DOI: https://doi.org/10.32515/2664-262X.2025.11(42).1.101-107
Technological Damage to Structures Made by 3D Printing
About the Authors
Oleksandr Tymoshenko, Associate Professor, PhD in Technics (Candidate of Technics Sciences), National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine , e-mail: timosaha@ukr.net, 0000-0003-0226-3755
Olha Musiienko, PhD, National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine , e-mail: olga.musinko@gmail.com, ORCID ID: 0000-0001-8255-3909
Yaroslav Demeshko, post-graduate, National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine , e-mail: demeshko.yaroslav.01@gmail.com, ORCID ID: 0009-0009-0863-4407
Abstract
This paper investigates aspects of technological damage to structures made using additive technologies, in particular, 3D printing. The main objective of the study is to analyze the effect of printing parameters, in particular the degree of filling, on the mechanical properties of PLA material, which is one of the most popular materials for 3D printing. The paper discusses in detail how the degree of filling of structures, which varies from 20% to 100%, affects their mechanical characteristics, in particular, tensile strength, Young's modulus, and fracture strain.
To investigate this, experimental tensile tests were conducted on PLA samples with different percentages of filling. The tests revealed that with an increase in the degree of filling of the structures, the material shows an increase in stiffness and strength, but at certain stages this effect ceases to be linear. The highest values of mechanical characteristics were recorded at 100% filling, but a decrease in the degree of filling led to a significant decrease in the strength of the material, especially at 20% filling, where significant deformation was recorded at lower loads. This indicates a significant influence of the internal structure of the material on its performance, which should be taken into account when designing structures for specific purposes.
The obtained results allow us to draw important conclusions regarding the optimization of 3D printing parameters for the manufacture of PLA structures, taking into account the requirements for mechanical properties. Evaluation of the effect of the degree of filling on the parameters of technological damage to the material allows us to develop recommendations for selecting optimal printing conditions depending on the type of product and its intended operating conditions. As a result of the study, the correlation between the mechanical properties of the material and the parameters of 3D printing was determined, which is key to the development of efficient and reliable structures in various fields of application of additive technologies.
Keywords
PLA, 3D printing, tensile testing, strength, Young's modulus, initial damage, damage parameter
Full Text:
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References
1. Srivastava, M., Rathee, S., Patel, V., Kumar, A., & Koppad, P. G. (2022). A review of various materials for additive manufacturing: Recent trends and processing issues. Journal of Materials Research and Technology, 21, 2612–2641. https://doi.org/10.1016/j.jmrt.2022.05.022.
2. Zalohin, M. Yu., Skliarov, V. V., Dovzhenko, J. S., & Brega, D. A. (2019). Experimental determination and comparative analysis of the PPH030GP, ABS and PLA polymer strength characteristics at different strain rates. Science & Technique, 18, 233–239. DOI:10.21122/2227-1031-2019-18-3-233-239.
3. Stoia, D. I., Marsavina, L., & Linul, E. (2021). Mode I critical energy release rate of additively manufactured polyamide samples. Theoretical and Applied Fracture Mechanics, 114, 102968. https://doi.org/10.1016/j.tafmec.2021.102968 [in English].
4. Singamneni, S., Behera, M. P., Truong, D., Le Guen, M. J., Macrae, E., & Pickering, K. (2021). Direct extrusion 3D printing for a softer PLA-based bio-polymer composite in pellet form. Journal of Materials Research and Technology, 15, 936–949. https://doi.org/10.1016/j.jmrt.2021.06.041.
5. Tao, Y., Kong, F., Li, Z., Zhang, J., Zhao, X., Yin, Q., Xing, D., & Li, P. (2021). A review on voids of 3D printed parts by fused filament fabrication. Journal of Materials Research and Technology, 15, 4860–4879. https://doi.org/10.1016/j.jmrt.2021.07.071.
