Formability Assessment of 3D-Printed ABS Sheets Using Nakajima Test

Formability Assessment of 3D-Printed ABS Sheets Using Nakajima Test | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Formability Assessment of 3D-Printed ABS Sheets Using Nakajima Test Abdolvahed Kami, Hamed Fakhri, Mehdi Hosseini, Hamid Mirtorabi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4735291/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This study explores the formability of acrylonitrile butadiene styrene (ABS) sheets produced by the fused filament fabrication 3D-printing process. The ABS sheets, fabricated with a diameter of 80 mm, were subjected to the Nakajima test. The investigation focused on assessing the impact of printing pattern (rectilinear, concentric, concentric/rectilinear), sheet thickness (0.8 mm, 1.4 mm, and 2 mm), and forming temperature (35°C, 70°C, and 90°C) on forming depth, utilizing a full factorial design of experiments comprising 27 conditions. Through the application of analysis of variance (ANOVA), a linear model for forming depth was derived, demonstrating high precision and reliability. Results indicate that as temperature increases, formability improves, reaching a maximum at 90°C with a rectilinear print pattern (15.95 mm depth). Conversely, the lowest forming depth (1.45 mm) occurred at 35°C with a concentric printing pattern. Sheet thickness showed minimal impact on forming depth, but forming force increased with thickness. Mechanical Engineering Materials Engineering 3D Printing Fused filament fabrication ABS sheets Formability Nakajima test Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 1. Introduction Fused filament fabrication (FFF) is a widely used technique for producing polymer components, including those made from acrylonitrile butadiene styrene (ABS), polyamides (PA), polylactic acid (PLA), polyether-ether-ketone (PEEK), and so on [ 1 ]. FFF allows for the creation of components with any shape complexity, suitable for both prototypes and final products [ 2 ]. Therefore, ensuring these components have acceptable mechanical characteristics is crucial. The mechanical characteristics assessment of 3D-printed polymers has been widely investigated. Most of these studies focus on static properties, such as tensile or compressive strength, or dynamic responses, including fatigue and impact resistance [ 3 , 4 ]. One primary reason for this focus lies in the expectation that components produced by 3D printing are intended for final use, necessitating assurance of their ability to withstand applied loads. Consequently, the mechanical properties of these components are extensively evaluated. However, there is a lack of knowledge regarding other plastic behavior properties, such as their response to varying loading conditions or conventional forming techniques, emphasizing the necessity for further exploration into the formability study of 3D-printed components. The scenarios in which the formability of 3D-printed components becomes of interest could involve hybrid manufacturing, combining additive manufacturing with conventional forming methods [ 5 ]. In such cases, components with simpler geometries, such as sheets, can be produced using additive processes and then formed into final shapes using dies [ 6 ]. Moreover, 3D-printed components are increasingly employed in die production, especially when the required production volume is low [ 7 – 9 ]. In such instances, it becomes essential to evaluate the durability and endurance of these dies. Several studies have explored the formability of metallic components created through 3D printing [ 10 , 11 ]. Additionally, there is existing research on the forming and formability of polymers [ 12 , 13 ] and polymer matrix composites [ 14 ]. However, research on the formability of 3D-printed polymer components is limited. The formability and failure behavior of additively made polymer sheets were studied by Rosa-Sainz, et al. [ 5 ]. Polycaprolactone (PCL) and polyethylene terephthalate glycol (PETG) were subjected to Nakajima formability testing. Their analysis encompassed evaluating various failure types under plastic deformation and assessing overall formability limits through forming limit diagrams and optical microscopy. The results revealed low ductility and early fracture in PETG, attributed to inadequate layer cohesion, while PCL demonstrated high formability and distinct failure modes such as interlayer gliding. Incremental sheet forming (ISF) was applied to PLA and PCL sheets made by FFF by Garcia-Romeu, et al. [ 15 ] They formed truncated cone shapes using modified ISF parameters. They evaluated temperature, forming forces, shape accuracy, and surface integrity and roughness. Feasibility windows were established, with PCL showing promise for prosthesis manufacturing due to its favorable formability. PLA, however, exhibited limited formability. Sorimpuk, et al. [ 16 ] thermoformed 3D-printed PLA/TPU multi-material specimens at various temperatures and investigated their formability and shape recovery. TPU was deposited onto PLA using FFF. Simple thermoforming tests were conducted, followed by reheating to evaluate shape memory. Results showed PLA/TPU specimens had better bending modulus than PLA alone at 60°C to 90°C. Thermoforming at 100°C or higher showed excellent shape retention and bonding while thermoforming at 60°C to 90°C demonstrated reasonable shape recovery. Recommended thermoforming temperatures were suggested based on application needs, aiding rapid prototyping of multi-material parts with tailored rigidity and shape memory. In this study, the formability characteristics of 3D-printed ABS sheets were investigated. The effects of variables such as printing pattern, sheet thickness, and forming temperature on the formability behavior of 3D-printed polymer components were studied. This research aims to advance the knowledge base surrounding hybrid AM processes and facilitate the development of optimized fabrication techniques for polymer-based components. 2. Material and Methods Disk-shaped sheets with a diameter of 80 mm were 3D printed using a desktop FFF machine. The samples are made of ABS, well-known for its high tensile strength and widespread use as a filament material in 3D printing. The samples were 3D printed using 1.75 mm diameter Xtrusion filaments (Xtrusion filament, Mashhad, Iran) with a 100% infill. Table 1 summarizes the conditions under which the parts were 3D printed. Table 1 . 3D printing condition of ABS sheets Process variable Operating condition Nozzle diameter (mm) 0.4 Filament diameter (mm) 1.75 Layer height (mm) 0.2 Top, bottom, and shell layers 2 Infill (%) 100 % Internal fill pattern Rectilinear, Concentric, Rectilinear and Concentric Printing speed (mm٫s) 25 Travel speed (mm٫s) 50 Nozzle temperature (°C) 245 Bed temperature (°C) 90 The samples were put through the Nakajima test, which involves pressing a sheet sample into a die cavity using a hemispherical punch. The punch was 50 mm in diameter. The tests were performed using a Santam STM-400 machine at a speed of 5 mm/min without the use of lubricant between the sample surface and the punch of the machine. The tests continued until the occurrence of sample failure (crack), which was identified through a noticeable decline in the force-displacement curves. Figure 1 shows the Nakajima test setup as well as how the sheet samples are placed on the die. To stop the sheet samples from moving, the die's surface is roughened. Furthermore, the blank holder, which is secured to the die with six screws, keeps the sheets from moving while the test is being conducted. The investigation into the formability of ABS sheets encompassed an examination of three variables: printing algorithm, thickness, and temperature. Each parameter was explored at three distinct levels, resulting in the implementation of a full factorial design of experiments, comprising 27 experiments as shown in Table 2. The samples were 3D printed at three different thicknesses of 0.8, 1.4, and 2 mm, and with three distinct printing patterns, rectilinear (R), concentric (C), and concentric/rectilinear (CR). In addition to these variables, the Nakajima tests were conducted at three temperatures: 35°C, 70°C, and 90°C. These temperatures were chosen to represent a range from low to high forming temperatures considering the thermal properties of ABS. Within this experimental framework, the depth of penetration was considered as the output variable. Table 2 . Full factorial design of experiments for formability assessment of ABS 3D-printed sheets, (R: Rectilinear, C: Concentric, CR: Concentric/Rectilinear) No. Printing Pattern Sheet Thickness (mm) Test Temperature (°C) No. Printing Pattern Sheet Thickness (mm) Test Temperature (°C) 1 R 0.8 35 15 C 1.4 90 2 R 0.8 70 16 C 2 35 3 R 0.8 90 17 C 2 70 4 R 1.4 35 18 C 2 90 5 R 1.4 70 19 CR 0.8 35 6 R 1.4 90 20 CR 0.8 70 7 R 2 35 21 CR 0.8 90 8 R 2 70 22 CR 1.4 35 9 R 2 90 23 CR 1.4 70 10 C 0.8 35 24 CR 1.4 90 11 C 0.8 70 25 CR 2 35 12 C 0.8 90 26 CR 2 70 13 C 1.4 35 27 CR 2 90 14 C 1.4 70 For the execution of these experiments, a round ceramic heating element was employed, encircling the mold and imparting heat to both the mold and the test sheet sample. Additionally, a thermostat was utilized to accurately regulate and attain the specified testing temperature. Upon reaching the desired temperature, the sheet underwent testing. The thermal equipment implemented in the tests is depicted in Figure 2. 