<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.3 20210610//EN" "JATS-journalpublishing1-3.dtd">
<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="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">zldm</journal-id><journal-title-group><journal-title xml:lang="ru">Заводская лаборатория. Диагностика материалов</journal-title><trans-title-group xml:lang="en"><trans-title>Industrial laboratory. Diagnostics of materials</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">1028-6861</issn><issn pub-type="epub">2588-0187</issn><publisher><publisher-name>ООО «Издательство «ТЕСТ-ЗЛ»</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.26896/1028-6861-2026-92-5-55-69</article-id><article-id custom-type="elpub" pub-id-type="custom">zldm-2831</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="ru"><subject>ИССЛЕДОВАНИЕ СТРУКТУРЫ И СВОЙСТВ. МЕХАНИКА МАТЕРИАЛОВ: ПРОЧНОСТЬ, РЕСУРС, БЕЗОПАСНОСТЬ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>TESTING OF STRUCTURE AND PARAMETERS. MECHANICAL TESTING METHODS</subject></subj-group></article-categories><title-group><article-title>CTOA: a tool for risk prevention in pipelines transporting dangerous gases</article-title><trans-title-group xml:lang="en"><trans-title>Materials mechanics: strength, durability, safety</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Pluvinage</surname><given-names>G.</given-names></name><name name-style="western" xml:lang="en"><surname>Pluvinage</surname><given-names>G.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Guy Pluvinage</p><p>1, Route d’Ars Laquenexy, Metz, 57078</p></bio><bio xml:lang="en"><p>Guy Pluvinage</p><p>1, Route d’Ars Laquenexy, Metz, 57078 </p></bio><email xlink:type="simple">pluvinage.guy@orange.fr</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Capelle</surname><given-names>J.</given-names></name><name name-style="western" xml:lang="en"><surname>Capelle</surname><given-names>J.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Julien Capelle</p><p>1, Route d’Ars Laquenexy, Metz, 57078</p></bio><bio xml:lang="en"><p>Julien Capelle</p><p>1, Route d’Ars Laquenexy, Metz, 57078 </p></bio><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>ENIM — University of Lorraine</institution><country>Франция</country></aff><aff xml:lang="en"><institution>ENIM — University of Lorraine</institution><country>France</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2026</year></pub-date><pub-date pub-type="epub"><day>27</day><month>05</month><year>2026</year></pub-date><volume>92</volume><issue>5</issue><fpage>55</fpage><lpage>69</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Pluvinage G., Capelle J., 2026</copyright-statement><copyright-year>2026</copyright-year><copyright-holder xml:lang="ru">Pluvinage G., Capelle J.</copyright-holder><copyright-holder xml:lang="en">Pluvinage G., Capelle J.</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.zldm.ru/jour/article/view/2831">https://www.zldm.ru/jour/article/view/2831</self-uri><abstract><p>This paper presents the Crack Tip Opening Angle (CTOA) as an effective fracture mechanics criterion for preventing risks associated with pipelines transporting hazardous gases such as hydrogen and ammonia. CTOA is used as a global parameter to characterize resistance to ductile crack propagation and to predict crack arrest conditions in pressurized pipelines. Unlike initiation-based fracture parameters, CTOA directly describes steady-state crack growth and is therefore well suited for assessing long-running cracks that may lead to catastrophic failures. The paper reviews the fracture behavior of pipeline steels, distinguishing between crack initiation and propagation, and highlights the advantages and limitations of the CTOA approach. Several CTOA measurement techniques are discussed, including direct optical methods, indirect load — displacement curve analysis, and