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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="en"><front><journal-meta><journal-id journal-id-type="publisher-id">donstu</journal-id><journal-title-group><journal-title xml:lang="en">Advanced Engineering Research (Rostov-on-Don)</journal-title><trans-title-group xml:lang="ru"><trans-title>Advanced Engineering Research (Rostov-on-Don)</trans-title></trans-title-group></journal-title-group><issn pub-type="epub">2687-1653</issn><publisher><publisher-name>Don State Technical University</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.23947/2687-1653-2024-24-3-215-226</article-id><article-id custom-type="edn" pub-id-type="custom">KVEMQM</article-id><article-id custom-type="elpub" pub-id-type="custom">donstu-2250</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>MECHANICS</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>МЕХАНИКА</subject></subj-group></article-categories><title-group><article-title>Increasing the Interlayer Fracture Toughness of Polymer Fabric Composites Using Local 3D-Reinforcement (Felting)</article-title><trans-title-group xml:lang="ru"><trans-title>Повышение межслойной трещиностойкости полимерных тканевых композитов с помощью локального трехмерного армирования (фелтинга)</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-7263-9274</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Форенталь</surname><given-names>Г. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Forental</surname><given-names>G. А.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Галина Анатольевна Форенталь, инженер-исследователь </p><p>454080, г. Челябинск, пр. Ленина, 76</p></bio><bio xml:lang="en"><p>Galina A. Forental, Research Engineer</p><p>76, Lenin Ave., Chelyabinsk, 454080</p></bio><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-7022-4865</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Сапожников</surname><given-names>С. Б.</given-names></name><name name-style="western" xml:lang="en"><surname>Sapozhnikov</surname><given-names>S. B.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Сергей Борисович Сапожников, доктор технических наук, профессор; ведущий ученый</p><p>454080, г. Челябинск, пр. Ленина, 76</p><p>140180, г. Жуковский, Московская область, ул. Жуковского, 1</p></bio><bio xml:lang="en"><p>Sergey B. Sapozhnikov, Dr.Sci. (Eng.), Professor of the Engineering Mechanics Department; Leading Scientist</p><p>76, Lenin Ave., Chelyabinsk, 454080</p><p>1, Zhukovsky Str., Zhukovsky, Moscow Region, 140180</p></bio><xref ref-type="aff" rid="aff-2"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Южно-Уральский государственный университет</institution><country>Россия</country></aff><aff xml:lang="en"><institution>South Ural State University</institution><country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="ru"><institution>Южно-Уральский государственный университет; Центральный аэрогидродинамический институт имени профессора Н.Е. Жуковского</institution><country>Россия</country></aff><aff xml:lang="en"><institution>South Ural State University; Central Aerohydrodynamic Institute</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2024</year></pub-date><pub-date pub-type="epub"><day>25</day><month>09</month><year>2024</year></pub-date><volume>24</volume><issue>3</issue><fpage>215</fpage><lpage>226</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Forental G.А., Sapozhnikov S.B., 2024</copyright-statement><copyright-year>2024</copyright-year><copyright-holder xml:lang="ru">Форенталь Г.А., Сапожников С.Б.</copyright-holder><copyright-holder xml:lang="en">Forental G.А., Sapozhnikov S.B.