The issue of residual stresses in additive technologies

. The paper considers the issue of residual stresses in 3D-printed plastic models. Most additive technologies create residual stresses in products. Residual stresses occur in the printed material due to its expansion when heated and contraction when cooled. Residual stresses and their intensity depend on the printing technology and technique. The paper discusses the impact of printing techniques and various printing nozzle diameters and model shapes (rectangular, circular) on the occurrence of residual stresses in specimens. As part of the study, in transparent models, residual stresses were detected using a PPU-7 polarization-projection unit. Two series of six specimens each have been printed. The first and second series models had the shape of a parallelepiped and a disk, respectively. The frequency-division multiplexing technology was chosen. In the study, the models were manufactured from a polyethylene terephthalate-glycol plastic filament. This material has a high optical sensitivity. Nozzles of two diameters (0.4 and 1 mm) were used to print specimens. Shell-less and single-and double-shell specimens were printed. The dependence of residual stresses on the specimen shape, the printing nozzle diameter, and the model shell thickness has been estimated. The study is focused on finding a technique for printing models from plastic filament, completely free of residual stresses in the specimen material. This is dictated by the photoelasticity requirements for piezo-optical materials, including some transparent plastics used in 3D printing.


Introduction
3D printing has gained the most popularity in the 21st century due to the affordability and practicability of manufacturing models [1]. Additive manufacturing (3D printing) is a process for creating parts based on layer by layer buildup of a physical body according to an electronic geometric model as opposed to subtractive (machining) and conventional shaping (casting, stamping) production. The main advantage of 3D printing is relatively high accuracy and speed of creating objects [2].
Additive technologies are currently represented by several printing methods differing in the source material and model manufacturing technique. Several basic 3D printing technologies can be distinguished such as, e.g., fusing modelling method fused deposition modeling (FDM), UV curing resin (SLA) and selective laser sintering (SLS) of polymer powders [2]. However, the FDM technology is accompanied by residual stresses in the material, which reduces the possibility of taking full advantage of the structure's load-bearing capacity and challenges the use of this-way-printed models in the photoelasticity technique [3][4][5][6][7][8]. The latter is of paramount importance for the authors of the paper.
Physical and physicomechanical processes arising in the material during and continuing after the part manufacture cause residual stresses. Fusion-bonded plastic is liquid; the fusing temperature may vary from 190 to 250°C and reach 600°C for some printers focused on certain plastic types, and is 230°C in our case of printing with plastic polyethylene terephthalate glycol (PETG). The temperature difference between the already deposited material layers causes residual stresses in the model, which reduce the product's safety factor. The safety factor is the ratio of ultimate to permissible stresses, where ultimate stresses are those causing the occurrence of structural failure signs or unacceptable plastic deformations of the material. In turn, the permissible stress is the maximum value for the given material, ensuring the required strength and reliability of the structure and its components under the given load [9].
In construction, 3D printing is an effective and promising technology [10] since it allows the creation of various building products [11]. The additive technology advantages include reduced labor, material consumption, and construction time, improved product quality, minimum hazardous waste, and the possibility of implementing any solutions [12][13][14].
3D printing primarily uses polymeric materials, superior to other materials in many ways. Their key advantages include lightweight, which allows reducing the weight of structures made of them, sufficiently high compressive and tensile strength surpassing that of many building materials, high corrosion resistance, etc. [15][16][17][18][19][20][21]. As a result, polymeric materials are more advantageous to use than many others.
The emergence of additive technologies and materials used in 3D printing necessitated studying the impact of printing techniques on the material properties and determining physicomechanical characteristics of new plastics. Recently, many papers have been published, devoted to the results of research in this area using a variety of materials and 3D printing technologies. E.g., [18] provides the results of testing cylindrical specimens made of acrylonitrile butadiene styrene (ABS) using FDM on a 3D printer with high, medium, and low fill density. [19] estimates the impact of a longitudinal and transverse build-up of the melt forming the product geometry on the formation of pores in the part and the product density impact on its strain-stress properties (hardness, strength, and compressive strain). The study performed in [20] shows the dependence of the specimen's compressive strength on the ABS plastic product's surface layer structure. The experiments involved specimens obtained by FDM 3D printing. Specimens were obtained with 20, 40, 60, and 80% fill of the part mold. [21] describes compression tests of specimens made of various materials using various printing technologies. Some specimens were made of REC ABS plastic using FDM printing technology, and others were obtained from PA-12 polyamide by SLS. [22] describes the compression tests of specimens made of two polymeric material types: ABS plastic and polylactide (PLA). Three ABS specimens with, respectively, 25, 50, and 100% fill and three similar PLA specimens were tested. Cylindrical models were printed. Compression tests were performed on an EU-100 machine. [23] provides the results of an experimental study of the strain-stress performance of ABS specimens. The test showed isotropic properties of the material by Young's modulus and anisotropic ones for elongation at break, yield stress, and strength. The study results include recommendations for positioning the product on the 3D printer table for maximum tensile strength. [24] shows that the strain-stress performance of parts manufactured at optimal printing parameters is very close to that of die-cast products. The study has also identified fundamental approaches to obtaining specimens with more than 200°C heat resistance and more than 100 MPa flexural and tensile strength. [25] provides the results of stress-to-rupture test of PLA specimens obtained by 3D printing in various process modes. The following parameters were varied: the specimen filling shape (triangle, hexagon (honeycomb), line, edge), nozzle temperature (190-205°C), and specimen filling factor (10-40%). The tests were performed on a Kason WDW-5 hydraulic tensile machine with the conditional yield stress as the key output parameter. The test showed a significant impact of the considered process parameters on the conditional yield stress, which varied within 16. 5-22.4 MPa. In the study, the most efficient filling shapes and factors and the nozzle temperature for printing PLA specimens were also defined. In [26], physical-mechanical tests of 3D-printed ABS and PLA specimens are described. The study compares the results with the properties of products obtained by other techniques. Based on experimental study, the possibility of using additive technologies in the manufacture of low-power turbogenerator impellers is proven.
Despite a large number of studies aimed at determining the physicomechanical properties of materials used in additive technologies, the residual stress issues have been understudied. The paper authors have previously searched for optically sensitive materials [27] and assessed various 3D models for residual stresses in the product material [28,29]. The paper considers issues such as whether the specimen shape, the printing nozzle diameter, and the printing technique affect the onset of residual stresses and their intensity.