6. Vidakis, N., Kechagias, J. D., Petousis, M., Vakouftsi, F., & Mountakis, N. (2023). The effects of FFF 3D printing parameters on energy consumption. Materials and Manufacturing Processes, 38(8), 915–932. https://doi.org/10.1080/10426914.2023.2191842.
7. Cai, L., Byrd, P., Zhang, H., Schlarman, K., Zhang, Y., Golub, M., & Zhang, J. (n.d.). Effect of printing orientation on strength of 3D printed ABS plastics.
8. Musiienko, O. S., Slobodianiuk, I. V., & Reminny, V. A. (2024). The influence of moisture content of polymeric materials on the mechanical characteristics of products printed by 3D printing. Sekcia 1 "Organisaciyno-ekonomichni Metodi realisacii innovaciynoi modeli rozvutky ekonomiky", p.148 [in Ukrainian].
9. Vălean, C., Marșavina, L., Mărghitaș, M., & others. (2020). The effect of crack insertion for FDM printed PLA materials on Mode I and Mode II fracture toughness. Procedia Structural Integrity, 28, 1134–1139. https://doi.org/10.1016/j.prostr.2020.10.134.
10. Rubashevsky, V. V., & Shykaev, S. M. (2020). Micnist i pruzhnist PLA + graphit composityv: experymentalny I teoretichniy analis. [Strength and elasticity of PLA + graphite composites: experimental and theoretical analysis.] p.145-154 [in Ukrainian].
11. Hussain, M., Khan, S. M., Shafiq, M., & Abbas, N. (n.d.). A review on PLA-based biodegradable materials for biomedical applications.
12. Lemaitre, J., & Desmorat, R. (2005). Engineering Damage Mechanics. Springer.
13. Badreddine, H., Saanouni, K., & Nguyen, T. D. (2015). Damage anisotropy and its effect on the plastic anisotropy evolution under finite strains. International Journal of Solids and Structures, 63, 11–31. https://doi.org/10.1016/j.ijsolstr.2015.02.009.
14. Lu, D., et al. (2022). Double scalar variables plastic-damage model for concrete. Journal of Engineering Mechanics, 148(2), 04021143. https://doi.org/10.1061/(ASCE)EM.1943-7889.0002049 [in English].
15. Xing, L., et al. (2022). A micromechanics-based damage constitutive model considering microstructure for aluminum alloys. International Journal of Plasticity, 157, 103390. doi.org/10.1016/j.ijplas.2022.103390.
16. Chausov, M. G., Maruschak, P. O., Hutsaylyuk, V., Śnieżek, L., & Pylypenko, A. P. (2018). Effect of complex combined loading mode on the fracture toughness of titanium alloys. Vacuum, 147, 51–57. https://doi.org/10.1016/j.vacuum.2017.10.010 [in English].
17. Betten, J. (1983). Damage tensors in continuum mechanics. Journal de mécanique théorique appliquée, 1, 13–32.
18. Shedbale, A. S., Sun, G., & Poh, L. H. (2021). A localizing gradient enhanced isotropic damage model with Ottosen equivalent strain for the mixed-mode fracture of concrete. International Journal of Mechanical Sciences, 199, 106410. https://doi.org/10.1016/j.ijmecsci.2021.106410 [in English].
19. Brünig, M., Koirala, S., & Gerke, S. (2024). Micro-mechanical numerical analysis on ductile damage in multiaxially loaded anisotropic metals. Computational Mechanics, 73(2), 223–232. https://doi.org/10.1007/s00466-023-02258-7.
20. Keshavarz, A., & Ghajar, R. (2019). Effect of isotropic and anisotropic damage and plasticity on ductile crack initiation. International Journal of Damage Mechanics, 28(6), 918–942. https://doi.org/10.1177/1056789519829691.
21. Xing, L., et al. (2022). A micromechanics-based damage constitutive model considering microstructure for aluminum alloys. International Journal of Plasticity, 157, 103390. https://doi.org/10.1016/j.ijplas.2022.103390.