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://www.vestnik-donstu.ru/jour/article/view/2250">https://www.vestnik-donstu.ru/jour/article/view/2250</self-uri><abstract><sec><title>Introduction</title><p>Introduction. One of the reasons for undesirable delamination of polymer composites with fabric reinforcement is low transverse shear properties. It is known that the reinforcement of polymer fabric composites in the Z direction reduces the sensitivity to delamination and increases the viscosity of interlayer fracture. Various methods of three-dimensional reinforcement of polymer fabric composites are proposed in the literature. However, they complicate the manufacturing process of the structure. The problem is solved by the method of three-dimensional reinforcement proposed in this article — felting. This is a local reinforcement of the composite in the Z direction with minimal production changes. The degree of Z-reinforcement is determined by the felting density, i.e., the number of needle punches per 1 cm² of the fabric package. The work is aimed at evaluating the effect of felting on the interlayer crack resistance of a composite material.</p></sec><sec><title>Materials and Methods</title><p>Materials and Methods. The interlayer fracture toughness GIIc was determined on a cross-woven fiberglass with felting of 10 cm-². The material was impregnated with Etal-370 resin and Etal-45 hardener. Experiments according to ASTM D7905M–14 and GOST 33685–2015 standards were carried out on an Instron 5900R test machine. The stress state at the crack tip was analyzed with regard to the nonlocal strength theory in the ANSYS Workbench program (option “static strength analysis”). The finite element method (FEM) was used.</p></sec><sec><title>Results</title><p>Results. The “load — displacement” curves were considered for the samples. Values GIIc were calculated. The results of ENF tests for felting density of 0 cm–² and 10 cm–² were summarized. Control samples and felting samples were compared. In the latter case, GIIс turned out to be ~33% higher. The stress state at the crack tip was calculated under DCB and ENF loading. The dependences of maximum normal and shear stresses, as well as displacements, were visualized in the form of graphs and color charts. To get the calculated “load — displacement” dependences using FEM, the reverse method of obtaining transverse shear constants was used. DCB loading showed that felting provided increasing the rupture strength in the Z direction to ~18%, by 39 to 46 MPa, and in the planes XZ— to ~16%, by 77 to 89 MPa.</p><p>Discussion and Conclusion. Felting as a method of local three-dimensional reinforcement enhances the interlayer crack resistance of polymer fabric composites. It provides reducing the area of stratifications after local impacts during the operation of structures. Flexible felting technology makes it possible to create zones with an arbitrary impact density, increasing fracture toughness only in the required places of structures. The FEM analysis of the stress state at the crack tip within the framework of the nonlocal strength theory has shown that in strength calculations, the stratification crack can be considered as a stress concentrator.</p></sec></abstract><trans-abstract xml:lang="ru"><sec><title>Введение</title><p>Введение. Одна из причин нежелательных расслоений полимерных композитов с тканевым армированием — низкие трансверсально-сдвиговые характеристики. Известно, что армирование полимерных тканевых композитов в направлении Z уменьшает чувствительность к расслоению и повышает вязкость межслойного разрушения. В литературе предлагаются разные способы трехмерного армирования полимерных тканевых композитов. Однако они усложняют процесс изготовления конструкции. Проблему решает предложенный в данной статье способ трехмерного армирования — фелтинг. Это локальное армирование композита в направлении Z при минимальных производственных изменениях. Степень Z-армирования определяется плотностью фелтинга, т.е. количеством ударов иглы на 1 см² тканевого пакета. Цель работы — оценить влияние фелтинга на межслойную трещиностойкость композитного материала.