Damage-Accounted Assessment of the Stress-Strain State of Structural Elements
Приведены и проанализированы инженерные методы расчета напряжений и деформаций в зонах концентрации при упругопластическом деформировании конструктивных элементов. Показано, что для оценки кинетики эффективных коэффициентов концентрации напряжений и деформаций наиболее приемлемой по точности являетс...
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Інститут проблем міцності ім. Г.С. Писаренко НАН України
2017
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| Schriftenreihe: | Проблемы прочности |
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| Zitieren: | Damage-Accounted Assessment of the Stress-Strain State of Structural Elements / Н.И. Бобырь, В.В. Коваль // Проблемы прочности. — 2017. — № 3. — С. 21-29. — Бібліогр.: 13 назв. — рос. |
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nasplib_isofts_kiev_ua-123456789-1736682025-02-09T17:10:35Z Damage-Accounted Assessment of the Stress-Strain State of Structural Elements Фактор поврежденности в оценке напряженно-деформированного состояния в зонах концентрации напряжений Бобырь, Н.И. Коваль, В.В. Научно-технический раздел Приведены и проанализированы инженерные методы расчета напряжений и деформаций в зонах концентрации при упругопластическом деформировании конструктивных элементов. Показано, что для оценки кинетики эффективных коэффициентов концентрации напряжений и деформаций наиболее приемлемой по точности является модификация Махутовым уравнения Нойбера. Введено понятие рассеянной поврежденности. Влияние рассеянных повреждений на оценку напряженно-деформированного состояния конструктивных элементов показано на примере упругопластического деформирования пластины с отверстием. Наведено і проаналізовано інженерні методи розрахунку напружень і деформацій у зонах концентрації при пружно-пластичному деформуванні конструктивних елементів. Показано, що для оцінки кінетики ефективних коефіцієнтів концентрації напружень і деформацій найбільш прийнятною за точністю є модифікація Махутовим рівняння Нойбера. Введено поняття розсіяної пошкодженості. Установлено ефективність використання параметра пошкодженості для оцінки вірогідності механічних властивостей ряда металічних матеріалів. Вплив розсіяних пошкоджень на оцінку напружено-деформованого стану конструктивних елементів показано на прикладі пружно-пластичного деформування пластини з отвором. Engineering calculation methods for stresses and strains in the concentration zones under elastoplastic deformation of structural elements are presented and analyzed. The Makhutov-modified Neuber equation is shown to be of the most reasonable accuracy for the assessment of kinetics of effective coefficients for stress and strain concentrations. The concept of scattered damage is introduced. The effect of scattered damages on the assessment of the stress-strain state of structural elements is demonstrated by the example of elastoplastic deformation of a hole-containing plate. 2017 Article Damage-Accounted Assessment of the Stress-Strain State of Structural Elements / Н.И. Бобырь, В.В. Коваль // Проблемы прочности. — 2017. — № 3. — С. 21-29. — Бібліогр.: 13 назв. — рос. 0556-171X https://nasplib.isofts.kiev.ua/handle/123456789/173668 539.4 ru Проблемы прочности application/pdf Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