fracture surface microtopography. The influence of material properties, specimen geometry, thickness, loading mode, and plastic constraint on CTOA values is examined, with particular emphasis on the significant scatter observed in experimental data. CTOA is implemented in finite element simulations using a node-release technique to model ductile crack propagation and arrest under internal pressure. The predicted arrest pressure and crack length are compared with established approaches such as the Battelle Two-Curves Method, showing good agreement. Once crack arrest is determined, the resulting breach size is used to calculate gas outflow rates. Finally, gas dispersion modeling, combined with CTOA-based fracture analysis, enables the determination of safety distances for toxic or explosive gas releases. A case study using ammonia and the ALOHA dispersion software demonstrates how CTOA can be integrated into a risk-based framework to ensure that lethal risk remains below regulatory thresholds over the pipeline’s service life.</p></abstract><trans-abstract xml:lang="en"><p>This paper presents the Crack Tip Opening Angle (CTOA) as an effective fracture mechanics criterion for preventing risks associated with pipelines transporting hazardous gases such as hydrogen and ammonia. CTOA is used as a global parameter to characterize resistance to ductile crack propagation and to predict crack arrest conditions in pressurized pipelines. Unlike initiation-based fracture parameters, CTOA directly describes steady-state crack growth and is therefore well suited for assessing long-running cracks that may lead to catastrophic failures. The paper reviews the fracture behavior of pipeline steels, distinguishing between crack initiation and propagation, and highlights the advantages and limitations of the CTOA approach. Several CTOA measurement techniques are discussed, including direct optical methods, indirect load — displacement curve analysis, and fracture surface microtopography. The influence of material properties, specimen geometry, thickness, loading mode, and plastic constraint on CTOA values is examined, with particular emphasis on the significant scatter observed in experimental data. CTOA is implemented in finite element simulations using a node-release technique to model ductile crack propagation and arrest under internal pressure. The predicted arrest pressure and crack length are compared with established approaches such as the Battelle Two-Curves Method, showing good agreement. Once crack arrest is determined, the resulting breach size is used to calculate gas outflow rates. Finally, gas dispersion modeling, combined with CTOA-based fracture analysis, enables the determination of safety distances for toxic or explosive gas releases. A case study using ammonia and the ALOHA dispersion software demonstrates how CTOA can be integrated into a risk-based framework to ensure that lethal risk remains below regulatory thresholds over the pipeline’s service life.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>Crack Tip Opening Angle (CTOA)</kwd><kwd>optical methods</kwd><kwd>indirect load — displacement curve analysis</kwd><kwd>and fracture surface microtopography</kwd><kwd>arrest pressure and crack length</kwd><kwd>safety distances</kwd></kwd-group><kwd-group xml:lang="en"><kwd>Crack Tip Opening Angle (CTOA)</kwd><kwd>optical methods</kwd><kwd>indirect load — displacement curve analysis</kwd><kwd>and fracture surface microtopography</kwd><kwd>arrest pressure and crack length</kwd><kwd>safety distances</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Pluvinage G. Elastoplastic fracture mechanics. — Toulouse: CEPADUES, 1989; Moscow: MIR, 1993.</mixed-citation><mixed-citation xml:lang="en">Pluvinage G. Elastoplastic fracture mechanics. — Toulouse: CEPADUES, 1989; Moscow: MIR, 1993.