3. Results and Discussion The values of the maximum penetration depth and maximum compressive force of the test samples, which are essential metrics for evaluating the mechanical properties and failure behavior of the materials, are presented in Table 3. Table 3. The values of the maximum penetration depth and maximum compressive force of the test samples No. Maximum compressive force (N) Maximum penetration depth (mm) No. Maximum compressive force (N) Maximum penetration depth (mm) 1 422 6.74 15 108 3.50 2 157 5.58 16 78 1.45 3 618 14.04 17 59 1.79 4 814 5.59 18 78 2.57 5 363 5.58 19 157 2.65 6 873 15.95 20 186 5.80 7 1001 7.55 21 265 5.55 8 363 7.28 22 324 3.11 9 1295 15.87 23 334 6.33 10 157 2.35 24 373 5.98 11 39 3.12 25 844 5.93 12 157 3.04 26 618 6.55 13 108 2.13 27 677 7.76 14 157 2.67 Figure 3 illustrates samples 4, 13, and 22 after Nakajima testing, during which the tests continued until sample failure occurred. These samples exhibit Rectilinear (R), Concentric (C), and Concentric/Rectilinear (CR) patterns, respectively. In this figure, the dashed lines depict the crack shape, the red arrows indicate the path of crack propagation, and the white arrows illustrate the direction of 3D printing rasters. Furthermore. the "W" value indicates the approximate length of the crack. As shown in Figure 3, in all samples, cracks occurred due to the separation of joints between adjacent rasters, following the 3D printing pattern. In samples with an R pattern, such as sample 4, the crack path is linear and follows the direction of the rasters. The separation of bonding between adjacent rasters resulted in sample failure. In samples with a C pattern, such as sample 14, the rasters in the consecutive layers had a slight mismatch, resulting in the creation of a through-thickness region with weak strength against shear load during the Nakajima test. Consequently, applying force during the test caused shear stress, leading to raster separation and crack propagation along the circular path. Although the circular pattern follows the shape of the samples, it renders them weak and prone to cracking during loading. Therefore, utilizing a circular pattern that follows the sample's shape is not feasible for Nakajima testing, where loading is normal to the surface of the sheet. The samples with the CR pattern, such as sample 22, have alternating raster patterns of circular and rectilinear. In these samples, cracks initiated from a layer with a circular pattern and propagated to a layer with a rectilinear pattern under increased force. Therefore, it can be inferred that the circular patterns are weaker than the linear patterns. The fracture behavior of the samples with different patterns, which are formed at a higher temperature is compared in Figure 4. These samples were deformed at 70°C. By comparing Figure 4 with Figure 3, it can be observed that an increase in forming temperature had a positive impact on the formability of the 3D-printed ABS sheets. The average penetration depth for the samples in Figure 4 is about 5 mm, whereas the average fracture depth for the samples in Figure 3 is about 3.6 mm. Therefore, similar to the formability enhancement observed in rolled sheet metals with an increase in forming temperature [17, 18], the formability of 3D-printed ABS sheets also improves as the forming temperature increases. Additionally, comparing the two figures shows that the fracture lines remain consistent across temperatures. Sample 11, with a C pattern, exhibits circular fracture lines, following the path of the raster. In sample 2, with an R printing pattern, the fracture path is linear and parallel to the raster lines. Finally, in sample 20 with a CR printing pattern, the fracture lines are both circular and linear. The fracture initially occurs in the layer with a circular raster pattern before progressing to the linear pattern. Despite this, the samples exhibited more deformation and showed deeper penetration differences at higher temperatures. To better understand the data provided in Table 3, the values are plotted in the form of a column graph, as illustrated in Figure 5. This graph outlines the impact of different printing patterns, sheet thicknesses, and test temperatures on the formability of 3D-printed ABS sheets. As shown in Figure 5, the R pattern exhibits a higher penetration depth compared to the C and CR patterns, indicating better performance under load. The linear arrangement of rasters contributes to greater structural integrity. Conversely, the C pattern shows the lowest penetration depths due to the circular arrangement of rasters. Higher temperatures (90°C) significantly improve penetration depth, suggesting that increased temperature enhances the ductility of ABS sheets. According to Table 3, a substantial increase in compressive force at 90°C is observed for the R and CR patterns, while the C pattern remains less influenced by temperature changes. Foltuţ, et al. [19] investigated the tensile properties of ABS printed at different orientations and temperatures, finding that higher temperatures improve ductility and that certain orientations, particularly 0° and 90°, yield higher tensile strengths compared to 45°. This aligns with the current study’s observation that formability increases with temperature and varies significantly with printing patterns. While Foltuţ, et al. [19] focused on tensile strength, the current study provides a comprehensive analysis of formability, contributing further insights into how pattern, thickness, and temperature influence the mechanical behavior of 3D-printed ABS. As depicted in Figure 5, while thicker sheets (2.0 mm) demonstrate higher formability, the forming depth exhibits minimal variation with changes in sample thickness. This behavior contrasts with that of metals, where sheet formability typically increases with thickness [20, 21]. This phenomenon may be attributed to the 3D printing process used to produce ABS sheets, as process parameters such as printing temperature and layer adhesion can significantly impact overall formability. Sample 6, printed with the R pattern and a thickness of 1.4 mm, demonstrated the best formability, achieving a forming depth of 15.95 mm (see Figure 6). The fracture occurred along the printing path between the rasters, consistent with the fracture behavior of samples with the R pattern. The increased forming temperature (90°C) significantly improved the formability, as sample 6’s forming depth was approximately three times greater than that of samples four and five, which were printed under the same conditions but formed at 35°C and 70°C, respectively. To assess the impact of the studied parameters on the formability of ABS sheets, an analysis of variance (ANOVA) was performed. Table 4 presents the results of this ANOVA, indicating the significance of the model terms through p-values below 0.05 and corresponding F-values. Specifically, forming temperature and printing pattern are identified as significant parameters, with p-values less than 0.0001 and F-values of 47.86 and 88.58, respectively. These findings are consistent with the discussions related to Figure 5. According to Table 4, the F-value of the predicted linear model is 52.66, suggesting the model's significance. The predicted linear model for forming depth demonstrates a high level of accuracy and reliability, as evidenced by the fit statistics in Table 5. The standard deviation of 0.2087 indicates that the predicted values are closely clustered around the mean, reflecting precision and consistency in the model's predictions. Furthermore, a predicted R² value of 0.873 offers an estimation of the model's predictive performance on novel data, underscoring its robustness and reliability. The coefficient of variation (C.V. %) of 13.24 suggests a relatively low percentage of variability relative to the mean, indicating good precision and reliability in the model's predictions. Finally, the adequate precision value of 22.639 indicates a robust signal-to-noise ratio, supporting the reliability of the model's predictions. Table 4 . ANOVA results for the effect of forming temperature, sheet thickness, and printing pattern on ABS sheet formability Source Sum of squares df Mean squares F-value P-value Model 9.100 4 2.270 52.660 < 0.0001 significant A- Test temperature 2.070 1 2.070 47.860 < 0.0001 B- Sheet thickness 0.004 1 0.004 0.093 0.7641 C- Printing pattern 7.650 2 3.830 88.580 < 0.0001 Residual 0.777 18 0.043 Cor total 9.870 22 Table 5 . Fit statistics for the linear model of forming depth Standard deviation Mean C.V. % R² Adjusted R² Predicted R² Adequate precision 0.2087 1.57 13.24 0.921 0.904 0.873 22.639 Figure 7 compares the predictions of the linear model with the actual forming depth. According to this figure, the model predictions are very close to the actual forming depth (45° line), indicating that the prediction model has high precision in the prediction of forming depth. The perturbation plot, illustrating the change in maximum forming depth in response to variations in the studied parameters, is presented in Figure 8. According to this figure, the temperature curve exhibits a positive slope, signifying that forming depth increases with elevated temperatures. The sheet thickness curve appears horizontal, indicating that this parameter does not significantly affect the formability. A comprehensive depiction of forming depth variations is provided by a 3D surface plot. Figure 9 presents a 3D surface diagram illustrating how forming depth changes with variations in sheet thickness and test temperature. In Figure 9a, sheet thickness demonstrates minimal influence on forming depth, while increasing test temperature shows a direct correlation with greater forming depth. The plot reveals that maximum forming depth occurs at a test temperature of 90°C, regardless of sheet thickness. Figure 9b displays a contour plot where parallel curves indicate no significant interaction between test temperature and sheet thickness. Moreover, the linear orientation of these curves suggests a linear relationship between forming depth and temperature changes. 4. Conclusions This study investigated the formability characteristics of 3D-printed ABS sheets using Nakajima tests, focusing on maximizing forming depth as the primary output parameter. The key findings can be summarized as follows: The formability of 3D-printed ABS sheets demonstrated significant improvement with increasing temperature. Maximum forming depth was achieved at 90°C, particularly with the R printing pattern, yielding a forming depth of 15.95 mm. In contrast, the lowest forming depth of 1.45 mm occurred at 35°C with the C printing pattern. Contrary to conventional expectations, changes in sheet thickness did not notably affect forming depth. The study revealed that, unlike traditional metal sheet formability, 3D-printed ABS sheets did not exhibit a clear correlation between thickness and formability. While forming depth remained largely unaffected by variations in sheet thickness, an increase in thickness did lead to higher observed forming forces. This suggests that mechanical requirements for forming force differ from those influencing forming depth in 3D-printed ABS sheets. This research contributes valuable insights into optimizing the formability of 3D-printed ABS components, highlighting the critical roles of printing patterns and temperature in achieving desired formability outcomes. These findings are essential for advancing hybrid additive manufacturing processes and enhancing the reliability and applicability of 3D-printed polymer components in various industrial applications. Declarations 5.1. Funding No funding was received for conducting this study. 5.2. Competing Interests The authors declare no conflicts of interest relevant to the content of this article. 