</p></sec><sec><title>Материалы и методы</title><p>Материалы и методы. Межслойную вязкость разрушения GIIc определяли на стеклоткани полотняного переплетения с фелтингом 10 см–². Материал пропитывали смолой Этал-370 и отвердителем Этал-45. Эксперименты по стандартам ASTM D7905M–14 и ГОСТ 33685–2015 проводили на испытательной машине Instron 5900R. Напряженное состояние у вершины трещины анализировали с позиции нелокальной теории прочности в программе Ansys Workbench (опция «статический прочностной анализ»). Задействовали метод конечных элементов (МКЭ).</p></sec><sec><title>Результаты исследования</title><p>Результаты исследования. Для образцов рассмотрели кривые «нагрузка — перемещение». Вычислили значения GIIс. Обобщили итоги ENF-испытаний для плотности фелтинга 0 см–² и 10 см–². Сравнили контрольные образцы и образцы с фелтингом. В последнем случае GIIс оказалась выше на ~33 %. Рассчитали напряженное состояние у вершины трещины при DCB- и ENF-нагружении. Визуализировали в виде графиков и цветовых диаграмм зависимости максимальных нормальных и касательных напряжений, а также перемещений. Для получения расчетных зависимостей «нагрузка — перемещение» с помощью МКЭ использовали обратный метод получения трансверсально-сдвиговых констант. Нагружение по схеме DCB показало, что фелтинг позволяет увеличить предел прочности на растяжение в направлении Z на ~18 %, с 39 до 46 МПа, а в плоскости XZ — на ~16 %, с 77 МПа до 89 МПа.</p></sec><sec><title>Обсуждение и заключение</title><p>Обсуждение и заключение. Фелтинг как способ локального трехмерного армирования усиливает межслойную трещиностойность полимерных тканевых композитов. Он позволяет сократить площадь расслоений после локальных ударов при эксплуатации конструкций. Гибкая технология фелтинга дает возможность создавать зоны с произвольной плотностью ударов, повышая трещиностойкость лишь в необходимых местах конструкций. МКЭ-анализ напряженного состояния у вершины трещины в рамках нелокальной теории прочности показал, что в прочностных расчетах трещину расслоения можно рассматривать как концентратор напряжений.</p></sec></trans-abstract><kwd-group xml:lang="ru"><kwd>армирование полимерных тканевых композитов</kwd><kwd>трансверсально-сдвиговая прочность</kwd><kwd>межслойная трещиностойкость</kwd><kwd>межслоевая вязкость разрушения</kwd><kwd>фелтинговое локальное трехмерное армирование</kwd></kwd-group><kwd-group xml:lang="en"><kwd>reinforcement of polymer fabric composites</kwd><kwd>transverse shear strength</kwd><kwd>interlayer crack resistance</kwd><kwd>interlaminar fracture toughness</kwd><kwd>felting local three-dimensional reinforcement</kwd></kwd-group><funding-group><funding-statement xml:lang="ru">Исследование выполнено в рамках Программы создания и развития научного центра мирового уровня «Сверхзвук» на 2020–2025 годы при финансовой поддержке Минобрнауки России (соглашение от 17 мая 2022 г. № 075–15–2022–1023).</funding-statement><funding-statement xml:lang="en">The research was done within the framework of the Program for the Creation and Development of the World-Class Scientific Center “Supersound” for 2020–2025 with the financial support of the Ministry of Education and Science of the Russian Federation (Agreement no. 075–15–2022–1023, dated May 17, 2022).</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Callister WD Jr., Rethwisch DG. Materials Science and Engineering: An Introduction. 10th edn. Hoboken, NJ: Wiley; 2018. 992 p. URL: https://www.wiley.com/en-us/Materials+Science+and+Engineering%3A+An+Introduction%2C+10th+Edition-p9781119405498 (accessed: 22.04.2024).</mixed-citation><mixed-citation xml:lang="en">Callister WD Jr., Rethwisch DG. Materials Science and Engineering: An Introduction. 10th edn. Hoboken, NJ: Wiley; 2018. 992 p. URL: https://www.wiley.com/en-us/Materials+Science+and+Engineering%3A+An+Introduction%2C+10th+Edition-p9781119405498 (accessed: 22.04.2024).</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Wei Tan, Falzon BG, Chiu LNS, Price M. Predicting Low Velocity Impact Damage and Compression-After-Impact (CAI) Behaviour of Composite Laminates. Composites Part A: Applied Science and Manufacturing. 