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Ernst H. A., Paris P. C., Landes J. D. Estimations on J-integral and tearing modulus from a single specimen test record / ASTM STP 743.1981. DOI: 10.1520/stp28814s</mixed-citation><mixed-citation xml:lang="en">Ernst H. A., Paris P. C., Landes J. D. Estimations on J-integral and tearing modulus from a single specimen test record / ASTM STP 743.1981. DOI: 10.1520/stp28814s</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Brocks W., Schwalbe K.-H., Zerbst U. Structural integrity assessment of thin-walled structures / Adv. Eng. Mater. 2006. Vol. 8(5). P. 319 – 327. DOI: 10.1002/adem.200600120</mixed-citation><mixed-citation xml:lang="en">Brocks W., Schwalbe K.-H., Zerbst U. Structural integrity assessment of thin-walled structures / Adv. Eng. Mater. 2006. Vol. 8(5). P. 319 – 327. DOI: 10.1002/adem.200600120</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Anderson T. L. Fracture toughness measurements for metals. — Columbus: Battelle Columbus Laboratories Report, 1973.</mixed-citation><mixed-citation xml:lang="en">Anderson T. L. Fracture toughness measurements for metals. — Columbus: Battelle Columbus Laboratories Report, 1973.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Chen C. R., Kolednik O., Scheider I., et al. On the determination of the cohesive zone parameters for the modelling of micro-ductile crack growth in thick specimens / Int. J. Fracture. 2003. Vol. 120(3). P. 517 – 536. DOI: 10.1023/a:1025426121928</mixed-citation><mixed-citation xml:lang="en">Chen C. R., Kolednik O., Scheider I., et al. On the determination of the cohesive zone parameters for the modelling of micro-ductile crack growth in thick specimens / Int. J. Fracture. 2003. Vol. 120(3). P. 517 – 536. DOI: 10.1023/a:1025426121928</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Gurson A. L. Continuum theory of ductile rupture by void nucleation and growth. Part I. Yield criteria and flow rules for porous ductile media / J. Eng. Mater. Technol. 1977. Vol. 99(1). P. 2 – 15. DOI: 10.1115/1.3443406</mixed-citation><mixed-citation xml:lang="en">Gurson A. L. Continuum theory of ductile rupture by void nucleation and growth. Part I. Yield criteria and flow rules for porous ductile media / J. Eng. Mater. Technol. 1977. Vol. 99(1). P. 2 – 15. DOI: 10.1115/1.3443406</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Andersson H. A. Finite element representation of stable crack growth / J. Mech. Phys. Solids. 1973. Vol. 21. P. 337 – 356.</mixed-citation><mixed-citation xml:lang="en">Andersson H. A. Finite element representation of stable crack growth / J. Mech. Phys. Solids. 1973. Vol. 21. P. 337 – 356.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Reuven R., McCowan C., Drexler E., et al. CTOA results for X65 and X100 pipeline steels: influence of displacement rate / Proc. of the Int. Pipeline Conf. — Calgary, 2008.</mixed-citation><mixed-citation xml:lang="en">Reuven R., McCowan C., Drexler E., et al. CTOA results for X65 and X100 pipeline steels: influence of displacement rate / Proc. of the Int. Pipeline Conf. — Calgary, 2008.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Ying Z., Li X., Cao Y., Zhang S. A novel method to determine critical CTOA by the load-displacement curve / Eng. Fracture Mech. 2020. Vol. 230. Art. 107013. DOI: 10.1016/j.engfracmech.2020.107013</mixed-citation><mixed-citation xml:lang="en">Ying Z., Li X., Cao Y., Zhang S. A novel method to determine critical CTOA by the load-displacement curve / Eng. Fracture Mech. 2020. Vol. 230. Art. 107013. DOI: 10.1016/j.engfracmech.2020.107013</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Schwalbe K.-H., Newman J. C. Jr., Shannon J. Jr. Fracture mechanics testing on specimens with low constraint — standardisation activities within ISO and ASTM / Eng. Fracture Mech. 2005. Vol. 72. P. 557 – 576. DOI: 10.1016/j.engfracmech.2004.04.006</mixed-citation><mixed-citation xml:lang="en">Schwalbe K.