5.3. Availability of data and materials The datasets utilized and analyzed in this study can be obtained from the corresponding author upon request. References A. Dey, I. N. Roan Eagle, N. J. J. o. m. Yodo, and m. processing, "A review on filament materials for fused filament fabrication," vol. 5, no. 3, p. 69, 2021. I. Gibson et al. , Additive manufacturing technologies . Springer, 2021. J. R. C. Dizon, A. H. Espera, Q. Chen, and R. C. Advincula, "Mechanical characterization of 3D-printed polymers," Additive Manufacturing, vol. 20, pp. 44-67, 2018/03/01/ 2018. F. Safari, A. Kami, and V. Abedini, "3D printing of Continuous Fiber Reinforced Composites: A Review of the Processing, Pre- and Post-Processing Effects on Mechanical Properties," Polymers and Polymer Composites, vol. 30, pp. 1-26, 2022. A. Rosa-Sainz, I. Ferrer, M. L. Garcia-Romeu, and G. Centeno, "Characterization of plastic formability and failure mechanisms in FDM additively manufactured PETG and PCL sheets," Polymer Testing, vol. 134, p. 108431, 2024/05/01/ 2024. M. Merklein, R. Schulte, and T. Papke, "An innovative process combination of additive manufacturing and sheet bulk metal forming for manufacturing a functional hybrid part," Journal of Materials Processing Technology, vol. 291, p. 117032, 2021/05/01/ 2021. N. Nakamura, K.-i. Mori, and Y. Abe, "Applicability of plastic tools additively manufactured by fused deposition modelling for sheet metal forming," The International Journal of Advanced Manufacturing Technology, vol. 108, no. 4, pp. 975-985, 2020/05/01 2020. N. Nakamura, K.-i. Mori, F. Abe, and Y. Abe, "Bending of sheet metals using plastic tools made with 3D printer," Procedia Manufacturing, vol. 15, pp. 737-742, 2018/01/01/ 2018. P. Frohn-Sörensen, M. Geueke, T. B. Tuli, C. Kuhnhen, M. Manns, and B. Engel, "3D printed prototyping tools for flexible sheet metal drawing," The International Journal of Advanced Manufacturing Technology, vol. 115, no. 7, pp. 2623-2637, 2021/08/01 2021. S. Rosenthal, M. Hahn, and A. E. Tekkaya, "Deep drawability of additively manufactured sheets with a structured core," International Journal of Material Forming, vol. 16, no. 2, p. 20, 2023/02/14 2023. S. Rosenthal et al. , "Forming properties of additively manufactured monolithic Hastelloy X sheets," Materials Science and Engineering: A, vol. 753, pp. 300-316, 2019/04/10/ 2019. P. Martins, L. Kwiatkowski, V. Franzen, A. Tekkaya, and M. Kleiner, "Single point incremental forming of polymers," CIRP annals, vol. 58, no. 1, pp. 229-232, 2009. A. Rosa-Sainz, G. Centeno, M. B. Silva, J. A. López-Fernández, A. J. Martínez-Donaire, and C. Vallellano, "On the Determination of Forming Limits in Polycarbonate Sheets," vol. 13, no. 4, p. 928, 2020. A. Bagheri, V. Asghari, and A. Kami, "Spin welding of 3D-printed and solid acrylonitrile–butadiene–styrene (ABS) components: a preliminary investigation," Archives of Civil and Mechanical Engineering, vol. 22, no. 3, p. 130, 2022/05/14 2022. M. L. Garcia-Romeu, I. Ferrer, C. Pasotti, J. Coma, A. Rosa-Sainz, and G. Centeno, "Preliminary study on the use of 3D printed biodegradable polymeric sheet for the manufacturing of medical prostheses by SPIF," Procedia CIRP, vol. 110, pp. 76-81, 2022/01/01/ 2022. N. P. Sorimpuk, W. H. Choong, and B.-L. Chua, "Thermoforming Characteristics of PLA/TPU Multi-Material Specimens Fabricated with Fused Deposition Modelling under Different Temperatures," vol. 14, no. 20, p. 4304, 2022. S. Pandre, A. Morchhale, N. Kotkunde, and S. K. Singh, "Influence of processing temperature on formability of thin-rolled DP590 steel sheet," Materials and Manufacturing Processes, vol. 35, no. 8, pp. 901-909, 2020/06/10 2020. A. Heidari, A. Ghassemi, and A. Atrian, "A numerical and experimental investigation of temperature effects on the formability of AA6063 sheets using different ductile fracture criteria," The International Journal of Advanced Manufacturing Technology, vol. 106, no. 5, pp. 2595-2611, 2020/01/01 2020. D. Foltuţ, E. Vălean, V. Dzitac, and L. Marşavina, "The influence of temperature on the mechanical properties of 3D printed and injection molded ABS," Materials Today: Proceedings, vol. 78, pp. 210-213, 2023/01/01/ 2023. D. Banabic, F. Barlat, O. Cazacu, and T. Kuwabara, "Advances in anisotropy of plastic behaviour and formability of sheet metals," International Journal of Material Forming, vol. 13, pp. 749-787, 2020. D. Peng, S. Chen, R. Darabi, A. Ghabussi, and M. Habibi, "Prediction of the bending and out-of-plane loading effects on formability response of the steel sheets," Archives of Civil and Mechanical Engineering, vol. 21, no. 2, p. 74, 2021. Additional Declarations The authors declare no competing interests. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4735291","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":326511320,"identity":"4a0cc210-6866-414d-b6be-0e54720684aa","order_by":0,"name":"Abdolvahed Kami","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAxklEQVRIiWNgGAWjYDACHiBOqEASYCNOyxmStTC2keIu/p7DTzc8nFcnpzu7+dkDhho7Bj7pA/i1SJxtM7uRuO2wsdmdY+YGDMeSGdj4EghYc54BpOVA4rYbCWYSDGwHGNh4COiQP8/+7UbinLr6bTfSv0kw/CNCi8HZHqAtDcwJZjdyzCQY24jQYnjmTNmNhGOHDbfdyCmTSOxL5iGoRe5M+rabP2rq5M1upG+T+PDNTk6+h4AWVJAAiadRMApGwSgYBZQCAJINQEvKTHmoAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0003-2148-3366","institution":"Semnan University","correspondingAuthor":true,"prefix":"","firstName":"Abdolvahed","middleName":"","lastName":"Kami","suffix":""},{"id":326512071,"identity":"0f9ec261-ad1b-4e7e-8ac3-972fd05eefd0","order_by":1,"name":"Hamed Fakhri","email":"","orcid":"","institution":"Semnan University","correspondingAuthor":false,"prefix":"","firstName":"Hamed","middleName":"","lastName":"Fakhri","suffix":""},{"id":326512072,"identity":"c48cdf25-34dd-4f8f-9ad3-1ecba77b3c3b","order_by":2,"name":"Mehdi Hosseini","email":"","orcid":"","institution":"Semnan University","correspondingAuthor":false,"prefix":"","firstName":"Mehdi","middleName":"","lastName":"Hosseini","suffix":""},{"id":326512073,"identity":"969ae4f9-c05a-4151-9fe1-27618aadd533","order_by":3,"name":"Hamid Mirtorabi","email":"","orcid":"","institution":"Semnan University","correspondingAuthor":false,"prefix":"","firstName":"Hamid","middleName":"","lastName":"Mirtorabi","suffix":""}],"badges":[],"createdAt":"2024-07-13 13:19:32","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-4735291/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4735291/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":60429012,"identity":"14ee4a8c-785a-41eb-b738-b3741496c425","added_by":"auto","created_at":"2024-07-16 15:59:34","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":200558,"visible":true,"origin":"","legend":"\u003cp\u003eNakajimatest die and placement of sheet sample in the die\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-4735291/v1/e1c3c6a7948273356b4d7de2.png"},{"id":60429005,"identity":"75220e07-aa10-480c-8e72-82223fc5f0c2","added_by":"auto","created_at":"2024-07-16 15:59:34","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":119863,"visible":true,"origin":"","legend":"\u003cp\u003eThermal testing equipment, (a) control set, comprising a thermostat and a thermocouple, and (b) ceramic heating element.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-4735291/v1/bd2d68b4ce2b4aa3ec6a17de.png"},{"id":60429736,"identity":"b1280590-9d8a-4fd4-9fed-c5f47410e386","added_by":"auto","created_at":"2024-07-16 16:07:34","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":291544,"visible":true,"origin":"","legend":"\u003cp\u003eIllustration of cracks and their growth path on samples with different print patterns (sheet thickness = 1.4 mm, test temperature 35°C); samples (a) 4, (b) 13, and (c) 22, with R, C, and CR patterns, respectively\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-4735291/v1/f248182fa26d5a8c4c103384.png"},{"id":60429740,"identity":"7580c281-ce0f-45b7-a235-1547f79678df","added_by":"auto","created_at":"2024-07-16 16:07:34","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":214239,"visible":true,"origin":"","legend":"\u003cp\u003eFailure of the sample with different print patterns at the test temperature of 70°C; samples (a) 11, (b) 2, and (c) 20 with the penetration depth of 3.12 mm, 5.98 mm, and 5.80 mm, respectively\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-4735291/v1/cc2652ae383e1547a93837b8.png"},{"id":60429007,"identity":"8dc888c7-11f9-4851-8e69-2d381bacda16","added_by":"auto","created_at":"2024-07-16 15:59:34","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":33029,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of penetration depths of ABS sheets for various studied parameters\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-4735291/v1/cfde07a89e88effdc885c999.png"},{"id":60429010,"identity":"8c5baaea-2ccd-4b5f-86cf-c05dc4e9cbcd","added_by":"auto","created_at":"2024-07-16 15:59:34","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":91161,"visible":true,"origin":"","legend":"\u003cp\u003eFailure of sample 6 at a maximum depth of penetration of 15.95 mm\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-4735291/v1/aebfe2db4597e26326f94588.png"},{"id":60429739,"identity":"7735e5f3-2f49-404e-a30e-ad3224f44d04","added_by":"auto","created_at":"2024-07-16 16:07:34","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":12790,"visible":true,"origin":"","legend":"\u003cp\u003eThe predicted versus actual forming depth of ABS sheets\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-4735291/v1/d349745e79b165f1824224dc.png"},{"id":60429008,"identity":"0e4688ae-2380-487b-865c-a9b27aaccb49","added_by":"auto","created_at":"2024-07-16 15:59:34","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":15357,"visible":true,"origin":"","legend":"\u003cp\u003ePerturbation plot comparing maximum forming depth in response to changes in forming temperature and sheet thickness\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-4735291/v1/d7cc7125ac614c8a6d4c5185.png"},{"id":60429013,"identity":"9962777a-0cb3-4621-9b7d-55fd425309b2","added_by":"auto","created_at":"2024-07-16 15:59:34","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":107495,"visible":true,"origin":"","legend":"\u003cp\u003e(a) 3D surface diagram and (b) contour diagram showing changes in forming depth with forming temperature and sheet thickness\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-4735291/v1/9cda0753b65dd68fde9e28b7.png"},{"id":60429759,"identity":"db2f853f-c300-44f8-824b-ffb686eed5eb","added_by":"auto","created_at":"2024-07-16 16:07:39","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1691498,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4735291/v1/b5add31a-919c-4326-b899-11eeab4fe1e8.pdf"},{"id":60429009,"identity":"2f9746c4-73ca-45b6-bcf0-4365d270c9dc","added_by":"auto","created_at":"2024-07-16 15:59:34","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":541812,"visible":true,"origin":"","legend":"","description":"","filename":"GraphicalAbstract.docx","url":"https://assets-eu.researchsquare.com/files/rs-4735291/v1/0244ebc7c9037b288deec02d.docx"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eFormability Assessment of 3D-Printed ABS Sheets Using Nakajima Test\u003c/strong\u003e\u003c/p\u003e","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eFused filament fabrication (FFF) is a widely used technique for producing polymer components, including those made from acrylonitrile butadiene styrene (ABS), polyamides (PA), polylactic acid (PLA), polyether-ether-ketone (PEEK), and so on [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. FFF allows for the creation of components with any shape complexity, suitable for both prototypes and final products [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. Therefore, ensuring these components have acceptable mechanical characteristics is crucial.