22. Yue, Z., et al. (2019). Failure prediction on steel sheet under different loading paths based on fully coupled ductile damage model. International Journal of Mechanical Sciences, 153, 1–9. https://doi.org/10.1016/j.ijmecsci.2019.105349.
23. DSTU EN ISO 527-3:2017. (2017). Plasmasy. Vysnachennya vlastivostey pid chas roztyguvannya. Chastyna 3. Umovy vyprobyvannya dlya plivok ta listiv. [Plastics. Determination of tensile properties. Part 3. Test conditions for films and sheets.] [in Ukrainian].
24. Tymoshenko, O. V., Musiienko, O. S., & Demeshko, Y. V. (2023). Vplyv struktury zapovnennya na micnist PLA-plastyku pry 3D-druci [Influence of the filling structure on the strength of PLA plastic in 3D printing.] p.60-62 [in Ukrainian].
Citations
1. Srivastava, M., Rathee, S., Patel, V., Kumar, A., Koppad, P. G. A review of various materials for additive manufacturing: recent trends and processing issues. Journal of Materials Research and Technology. 2022. Vol. 21. P. 2612–2641.
2. Залохін, М. Ю., Скляров, В. В., Довженко, Ю. С., Брега, Д. А. Експериментальне визначення та порівняльний аналіз міцнісних характеристик полімерів PPH030GP, ABS і PLA при різних швидкостях деформування. Science & Technique. 2019. №18. С. 233–239.
3. Stoia, D. I., Marsavina, L., Linul, E. Mode I critical energy release rate of additively manufactured polyamide samples. Theoretical and Applied Fracture Mechanics. 2021. Vol. 114. Article 102968.
4. Singamneni, S., Behera, M. P., Truong, D., Le Guen, M. J., Macrae, E., Pickering, K. Direct extrusion 3D printing for a softer PLA-based bio-polymer composite in pellet form. Journal of Materials Research and Technology. 2021. Vol. 15. P. 936–949.
5. Tao, Y., Kong, F., Li, Z., Zhang, J., Zhao, X., Yin, Q., Xing, D., Li, P. A review on voids of 3D printed parts by fused filament fabrication. Journal of Materials Research and Technology. 2021. Vol. 15. P. 4860–4879.
6. Vidakis, N., Kechagias, J. D., Petousis, M., Vakouftsi, F., Mountakis, N. The effects of FFF 3D printing parameters on energy consumption. Materials and Manufacturing Processes. 2023. Vol. 38, No. 8. P. 915–932.
7. Cai, L., Byrd, P., Zhang, H., Schlarman, K., Zhang, Y., Golub, M., Zhang, J. Effect of printing orientation on strength of 3D printed ABS plastics. Materials Today: Proceedings. 2022. Vol. 56. P. 453–460.
8. Мусієнко, О. С., Слободянюк, І. В., Ремінний, В. А. Вплив вологості полімерних матеріалів на механічні характеристики виробів, надрукованих методом 3D-друку. Організаційно-економічні методи реалізації інноваційної моделі розвитку економіки. 2024. С. 148.
9. Vălean, C., Marșavina, L., Mărghitaș, M., et al. The effect of crack insertion for FDM printed PLA materials on Mode I and Mode II fracture toughness. Procedia Structural Integrity. 2020. Vol. 28. P. 1134–1139.
10. Rubashevskyi, V., Shukayev, S. Міцність і пружність PLA+ графіт композитів: експериментальний і теоретичний аналіз // Mechanics and Advanced Technologies. 2023. Vol. 7, No. 2 (98). С. 145–154.
11. Hussain, M., Khan, S. M., Shafiq, M., Abbas, N. A review on PLA-based biodegradable materials for biomedical applications. Journal of Polymer Research. 2022. Vol. 29. Article 123.