-H., Newman J. C. Jr., Shannon J. Jr. Fracture mechanics testing on specimens with low constraint — standardisation activities within ISO and ASTM / Eng. Fracture Mech. 2005. Vol. 72. P. 557 – 576. DOI: 10.1016/j.engfracmech.2004.04.006</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Lloyd W. R., McClintock F. A. Microtopography for ductile fracture process characterization. Part 2. Application for CTOA analysis / Eng. Fracture Mech. 2003. Vol. 70(3 – 4). P. 403 – 415. DOI: 10.1520/stp16391s</mixed-citation><mixed-citation xml:lang="en">Lloyd W. R., McClintock F. A. Microtopography for ductile fracture process characterization. Part 2. Application for CTOA analysis / Eng. Fracture Mech. 2003. Vol. 70(3 – 4). P. 403 – 415. DOI: 10.1520/stp16391s</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Ben Amara M., Pluvinage G., Capelle J., Azari Z. Crack tip opening angle as a fracture resistance parameter to describe ductile crack extension and arrest in steel pipes under service pressure / Phys. Mesomech. 2015. Vol. 18(4). P. 355 – 369.</mixed-citation><mixed-citation xml:lang="en">Ben Amara M., Pluvinage G., Capelle J., Azari Z. Crack tip opening angle as a fracture resistance parameter to describe ductile crack extension and arrest in steel pipes under service pressure / Phys. Mesomech. 2015. Vol. 18(4). P. 355 – 369.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Baba K. E., Pluvinage G., Capelle J. Security length associated with the risk of ammonia tank leak using CTOA criterion and ALOHA software / J. Energy Power Technol. 2024. Vol. 6(4). DOI: 10.21926/jept.2404018</mixed-citation><mixed-citation xml:lang="en">Baba K. E., Pluvinage G., Capelle J. Security length associated with the risk of ammonia tank leak using CTOA criterion and ALOHA software / J. Energy Power Technol. 2024. Vol. 6(4). DOI: 10.21926/jept.2404018</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Heerens J., Schödel M. On the determination of crack tip opening angle (CTOA) using light microscopy and a five-measurement technique / Eng. Fracture Mech. 2003. Vol. 70(3 – 4). P. 417 – 426. DOI: 10.1016/s0013-7944(02)00128-5</mixed-citation><mixed-citation xml:lang="en">Heerens J., Schödel M. On the determination of crack tip opening angle (CTOA) using light microscopy and a five-measurement technique / Eng. Fracture Mech. 2003. Vol. 70(3 – 4). P. 417 – 426. DOI: 10.1016/s0013-7944(02)00128-5</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Dawicke D. S., Sutton M. A. CTOA and crack-tunneling measurements in thin sheet 2024-T3 aluminum alloy / Exp. Mech. 1994. Vol. 34(4). P. 357 – 368.</mixed-citation><mixed-citation xml:lang="en">Dawicke D. S., Sutton M. A. CTOA and crack-tunneling measurements in thin sheet 2024-T3 aluminum alloy / Exp. Mech. 1994. Vol. 34(4). P. 357 – 368.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Xu S., Petri N., Tyson W. R. Evaluation of CTOA from load versus load-line displacement for C(T) specimens / Eng. Fracture Mech. 2009. Vol. 76(13). P. 2126 – 2134. DOI: 10.1016/j.engfracmech.2009.04.023</mixed-citation><mixed-citation xml:lang="en">Xu S., Petri N., Tyson W. R. Evaluation of CTOA from load versus load-line displacement for C(T) specimens / Eng. Fracture Mech. 2009. Vol. 76(13). P. 2126 – 2134. DOI: 10.1016/j.engfracmech.2009.04.023</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Lloyd W. R., McClintock F. A. Microtopography for ductile fracture process characterization. Part 2. Application for CTOA analysis / Eng. Fracture Mech. 2003. Vol. 70(3 – 4). P. 403 – 415.</mixed-citation><mixed-citation xml:lang="en">Lloyd W. R., McClintock F. A. Microtopography for ductile fracture process characterization. Part 2. Application for CTOA analysis / Eng. Fracture Mech. 2003. Vol. 70(3 – 4). P. 403 – 415.