Russian |
| topic |
Научно-технический раздел Научно-технический раздел |
| spellingShingle |
Научно-технический раздел Научно-технический раздел Бобырь, Н.И. Коваль, В.В. Damage-Accounted Assessment of the Stress-Strain State of Structural Elements Проблемы прочности |
| description |
Приведены и проанализированы инженерные методы расчета напряжений и деформаций в зонах концентрации при упругопластическом деформировании конструктивных элементов. Показано, что для оценки кинетики эффективных коэффициентов концентрации напряжений и деформаций наиболее приемлемой по точности является модификация Махутовым уравнения Нойбера. Введено понятие рассеянной поврежденности. Влияние рассеянных повреждений на оценку напряженно-деформированного состояния конструктивных элементов показано на примере упругопластического деформирования пластины с отверстием. |
| format |
Article |
| author |
Бобырь, Н.И. Коваль, В.В. |
| author_facet |
Бобырь, Н.И. Коваль, В.В. |
| author_sort |
Бобырь, Н.И. |
| title |
Damage-Accounted Assessment of the Stress-Strain State of Structural Elements |
| title_short |
Damage-Accounted Assessment of the Stress-Strain State of Structural Elements |
| title_full |
Damage-Accounted Assessment of the Stress-Strain State of Structural Elements |
| title_fullStr |
Damage-Accounted Assessment of the Stress-Strain State of Structural Elements |
| title_full_unstemmed |
Damage-Accounted Assessment of the Stress-Strain State of Structural Elements |
| title_sort |
damage-accounted assessment of the stress-strain state of structural elements |
| publisher |
Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| publishDate |
2017 |
| topic_facet |
Научно-технический раздел |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/173668 |
| citation_txt |
Damage-Accounted Assessment of the Stress-Strain State of Structural Elements / Н.И. Бобырь, В.В. Коваль // Проблемы прочности. — 2017. — № 3. — С. 21-29. — Бібліогр.: 13 назв. — рос. |
| series |
Проблемы прочности |
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2025-11-28T11:16:00Z |
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2025-11-28T11:16:00Z |
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| fulltext |
ÓÄÊ 539.4
Ôàêòîð ïîâðåæäåííîñòè â îöåíêå íàïðÿæåííî-äåôîðìèðîâàííîãî
ñîñòîÿíèÿ â çîíàõ êîíöåíòðàöèè íàïðÿæåíèé
Í. È. Áîáûðü, Â. Â. Êîâàëü
Íàöèîíàëüíûé òåõíè÷åñêèé óíèâåðñèòåò Óêðàèíû “Êèåâñêèé ïîëèòåõíè÷åñêèé èíñòèòóò
èìåíè Èãîðÿ Ñèêîðñêîãî”, Êèåâ, Óêðàèíà
mmidpm@gmail.com
Ïðèâåäåíû è ïðîàíàëèçèðîâàíû èíæåíåðíûå ìåòîäû ðàñ÷åòà íàïðÿæåíèé è äåôîðìàöèé â
çîíàõ êîíöåíòðàöèè ïðè óïðóãîïëàñòè÷åñêîì äåôîðìèðîâàíèè êîíñòðóêòèâíûõ ýëåìåíòîâ.
Ïîêàçàíî, ÷òî äëÿ îöåíêè êèíåòèêè ýôôåêòèâíûõ êîýôôèöèåíòîâ êîíöåíòðàöèè íàïðÿæåíèé
è äåôîðìàöèé íàèáîëåå ïðèåìëåìîé ïî òî÷íîñòè ÿâëÿåòñÿ ìîäèôèêàöèÿ Ìàõóòîâûì óðàâ-
íåíèÿ Íîéáåðà. Ââåäåíî ïîíÿòèå ðàññåÿííîé ïîâðåæäåííîñòè. Âëèÿíèå ðàññåÿííûõ ïîâðåæ-
äåíèé íà îöåíêó íàïðÿæåííî-äåôîðìèðîâàííîãî ñîñòîÿíèÿ êîíñòðóêòèâíûõ ýëåìåíòîâ ïîêà-
çàíî íà ïðèìåðå óïðóãîïëàñòè÷åñêîãî äåôîðìèðîâàíèÿ ïëàñòèíû ñ îòâåðñòèåì.
Êëþ÷åâûå ñëîâà: êîíöåíòðàöèÿ íàïðÿæåíèé è äåôîðìàöèé, ïîâðåæäåííîñòü, ìåòîäû
ðàñ÷åòà íàïðÿæåííî-äåôîðìèðîâàííîãî ñîñòîÿíèÿ, ìåõàíè÷åñêèå ñâîéñòâà êîíñòðóê-
öèîííûõ ìàòåðèàëîâ.
