Modelling and characterising FFF process of semi-crystalline polymers: Warpage formation and mechanism analysis

Abstract

Fused filament fabrication (FFF) is commonly utilised for 3D printing of semi-crystalline polymers, i.e., polypropylene (PP), while warpage deformation can often be observed in the printed products, with significantly reduced surface quality and mechanical properties. This study develops computational models for predicting rectangular boxes made of PP with different thicknesses under the FFF process to study the stress concentration and warpage mechanisms during 3D printing. Numerical models were established based on heat transfer, thermoelasticity, and crystallisation kinetics, with an activating elemental approach to calculate the FFF process of PP. The numerical models were validated with repetitive printing tests to study the mechanisms and relationships of stress conditions and warpage formation in PP boxes under FFF. The results show that the boxes with the thinnest thickness exhibited mostly severe warpage deformation (6.8 mm/5.9 mm in experiment and simulation, respectively), which is much more than that of the thickest box (1.3 mm/1.6 mm in experiment and simulation, respectively). The average crystallinity of the three boxes increases as the box thickness increases, but to a lesser extent. In terms of residual stress, the thinner box has a smaller residual stress (25.1 MPa, almost 45% of the thicker box).

Introduction

Fused filament manufacturing (FFF), recognized as a foremost additive manufacturing (AM) technology, is distinguished by its exceptional scalability and cost-effective manufacturing capabilities.^1,2 In FFF, thermoplastic polymers as raw materials are melted and subsequently extruded through nozzle to fabricate the structures layer-by-layer.^3,4 While FFF has big advantages in operational convenience and rapid manufacturing, there are drawbacks in the mechanical performance of the printed components, when compared to those fabricated using conventional manners.^5,6 Some of the reasons are because of the physical and chemical properties of raw materials and the printing process using FFF.^7,8 Specifically, it is to note that most of the crucial drawbacks are shrinkage, warpage and thermal deformation of printed components, leading to low mechanical properties of the printed products. ⁹

As the FFF process gains widespread popularity, a growing number of scholars are engaging in the adjustment of printing conditions and various parameters through diverse simulation software and experimental methodologies. These endeavours aim to curtail the buildup of residual stress within printed components, ultimately striving to mitigate warping phenomena.^10,11 Xu et al. ¹² have emphasised that cooling conditions are pivotal in governing shrinkage, with processing variables and material characteristics concurrently influencing material stress.

Empirical evidence has demonstrated the significant impact of material thermal viscoelasticity and parameters during manufacturing on both residual stress and warpage tendencies. Kabanemi et al. ¹³ have investigated the influence of the polymer cooling process on residual stress and warping tendencies. Recent investigations by Samy et al. ¹⁴ have indicated that printing parameters, including ambient temperature and printing speed, wield substantial influence over residual stress levels. Spoerk et al. ¹⁵ have conducted a comprehensive analysis of warping phenomena, pinpointing layer thickness, geometrical attributes, stack length, and deposition rate as factors which can modulate residual stress distribution in fabricated parts.

The primary objective of this research is to conduct an in-depth analysis of structural thickness within the context of 3D printing. Moreover, the study aims to comprehensively explore the impact of thickness parameters on the final quality of polypropylene (PP) mouldings. The acquired knowledge in this study provides valuable guidance in determining optimal thickness parameters aimed at mitigating warping issues in FFF printed components. The selection of PP material is deliberate, stemming from its distinctive semi-crystalline properties that facilitate a precise characterisation of its crystallinity. Additionally, PP is one of the most prevalent materials employed in 3D printing applications.

In this investigation, the crystalline characteristics of the printed components were meticulously examined through experiments. Subsequently, a software-based simulation was performed to replicate the printing process. The outcomes of these simulations were used to assess critical aspects such as temperature evolution, distribution of residual stress, and warpage within the printed structures. Comprehensively comparing empirical findings and simulation results offers a systematic in-depth understanding of the interrelationships between crystallinity, residual stress, and warping tendencies.