12. Lemaitre, J., Desmorat, R. Engineering Damage Mechanics. Paris: Springer, 2005. 380 p.
13. Badreddine, H., Saanouni, K., Nguyen, T. D. Damage anisotropy and its effect on the plastic anisotropy evolution under finite strains. International Journal of Solids and Structures. 2015. Vol. 63. P. 11–31.
14. Lu, D., et al. Double scalar variables plastic-damage model for concrete. Journal of Engineering Mechanics. 2022. Vol. 148, No. 2. Article 04021143.
15. Xing, L., et al. A micromechanics-based damage constitutive model considering microstructure for aluminum alloys. International Journal of Plasticity. 2022. Vol. 157. Article 103390.
16. Chausov, M. G., Maruschak, P. O., Hutsaylyuk, V., Śnieżek, L., Pylypenko, A. P. Effect of complex combined loading mode on the fracture toughness of titanium alloys. Vacuum. 2018. Vol. 147. P. 51–57.
17. Betten, J. Damage tensors in continuum mechanics. Journal de Mécanique Théorique et Appliquée. 1983. No. 1. P. 13–32.
18. Shedbale, A. S., Sun, G., Poh, L. H. A localizing gradient enhanced isotropic damage model with Ottosen equivalent strain for the mixed-mode fracture of concrete. International Journal of Mechanical Sciences. 2021. Vol. 199. Article 106410.
19. Brünig, M., Koirala, S., Gerke, S. Micro-mechanical numerical analysis on ductile damage in multiaxially loaded anisotropic metals. Computational Mechanics. 2024. Vol. 73, No. 2. P. 223–232.
20. Keshavarz, A., Ghajar, R. Effect of isotropic and anisotropic damage and plasticity on ductile crack initiation. International Journal of Damage Mechanics. 2019. Vol. 28, No. 6. P. 918–942.
21. Xing L., et al. A micromechanics-based damage constitutive model considering microstructure for aluminum alloys. International Journal of Plasticity. 2022. Vol. 157. P. 103390.
22. Yue, Z., et al. Failure prediction on steel sheet under different loading paths based on fully coupled ductile damage model. International Journal of Mechanical Sciences. 2019. Vol. 153. P. 1–9.
23. ДСТУ EN ISO 527-3:2017. Пластмаси. Визначення властивостей під час розтягування. Частина 3. Умови випробування для плівок і листів (EN ISO 527-3:1995; AC:2002, IDT; ISO 527-3:1995; Cor.1:2001, IDT).
24. Тимошенко, О. В., Мусієнко, О. С., Демешко, Я. В. Вплив структури заповнення на міцність PLA-пластику при 3D-друці. Прогресивна техніка, технологія та інженерна освіта. 2024. С. 60–62.
Copyright (c) 2025 Oleksandr Tymoshenko, Olha Musiienko, Yaroslav Demeshko
Technological Damage to Structures Made by 3D Printing
About the Authors
Oleksandr Tymoshenko, Associate Professor, PhD in Technics (Candidate of Technics Sciences), National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine , e-mail: timosaha@ukr.net, 0000-0003-0226-3755
Olha Musiienko, PhD, National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine , e-mail: olga.musinko@gmail.com, ORCID ID: 0000-0001-8255-3909
Yaroslav Demeshko, post-graduate, National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine , e-mail: demeshko.yaroslav.01@gmail.com, ORCID ID: 0009-0009-0863-4407
Abstract
Keywords
Full Text:
PDFReferences
1. Srivastava, M., Rathee, S., Patel, V., Kumar, A., & Koppad, P. G. (2022). A review of various materials for additive manufacturing: Recent trends and processing issues. Journal of Materials Research and Technology, 21, 2612–2641. https://doi.org/10.1016/j.jmrt.2022.05.022.