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Lloyd W. R. Microtopography for ductile fracture process characterization. Part 1. Theory and methodology / Eng. Fracture Mech. 2003. Vol. 70(3 – 4). P. 387 – 401. DOI: 10.1016/s0013-7944(02)00126-1</mixed-citation><mixed-citation xml:lang="en">Lloyd W. R. Microtopography for ductile fracture process characterization. Part 1. Theory and methodology / Eng. Fracture Mech. 2003. Vol. 70(3 – 4). P. 387 – 401. DOI: 10.1016/s0013-7944(02)00126-1</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Reuven R., McCowan C., Drexler E., Shtechman A., Darcis P., Treinen M., Smith R., Merritt J., Siewert T., McColskey J. D. CTOA results for X65 and X100 pipeline steels: influence of displacement rate / Proc. of the 7th Int. Pipeline Conf. — Calgary, 2008.</mixed-citation><mixed-citation xml:lang="en">Reuven R., McCowan C., Drexler E., Shtechman A., Darcis P., Treinen M., Smith R., Merritt J., Siewert T., McColskey J. D. CTOA results for X65 and X100 pipeline steels: influence of displacement rate / Proc. of the 7th Int. Pipeline Conf. — Calgary, 2008.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Xu S., Tyson W. R., Eagleson R., McCowan C. N., Drexler E. S., McCloskey J. D. Measurement of CTOA of pipe steels using MDCB and DWTT specimens / International Pipeline Conference IPC2010-31076. 2011. P. 269 – 278.</mixed-citation><mixed-citation xml:lang="en">Xu S., Tyson W. R., Eagleson R., McCowan C. N., Drexler E. S., McCloskey J. D. Measurement of CTOA of pipe steels using MDCB and DWTT specimens / International Pipeline Conference IPC2010-31076. 2011. P. 269 – 278.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">O’Donoghue P. E., Kanninen M. F., Leung C. P., et al. Development and validation of a dynamic fracture propagation model for gas transmission pipelines / Int. J. Pressure Vessels Piping. 1997. Vol. 70. P. 11 – 25. DOI: 10.1016/s0308-0161(97)00015-x</mixed-citation><mixed-citation xml:lang="en">O’Donoghue P. E., Kanninen M. F., Leung C. P., et al. Development and validation of a dynamic fracture propagation model for gas transmission pipelines / Int. J. Pressure Vessels Piping. 1997. Vol. 70. P. 11 – 25. DOI: 10.1016/s0308-0161(97)00015-x</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Cao Y., Zhen Y., Liu Y., Niu R. Study on CTOA evolutions during dynamic crack propagation of pipelines / Eng. Fracture Mech. 2022. DOI: 10.1016/j.engfracmech.2022.108651</mixed-citation><mixed-citation xml:lang="en">Cao Y., Zhen Y., Liu Y., Niu R. Study on CTOA evolutions during dynamic crack propagation of pipelines / Eng. Fracture Mech. 2022. DOI: 10.1016/j.engfracmech.2022.108651</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Ben Amara M., Pluvinage G., Capelle J., Azari Z. The CTOA as a parameter of resistance to crack extension in pipes under internal pressure / Lecture Notes Mech. Eng. 2017. P. 59 – 88. DOI: 10.1007/978-3-319-75677-3_3</mixed-citation><mixed-citation xml:lang="en">Ben Amara M., Pluvinage G., Capelle J., Azari Z. The CTOA as a parameter of resistance to crack extension in pipes under internal pressure / Lecture Notes Mech. Eng. 2017. P. 59 – 88. DOI: 10.1007/978-3-319-75677-3_3</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Creuzet M. Comparaison de mesures CTOA faites sur éprouvettes standard et tubulaires entaillées issues de tubes SMLS / Rapport interne, Metz, 2024.</mixed-citation><mixed-citation xml:lang="en">Creuzet M. Comparaison de mesures CTOA faites sur éprouvettes standard et tubulaires entaillées issues de tubes SMLS / Rapport interne, Metz, 2024.</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Attikpo T., Delosges H., Pluvinage G., Capelle J. A new CTOA test based on opening bi-cracked tubular specimens by driving in a conical mandrel / À paraître.</mixed-citation><mixed-citation xml:lang="en">Attikpo T., Delosges H., Pluvinage G., Capelle J. A new CTOA test based on opening bi-cracked tubular specimens by driving in a conical mandrel / À paraître.