Ââåäåíèå. Ïîâûøåíèå äîñòîâåðíîñòè îöåíêè íàïðÿæåííî-äåôîðìèðîâàííîãî
ñîñòîÿíèÿ (ÍÄÑ) ýëåìåíòîâ êîíñòðóêöèé è ïðîãíîçèðîâàíèÿ èõ ðåñóðñà êàê íà
ñòàäèè ïðîåêòèðîâàíèÿ, òàê è íà ñòàäèè ýêñïëóàòàöèè â íàñòîÿùåå âðåìÿ îáóñëîâ-
ëåíî ââåäåíèåì â ñèñòåìó îïðåäåëÿþùèõ óðàâíåíèé ïàðàìåòðîâ ïîâðåæäåííîñòè,
êàê ïðàâèëî, â âèäå êèíåòè÷åñêèõ óðàâíåíèé [1–4]. Ïðè ýòîì äëÿ èíæåíåðíûõ
ðàñ÷åòîâ èñïîëüçóþò ôåíîìåíîëîãè÷åñêèé ïîäõîä, êîòîðûé áàçèðóåòñÿ íà îñíîâíûõ
ïîëîæåíèÿõ êîíòèíóàëüíîé ìåõàíèêè ïîâðåæäåíèé (ÊÌÏ). Èäåè ýòîãî ïîäõîäà âïåð-
âûå áûëè ñôîðìóëèðîâàíû â ðàáîòàõ [1, 2] ïðèìåíèòåëüíî ê ðàçðóøåíèþ â óñëîâèÿõ
îäíîîñíîé ïîëçó÷åñòè.
 íàñòîÿùåå âðåìÿ ìîäåëü ÊÌÏ óñïåøíî ïðèìåíÿåòñÿ â êà÷åñòâå óíèâåðñàëü-
íîãî ìåòîäà ðåøåíèÿ ðàçëè÷íûõ çàäà÷ ðàçðóøåíèÿ íà ñòàäèè çàðîæäåíèÿ ìàêðî-
òðåùèíû. Äëÿ íà÷àëüíî-èçîòðîïíîãî â íåïîâðåæäåííîãî ìàòåðèàëà â ýòîì ñëó÷àå
ïðèíèìàåòñÿ ñëåäóþùåå:
òåðìîñèëîâîå ýêñïëóàòàöèîííîå íàãðóæåíèå (äåôîðìèðîâàíèå) ñîïðîâîæäàåòñÿ
íàêîïëåíèåì ðàññåÿííûõ ïîâðåæäåíèé â âèäå íåïðåðûâíûõ è íåîáðàòèìûõ ìèêðî-
ñòðóêòóðíûõ èçìåíåíèé â ìàòåðèàëå;
ðàññåÿííûå ïîâðåæäåíèÿ ðàâíîìåðíî âîçíèêàþò è ðàçâèâàþòñÿ â êàæäîì ðåïðå-
çåíòàòèâíîì ñòðóêòóðíîì ýëåìåíòå ìàòåðèàëà;
â êà÷åñòâå òàêîãî ðåïðåçåíòàòèâíîãî ýëåìåíòà îðèåíòèðîâî÷íî ïðèíèìàåòñÿ
ëèíåéíûé ðàçìåð çåðíà â ïîëèêðèñòàëëè÷åñêîì ìàòåðèàëå;
íàëè÷èå ïîðîãà ïîâðåæäåííîñòè (ïðåäåë ïðîïîðöèîíàëüíîñòè äëÿ çàäà÷ òåîðèè
ïëàñòè÷íîñòè è ïðåäåë âûíîñëèâîñòè äëÿ èíæåíåðíûõ);
ðàññåÿííûå ïîâðåæäåíèÿ èíòåãðàëüíî âëèÿþò íà äåãðàäàöèþ îñíîâíûõ ìåõàíè-
÷åñêèõ õàðàêòåðèñòèê êîíñòðóêöèîííûõ ìàòåðèàëîâ ïðè ðàçëè÷íûõ âèäàõ íàãðóæå-
íèÿ;
âëèÿíèå ïåðâîãî èíâàðèàíòà òåíçîðà íàïðÿæåíèé I T1 ( )� íà êèíåòèêó ïðîöåññà
ðàññåÿííîãî ðàçðóøåíèÿ;
íåëèíåéíàÿ çàâèñèìîñòü íàêîïëåíèÿ ïîâðåæäåíèé â êîíñòðóêöèîííîì ìàòåðè-
àëå îò íàïðÿæåíèé, äåôîðìàöèé, âðåìåíè èëè ÷èñëà öèêëîâ.
