization during printing for the 10 s layer time system is 11% lower than for conditions with longer layer times. This lower slope is related to the higher layer temperature associated with a shorter layer time as can be seen in Fig. 4a. For a layer time of 10 s, layer 5 stays above the fast crystallization temperature range until 80 s (when the final layer is added), which results in slower crystallization. After 80 s, the temperature briefly lowers to the crystallization-favored range and crystallization continues at a similar rate, followed by slower crystallization as the system cools. For models with longer layer times, the initial fast crystallization continues up to when the final layer is printed and then transitions to slower crystallization. Lower layer times result in slower crystallization and higher layer temperature during printing, which can suppress warpage. This result is consistent with previously reported experimental results19.

Interestingly, the crystallinity after printing is completed (t > 192 s) is similar for all models regardless of the layer time, which is related to Technomelt PA 6910’s slow crystallization at a wide range of temperatures, including at room temperature. This result is consistent with the similar final crystallinity measured for specimens from hollow boxes with different wall lengths, which provides validation of this model19.

Layer 5 temperatures from models with and without coupled crystallization kinetics are shown in Fig. 5. The released heat from crystallization is minimal and both models show similar thermal profiles. The low melting enthalpy of Technomelt PA 6910 and its slow crystallization over time prevents sudden and significant heat release during printing. The enlarged region of the graph shows the largest temperature difference between the models, which occurs immediately after printing of the final layer (layer 8). The coupled model exhibits a slightly higher layer temperature (< 1 °C), demonstrating the model’s ability to capture released heat during crystallization.

Layer 5 thermal profiles for Technomelt PA 6910 heat transfer models for a layer time of 16 s with and without coupled crystallization kinetics. The insert shows temperatures for the two models immediately after the final layer is printed.

Since Technomelt PA 6910 showed relative crystallization that converged to the same level for all models, we chose to compare its behavior to another polyamide that can be printed via FFF. This is a commercially available blend of PA 6 and PA 66, which will be referred to as PA 6/66. Time-temperature profiles from the coupled thermal model with crystallization kinetics for printed boxes of PA 6/66 with different layer times are shown in Fig. 6. In all models, the first layer quickly cools from the extrusion temperature of 250 °C to the bed temperature of 60 °C due to heat conduction between the first layer and the print bed. Similar to Technomelt PA 6901, a steady state temperature profile is observed after layer 4, and, excluding the higher extrusion temperature, thermal profiles for PA 6/66 closely resemble those of Technomelt PA 6910. However, PA 6/66’s crystallization window is between 70 °C and 160 °C, with a fast crystallization window between 120 °C and 130 °C. Additionally, PA 6/66 crystallizes much more rapidly than Technomelt PA under almost all conditions: Technomelt PA 6910’s half time crystallization (t0.5) values range from 40 s to 800 s, while t0.5 values for PA 6/66 fall between 5 and 80 s20. Both crystallization window and t0.5 affect the amount of crystallization in a given location.

Simulated time-temperature profile of printing the first eight layers of PA 6/66 for layer times of: (a) 10 s (box side length of 25 mm); (b) 16 s (40 mm); (c) 24 s (60 mm). Temperatures for a given layer are reported for the center of that layer’s top surface. The crystallization window is between the dashed lines.

Temperature profiles for layer 5 of PA 6/66 models with different layer times are shown in Fig. 7a. Similar to Technomelt PA 6910, deposition of layer 6 results in a temperature spike in layer 5 due to incoming heat from the new layer. From FSC, PA 6/66’s melting temperature decreases with increasing cooling rate, reaching a plateau value of 156 °C. For a processing-relevant cooling rate, PA 6/66 will exhibit a Tg of approximately 65 °C20. Since all the temperature spikes in layer 5 are below 156 °C, the interface is not re-melting upon deposition of layer 6, although there is a short amount of time above Tg for interlayer chain reptation and crystallization. This limited time for crystallization is apparent in Fig. 7b, where relative crystallinity exhibits a beveled stepwise shape. Relative crystallinity increases in a decaying manner upon deposition of each subsequent layer, but crystallinity rapidly stops evolving after each layer is deposited. Relative crystallinity for the PA 6/66 systems is also highly dependent on layer time, with short layer times associated with higher crystallinity from the higher temperatures. The relative crystallinity of PA 6/66 is much lower than Technomelt PA 6910 because, although PA 6/66 crystallizes more rapidly, the system spends very little time within the crystallization window. These results highlight the importance of crystallization conditions as well as kinetics in achieving crystallinity in FFF parts.

(a) Temperature profile and (b) relative crystallinity of layer 5 as a function of cooling time for PA 6/66 models with different layer times/box lengths. Temperatures are taken from the center of layer 5’s top surface and relative crystallization is taken from the center of layer 5’s cross-section. The crystallization window is between the dashed lines and the fast crystallization window is shaded gray.