\u003c/p\u003e \u003cp\u003eThe mechanical characteristics assessment of 3D-printed polymers has been widely investigated. Most of these studies focus on static properties, such as tensile or compressive strength, or dynamic responses, including fatigue and impact resistance [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. One primary reason for this focus lies in the expectation that components produced by 3D printing are intended for final use, necessitating assurance of their ability to withstand applied loads. Consequently, the mechanical properties of these components are extensively evaluated. However, there is a lack of knowledge regarding other plastic behavior properties, such as their response to varying loading conditions or conventional forming techniques, emphasizing the necessity for further exploration into the formability study of 3D-printed components. The scenarios in which the formability of 3D-printed components becomes of interest could involve hybrid manufacturing, combining additive manufacturing with conventional forming methods [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. In such cases, components with simpler geometries, such as sheets, can be produced using additive processes and then formed into final shapes using dies [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. Moreover, 3D-printed components are increasingly employed in die production, especially when the required production volume is low [\u003cspan additionalcitationids=\"CR8\" citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. In such instances, it becomes essential to evaluate the durability and endurance of these dies.\u003c/p\u003e \u003cp\u003eSeveral studies have explored the formability of metallic components created through 3D printing [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. Additionally, there is existing research on the forming and formability of polymers [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e] and polymer matrix composites [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. However, research on the formability of 3D-printed polymer components is limited. The formability and failure behavior of additively made polymer sheets were studied by Rosa-Sainz, et al. [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. Polycaprolactone (PCL) and polyethylene terephthalate glycol (PETG) were subjected to Nakajima formability testing. Their analysis encompassed evaluating various failure types under plastic deformation and assessing overall formability limits through forming limit diagrams and optical microscopy. The results revealed low ductility and early fracture in PETG, attributed to inadequate layer cohesion, while PCL demonstrated high formability and distinct failure modes such as interlayer gliding. Incremental sheet forming (ISF) was applied to PLA and PCL sheets made by FFF by Garcia-Romeu, et al. [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e] They formed truncated cone shapes using modified ISF parameters. They evaluated temperature, forming forces, shape accuracy, and surface integrity and roughness. Feasibility windows were established, with PCL showing promise for prosthesis manufacturing due to its favorable formability. PLA, however, exhibited limited formability. Sorimpuk, et al. [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e] thermoformed 3D-printed PLA/TPU multi-material specimens at various temperatures and investigated their formability and shape recovery. TPU was deposited onto PLA using FFF. Simple thermoforming tests were conducted, followed by reheating to evaluate shape memory. Results showed PLA/TPU specimens had better bending modulus than PLA alone at 60\u0026deg;C to 90\u0026deg;C. Thermoforming at 100\u0026deg;C or higher showed excellent shape retention and bonding while thermoforming at 60\u0026deg;C to 90\u0026deg;C demonstrated reasonable shape recovery. Recommended thermoforming temperatures were suggested based on application needs, aiding rapid prototyping of multi-material parts with tailored rigidity and shape memory.\u003c/p\u003e \u003cp\u003eIn this study, the formability characteristics of 3D-printed ABS sheets were investigated. The effects of variables such as printing pattern, sheet thickness, and forming temperature on the formability behavior of 3D-printed polymer components were studied. This research aims to advance the knowledge base surrounding hybrid AM processes and facilitate the development of optimized fabrication techniques for polymer-based components.\u003c/p\u003e"},{"header":"2. Material and Methods","content":"\u003cp\u003eDisk-shaped sheets with a diameter of 80 mm were 3D printed using a desktop FFF machine. The samples are made of ABS, well-known for its high tensile strength and widespread use as a filament material in 3D printing. The samples were 3D printed using 1.75 mm diameter\u003cspan dir=\"RTL\"\u003e\u0026nbsp;\u003c/span\u003eXtrusion\u003cspan dir=\"RTL\"\u003e\u0026nbsp;\u003c/span\u003efilaments (Xtrusion filament, Mashhad, Iran) with a 100% infill. Table 1 summarizes the conditions under which the parts were 3D printed.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 1\u003c/strong\u003e. 3D printing condition of ABS sheets\u003c/p\u003e\n\u003cdiv align=\"center\"\u003e\n \u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"84%\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd width=\"37.37373737373738%\"\u003e\n \u003cp\u003e\u003cstrong\u003eProcess variable\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"62.62626262626262%\"\u003e\n \u003cp\u003e\u003cstrong\u003eOperating condition\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"37.37373737373738%\"\u003e\n \u003cp\u003eNozzle diameter (mm)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"62.62626262626262%\"\u003e\n \u003cp\u003e0.4\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"37.37373737373738%\"\u003e\n \u003cp\u003eFilament diameter (mm)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"62.62626262626262%\"\u003e\n \u003cp\u003e1.75\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"37.37373737373738%\"\u003e\n \u003cp\u003eLayer height (mm)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"62.62626262626262%\"\u003e\n \u003cp\u003e0.2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"37.37373737373738%\"\u003e\n \u003cp\u003eTop, bottom, and shell layers\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"62.62626262626262%\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"37.37373737373738%\"\u003e\n \u003cp\u003eInfill (%)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"62.62626262626262%\"\u003e\n \u003cp\u003e100\u0026nbsp;%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"37.37373737373738%\"\u003e\n \u003cp\u003eInternal fill pattern\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"62.62626262626262%\"\u003e\n \u003cp\u003eRectilinear, Concentric, Rectilinear and Concentric\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"37.37373737373738%\"\u003e\n \u003cp\u003ePrinting speed (mm٫s)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"62.62626262626262%\"\u003e\n \u003cp\u003e25\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"37.37373737373738%\"\u003e\n \u003cp\u003eTravel speed (mm٫s)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"62.62626262626262%\"\u003e\n \u003cp\u003e50\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"37.37373737373738%\"\u003e\n \u003cp\u003eNozzle temperature (\u0026deg;C)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"62.62626262626262%\"\u003e\n \u003cp\u003e245\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"37.37373737373738%\"\u003e\n \u003cp\u003eBed temperature (\u0026deg;C)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"62.62626262626262%\"\u003e\n \u003cp\u003e90\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eThe samples were put through the Nakajima test, which involves pressing a sheet sample into a die cavity using a hemispherical punch. The punch was 50 mm in diameter. The tests were performed using a Santam STM-400 machine at a speed of 5 mm/min without the use of lubricant between the sample surface and the punch of the machine. The tests continued until the occurrence of sample failure (crack), which was identified through a noticeable decline in the force-displacement curves. Figure 1 shows the Nakajima test setup as well as how the sheet samples are placed on the die. To stop the sheet samples from moving, the die\u0026apos;s surface is roughened. Furthermore, the blank holder, which is secured to the die with six screws, keeps the sheets from moving while the test is being conducted.\u003c/p\u003e\n\u003cp\u003eThe investigation into the formability of ABS sheets encompassed an examination of three variables: printing algorithm, thickness, and temperature. Each parameter was explored at three distinct levels, resulting in the implementation of a full factorial design of experiments, comprising 27 experiments as shown in Table 2. The samples were 3D printed at three different thicknesses of 0.8, 1.4, and 2 mm, and with three distinct printing patterns, rectilinear (R), concentric (C), and concentric/rectilinear (CR). In addition to these variables, the Nakajima tests were conducted at three temperatures: 35\u0026deg;C, 70\u0026deg;C, and 90\u0026deg;C. These temperatures were chosen to represent a range from low to high forming temperatures considering the thermal properties of ABS. Within this experimental framework, the depth of penetration was considered as the output variable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 2\u003c/strong\u003e. Full factorial design of experiments for formability assessment of ABS 3D-printed sheets, (R: Rectilinear, C: Concentric, CR: Concentric/Rectilinear)\u003c/p\u003e\n\u003cdiv align=\"center\"\u003e\n \u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"98%\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd width=\"6.315789473684211%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003eNo.