Materials and methods

Materials

The Ultimaker ³ printer was employed for the AM of PP structures. For this purpose, the compatible Ultimaker PP filament with the filament code CAS# 9010-79-1 was selected. The printing process was executed with these parameters: a nozzle diameter of 0.5 mm (layer thickness), an extrusion temperature of 220°C, and a heated bed temperature of 90°C. The printing parameters were chosen according to both the recommendations of the manufacturer’s technical manual and the previous testing experience. The elevated heated bed temperature serves the purpose of preventing detachment of prints from the bed surface, a common practice in the field.^16,17 Three specimens were manufactured, each specimen assumes the form of a vertically oriented square tube (ST) with a side length of 6 cm. The wall thickness of ST specimen A was 0.5 mm (1 layer), for ST specimen B this was 1.0 mm (2 layers), and for ST specimen C it was 1.5 mm (3 layers). Three specimens denoted as ST-A, ST-B and ST-C, respectively.

Figure 1(a) delineates the dimensions of the model and the specimens, visually representing the structural attributes. Figure 1(b) illustrates the measurement points for subsequent testing on specimens ST-A, ST-B and ST-C. To ensure a robust assessment, five distinct measurement points were identified for each specimen. These measurement points are strategically positioned at both the four corners of the initial print surface of the specimen, and additionally, at the precise centre.

Figure 1.

(a) Dimensions of the model and specimen and (b) measurement points on specimens.

According to geometric dimensions of the standard D638 Type I specimens, three dog-bone (DB) shaped specimens with different thickness were applied to characterise the effect of printing thickness on mechanical performance. Correspondingly, the specimens with one, two, and three layers were fabricated and noted as DB-A, DB-B, and DB-C, respectively.

Test methods

Figure 2 illustrates a micrometre measurement setup comprising a micrometre instrument and an adjustable supporting plane. The specimen’s displacement was achieved by manipulating the knob on the measurement table. The micrometre’s probe gauged the extent of out-of-surface warpage exhibited by the ST specimen.

Figure 2.

Micrometre measurement setup.

To characterise the internal crystallisation of different specimens, they were immersed in liquid nitrogen as a cryogenic treatment, then removed to induce embrittlement. The fractured specimens were subsequently embedded in epoxy resin for curing. Subsequently, the epoxy-embedded specimens were meticulous polished utilizing the EcoMet 30 dual-disc automatic polisher. During the polishing procedure, a continuous flow of ice water was maintained to mitigate the potential of recrystallisation prompted by frictional heating.

An IKA RCT Basic model magnetic stirrer was employed to prepare an etching solution comprised of 98% sulphuric acid, deionized water, and chromium trioxide (20 mL: 80 mL: 50 g, respectively). The etching process was conducted through heating in an oil bath for 15 min at 80°C. ¹⁸ Following this, the specimens were thoroughly rinsed to eliminate the residual etching solution, after which the specimens were dried at room temperature. Platinum powder was applied onto the surface of specimens using a Hitachi MC1000 gold-spraying instrument. Subsequently, three platinum-sprayed specimens were observed by a Hitachi TM4000Plus scanning electron microscope (SEM) under 15 k voltage. ¹⁹

Numerical modelling

Numerical modelling assists comprehension of the intricate thermal dynamics of materials and facilitates accurate determination of essential parameters e.g. residual stress, warpage, and crystallinity. The numerical model (Figure 3), through MSC Digimat software, enable the integration of heat transfer, thermoelasticity, and crystallisation kinetics. The formulation began by accounting for boundary conditions encompassing heat radiation and heat conduction, thereby predicting temperature distribution via the thermal model grounded in the governing principles of heat transfer equilibrium. Temperature distribution was subsequently used coupled to develop the thermoelastic model, calculating its strain, stress, and warpage. Given the inherently non-isothermal character of the crystallisation process, the crystallisation kinetic equation posited by Nakamura was incorporated into the model to calculate crystallinity. ²⁰

Figure 3.