2015;71:212–226. https://doi.org/10.1016/j.compositesa.2015.01.025</mixed-citation><mixed-citation xml:lang="en">Wei Tan, Falzon BG, Chiu LNS, Price M. Predicting Low Velocity Impact Damage and Compression-After-Impact (CAI) Behaviour of Composite Laminates. Composites Part A: Applied Science and Manufacturing. 2015;71:212–226. https://doi.org/10.1016/j.compositesa.2015.01.025</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Balasubramani Veerappan, S Rajendra Boopathy. Prediction of Residual Tensile Strength of Laminated Composite Plates after Low Velocity Impact. ARPN Journal of Engineering and Applied Sciences. 2014;9(3):320–325.</mixed-citation><mixed-citation xml:lang="en">Balasubramani Veerappan, S Rajendra Boopathy. Prediction of Residual Tensile Strength of Laminated Composite Plates after Low Velocity Impact. ARPN Journal of Engineering and Applied Sciences. 2014;9(3):320–325.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Abrate S. Impact on Composite Structures. Cambridge: Cambridge University Press; 2009. 289 p. https://doi.org/10.1017/CBO9780511574504</mixed-citation><mixed-citation xml:lang="en">Abrate S. Impact on Composite Structures. Cambridge: Cambridge University Press; 2009. 289 p. https://doi.org/10.1017/CBO9780511574504</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Liyong Tong, Mouritz AP, Bannister MK. 3D Fibre Reinforced Polymer Composites. Amsterdam: Elsevier Science; 2002. 254 p. https://doi.org/10.1016/B978-0-08-043938-9.X5012-1</mixed-citation><mixed-citation xml:lang="en">Liyong Tong, Mouritz AP, Bannister MK. 3D Fibre Reinforced Polymer Composites. Amsterdam: Elsevier Science; 2002. 254 p. https://doi.org/10.1016/B978-0-08-043938-9.X5012-1</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Jinlian Hu. 3-D Fibrous Assemblies: Properties, Applications and Modeling of Three-Dimensional Textile Structures. Sawston, Cambridge: Woodhead Publishing; 2008. 280 p.</mixed-citation><mixed-citation xml:lang="en">Jinlian Hu. 3-D Fibrous Assemblies: Properties, Applications and Modeling of Three-Dimensional Textile Structures. Sawston, Cambridge: Woodhead Publishing; 2008. 280 p.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Chen Xiaoming, Zhao Yufen, Zhang Chunyan, Wang Xiaoxu, Chen Li. Robot Needle-Punching for Manufacturing Composite Performs. Robotics and Computer-Integrated Manufacturing. 2018;50:132–139. https://doi.org/10.1016/j.rcim.2017.09.008</mixed-citation><mixed-citation xml:lang="en">Chen Xiaoming, Zhao Yufen, Zhang Chunyan, Wang Xiaoxu, Chen Li. Robot Needle-Punching for Manufacturing Composite Performs. Robotics and Computer-Integrated Manufacturing. 2018;50:132–139. https://doi.org/10.1016/j.rcim.2017.09.008</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Forental GA, Kheruvimov AV, Nikonov AV, Sapozhnikov SB. Stack Fabric Felting to Get PCM Gllc Improvement and LVI Tolerance. IOP Conference Series: Materials Science and Engineering. 2021;1024(1):012001. https://doi.org/10.1088/1757-899X/1024/1/012001</mixed-citation><mixed-citation xml:lang="en">Forental GA, Kheruvimov AV, Nikonov AV, Sapozhnikov SB. Stack Fabric Felting to Get PCM Gllc Improvement and LVI Tolerance. IOP Conference Series: Materials Science and Engineering. 2021;1024(1):012001. https://doi.org/10.1088/1757-899X/1024/1/012001</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Sham MS, Venkatesha CS, Jayaraju T. Experimental Methods of Determining Fracture Toughness of Fiber Reinforced Polymer Composites under Various Loading Conditions. Journal of Minerals and Materials Characterization and Engineering. 2011;10(13):1263–1275. http://doi.org/10.4236/jmmce.2011.1013099</mixed-citation><mixed-citation xml:lang="en">Sham MS, Venkatesha CS, Jayaraju T. Experimental Methods of Determining Fracture Toughness of Fiber Reinforced Polymer Composites under Various Loading Conditions. Journal of Minerals and Materials Characterization and Engineering. 