Materials and Methods
As part of the study, the FDM printing technology has been considered since it is characterized by residual stresses in the model. Fusion-bonded plastic is liquid. The printing technology is as follows: the filament is fed into the print head using guide rollers or screws and extruded through a special nozzle heating the material and depositing it onto the previous layer. A specially programmed system then regulates the supply of material and controls the head and table motion to properly build up the material and obtain the desired shape [2]. When printing models, various parameters may be varied, e.g., the layer height or preventing the intersection of layers. In this study, the models have different shell thicknesses. The shell is a plastic layer deposited along the outer model boundaries. When printing, a shell is first created, and then the inner space is filled with plastic; after depositing one layer, the next one is built up. A similar algorithm is used to create double-shell models. The model can also be absolutely shell-less.
In the study, specimens were printed on a FLSUN QQ 3D printer shown in Fig. 1.

Fig. 1. FLSUN QQ 3D Printer
An optically sensitive PETG plastic filament was used in printing [30], and residual stresses in the models were defined by photoelasticity.
Photoelasticity is a technique for measuring and further analyzing the stress parameters of transparent bodies. It is an experimental technique, widely used to solve deformable solid body mechanics problems, where stresses and strains are related by Hooke's law, which allows determining the distribution of stresses (strains) using transparent models in the study area without the tools of the mathematical theory of elasticity. On the other hand, due to the representativeness of optical information, it illustrates well the solutions obtained using this theory.
Experiments to determine the residual stresses were performed on a PPU-7 polarizationprojection unit, the scheme of which is shown in Fig. 2. The technique is based on the transillumination of optically sensitive material with a light beam. When a light beam passes through the material, birefringence occurs. Birefringence is used to both produce and transform polarized light. As a result, an interference fringe pattern called also the isochrome field emerges on the screen. When the model is transilluminated with white light, color fringes emerge on the screen, characterized by a certain alternation of colors. Dark regions have zero optical path difference. The relationship between the model's interference fringe pattern and the stress-strain state (SSS) is determined by the fact that isochromatic lines are the locus of points with the same main stress difference in the plane.
In this study, two specimen types have been used to determine the residual stresses, i.e., a 7×0.5×1.5 cm parallelepiped shown in Fig. 3 and a disk 0.5 cm thick and 2.5 cm in diameter shown in Fig. 4. The dimensions in the figures are given in millimeters. In total, four model series were printed to study. Each series comprised three specimens. Each series included double-shell, single-shell, and no shell-less models. The first and second series were parallelepiped specimens printed using 0.4 mm and 1 mm diameter nozzles, respectively. The third and fourth ones were disk specimens, also printed using 0.4 mm and 1 mm diameter nozzles.