</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">Mouwakeh M., Pluvinage G., Masri S. Failure of water pipes containing surface cracks using limit analysis notions / Res. J. Aleppo Univ. Eng. Sci. Ser. 2011. Vol. 63.</mixed-citation><mixed-citation xml:lang="en">Mouwakeh M., Pluvinage G., Masri S. Failure of water pipes containing surface cracks using limit analysis notions / Res. J. Aleppo Univ. Eng. Sci. Ser. 2011. Vol. 63.</mixed-citation></citation-alternatives></ref><ref id="cit27"><label>27</label><citation-alternatives><mixed-citation xml:lang="ru">Henry B. S., Luxmore A. R. The stress triaxiality constraint and the Q-value as a ductile fracture parameter / Eng. Fracture Mech. 1997. Vol. 57. P. 375 – 390. DOI: 10.1016/s0013-7944(96)00158-6</mixed-citation><mixed-citation xml:lang="en">Henry B. S., Luxmore A. R. The stress triaxiality constraint and the Q-value as a ductile fracture parameter / Eng. Fracture Mech. 1997. Vol. 57. P. 375 – 390. DOI: 10.1016/s0013-7944(96)00158-6</mixed-citation></citation-alternatives></ref><ref id="cit28"><label>28</label><citation-alternatives><mixed-citation xml:lang="ru">Hadj Meliani M., Matvienko Y. G., Pluvinage G. Two-parameter fracture criterion (Kr, c-Tef, c) based on notch fracture mechanics / Int. J. Fracture. 2011. Vol. 167. P. 173 – 182. DOI: 10.1007/s10704-011-9609-6</mixed-citation><mixed-citation xml:lang="en">Hadj Meliani M., Matvienko Y. G., Pluvinage G. Two-parameter fracture criterion (Kr, c-Tef, c) based on notch fracture mechanics / Int. J. Fracture. 2011. Vol. 167. P. 173 – 182. DOI: 10.1007/s10704-011-9609-6</mixed-citation></citation-alternatives></ref><ref id="cit29"><label>29</label><citation-alternatives><mixed-citation xml:lang="ru">Ruggieri C., Gao X., Dodds R. H. Transferability of elastic-plastic fracture toughness using the Weibull stress approach / Eng. Fracture Mech. 2000. Vol. 67. P. 101 – 117. DOI: 10.1016/s0013-7944(99)00123-3</mixed-citation><mixed-citation xml:lang="en">Ruggieri C., Gao X., Dodds R. H. Transferability of elastic-plastic fracture toughness using the Weibull stress approach / Eng. Fracture Mech. 2000. Vol. 67. P. 101 – 117. DOI: 10.1016/s0013-7944(99)00123-3</mixed-citation></citation-alternatives></ref><ref id="cit30"><label>30</label><citation-alternatives><mixed-citation xml:lang="ru">Nikishkov G. P. Algorithm and computer program for the three-term asymptotic expansion of elastic-plastic crack-tip fields / Eng. Fracture Mech. 1995. Vol. 50. P. 65 – 83. DOI: 10.1016/0013-7944(95)00022-W</mixed-citation><mixed-citation xml:lang="en">Nikishkov G. P. Algorithm and computer program for the three-term asymptotic expansion of elastic-plastic crack-tip fields / Eng. Fracture Mech. 1995. Vol. 50. P. 65 – 83. DOI: 10.1016/0013-7944(95)00022-W</mixed-citation></citation-alternatives></ref><ref id="cit31"><label>31</label><citation-alternatives><mixed-citation xml:lang="ru">Chao Y. J., Lam P. S. Use of constraint parameter A2 determined from displacement in predicting fracture events / Eng. Fracture Mech. 1998. Vol. 61(5 – 6). P. 487 – 502. DOI: 10.1016/s0013-7944(97)00140-9</mixed-citation><mixed-citation xml:lang="en">Chao Y. J., Lam P. S. Use of constraint parameter A2 determined from displacement in predicting fracture events / Eng. Fracture Mech. 1998. Vol. 61(5 – 6). P. 487 – 502. DOI: 10.1016/s0013-7944(97)00140-9</mixed-citation></citation-alternatives></ref><ref id="cit32"><label>32</label><citation-alternatives><mixed-citation xml:lang="ru">Zhu X. K., Lam P. S., Chao Y. J. Constraint-dependent CTOA determination for stable ductile crack growth / Eng. Fracture Mech. 2022. Vol. 271. Art. 108651. DOI: 10.1016/j.engfracmech.2022.108651</mixed-citation><mixed-citation xml:lang="en">Zhu X. K., Lam P. S., Chao Y. J. Constraint-dependent CTOA determination for stable ductile crack growth / Eng. Fracture Mech. 2022. Vol. 271. Art. 108651. DOI: 10.1016/j.engfracmech.2022.108651</mixed-citation></citation-alternatives></ref><ref id="cit33"><label>33</label><citation-alternatives><mixed-citation xml:lang="ru">Eiber R. J. Fracture propagation / Proc. of the 4th Symp. on Line Pipe Research. — Houston: AGA, 1969.