\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.578947368421053%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003ePrinting\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003ePattern\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.736842105263158%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003eSheet Thickness\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e(mm)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.894736842105264%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003eTest Temperature\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e(\u0026deg;C)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"6.315789473684211%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003eNo.\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.578947368421053%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003ePrinting\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003ePattern\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.68421052631579%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003eSheet Thickness\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e(mm)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.894736842105264%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003eTest Temperature\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e(\u0026deg;C)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"6.315789473684211%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.578947368421053%\"\u003e\n \u003cp\u003eR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.736842105263158%\"\u003e\n \u003cp\u003e0.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.894736842105264%\"\u003e\n \u003cp\u003e35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"6.315789473684211%\"\u003e\n \u003cp\u003e15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.578947368421053%\"\u003e\n \u003cp\u003eC\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.68421052631579%\"\u003e\n \u003cp\u003e1.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.894736842105264%\"\u003e\n \u003cp\u003e90\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"6.315789473684211%\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.578947368421053%\"\u003e\n \u003cp\u003eR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.736842105263158%\"\u003e\n \u003cp\u003e0.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.894736842105264%\"\u003e\n \u003cp\u003e70\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"6.315789473684211%\"\u003e\n \u003cp\u003e16\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.578947368421053%\"\u003e\n \u003cp\u003eC\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.68421052631579%\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.894736842105264%\"\u003e\n \u003cp\u003e35\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"6.315789473684211%\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.578947368421053%\"\u003e\n \u003cp\u003eR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.736842105263158%\"\u003e\n \u003cp\u003e0.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.894736842105264%\"\u003e\n \u003cp\u003e90\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"6.315789473684211%\"\u003e\n \u003cp\u003e17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.578947368421053%\"\u003e\n \u003cp\u003eC\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.68421052631579%\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.894736842105264%\"\u003e\n \u003cp\u003e70\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"6.315789473684211%\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.578947368421053%\"\u003e\n \u003cp\u003eR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.736842105263158%\"\u003e\n \u003cp\u003e1.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.894736842105264%\"\u003e\n \u003cp\u003e35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"6.315789473684211%\"\u003e\n \u003cp\u003e18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.578947368421053%\"\u003e\n \u003cp\u003eC\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.68421052631579%\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.894736842105264%\"\u003e\n \u003cp\u003e90\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"6.315789473684211%\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.578947368421053%\"\u003e\n \u003cp\u003eR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.736842105263158%\"\u003e\n \u003cp\u003e1.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.894736842105264%\"\u003e\n \u003cp\u003e70\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"6.315789473684211%\"\u003e\n \u003cp\u003e19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.578947368421053%\"\u003e\n \u003cp\u003eCR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.68421052631579%\"\u003e\n \u003cp\u003e0.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.894736842105264%\"\u003e\n \u003cp\u003e35\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"6.315789473684211%\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.578947368421053%\"\u003e\n \u003cp\u003eR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.736842105263158%\"\u003e\n \u003cp\u003e1.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.894736842105264%\"\u003e\n \u003cp\u003e90\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"6.315789473684211%\"\u003e\n \u003cp\u003e20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.578947368421053%\"\u003e\n \u003cp\u003eCR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.68421052631579%\"\u003e\n \u003cp\u003e0.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.894736842105264%\"\u003e\n \u003cp\u003e70\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"6.315789473684211%\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.578947368421053%\"\u003e\n \u003cp\u003eR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.736842105263158%\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.894736842105264%\"\u003e\n \u003cp\u003e35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"6.315789473684211%\"\u003e\n \u003cp\u003e21\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.578947368421053%\"\u003e\n \u003cp\u003eCR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.68421052631579%\"\u003e\n \u003cp\u003e0.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.894736842105264%\"\u003e\n \u003cp\u003e90\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"6.315789473684211%\"\u003e\n \u003cp\u003e8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.578947368421053%\"\u003e\n \u003cp\u003eR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.736842105263158%\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.894736842105264%\"\u003e\n \u003cp\u003e70\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"6.315789473684211%\"\u003e\n \u003cp\u003e22\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.578947368421053%\"\u003e\n \u003cp\u003eCR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.68421052631579%\"\u003e\n \u003cp\u003e1.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.894736842105264%\"\u003e\n \u003cp\u003e35\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"6.315789473684211%\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.578947368421053%\"\u003e\n \u003cp\u003eR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.736842105263158%\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.894736842105264%\"\u003e\n \u003cp\u003e90\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"6.315789473684211%\"\u003e\n \u003cp\u003e23\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.578947368421053%\"\u003e\n \u003cp\u003eCR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.68421052631579%\"\u003e\n \u003cp\u003e1.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.894736842105264%\"\u003e\n \u003cp\u003e70\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"6.315789473684211%\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.578947368421053%\"\u003e\n \u003cp\u003eC\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.736842105263158%\"\u003e\n \u003cp\u003e0.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.894736842105264%\"\u003e\n \u003cp\u003e35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"6.315789473684211%\"\u003e\n \u003cp\u003e24\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.578947368421053%\"\u003e\n \u003cp\u003eCR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.68421052631579%\"\u003e\n \u003cp\u003e1.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.894736842105264%\"\u003e\n \u003cp\u003e90\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"6.315789473684211%\"\u003e\n \u003cp\u003e11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.578947368421053%\"\u003e\n \u003cp\u003eC\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.736842105263158%\"\u003e\n \u003cp\u003e0.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.894736842105264%\"\u003e\n \u003cp\u003e70\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"6.315789473684211%\"\u003e\n \u003cp\u003e25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.578947368421053%\"\u003e\n \u003cp\u003eCR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.68421052631579%\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.894736842105264%\"\u003e\n \u003cp\u003e35\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"6.315789473684211%\"\u003e\n \u003cp\u003e12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.578947368421053%\"\u003e\n \u003cp\u003eC\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.736842105263158%\"\u003e\n \u003cp\u003e0.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.894736842105264%\"\u003e\n \u003cp\u003e90\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"6.315789473684211%\"\u003e\n \u003cp\u003e26\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.578947368421053%\"\u003e\n \u003cp\u003eCR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.68421052631579%\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.894736842105264%\"\u003e\n \u003cp\u003e70\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"6.315789473684211%\"\u003e\n \u003cp\u003e13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.578947368421053%\"\u003e\n \u003cp\u003eC\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.736842105263158%\"\u003e\n \u003cp\u003e1.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.894736842105264%\"\u003e\n \u003cp\u003e35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"6.315789473684211%\"\u003e\n \u003cp\u003e27\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.578947368421053%\"\u003e\n \u003cp\u003eCR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.68421052631579%\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.894736842105264%\"\u003e\n \u003cp\u003e90\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"6.315789473684211%\"\u003e\n \u003cp\u003e14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.578947368421053%\"\u003e\n \u003cp\u003eC\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.736842105263158%\"\u003e\n \u003cp\u003e1.