Layer 5 temperatures from PA 6/66 models with and without coupled crystallization kinetics are shown in Fig. 8. The maximum temperature difference between the models is 6.3 °C, which is substantially higher than what was observed for Technomelt PA 6910. This maximum temperature difference occurs during layer 5’s deposition, with crystallization increasing the temperature. It is interesting to note that the maximum temperature difference for PA 6/66 and Technomelt PA 6910 occur at different points in the printing process (i.e., during printing of the layer of interest vs. when printing has completed), highlighting the importance of material properties on thermal behavior, especially for semicrystalline polymers.

Layer 5 thermal profiles for PA 6/66 heat transfer models for a layer time of 16 s with and without coupled crystallization kinetics. The insert shows temperatures for the two models immediately after the final layer is printed.

Crystallinity evolution in Technomelt PA 6910 with different layers times is shown in Fig. 9. Newly deposited layers show low crystallinity due to a lower given time for their crystallization. However, adding layers on top of them provides enough annealing time for further crystallization. The last layer exhibits lower crystallinity compared to previous layers even after 300 s of cooling due to the absence of material above that leads to faster cooling below the fast crystallization temperature range.

Crystallinity in Technomelt 6910 during modeling of printing for layer times of (a) 10s; (b) 16 s; (c) 24 s. Each layer cooled down for one layer time (TL) and the legend indicates relative crystallinity for each layer. Note that each time uses the full color scale; for reference, relative crystallinity ranges for 8TL + 300 s are 0.60 to 0.69, 0.61 to 0.77, and 0.61 to 0.82 for layers times of 10 s, 16 s, and 24 s, respectively.

Similar trends in crystallinity are observed for all layer times, although the final maximum crystallization increases slightly with increasing layer time. This is because models with longer layer times give earlier layers more time to crystallize within the modeled timeframe: 8TL + 300 s = 380 s for a layer time of 10 s vs. 492 s for a layer time of 24 s.

Figure 10 shows crystallinity evolution in PA 6/66 for the three investigated layer times. Similar levels of crystallinity are observed for the final layers at each layer time. For earlier layers, lower layer times result in increased and earlier crystallinity. Limited variation in crystallinity is observed across the cross-section of a given road, indicating that crystallinity is constant within a single layer.

Crystallinity in PA 6/66 during modeling of printing for layer times of (a) 10s; (b) 16 s; (c) 24 s. Each layer cooled for one layer time (TL) and the legend indicates relative crystallinity for each layer. Note that each time uses the full color scale; for reference, relative crystallinity ranges for 8TL + 300 s are 0.00458 to 0.217, 0.00256 to 0.120, and 0.00132 to 0.0846 for layers times of 10 s, 16 s, and 24 s, respectively.

PA 6/66 crystallinity results were compared to experimental levels of crystallinity in 8 layer boxes of PA 6/66, as determined from melting enthalpy in DSC. Results are shown in Fig. 11. All melting enthalpies fall within a narrow range (31.15 ± 0.48 J/g to 36.57 ± 2.22 J/g), consistent with the narrow range of relative crystallinity values predicted by the finite element model. These values for the enthalpy of melting are consistent with 86–100% relative crystallinity (note that 100% relative crystallinity indicates that all crystallization that can be achieved in this particular formulation has been realized), which is much higher than the predicted relatively crystallinity values.

Enthalpy of melting from DSC of 8 layer boxes of PA 6/66 and associated relative crystallinity. Error bars indicate standard deviation.

One possible source of error is the environmental temperature, which was experimentally measured to be 26 °C; however, this measurement was taken some distance from the printed structure. Average temperatures near a hot end while extruding at similar temperatures were measured to range from 70.5 °C to 83 °C (Adisa, A. O., Kamzer, D. O.; Peterson, A. M.: Modeling the effects of thermal contact resistance on mechanical properties in material extrusion additive manufacturing, submitted), so it would be reasonable that environmental temperatures near the printed structure would be higher than 26 °C. To investigate the effect of environmental temperature on crystallization, we compared the base case to two alternatives: (1) Air temperature of 40 °C on the sides of the print and 80 °C on the top surface; (2) Air temperature of 60 °C on the sides of the print and 80 °C on the top surface. Results are shown in Fig. 12. Increasing the environmental temperatures increases the relative crystallinity, which represents a promising approach to increase crystallinity of printed structures. However, even with the highest environmental temperatures, the predicted crystallinity ranges from 53 to 78%, which is still lower than the measured values. This indicates contributions from another crystallization mechanism. A non-thermal mechanism, such as flow-induced crystallization, may also be contributing to crystallization in the PA 6/66 system. Flow-induced crystallization has been widely studied in PA 6 and PA 66, thanks in part to the industrial importance of Nylon fibers30,31,32,33. Although 100% relative crystallinity can be achieved in printed PA 6/66, the total crystallinity is still quite low as compared to pure PA 6 or PA 66 – for comparison, the enthalpy of melting of perfect PA 6 and PA 66 crystals are reported as 176.4 J/g and 188.1 J/g, respectively34,35. It may be advantageous for semicrystalline polymers used in FFF to exhibit lower levels of crystallinity to reduce the potential for warpage15,19.