2. Zalohin, M. Yu., Skliarov, V. V., Dovzhenko, J. S., & Brega, D. A. (2019). Experimental determination and comparative analysis of the PPH030GP, ABS and PLA polymer strength characteristics at different strain rates. Science & Technique, 18, 233–239. DOI:10.21122/2227-1031-2019-18-3-233-239.
3. Stoia, D. I., Marsavina, L., & Linul, E. (2021). Mode I critical energy release rate of additively manufactured polyamide samples. Theoretical and Applied Fracture Mechanics, 114, 102968. https://doi.org/10.1016/j.tafmec.2021.102968 [in English].
4. Singamneni, S., Behera, M. P., Truong, D., Le Guen, M. J., Macrae, E., & Pickering, K. (2021). Direct extrusion 3D printing for a softer PLA-based bio-polymer composite in pellet form. Journal of Materials Research and Technology, 15, 936–949. https://doi.org/10.1016/j.jmrt.2021.06.041.
5. Tao, Y., Kong, F., Li, Z., Zhang, J., Zhao, X., Yin, Q., Xing, D., & Li, P. (2021). A review on voids of 3D printed parts by fused filament fabrication. Journal of Materials Research and Technology, 15, 4860–4879. https://doi.org/10.1016/j.jmrt.2021.07.071.
6. Vidakis, N., Kechagias, J. D., Petousis, M., Vakouftsi, F., & Mountakis, N. (2023). The effects of FFF 3D printing parameters on energy consumption. Materials and Manufacturing Processes, 38(8), 915–932. https://doi.org/10.1080/10426914.2023.2191842.
7. Cai, L., Byrd, P., Zhang, H., Schlarman, K., Zhang, Y., Golub, M., & Zhang, J. (n.d.). Effect of printing orientation on strength of 3D printed ABS plastics.
8. Musiienko, O. S., Slobodianiuk, I. V., & Reminny, V. A. (2024). The influence of moisture content of polymeric materials on the mechanical characteristics of products printed by 3D printing. Sekcia 1 "Organisaciyno-ekonomichni Metodi realisacii innovaciynoi modeli rozvutky ekonomiky", p.148 [in Ukrainian].
9. Vălean, C., Marșavina, L., Mărghitaș, M., & others. (2020). The effect of crack insertion for FDM printed PLA materials on Mode I and Mode II fracture toughness. Procedia Structural Integrity, 28, 1134–1139. https://doi.org/10.1016/j.prostr.2020.10.134.
10. Rubashevsky, V. V., & Shykaev, S. M. (2020). Micnist i pruzhnist PLA + graphit composityv: experymentalny I teoretichniy analis. [Strength and elasticity of PLA + graphite composites: experimental and theoretical analysis.] p.145-154 [in Ukrainian].
11. Hussain, M., Khan, S. M., Shafiq, M., & Abbas, N. (n.d.). A review on PLA-based biodegradable materials for biomedical applications.
12. Lemaitre, J., & Desmorat, R. (2005). Engineering Damage Mechanics. Springer.
13. Badreddine, H., Saanouni, K., & Nguyen, T. D. (2015). Damage anisotropy and its effect on the plastic anisotropy evolution under finite strains. International Journal of Solids and Structures, 63, 11–31. https://doi.org/10.1016/j.ijsolstr.2015.02.009.
14. Lu, D., et al. (2022). Double scalar variables plastic-damage model for concrete. Journal of Engineering Mechanics, 148(2), 04021143. https://doi.org/10.1061/(ASCE)EM.1943-7889.0002049 [in English].
15. Xing, L., et al. (2022). A micromechanics-based damage constitutive model considering microstructure for aluminum alloys. International Journal of Plasticity, 157, 103390. doi.org/10.1016/j.ijplas.2022.103390.
16. Chausov, M. G., Maruschak, P. O., Hutsaylyuk, V., Śnieżek, L., & Pylypenko, A. P. (2018). Effect of complex combined loading mode on the fracture toughness of titanium alloys. Vacuum, 147, 51–57. https://doi.org/10.1016/j.vacuum.2017.10.010 [in English].