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.894736842105264%\"\u003e\n \u003cp\u003e70\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"6.315789473684211%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.578947368421053%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"13.68421052631579%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"17.894736842105264%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eFor the execution of these experiments, a round ceramic heating element was employed, encircling the mold and imparting heat to both the mold and the test sheet sample. Additionally, a thermostat was utilized to accurately regulate and attain the specified testing temperature. Upon reaching the desired temperature, the sheet underwent testing. The thermal equipment implemented in the tests is depicted in Figure 2.\u003c/p\u003e"},{"header":"3. Results and Discussion","content":"\u003cp\u003eThe values of the maximum penetration depth and maximum compressive force of the test samples, which are essential metrics for evaluating the mechanical properties and failure behavior of the materials, are presented in Table 3.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 3.\u0026nbsp;\u003c/strong\u003eThe values of the maximum penetration depth and maximum compressive force of the test samples\u003c/p\u003e\n\u003cdiv align=\"center\"\u003e\n \u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"582\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd width=\"12.32876712328767%\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eNo.\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e\u003cstrong\u003eMaximum compressive force\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e(N)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e\u003cstrong\u003eMaximum penetration depth (mm)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.32876712328767%\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eNo.\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e\u003cstrong\u003eMaximum compressive force\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e(N)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e\u003cstrong\u003eMaximum\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003epenetration depth (mm)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"12.32876712328767%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e422\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e6.74\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.32876712328767%\"\u003e\n \u003cp\u003e15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e108\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e3.50\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"12.32876712328767%\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e157\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e5.58\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.32876712328767%\"\u003e\n \u003cp\u003e16\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e78\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e1.45\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"12.32876712328767%\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e618\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e14.04\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.32876712328767%\"\u003e\n \u003cp\u003e17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e59\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e1.79\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"12.32876712328767%\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e814\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e5.59\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.32876712328767%\"\u003e\n \u003cp\u003e18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e78\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e2.57\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"12.32876712328767%\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e363\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e5.58\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.32876712328767%\"\u003e\n \u003cp\u003e19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e157\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e2.65\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"12.32876712328767%\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e873\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e15.95\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.32876712328767%\"\u003e\n \u003cp\u003e20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e186\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e5.80\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"12.32876712328767%\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e1001\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e7.55\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.32876712328767%\"\u003e\n \u003cp\u003e21\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e265\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e5.55\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"12.32876712328767%\"\u003e\n \u003cp\u003e8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e363\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e7.28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.32876712328767%\"\u003e\n \u003cp\u003e22\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e324\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e3.11\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"12.32876712328767%\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e1295\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e15.87\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.32876712328767%\"\u003e\n \u003cp\u003e23\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e334\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e6.33\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"12.32876712328767%\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e157\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e2.35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.32876712328767%\"\u003e\n \u003cp\u003e24\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e373\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e5.98\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"12.32876712328767%\"\u003e\n \u003cp\u003e11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e39\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e3.12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.32876712328767%\"\u003e\n \u003cp\u003e25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e844\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e5.93\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"12.32876712328767%\"\u003e\n \u003cp\u003e12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e157\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e3.04\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.32876712328767%\"\u003e\n \u003cp\u003e26\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e618\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e6.55\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"12.32876712328767%\"\u003e\n \u003cp\u003e13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e108\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e2.13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.32876712328767%\"\u003e\n \u003cp\u003e27\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e677\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e7.76\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"12.32876712328767%\"\u003e\n \u003cp\u003e14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e157\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e2.67\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"12.32876712328767%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.835616438356166%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eFigure 3 illustrates samples 4, 13, and 22 after Nakajima testing, during which the tests continued until sample failure occurred. These samples exhibit Rectilinear (R), Concentric (C), and Concentric/Rectilinear (CR) patterns, respectively. In this figure, the dashed lines depict the crack shape, the red arrows indicate the path of crack propagation, and the white arrows illustrate the direction of 3D printing rasters. Furthermore. the \u0026quot;W\u0026quot; value indicates the approximate length of the crack.\u003c/p\u003e\n\u003cp\u003eAs shown in Figure 3, in all samples, cracks occurred due to the separation of joints between adjacent rasters, following the 3D printing pattern. In samples with an R pattern, such as sample 4, the crack path is linear and follows the direction of the rasters. The separation of bonding between adjacent rasters resulted in sample failure. In samples with a C pattern, such as sample 14, the rasters in the consecutive layers had a slight mismatch, resulting in the creation of a through-thickness region with weak strength against shear load during the Nakajima test. Consequently, applying force during the test caused shear stress, leading to raster separation and crack propagation along the circular path. Although the circular pattern follows the shape of the samples, it renders them weak and prone to cracking during loading. Therefore, utilizing a circular pattern that follows the sample\u0026apos;s shape is not feasible for Nakajima testing, where loading is normal to the surface of the sheet.\u003c/p\u003e\n\u003cp\u003eThe samples with the CR pattern, such as sample 22, have alternating raster patterns of circular and rectilinear. In these samples, cracks initiated from a layer with a circular pattern and propagated to a layer with a rectilinear pattern under increased force. Therefore, it can be inferred that the circular patterns are weaker than the linear patterns.\u003c/p\u003e\n\u003cp\u003eThe fracture behavior of the samples with different patterns, which are formed at a higher temperature is compared in Figure 4. These samples were deformed at 70\u0026deg;C. By comparing Figure 4 with Figure 3, it can be observed that an increase in forming temperature had a positive impact on the formability of the 3D-printed ABS sheets. The average penetration depth for the samples in Figure 4 is about 5 mm, whereas the average fracture depth for the samples in Figure 3 is about 3.6 mm. Therefore, similar to the formability enhancement observed in rolled sheet metals with an increase in forming temperature [17, 18], the formability of 3D-printed ABS sheets also improves as the forming temperature increases.