2011;10(13):1263–1275. http://doi.org/10.4236/jmmce.2011.1013099</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Pinho S, Robinson P, Iannucci L. Developing a Four Point Bend Specimen to Measure the Mode I Intralaminar Fracture Toughness of Unidirectional Laminated Composites. Composites Science and Technology. 2009;69(7–8): 1303–1309. https://doi.org/10.1016/j.compscitech.2009.03.007</mixed-citation><mixed-citation xml:lang="en">Pinho S, Robinson P, Iannucci L. Developing a Four Point Bend Specimen to Measure the Mode I Intralaminar Fracture Toughness of Unidirectional Laminated Composites. Composites Science and Technology. 2009;69(7–8): 1303–1309. https://doi.org/10.1016/j.compscitech.2009.03.007</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Issam Tawk, Jihad Rishmany, Nicolas Saba, Pablo Navarro, Jean-Francois Ferrero. Experimental Study of the Interlaminar Fracture of Composite Materials in Mode III by MSCB Test. Composite Structures. 2020;233:111548. https://doi.org/10.1016/j.compstruct.2019.111548</mixed-citation><mixed-citation xml:lang="en">Issam Tawk, Jihad Rishmany, Nicolas Saba, Pablo Navarro, Jean-Francois Ferrero. Experimental Study of the Interlaminar Fracture of Composite Materials in Mode III by MSCB Test. Composite Structures. 2020;233:111548. https://doi.org/10.1016/j.compstruct.2019.111548</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Hossein Saidpour, Mehdi Barikani, Multu Sezen. Mode-II Interlaminar Fracture Toughness of Carbon/Epoxy Laminates. Iranian Polymer Journal. 2003;12(5):389–400.</mixed-citation><mixed-citation xml:lang="en">Hossein Saidpour, Mehdi Barikani, Multu Sezen. Mode-II Interlaminar Fracture Toughness of Carbon/Epoxy Laminates. Iranian Polymer Journal. 2003;12(5):389–400.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Sham Prasad MS, Venkatesha CS, Jayaraju T. Experimental Methods of Determining Fracture Toughness of Fiber Reinforced Polymer Composites under Various Loading Conditions. Journal of Minerals and Materials Characterization and Engineering. 2011;10(13):1263–1275. http://doi.org/10.4236/jmmce.2011.1013099</mixed-citation><mixed-citation xml:lang="en">Sham Prasad MS, Venkatesha CS, Jayaraju T. Experimental Methods of Determining Fracture Toughness of Fiber Reinforced Polymer Composites under Various Loading Conditions. Journal of Minerals and Materials Characterization and Engineering. 2011;10(13):1263–1275. http://doi.org/10.4236/jmmce.2011.1013099</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Ying Zeng, Hong-Yuan Liu, Yiu-Wing Mai, Xu-Sheng Du. Improving Interlaminar Fracture Toughness of Carbon Fibre/Epoxy Laminates by Incorporation of Nano-Particles. Composites Part B: Engineering. 2012;43(1):90–94. https://doi.org/10.1016/j.compositesb.2011.04.036</mixed-citation><mixed-citation xml:lang="en">Ying Zeng, Hong-Yuan Liu, Yiu-Wing Mai, Xu-Sheng Du. Improving Interlaminar Fracture Toughness of Carbon Fibre/Epoxy Laminates by Incorporation of Nano-Particles. Composites Part B: Engineering. 2012;43(1):90–94. https://doi.org/10.1016/j.compositesb.2011.04.036</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Kadhum A, Muslim ZR, Jaffer HI. Interlaminar Fracture of Micro and Nano Composites Special. Acta Physica Polonica: Series A. 2019;135(5):1126–1128. http://doi.org/10.12693/APhysPolA.135.1126</mixed-citation><mixed-citation xml:lang="en">Kadhum A, Muslim ZR, Jaffer HI. Interlaminar Fracture of Micro and Nano Composites Special. Acta Physica Polonica: Series A. 2019;135(5):1126–1128. http://doi.org/10.12693/APhysPolA.135.1126</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Форенталь Г.А., Сапожников С.Б. Перспективы технологии фелтинга для локального трехмерного армирования полимерных тканевых композитов. Композиты и наноструктуры. 