17. Betten, J. (1983). Damage tensors in continuum mechanics. Journal de mécanique théorique appliquée, 1, 13–32.
18. Shedbale, A. S., Sun, G., & Poh, L. H. (2021). A localizing gradient enhanced isotropic damage model with Ottosen equivalent strain for the mixed-mode fracture of concrete. International Journal of Mechanical Sciences, 199, 106410. https://doi.org/10.1016/j.ijmecsci.2021.106410 [in English].
19. Brünig, M., Koirala, S., & Gerke, S. (2024). Micro-mechanical numerical analysis on ductile damage in multiaxially loaded anisotropic metals. Computational Mechanics, 73(2), 223–232. https://doi.org/10.1007/s00466-023-02258-7.
20. Keshavarz, A., & Ghajar, R. (2019). Effect of isotropic and anisotropic damage and plasticity on ductile crack initiation. International Journal of Damage Mechanics, 28(6), 918–942. https://doi.org/10.1177/1056789519829691.
21. Xing, L., et al. (2022). A micromechanics-based damage constitutive model considering microstructure for aluminum alloys. International Journal of Plasticity, 157, 103390. https://doi.org/10.1016/j.ijplas.2022.103390.
22. Yue, Z., et al. (2019). Failure prediction on steel sheet under different loading paths based on fully coupled ductile damage model. International Journal of Mechanical Sciences, 153, 1–9. https://doi.org/10.1016/j.ijmecsci.2019.105349.
23. DSTU EN ISO 527-3:2017. (2017). Plasmasy. Vysnachennya vlastivostey pid chas roztyguvannya. Chastyna 3. Umovy vyprobyvannya dlya plivok ta listiv. [Plastics. Determination of tensile properties. Part 3. Test conditions for films and sheets.] [in Ukrainian].
24. Tymoshenko, O. V., Musiienko, O. S., & Demeshko, Y. V. (2023). Vplyv struktury zapovnennya na micnist PLA-plastyku pry 3D-druci [Influence of the filling structure on the strength of PLA plastic in 3D printing.] p.60-62 [in Ukrainian].
Citations
1. Srivastava, M., Rathee, S., Patel, V., Kumar, A., Koppad, P. G. A review of various materials for additive manufacturing: recent trends and processing issues. Journal of Materials Research and Technology. 2022. Vol. 21. P. 2612–2641.
2. Залохін, М. Ю., Скляров, В. В., Довженко, Ю. С., Брега, Д. А. Експериментальне визначення та порівняльний аналіз міцнісних характеристик полімерів PPH030GP, ABS і PLA при різних швидкостях деформування. Science & Technique. 2019. №18. С. 233–239.
3. Stoia, D. I., Marsavina, L., Linul, E. Mode I critical energy release rate of additively manufactured polyamide samples. Theoretical and Applied Fracture Mechanics. 2021. Vol. 114. Article 102968.
4. Singamneni, S., Behera, M. P., Truong, D., Le Guen, M. J., Macrae, E., Pickering, K. Direct extrusion 3D printing for a softer PLA-based bio-polymer composite in pellet form. Journal of Materials Research and Technology. 2021. Vol. 15. P. 936–949.
5. Tao, Y., Kong, F., Li, Z., Zhang, J., Zhao, X., Yin, Q., Xing, D., Li, P. A review on voids of 3D printed parts by fused filament fabrication. Journal of Materials Research and Technology. 2021. Vol. 15. P. 4860–4879.
6. Vidakis, N., Kechagias, J. D., Petousis, M., Vakouftsi, F., Mountakis, N. The effects of FFF 3D printing parameters on energy consumption. Materials and Manufacturing Processes. 2023. Vol. 38, No. 8. P. 915–932.