\u003c/p\u003e\n\u003cp\u003eAdditionally, comparing the two figures shows that the fracture lines remain consistent across temperatures. Sample 11, with a C pattern, exhibits circular fracture lines, following the path of the raster. In sample 2, with an R printing pattern, the fracture path is linear and parallel to the raster lines. Finally, in sample 20 with a CR printing pattern, the fracture lines are both circular and linear. The fracture initially occurs in the layer with a circular raster pattern before progressing to the linear pattern. Despite this, the samples exhibited more deformation and showed deeper penetration differences at higher temperatures.\u003c/p\u003e\n\u003cp\u003eTo better understand the data provided in Table 3, the values are plotted in the form of a column graph, as illustrated in Figure 5. This graph outlines the impact of different printing patterns, sheet thicknesses, and test temperatures on the formability of 3D-printed ABS sheets. As shown in Figure 5, the R pattern exhibits a higher penetration depth compared to the C and CR patterns, indicating better performance under load. The linear arrangement of rasters contributes to greater structural integrity. Conversely, the C pattern shows the lowest penetration depths due to the circular arrangement of rasters. Higher temperatures (90\u0026deg;C) significantly improve penetration depth, suggesting that increased temperature enhances the ductility of ABS sheets. According to Table 3, a substantial increase in compressive force at 90\u0026deg;C is observed for the R and CR patterns, while the C pattern remains less influenced by temperature changes.\u0026nbsp;Foltuţ, et al. [19]\u0026nbsp;investigated the tensile properties of ABS printed at different orientations and temperatures, finding that higher temperatures improve ductility and that certain orientations, particularly 0\u0026deg; and 90\u0026deg;, yield higher tensile strengths compared to 45\u0026deg;. This aligns with the current study\u0026rsquo;s observation that formability increases with temperature and varies significantly with printing patterns. While\u0026nbsp;Foltuţ, et al. [19]\u0026nbsp;focused on tensile strength, the current study provides a comprehensive analysis of formability, contributing further insights into how pattern, thickness, and temperature influence the mechanical behavior of 3D-printed ABS.\u003c/p\u003e\n\u003cp\u003eAs depicted in Figure 5, while thicker sheets (2.0 mm) demonstrate higher formability, the forming depth exhibits minimal variation with changes in sample thickness. This behavior contrasts with that of metals, where sheet formability typically increases with thickness\u0026nbsp;[20, 21]. This phenomenon may be attributed to the 3D printing process used to produce ABS sheets, as process parameters such as printing temperature and layer adhesion can significantly impact overall formability.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;Sample 6, printed with the R pattern and a thickness of 1.4 mm, demonstrated the best formability, achieving a forming depth of 15.95 mm (see Figure 6). The fracture occurred along the printing path between the rasters, consistent with the fracture behavior of samples with the R pattern. The increased forming temperature (90\u0026deg;C) significantly improved the formability, as sample 6\u0026rsquo;s forming depth was approximately three times greater than that of samples four and five, which were printed under the same conditions but formed at 35\u0026deg;C and 70\u0026deg;C, respectively.\u003c/p\u003e\n\u003cp\u003eTo assess the impact of the studied parameters on the formability of ABS sheets, an analysis of variance (ANOVA) was performed. Table 4 presents the results of this ANOVA, indicating the significance of the model terms through p-values below 0.05 and corresponding F-values. Specifically, forming temperature and printing pattern are identified as significant parameters, with p-values less than 0.0001 and F-values of 47.86 and 88.58, respectively. These findings are consistent with the discussions related to Figure 5. According to Table 4, the F-value of the predicted linear model is 52.66, suggesting the model\u0026apos;s significance. The predicted linear model for forming depth demonstrates a high level of accuracy and reliability, as evidenced by the fit statistics in Table 5. The standard deviation of 0.2087 indicates that the predicted values are closely clustered around the mean, reflecting precision and consistency in the model\u0026apos;s predictions. Furthermore, a predicted R\u0026sup2; value of 0.873 offers an estimation of the model\u0026apos;s predictive performance on novel data, underscoring its robustness and reliability. The coefficient of variation (C.V. %) of 13.24 suggests a relatively low percentage of variability relative to the mean, indicating good precision and reliability in the model\u0026apos;s predictions. Finally, the adequate precision value of 22.639 indicates a robust signal-to-noise ratio, supporting the reliability of the model\u0026apos;s predictions.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 4\u003c/strong\u003e. ANOVA results for the effect of forming temperature, sheet thickness, and printing pattern on ABS sheet formability\u003c/p\u003e\n\u003cdiv align=\"center\"\u003e\n \u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\n \u003cp\u003e\u003cstrong\u003eSource\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e\u003cstrong\u003eSum of squares\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e\u003cstrong\u003edf\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e\u003cstrong\u003eMean squares\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e\u003cstrong\u003eF-value\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e\u003cstrong\u003eP-value\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd\u003e\n \u003cp\u003eModel\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e9.100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e2.270\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e52.660\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e\u0026lt; 0.0001\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003esignificant\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd\u003e\n \u003cp\u003eA- Test temperature\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e2.070\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e2.070\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e47.860\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e\u0026lt; 0.0001\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd\u003e\n \u003cp\u003eB- Sheet thickness\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e0.004\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e0.004\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e0.093\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e0.7641\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd\u003e\n \u003cp\u003eC- Printing pattern\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e7.650\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e3.830\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e88.580\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e\u0026lt; 0.0001\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd\u003e\n \u003cp\u003eResidual\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e0.777\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e0.043\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd\u003e\n \u003cp\u003eCor total\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e9.870\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e22\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003e\u003cstrong\u003eTable 5\u003c/strong\u003e.\u0026nbsp;Fit statistics for the linear model of forming depth\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd width=\"14.285714285714286%\"\u003e\n \u003cp\u003e\u003cstrong\u003eStandard deviation\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.285714285714286%\"\u003e\n \u003cp\u003e\u003cstrong\u003eMean\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.285714285714286%\"\u003e\n \u003cp\u003e\u003cstrong\u003eC.V. %\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.285714285714286%\"\u003e\n \u003cp\u003e\u003cstrong\u003eR\u0026sup2;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.285714285714286%\"\u003e\n \u003cp\u003e\u003cstrong\u003eAdjusted R\u0026sup2;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.285714285714286%\"\u003e\n \u003cp\u003e\u003cstrong\u003ePredicted R\u0026sup2;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.285714285714286%\"\u003e\n \u003cp\u003e\u003cstrong\u003eAdequate precision\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"14.285714285714286%\"\u003e\n \u003cp\u003e0.2087\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.285714285714286%\"\u003e\n \u003cp\u003e1.57\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.285714285714286%\"\u003e\n \u003cp\u003e13.24\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.285714285714286%\"\u003e\n \u003cp\u003e0.921\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.285714285714286%\"\u003e\n \u003cp\u003e0.904\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.285714285714286%\"\u003e\n \u003cp\u003e0.873\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.285714285714286%\"\u003e\n \u003cp\u003e22.639\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eFigure 7 compares the predictions of the linear model with the actual forming depth. According to this figure, the model predictions are very close to the actual forming depth (45\u0026deg; line), indicating that the prediction model has high precision in the prediction of forming depth.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;The perturbation plot, illustrating the change in maximum forming depth in response to variations in the studied parameters, is presented in Figure 8. According to this figure, the temperature curve exhibits a positive slope, signifying that forming depth increases with elevated temperatures. The sheet thickness curve appears horizontal, indicating that this parameter does not significantly affect the formability.\u003c/p\u003e\n\u003cp\u003eA comprehensive depiction of forming depth variations is provided by a 3D surface plot. Figure 9 presents a 3D surface diagram illustrating how forming depth changes with variations in sheet thickness and test temperature. In Figure 9a, sheet thickness demonstrates minimal influence on forming depth, while increasing test temperature shows a direct correlation with greater forming depth. The plot reveals that maximum forming depth occurs at a test temperature of 90\u0026deg;C, regardless of sheet thickness. Figure 9b displays a contour plot where parallel curves indicate no significant interaction between test temperature and sheet thickness. Moreover, the linear orientation of these curves suggests a linear relationship between forming depth and temperature changes.