2022;14(4):233–245. https://doi.org/10.36236/1999-7590-2022-14-4-233-245233</mixed-citation><mixed-citation xml:lang="en">Forental GA, Sapozhnikov SB. Prospects of Felting Technology for Local 3D-Reinforcement of Polymer Fabric Composites. Composites and Nanostructures. 2022;14(56):233–245. https://doi.org/36.10236/1999-7590-2022-14-4-233-245233</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Maimi P, Gonzalez EV, Gascons N, Ripoll L. Size Effect Law and Critical Distance Theories to Predict the Nominal Strength of Quasibrittle Structures. Applied Mechanics Reviews. 2013;65(2):020803. https://doi.org/10.1115/1.4024163</mixed-citation><mixed-citation xml:lang="en">Maimi P, Gonzalez EV, Gascons N, Ripoll L. Size Effect Law and Critical Distance Theories to Predict the Nominal Strength of Quasibrittle Structures. Applied Mechanics Reviews. 2013;65(2):020803. https://doi.org/10.1115/1.4024163</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Hoang Thai Nguyen, A Abdullah Dönmez, Zdenek P Bazant. Structural Strength Scaling Law for Fracture of Plastic-Hardening Metals and Testing of Fracture Properties. Extreme Mechanics Letters. 2021;43(1):101141. https://doi.org/10.1016/j.eml.2020.101141</mixed-citation><mixed-citation xml:lang="en">Hoang Thai Nguyen, A Abdullah Dönmez, Zdenek P Bazant. Structural Strength Scaling Law for Fracture of Plastic-Hardening Metals and Testing of Fracture Properties. Extreme Mechanics Letters. 2021;43(1):101141. https://doi.org/10.1016/j.eml.2020.101141</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Taylor D. The Theory of Critical Distances: A New Perspective in Fracture Mechanics. Amsterdam: Elsevier Science; 2007. 306 p. https://doi.org/10.1016/B978-0-08-044478-9.X5000-5</mixed-citation><mixed-citation xml:lang="en">Taylor D. The Theory of Critical Distances: A New Perspective in Fracture Mechanics. Amsterdam: Elsevier Science; 2007. 306 p. https://doi.org/10.1016/B978-0-08-044478-9.X5000-5</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Mahmoodi MJ, Khamehchi M. Finite Element Analysis of Free Corner Effects in Composite Laminates Based on a Global–Local Model. Archive of Applied Mechanics. 2023;93(12):4327–4350. http://doi.org/10.1007/s00419-023-02494-1</mixed-citation><mixed-citation xml:lang="en">Mahmoodi MJ, Khamehchi M. Finite Element Analysis of Free Corner Effects in Composite Laminates Based on a Global–Local Model. Archive of Applied Mechanics. 2023;93(12):4327–4350. http://doi.org/10.1007/s00419-023-02494-1</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Jaehong Lee, Zafer Gurdal, O Hayden Griffin Jr. Layer-Wise Approach for the Bifurcation Problem in Laminated Composites with Delaminations. AIAA Journal. 1993;31(2):331–338. https://doi.org/10.2514/3.11672</mixed-citation><mixed-citation xml:lang="en">Jaehong Lee, Zafer Gurdal, O Hayden Griffin Jr. Layer-Wise Approach for the Bifurcation Problem in Laminated Composites with Delaminations. AIAA Journal. 1993;31(2):331–338. https://doi.org/10.2514/3.11672</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Сапожников С.Б. Разрушение тканевых композитов с концентраторами напряжений: учет неупругого деформирования в численном моделировании. Композиты и наноструктуры. 2020;2(46):31–39. https://doi.org/10.36236/1999-7590-2020-12-2-31-39</mixed-citation><mixed-citation xml:lang="en">Sapozhnikov SB. Failure of Fabric Reinforced Composite with Concentrators: Implementation of Inelastic Deformation in Numerical Simulation. Composites and Nanostructures. 2020;12(45):31–39. https://doi.org/10.36236/1999-7590-2020-12-2-31-39</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Barbero EJ. Introduction to Composite Materials Design, 2nd ed. Boca Raton: CRC Press; 2011. 562 p. https://doi.org/10.1201/9781439894132</mixed-citation><mixed-citation xml:lang="en">Barbero EJ. Introduction to Composite Materials Design, 2nd ed. Boca Raton: CRC Press; 2011. 562 p. https://doi.org/10.1201/9781439894132</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