Flowchart of numerical modelling. ²⁰

Computational parameters and boundary conditions

The model was discretised through voxel elements, partitioned into hexahedral components measuring 0.5 mm in length, width, and height, for facilitate subsequent analysis. Voxel elements, different to traditional mesh elements, can offer better regularity and alignment with the real-world structural properties, leading to more accurate finite element calculations.^21,22 The software sequentially executed printing and analysis layer by layer, in alignment with how actual printing occurs. As depicted in Figure 4(a), the printer nozzle material for the ST specimen counterclockwise. Upon completion of a specific print stratum, the print head ascends along the Z-axis by a defined distance, which initiates printing for subsequent layer. Figure 4(a) depicts a demonstration of the sequential activation of voxel mesh elements, highlighted in yellow. ²¹ Figure 4(b) provides the meshing process during simulation. ²¹

Figure 4.

(a) Schematic to illustrate the calculation with activating elements and (b) meshwork of the final printed specimen.

The numerical parameters are listed in Figure 5 and Table 1. Thermal radiation was calculated using the Stefan-Boltzmann constant and emissivity, while thermal convection was determined by the convection coefficient. Crystallinity was computed using the Avrami index and crystallisation rate constant. The crystallinity of thermoplastic polymers was determined by calculating the integrated area of the crystalline peak from the heat flux-temperature plot obtained through experiments with differential scanning calorimetry (DSC). ²³ The shape, scale and magnitude parameters within the Nakamura crystallisation kinetics model were operationalized to fit with experimental outcomes depicting the variation of crystallinity with temperature. ²⁰

Figure 5.

(a) Specific volume (b) specific heat capacity (c) Young’s modulus and (d) thermal conductivity versus temperature.^24–27

Table 1.

Primary material parameters used in the numerical simulation.

Parameter	Value
Poisson ratio	0.42 28
Coefficient of thermal expansion (1/°C)	1.1 × 10−6 29
Emissivity	0.94 30
Stefan-Boltzmann constant (mW/(mm2·K4))	5.67 × 10−11 31
Convection coefficient (mW/(mm2·K))	0.015 32
Glass transition temperature (°C)	−10 33
Avrami index	2.93 34
Crystallisation rate constant (min−1)	7.01 × 10−4 34
Shape parameter	2.5
Scale parameter	148
Magnitude parameter	2.8

Results and discussion

Figure 6(a)–(c) illustrate the results obtained from DSC experiments performed at specific measurement points corresponding to ST-A, ST-B and ST-C. The distinct heat flow peak signifies a heat absorption process, indicating the crystallisation melting process. Within this thermal zone, the internal molecular chain structure undergoes disruption during melt crystallisation, which is succeeded by the subsequent reorganisation into a more condensed and well-ordered molecular chain configuration.

Figure 6.

DSC results of (a) ST-A, (b) ST-B and (c) ST-C specimens.

Figure 7 presents the temperature distribution throughout the printing process. Notably, in the uppermost layer, the newly deposited material initiates a continuous heat transfer towards the downward direction. The central segment of the print filament cools to ambient temperature, while the lower portion is affected by the heated bed, resulting in an ongoing upward heat transfer. The calculation of warpage is shown in Figure 7, where d₀ presents the initial distance from the wall to the central plane of the square tube, i.e., 30 mm, and d presents the distance from the deformed wall to the central plane. Here, |d - d₀ | is the absolute warpage, while the concave deformation is marked with “‒” and the convex deformation is marked with “+” for better differentiation.

Figure 7.

Temperature distribution with measurement points and warpage deformation of (a) ST-A, (b) ST-B and (c) ST-C specimens.