\u003c/p\u003e"},{"header":"4. Conclusions","content":"\u003cp\u003eThis study investigated the formability characteristics of 3D-printed ABS sheets using Nakajima tests, focusing on maximizing forming depth as the primary output parameter. The key findings can be summarized as follows:\u003c/p\u003e \u003cp\u003eThe formability of 3D-printed ABS sheets demonstrated significant improvement with increasing temperature. Maximum forming depth was achieved at 90\u0026deg;C, particularly with the R printing pattern, yielding a forming depth of 15.95 mm. In contrast, the lowest forming depth of 1.45 mm occurred at 35\u0026deg;C with the C printing pattern. Contrary to conventional expectations, changes in sheet thickness did not notably affect forming depth. The study revealed that, unlike traditional metal sheet formability, 3D-printed ABS sheets did not exhibit a clear correlation between thickness and formability. While forming depth remained largely unaffected by variations in sheet thickness, an increase in thickness did lead to higher observed forming forces. This suggests that mechanical requirements for forming force differ from those influencing forming depth in 3D-printed ABS sheets. This research contributes valuable insights into optimizing the formability of 3D-printed ABS components, highlighting the critical roles of printing patterns and temperature in achieving desired formability outcomes. These findings are essential for advancing hybrid additive manufacturing processes and enhancing the reliability and applicability of 3D-printed polymer components in various industrial applications.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003e5.1. Funding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNo funding was received for conducting this study.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e5.2. Competing Interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no conflicts of interest relevant to the content of this article.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e5.3. Availability of data and materials\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe datasets utilized and analyzed in this study can be obtained from the corresponding author upon request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eA. Dey, I. N. Roan Eagle, N. J. J. o. m. Yodo, and m. processing, \u0026quot;A review on filament materials for fused filament fabrication,\u0026quot; vol. 5, no. 3, p. 69, 2021.\u003c/li\u003e\n\u003cli\u003eI. Gibson\u003cem\u003e et al.\u003c/em\u003e, \u003cem\u003eAdditive manufacturing technologies\u003c/em\u003e. Springer, 2021.\u003c/li\u003e\n\u003cli\u003eJ. R. C. Dizon, A. H. Espera, Q. Chen, and R. C. Advincula, \u0026quot;Mechanical characterization of 3D-printed polymers,\u0026quot; \u003cem\u003eAdditive Manufacturing, \u003c/em\u003evol. 20, pp. 44-67, 2018/03/01/ 2018.\u003c/li\u003e\n\u003cli\u003eF. Safari, A. Kami, and V. Abedini, \u0026quot;3D printing of Continuous Fiber Reinforced Composites: A Review of the Processing, Pre- and Post-Processing Effects on Mechanical Properties,\u0026quot; \u003cem\u003ePolymers and Polymer Composites, \u003c/em\u003evol. 30, pp. 1-26, 2022.\u003c/li\u003e\n\u003cli\u003eA. Rosa-Sainz, I. Ferrer, M. L. Garcia-Romeu, and G. Centeno, \u0026quot;Characterization of plastic formability and failure mechanisms in FDM additively manufactured PETG and PCL sheets,\u0026quot; \u003cem\u003ePolymer Testing, \u003c/em\u003evol. 134, p. 108431, 2024/05/01/ 2024.\u003c/li\u003e\n\u003cli\u003eM. Merklein, R. Schulte, and T. Papke, \u0026quot;An innovative process combination of additive manufacturing and sheet bulk metal forming for manufacturing a functional hybrid part,\u0026quot; \u003cem\u003eJournal of Materials Processing Technology, \u003c/em\u003evol. 291, p. 117032, 2021/05/01/ 2021.\u003c/li\u003e\n\u003cli\u003eN. Nakamura, K.-i. Mori, and Y. Abe, \u0026quot;Applicability of plastic tools additively manufactured by fused deposition modelling for sheet metal forming,\u0026quot; \u003cem\u003eThe International Journal of Advanced Manufacturing Technology, \u003c/em\u003evol. 108, no. 4, pp. 975-985, 2020/05/01 2020.\u003c/li\u003e\n\u003cli\u003eN. Nakamura, K.-i. Mori, F. Abe, and Y. Abe, \u0026quot;Bending of sheet metals using plastic tools made with 3D printer,\u0026quot; \u003cem\u003eProcedia Manufacturing, \u003c/em\u003evol. 15, pp. 737-742, 2018/01/01/ 2018.\u003c/li\u003e\n\u003cli\u003eP. Frohn-S\u0026ouml;rensen, M. Geueke, T. B. Tuli, C. Kuhnhen, M. Manns, and B. Engel, \u0026quot;3D printed prototyping tools for flexible sheet metal drawing,\u0026quot; \u003cem\u003eThe International Journal of Advanced Manufacturing Technology, \u003c/em\u003evol. 115, no. 7, pp. 2623-2637, 2021/08/01 2021.\u003c/li\u003e\n\u003cli\u003eS. Rosenthal, M. Hahn, and A. E. Tekkaya, \u0026quot;Deep drawability of additively manufactured sheets with a structured core,\u0026quot; \u003cem\u003eInternational Journal of Material Forming, \u003c/em\u003evol. 16, no. 2, p. 20, 2023/02/14 2023.\u003c/li\u003e\n\u003cli\u003eS. Rosenthal\u003cem\u003e et al.\u003c/em\u003e, \u0026quot;Forming properties of additively manufactured monolithic Hastelloy X sheets,\u0026quot; \u003cem\u003eMaterials Science and Engineering: A, \u003c/em\u003evol. 753, pp. 300-316, 2019/04/10/ 2019.\u003c/li\u003e\n\u003cli\u003eP. Martins, L. Kwiatkowski, V. Franzen, A. Tekkaya, and M. Kleiner, \u0026quot;Single point incremental forming of polymers,\u0026quot; \u003cem\u003eCIRP annals, \u003c/em\u003evol. 58, no. 1, pp. 229-232, 2009.\u003c/li\u003e\n\u003cli\u003eA. Rosa-Sainz, G. Centeno, M. B. Silva, J. A. L\u0026oacute;pez-Fern\u0026aacute;ndez, A. J. Mart\u0026iacute;nez-Donaire, and C. Vallellano, \u0026quot;On the Determination of Forming Limits in Polycarbonate Sheets,\u0026quot; vol. 13, no. 4, p. 928, 2020.\u003c/li\u003e\n\u003cli\u003eA. Bagheri, V. Asghari, and A. Kami, \u0026quot;Spin welding of 3D-printed and solid acrylonitrile\u0026ndash;butadiene\u0026ndash;styrene (ABS) components: a preliminary investigation,\u0026quot; \u003cem\u003eArchives of Civil and Mechanical Engineering, \u003c/em\u003evol. 22, no. 3, p. 130, 2022/05/14 2022.\u003c/li\u003e\n\u003cli\u003eM. L. Garcia-Romeu, I. Ferrer, C. Pasotti, J. Coma, A. Rosa-Sainz, and G. Centeno, \u0026quot;Preliminary study on the use of 3D printed biodegradable polymeric sheet for the manufacturing of medical prostheses by SPIF,\u0026quot; \u003cem\u003eProcedia CIRP, \u003c/em\u003evol. 110, pp. 76-81, 2022/01/01/ 2022.\u003c/li\u003e\n\u003cli\u003eN. P. Sorimpuk, W. H. Choong, and B.-L. Chua, \u0026quot;Thermoforming Characteristics of PLA/TPU Multi-Material Specimens Fabricated with Fused Deposition Modelling under Different Temperatures,\u0026quot; vol. 14, no. 20, p. 4304, 2022.\u003c/li\u003e\n\u003cli\u003eS. Pandre, A. Morchhale, N. Kotkunde, and S. K. Singh, \u0026quot;Influence of processing temperature on formability of thin-rolled DP590 steel sheet,\u0026quot; \u003cem\u003eMaterials and Manufacturing Processes, \u003c/em\u003evol. 35, no. 8, pp. 901-909, 2020/06/10 2020.\u003c/li\u003e\n\u003cli\u003eA. Heidari, A. Ghassemi, and A. Atrian, \u0026quot;A numerical and experimental investigation of temperature effects on the formability of AA6063 sheets using different ductile fracture criteria,\u0026quot; \u003cem\u003eThe International Journal of Advanced Manufacturing Technology, \u003c/em\u003evol. 106, no. 5, pp. 2595-2611, 2020/01/01 2020.\u003c/li\u003e\n\u003cli\u003eD. Foltuţ, E. Vălean, V. Dzitac, and L. Marşavina, \u0026quot;The influence of temperature on the mechanical properties of 3D printed and injection molded ABS,\u0026quot; \u003cem\u003eMaterials Today: Proceedings, \u003c/em\u003evol. 78, pp. 210-213, 2023/01/01/ 2023.\u003c/li\u003e\n\u003cli\u003eD. Banabic, F. Barlat, O. Cazacu, and T. Kuwabara, \u0026quot;Advances in anisotropy of plastic behaviour and formability of sheet metals,\u0026quot; \u003cem\u003eInternational Journal of Material Forming, \u003c/em\u003evol. 13, pp. 749-787, 2020.\u003c/li\u003e\n\u003cli\u003eD. Peng, S. Chen, R. Darabi, A. Ghabussi, and M. Habibi, \u0026quot;Prediction of the bending and out-of-plane loading effects on formability response of the steel sheets,\u0026quot; \u003cem\u003eArchives of Civil and Mechanical Engineering, \u003c/em\u003evol. 21, no. 2, p. 74, 2021.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Semnan University","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"3D Printing, Fused filament fabrication, ABS sheets, Formability, Nakajima test","lastPublishedDoi":"10.21203/rs.3.rs-4735291/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4735291/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study explores the formability of acrylonitrile butadiene styrene (ABS) sheets produced by the fused filament fabrication 3D-printing process. The ABS sheets, fabricated with a diameter of 80 mm, were subjected to the Nakajima test. The investigation focused on assessing the impact of printing pattern (rectilinear, concentric, concentric/rectilinear), sheet thickness (0.8 mm, 1.4 mm, and 2 mm), and forming temperature (35\u0026deg;C, 70\u0026deg;C, and 90\u0026deg;C) on forming depth, utilizing a full factorial design of experiments comprising 27 conditions. Through the application of analysis of variance (ANOVA), a linear model for forming depth was derived, demonstrating high precision and reliability. Results indicate that as temperature increases, formability improves, reaching a maximum at 90\u0026deg;C with a rectilinear print pattern (15.95 mm depth). Conversely, the lowest forming depth (1.45 mm) occurred at 35\u0026deg;C with a concentric printing pattern. Sheet thickness showed minimal impact on forming depth, but forming force increased with thickness.\u003c/p\u003e","manuscriptTitle":"Formability Assessment of 3D-Printed ABS Sheets Using Nakajima Test","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-07-16 15:59:29","doi":"10.21203/rs.3.rs-4735291/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"06c24741-ed29-4141-8d8b-a6500e13c64c","owner":[],"postedDate":"July 16th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":34550767,"name":"Mechanical Engineering"},{"id":34550768,"name":"Materials Engineering"}],"tags":[],"updatedAt":"2024-07-16T15:59:29+00:00","versionOfRecord":[],"versionCreatedAt":"2024-07-16 15:59:29","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4735291","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4735291","identity":"rs-4735291","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}