</mixed-citation><mixed-citation xml:lang="en">Eiber R. J. Fracture propagation / Proc. of the 4th Symp. on Line Pipe Research. — Houston: AGA, 1969.</mixed-citation></citation-alternatives></ref><ref id="cit34"><label>34</label><citation-alternatives><mixed-citation xml:lang="ru">Maxey W. A. Fracture initiation, propagation, and arrest / Proc. of the 5th Symp. on Line Pipe Research. — PRCI, 1974.</mixed-citation><mixed-citation xml:lang="en">Maxey W. A. Fracture initiation, propagation, and arrest / Proc. of the 5th Symp. on Line Pipe Research. — PRCI, 1974.</mixed-citation></citation-alternatives></ref><ref id="cit35"><label>35</label><citation-alternatives><mixed-citation xml:lang="ru">Demofonti G., Mannucci G., Hillenbrand H. G., Harris D. Evaluation of X100 steel pipes for high-pressure gas pipelines by full-scale tests / Int. Pipeline Conference. — Calgary, 2004.</mixed-citation><mixed-citation xml:lang="en">Demofonti G., Mannucci G., Hillenbrand H. G., Harris D. Evaluation of X100 steel pipes for high-pressure gas pipelines by full-scale tests / Int. Pipeline Conference. — Calgary, 2004.</mixed-citation></citation-alternatives></ref><ref id="cit36"><label>36</label><citation-alternatives><mixed-citation xml:lang="ru">Maxey W. A. Dynamic crack propagation in line pipe / Analytical and Experimental Fracture Mechanics // G. C. Sih, M. Mirabile, Eds., 1981. P. 109 – 123.</mixed-citation><mixed-citation xml:lang="en">Maxey W. A. Dynamic crack propagation in line pipe / Analytical and Experimental Fracture Mechanics // G. C. Sih, M. Mirabile, Eds., 1981. P. 109 – 123.</mixed-citation></citation-alternatives></ref><ref id="cit37"><label>37</label><citation-alternatives><mixed-citation xml:lang="ru">Sugie E., Matsuoka M., Akiyama H., Mimura T., Kawaguchi Y. Shear crack propagation in gas-pressurized pipelines / J. Press. Vessel Technol. (ASME). 1982. Vol. 104(4). P. 338 – 343. DOI: 10.1115/1.3269759</mixed-citation><mixed-citation xml:lang="en">Sugie E., Matsuoka M., Akiyama H., Mimura T., Kawaguchi Y. Shear crack propagation in gas-pressurized pipelines / J. Press. Vessel Technol. (ASME). 1982. Vol. 104(4). P. 338 – 343. DOI: 10.1115/1.3269759</mixed-citation></citation-alternatives></ref><ref id="cit38"><label>38</label><citation-alternatives><mixed-citation xml:lang="ru">Higuchi R., Makino H., Takeuchi I. New concept and test method on running ductile fracture arrest for high-pressure gas pipelines / 24th World Gas Conf. — Buenos Aires, 2009. P. 2730 – 2737.</mixed-citation><mixed-citation xml:lang="en">Higuchi R., Makino H., Takeuchi I. New concept and test method on running ductile fracture arrest for high-pressure gas pipelines / 24th World Gas Conf. — Buenos Aires, 2009. P. 2730 – 2737.</mixed-citation></citation-alternatives></ref><ref id="cit39"><label>39</label><citation-alternatives><mixed-citation xml:lang="ru">Kiefner J. F., Eiber R. J., Duffy A. R. Ductile fracture initiation, propagation and arrest in cylindrical vessels / ASTM STP 514.1972. P. 70 – 81.</mixed-citation><mixed-citation xml:lang="en">Kiefner J. F., Eiber R. J., Duffy A. R. Ductile fracture initiation, propagation and arrest in cylindrical vessels / ASTM STP 514.1972. P. 70 – 81.</mixed-citation></citation-alternatives></ref><ref id="cit40"><label>40</label><citation-alternatives><mixed-citation xml:lang="ru">Ben Amara M., Capelle J., Azari Z., Pluvinage G. Modelling crack propagation and arrest in gas pipes using CTOA criterion / J. Pipes Eng. 2016. Vol. 15. P. 243 – 256.