Table 2 lists both numerical and experimental crystallinity results at 5 measurement points. Evidently, the crystallinity increases with the increment of wall thickness. The reason can be explained that filaments undergo more cycles of reheating, resulting in an elevated crystallinity in thicker specimens with wall. For the five measurement points as shown in Figure 7, points 3 and 4, situated at the lowest layer, receive the most significant thermal influence due to the heating from both the overlying newly deposited layers and the heated build platform. Consequently, the materials at these two points can possess the highest crystallinity. On the contrary, minimal additional heating from subsequent depositions can be seen at points 1 and 2, and the relevant materials present lowest crystallinity.

Table 2.

Crystallinities of the specimens at five points in between simulation and experiment.

	Simulation			Experiment
	ST-A (%)	ST-B (%)	ST-C (%)	ST-A (%)	ST-B (%)	ST-C (%)
Point 1	17.9	18.2	18.8	17.5	17.8	18.6
Point 2	17.9	18.2	18.9	17.3	17.4	19.3
Point 3	18.6	18.9	19.3	17.3	17.3	17.4
Point 4	18.6	18.9	19.3	16.9	17.9	18.2
Point 5	18.2	18.5	19.0	19.1	18.6	17.3

Figure 8 shows the (maximum) warpage of 3D-printed specimens in both experiments and simulations where the analysis of von Mises stress is also exhibited. By observation, the numerical results are well agreed with the experimental results. Apparently, the warpage phenomenon is gradually mitigated as the wall thickness increases, which is aligned with the findings in the previous study. ³⁵

Figure 8.

Comparison of the absolute warpage in both experiments and simulations for (a) ST-A, (b) ST-B and (c) ST-C specimens.

Figure 9 illustrates the warpage deformation in both simulation and experimental results along the vertical white measurement line shown in Figure 7. This delineated measurement line conforms to the upward direction in Figure 4. It is evident that the warpages by experiments are slightly lower than corresponding ones by simulation. The difference between the experimental and the numerical results is mainly due to the boundary condition in the printing bed, where the simulation cannot perfectly replicate the experimental boundary condition with tight bonding during printing process. However, the basic trend in warpage is similar, illustrating that the maximum warpage occurs in the lower midsection, not in the middle region.

Figure 9.

The warpage versus height from bottom to upper according to the measurement line for (a) ST-A, (b) ST-B and (c) ST-C specimens.

This observation conveys that the lower segment of the specimens experiences a more pronounced warping tendency than their upper counterparts. This can be attributed to the dynamic process of FFF, where successive layers exert compression on previously deposited ones as these successive layers have higher shrinkage rates. The shrinkage of these subsequently printed layers is restrained by the previously printed layers, leading to pronounced warping effect in the lower part of the structures. ³⁶ These findings also align with similar warpage mechanisms from previous investigations,^37,38 consolidating that the upper sections of printed layers tend to experience less warping than the corresponding lower counterparts.

Furthermore, since the bottom of the specimen was fixed onto the bed during printing and the comparatively weak stiffness of the thin-walled specimen, warping is significantly observed due to the residual stresses. Consequently, the bottom areas of the specimens experience more accumulated residual thermal stresses with greater warpage deformations as compared to other areas. In contrast, the upper areas are primarily constrained by the previously deposited layers of PP. Besides, PP has a glass transition temperature (T_g is between −15°C and 0°C) lower than room temperature, making it prone to deformation under ambient conditions. ³³ Therefore, during curing process, the residual thermal stresses generated in the upper are effectively released and transferred to its lower sections, resulting in less warpage deformations. ³⁹

Figure 10 illustrates the stress distribution within the three ST specimens. The residual stresses in the specimens are mainly concentrated in each edge, with the four vertical edges having the highest concentration. This is primarily due to the residual stresses that develop within each wall during printing, compounded by the geometric changes with structural stiffness variation at the edges, which aggravate the stress concentration accordingly. The numerical analysis indicates a trend that the residual stresses rise as the wall thickness increases. Considerably higher residual stresses are apparent in the ST-C specimen (56.4 MPa) compared to those in the ST-A wall specimen (25.1 MPa).