7. Cai, L., Byrd, P., Zhang, H., Schlarman, K., Zhang, Y., Golub, M., Zhang, J. Effect of printing orientation on strength of 3D printed ABS plastics. Materials Today: Proceedings. 2022. Vol. 56. P. 453–460.
8. Мусієнко, О. С., Слободянюк, І. В., Ремінний, В. А. Вплив вологості полімерних матеріалів на механічні характеристики виробів, надрукованих методом 3D-друку. Організаційно-економічні методи реалізації інноваційної моделі розвитку економіки. 2024. С. 148.
9. Vălean, C., Marșavina, L., Mărghitaș, M., et al. The effect of crack insertion for FDM printed PLA materials on Mode I and Mode II fracture toughness. Procedia Structural Integrity. 2020. Vol. 28. P. 1134–1139.
10. Rubashevskyi, V., Shukayev, S. Міцність і пружність PLA+ графіт композитів: експериментальний і теоретичний аналіз // Mechanics and Advanced Technologies. 2023. Vol. 7, No. 2 (98). С. 145–154.
11. Hussain, M., Khan, S. M., Shafiq, M., Abbas, N. A review on PLA-based biodegradable materials for biomedical applications. Journal of Polymer Research. 2022. Vol. 29. Article 123.
12. Lemaitre, J., Desmorat, R. Engineering Damage Mechanics. Paris: Springer, 2005. 380 p.
13. Badreddine, H., Saanouni, K., Nguyen, T. D. Damage anisotropy and its effect on the plastic anisotropy evolution under finite strains. International Journal of Solids and Structures. 2015. Vol. 63. P. 11–31.
14. Lu, D., et al. Double scalar variables plastic-damage model for concrete. Journal of Engineering Mechanics. 2022. Vol. 148, No. 2. Article 04021143.
15. Xing, L., et al. A micromechanics-based damage constitutive model considering microstructure for aluminum alloys. International Journal of Plasticity. 2022. Vol. 157. Article 103390.
16. Chausov, M. G., Maruschak, P. O., Hutsaylyuk, V., Śnieżek, L., Pylypenko, A. P. Effect of complex combined loading mode on the fracture toughness of titanium alloys. Vacuum. 2018. Vol. 147. P. 51–57.
17. Betten, J. Damage tensors in continuum mechanics. Journal de Mécanique Théorique et Appliquée. 1983. No. 1. P. 13–32.
18. Shedbale, A. S., Sun, G., Poh, L. H. A localizing gradient enhanced isotropic damage model with Ottosen equivalent strain for the mixed-mode fracture of concrete. International Journal of Mechanical Sciences. 2021. Vol. 199. Article 106410.
19. Brünig, M., Koirala, S., Gerke, S. Micro-mechanical numerical analysis on ductile damage in multiaxially loaded anisotropic metals. Computational Mechanics. 2024. Vol. 73, No. 2. P. 223–232.
20. Keshavarz, A., Ghajar, R. Effect of isotropic and anisotropic damage and plasticity on ductile crack initiation. International Journal of Damage Mechanics. 2019. Vol. 28, No. 6. P. 918–942.
21. Xing L., et al. A micromechanics-based damage constitutive model considering microstructure for aluminum alloys. International Journal of Plasticity. 2022. Vol. 157. P. 103390.
22. Yue, Z., et al. Failure prediction on steel sheet under different loading paths based on fully coupled ductile damage model. International Journal of Mechanical Sciences. 2019. Vol. 153. P. 1–9.
23. ДСТУ EN ISO 527-3:2017. Пластмаси. Визначення властивостей під час розтягування. Частина 3. Умови випробування для плівок і листів (EN ISO 527-3:1995; AC:2002, IDT; ISO 527-3:1995; Cor.1:2001, IDT).
24. Тимошенко, О. В., Мусієнко, О. С., Демешко, Я. В. Вплив структури заповнення на міцність PLA-пластику при 3D-друці. Прогресивна техніка, технологія та інженерна освіта. 2024. С. 60–62.