</mixed-citation><mixed-citation xml:lang="en">Ben Amara M., Capelle J., Azari Z., Pluvinage G. Modelling crack propagation and arrest in gas pipes using CTOA criterion / J. Pipes Eng. 2016. Vol. 15. P. 243 – 256.</mixed-citation></citation-alternatives></ref><ref id="cit41"><label>41</label><citation-alternatives><mixed-citation xml:lang="ru">EGIG. 7th Report of the European Gas Pipeline Incident Data Group. Incidents 1970 – 2007. — EGIG, 2008.</mixed-citation><mixed-citation xml:lang="en">EGIG. 7th Report of the European Gas Pipeline Incident Data Group. Incidents 1970 – 2007. — EGIG, 2008.</mixed-citation></citation-alternatives></ref><ref id="cit42"><label>42</label><citation-alternatives><mixed-citation xml:lang="ru">GESIP. Guide méthodologique pour l’étude de sécurité des canalisations de transport / Rapport no 2008/01.2014.</mixed-citation><mixed-citation xml:lang="en">GESIP. Guide méthodologique pour l’étude de sécurité des canalisations de transport / Rapport no 2008/01.2014.</mixed-citation></citation-alternatives></ref><ref id="cit43"><label>43</label><citation-alternatives><mixed-citation xml:lang="ru">ASME B31.12. Hydrogen Piping and Pipelines. — New York: American Society of Mechanical Engineers, 2012. — 258 p.</mixed-citation><mixed-citation xml:lang="en">ASME B31.12. Hydrogen Piping and Pipelines. — New York: American Society of Mechanical Engineers, 2012. — 258 p.</mixed-citation></citation-alternatives></ref><ref id="cit44"><label>44</label><citation-alternatives><mixed-citation xml:lang="ru">Tsao C. K., Perry W. W. Modifications to the vulnerability model (VM4) for marine spills / US Coast Guard Report ADA-075-231.1979.</mixed-citation><mixed-citation xml:lang="en">Tsao C. K., Perry W. W. Modifications to the vulnerability model (VM4) for marine spills / US Coast Guard Report ADA-075-231.1979.</mixed-citation></citation-alternatives></ref><ref id="cit45"><label>45</label><citation-alternatives><mixed-citation xml:lang="ru">National Research Council. Acute exposure guideline levels for ammonia. — Washington, D.C.: National Academies Press, 2008.</mixed-citation><mixed-citation xml:lang="en">National Research Council. Acute exposure guideline levels for ammonia. — Washington, D.C.: National Academies Press, 2008.</mixed-citation></citation-alternatives></ref><ref id="cit46"><label>46</label><citation-alternatives><mixed-citation xml:lang="ru">INERIS. Formalisation du savoir et des outils dans le domaine des risques majeurs / Rapport DRA-14-133133-02917A. — Paris, 2014.</mixed-citation><mixed-citation xml:lang="en">INERIS. Formalisation du savoir et des outils dans le domaine des risques majeurs / Rapport DRA-14-133133-02917A. — Paris, 2014.</mixed-citation></citation-alternatives></ref><ref id="cit47"><label>47</label><citation-alternatives><mixed-citation xml:lang="ru">Sévêque J. L. Étude de dangers des ICPE — Analyse des scénarios / Techniques de l’Ingénieur. 2006. DOI: 10.51257/a-v1-g4211.</mixed-citation><mixed-citation xml:lang="en">Sévêque J. L. Étude de dangers des ICPE — Analyse des scénarios / Techniques de l’Ingénieur. 2006. DOI: 10.51257/a-v1-g4211.</mixed-citation></citation-alternatives></ref><ref id="cit48"><label>48</label><citation-alternatives><mixed-citation xml:lang="ru">U.S. Environmental Protection Agency. ALOHA Software. — Washington, D.C., 2024.</mixed-citation><mixed-citation xml:lang="en">U.S. Environmental Protection Agency. ALOHA Software. — Washington, D.C., 2024.</mixed-citation></citation-alternatives></ref><ref id="cit49"><label>49</label><citation-alternatives><mixed-citation xml:lang="ru">Jones R., Lehr W., Simecek-Beatty D., Reynolds M. ALOHA® 5.4.4. Technical documentation. — Seattle: NOAA, 2013.</mixed-citation><mixed-citation xml:lang="en">Jones R., Lehr W., Simecek-Beatty D., Reynolds M. ALOHA® 5.4.4. Technical documentation. — Seattle: NOAA, 2013.</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>