Figure 10.

Stress distribution in (a) ST-A (b) ST-B and (c) ST-C specimens.

Figure 11 illustrates the relationships between the crystallinity and either von Mises stress or ultimate warpage across different points in three ST specimens. Notably, for Figures 11 and 12, all the measurement points were selected at Point 5 from Figure 1(b). There is a notable positive correlation between crystallinity and von Mises stress. However, the connection between crystallinity and warpage is less distinct in this context, owing to the intricate interplay of printing parameters. This aligns with the conclusion made by Spoerk,^15,40 that elevating the ambient temperature for more heating process results in increased crystallinity, with a reduction in warpage and improvement in dimensional stability.

Figure 11.

Ultimate warpage and von Mises stress versus crystallinity for (a) ST-A, (b) ST-B and (c) ST-C specimens.

Figure 12.

The crystals of (a) ST-A, (b) ST-B and (c) ST-C specimens.

Figure 12 depicts the SEM results of three ST specimens. The internal volume of PP crystallites in the 1.5-mm specimen is significantly greater than in the 0.5-mm specimen. This is due to increased reheating from newly deposited material for the thicker specimens during printing, resulting in more thorough heating. As such, thicker specimens possess higher crystallinity with larger crystals,^14,41 which is consistent with the corresponding results of crystallinity in Figure 11. Stiffness of PP increases with the higher crystallinity due to the limit on chain movement from crystals. ⁴² The warpage of the thinner specimens is much greater due to their poor stiffness. This matches the simulation results presented in Figure 9.

As shown in the Figure 13, both Young’s modulus and yield strength increase with the increment of the specimen’s thickness, attributed to the increase in crystallinity. Because of the stiffness enhancement, the warpage is mitigated. This phenomenon can be well consolidated with the analyses of Figures 11 and 12 on the effect of crystallinity on warpage.

Figure 13.

Tensile mechanical properties of specimens with different thicknesses (a) Stress-strain curve (b) Young’s modulus and yield strength.

Conclusions

In this study, the effect of the wall thickness and the residual stresses, crystallinity, and warpage of 3D-printed specimens by FFF were numerically and experimentally analysed. The main conclusions can be summarised as follows.

(1) A numerical model with coupled multi-physical field, encompassing heat transfer, thermoelasticity, and crystallisation kinetics, was developed to predict FFF process and mechanical performance of 3D-printed specimens. Voxel elements and some critical parameters were specifically determined to reflect the actual FFF process with enhanced numerical accuracy.

(2) The results from both simulations and experiments reveal that, the average crystallinity is higher with the thicker specimens, and generally, the lower layers exhibited greater crystallinity compared to the upper layers in the 3D-printed specimens. Furthermore, stresses simulation shows that the maximum stress in the thicker specimen (56.4 MPa) is larger than that of the thinner specimen (25.1 MPa). Besides, both experimental and simulated data demonstrate that the thicker specimens possess higher printing quality with less warpage (1.3 mm/1.6 mm for experimental and simulated warpage results, respectively) when compared to those of the thinner ones (6.8 mm/5.9 mm for experimental and simulated warpage results, respectively).

(3) The size of internal crystallisation within the specimens is positively correlated with specimen thickness, thereby corroborating the interconnectedness of temperature and crystalline attributes. Besides, the effect of crystallinity on mechanical properties show that the warpage increases with the reduction of stiffness attributed to the decreased crystallinity with smaller crystals in thinner specimens.

(4) The results and conclusions of this study can provide useful information for manufacture process optimisation and printing quality improvement for industrial applications. In addition, it is recommended to elevate the chamber temperature so as to mitigate the warpage phenomenon during FFF. Besides, the optimisation of printing parameters, e.g., chamber temperature, printing speed, etc. Based on present model will also be part of our future work.