Results and Discussion
During the tests, interference fringe patterns were obtained, and residual stresses were estimated. All specimens were marked depending on the shell. Shell-less specimens were marked «0», and double-and single-shell ones, respectively, «1» and «2».
The first series of experiments was focused on analyzing residual stresses in parallelepiped specimens. They were printed with a 1 mm diameter nozzle. As mentioned above, the specimens have been placed in the PPU-7 unit, and the interference fringe patterns obtained by transilluminating them are shown in Fig. 5.

Fig. 5. Interference Fringe Patterns of Specimens Printed Using a 1 mm Diameter Nozzle
Specimen «0» was printed without a shell and had no residual stresses. However, specimen «1» printed with a single shell already had residual stresses at the model's bodyshell interface. Specimen «2» has a double shell thickness compared to that of «1», which led to the stress propagation deep into the model. Moreover, the greatest residual stress intensity, according to Fig. 5, was in the shell itself. In Fig. 5, residual stresses in models «1» and «2» are highlighted in red. Specimens «1» and «2» had the first-order interference fringe. It is worth noting that each fringe order has an individual color spectrum.
Parallelepiped specimens were also printed for the second series of experiments but using a 0.4 mm diameter nozzle. The corresponding interference fringe patterns are shown in Fig.  6. Note that printing with a small nozzle deteriorates the model transparency; as for residual stresses, their presence is visible in specimen «2». Specimens «0» and «1» have no residual stresses. Specimen «2» has residual stresses in both the shell and the middle of the model. The residual stress areas are circled in red. The interference fringe corresponds to the first order.
For the third series of experiments, discs were printed with a 1 mm diameter nozzle. The interference fringe patterns obtained by photoelasticity are shown in Fig. 7. Pattern «0» was printed shell-less. An analysis of its interference fringe patterns shows that this printing technique creates no residual stresses. However, already in the single-shell specimen «1», residual stresses are observed. They are located both in the shell and at the shell-specimen body interface. Estimating the stress state of the double-shell specimen «2» also shows residual stresses that prevail inside the shell. The residual stress areas are circled in red in Fig. 7. The interference fringe is of the first order.
For the fourth series of experiments, disk specimens were printed with a 0.4 mm diameter nozzle. The resulting interference fringe patterns are shown in Fig. 8. The transparency has deteriorated as with the previous specimens printed with a 0.4 mm diameter nozzle. Specimens «0» and «1» have no residual stresses. Specimen «2» had residual stresses mainly in the shell. The residual stress areas are circled in red. The interference fringe corresponds to the first order.

Conclusion
The analysis of the 3D printing technique with nozzles of different diameters (0.4 mm and 1 mm) performed in the study shows that the use of a smaller diameter nozzle leads to a deterioration in material transparency. The study results herein are exploratory and are aimed at providing the photoelasticity technique with new optically sensitive materials used in 3D printing. Transparency is one of the requirements for optically sensitive materials. Another important requirement for materials used to manufacture models in the polarization-optical method is the absence of residual stresses. Printing shelled models with a larger diameter nozzle and thicker shells leads to the emergence of residual stresses in both the model shell and body. In summary: when using PETG models in photoelasticity, the use of small diameter nozzles (0.4 mm) should be avoided; when choosing a printing technique, preference should be givento shell-less models. The specimen shape does not affect the emergence of residual stresses.