Final (at t = 8TL + 300s) relative crystallinity for PA 6/66 for a layer time of 10 s with different environmental temperatures. (a) 26 °C (i.e., base case shown in Fig. 10a); (b) sides of print at 40 °C, top surface at 80 °C; (c) sides of print at 60 °C, top surface at 80 °C.

This work aims to study the effect of crystallization kinetics on heat transfer during FFF of two semicrystalline polyamides. A 2D model was developed based on an experimental system of single road width hollow boxes with wall lengths of 25 mm, 40 mm, and 60 mm. Each material’s crystallization kinetics was coupled to the heat transfer model.

Initial crystallization is faster for models with longer layer times due to their longer time at temperatures where crystallization is favored. The second phase of crystallization occurs slowly during cooling of the layers down to room temperature. For Technomelt PA 6910, this results in a similar final crystallinity for all layer times due to its slow crystallization at a wide range of temperatures, including at room temperature. For PA 6/66, crystallinity in intermediate layer decreases with increasing layer time due to this material’s rapid crystallization kinetics at relatively high temperatures. The model effectively captures released heat during crystallization. The released heat during crystallization of Technomelt PA 6910 increased the layer temperature by less than 1 °C due to its low melting enthalpy. Due to PA 6/66’s higher melting enthalpy and faster crystallization kinetics, the released heat during crystallization for this material increased the layer temperature by up to 6.3 °C.

Results from the coupled model provide insight about the significance of heat generated during crystallization on temperature profiles in different layers of FFF. Additionally, the model can predict the time and location of formation of crystallites within the built structure, which can enable optimizing printing parameters to control crystallization-induced warpage and improving weld strength between layers. Crystallization-induced warpage can be caused by different amounts of crystallization in proximate portions of a printed part and by high amounts of crystallization near areas that have already achieved their final morphology (i.e., cooled to a point where no more crystallization is possible and the amorphous regions are below Tg). One example of the potential impact of this work is to use this approach to identify if there will be high gradients in crystallinity or areas where large amount of crystallization are predicted to occur near portions of a printed structure that have already substantially cooled. If the model identifies either of these issues, then toolpaths can be re-designed or different processing conditions (e.g., print speeds, extrusion temperatures) can be used to ameliorate. One limitation of this work is that the model does not consider flow-induced crystallization, which could substantially increase the amount of crystallinity. Extending the models to incorporate flow-induced crystallization is a goal of future work.

Combined, these results demonstrate that crystallization kinetics dramatically affects the importance of processing parameters on crystallinity development within material extrusion additively manufactured structures. Materials with fast crystallization at temperatures higher than ambient are much more sensitive to processing conditions because the material only gives limited time for crystallinity to evolve. However, these types of materials also provide a larger increase in temperature due to crystallization enthalpy, which may help increase the amount of crystallinity. For example, increasing the environmental temperature can substantially increase crystallinity. Materials with slower crystallization at temperatures that include ambient can continue to evolve crystallinity over long time periods, resulting in crystallinity that does not depend on layer time. For situations where processing parameters affect crystallinity, it is recommended that part and processing design occur in concert to achieve structures with desired properties.

The datasets generated during the current study are available from the corresponding author on reasonable request.

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The authors acknowledge financial support from the National Science Foundation (CMMI-1853480). The authors also thank Henkel Corporation for providing Technomelt PA 6910 and thank Charles Paul, Luca Marchese, and Tim Welters of Henkel Corporation for insightful conversations and guidance.

Department of Plastics Engineering, University of Massachusetts Lowell, 1 University Ave, Lowell, MA, 01854, USA

Masoumeh Pourali, Ahmed Adisa, Shalmali Salunke & Amy M. Peterson

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Masoumeh Pourali: Conceptualization, Methodology, Software, Validation, Formal Analysis, Investigation, Writing – Original Draft, Visualization. Ahmed Adisa: Formal Analysis, Investigation, Writing - Original Draft. Shalmali Salunke: Methodology, Software, Validation, Formal Analysis, Investigation. Amy Peterson: Conceptualization, Methodology, Resources, Writing – Review & Editing, Supervision, Project Administration, Funding Acquisition.

Correspondence to Amy M. Peterson.

The authors declare no competing interests.

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Pourali, M., Adisa, A., Salunke, S. et al. Crystallization modeling of two semi-crystalline polyamides during material extrusion additive manufacturing. Sci Rep 14, 26297 (2024). https://doi.org/10.1038/s41598-024-77635-9

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Received: 05 June 2024

Accepted: 23 October 2024

Published: 01 November 2024

DOI: https://doi.org/10.1038/s41598-024-77635-9

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