© Í. È. ÁÎÁÛÐÜ, Â. Â. ÊÎÂÀËÜ, 2017
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2017, ¹ 3 21
 êà÷åñòâå ïàðàìåòðà ïîâðåæäåííîñòè â ïåðâîì ïðèáëèæåíèè ïðèíèìàþò ñêà-
ëÿðíûé ïàðàìåòð, îñíîâàííûé íà äåôîðìàöèîííîì èëè ýíåðãåòè÷åñêîì ïîäõîäå. Â
ÊÌÏ èñïîëüçóåòñÿ, êàê ïðàâèëî, ýíåðãåòè÷åñêèé ïîäõîä. Îí áàçèðóåòñÿ íà ðåçóëü-
òàòàõ èññëåäîâàíèé â îáëàñòè ìàòåðèàëîâåäåíèÿ è ìåõàíèêè ïîâðåæäåíèé, à òàêæå íà
íåêîòîðûõ ðàçäåëàõ òåðìîäèíàìèêè íåîáðàòèìûõ ïðîöåññîâ, òåîðèè èíâàðèàíòîâ,
òåíçîðíîãî àíàëèçà è ìåõàíèêå òâåðäîãî äåôîðìèðóåìîãî òåëà [3, 4].
 çîíàõ êîíöåíòðàöèè, ãäå íàáëþäàåòñÿ ñóùåñòâåííî íåîäíîðîäíîå ðàñïðå-
äåëåíèå àìïëèòóäíûõ çíà÷åíèé íàïðÿæåíèé è äåôîðìàöèé â ïðîöåññå öèêëè÷åñêîãî
óïðî÷íåíèÿ èëè ðàçóïðî÷íåíèÿ, âåðîÿòíîå ëîêàëüíîå óïðóãîïëàñòè÷åñêîå äåôîðìè-
ðîâàíèå ñîïðîâîæäàåòñÿ íàêîïëåíèåì ðàññåÿííûõ ïîâðåæäåíèé.
Ïðèìåíèòåëüíî ê ìàëîöèêëîâîìó íàãðóæåíèþ â íàñòîÿùåå âðåìÿ ðàçâèâàþòñÿ
äâà îñíîâíûõ íàïðàâëåíèÿ: ïåðâîå ïðåäóñìàòðèâàåò ÷èñëåííîå ìîäåëèðîâàíèå ïðî-
öåññîâ ìàëîöèêëîâîãî íàãðóæåíèÿ (äåôîðìèðîâàíèÿ) êîíñòðóêöèîííûõ ìàòåðèàëîâ
íà îñíîâå êîíöåïöèè îáîáùåííîé äèàãðàììû öèêëè÷åñêîãî äåôîðìèðîâàíèÿ [5];
âòîðîå (ìåíåå òðóäîåìêîå) áàçèðóåòñÿ íà ðàçðàáîòêå ïðèáëèæåííûõ èíæåíåðíûõ
ìåòîäîâ îöåíêè èçìåíåíèÿ â ïðîöåññå òåðìîñèëîâîãî íàãðóæåíèÿ ýôôåêòèâíûõ
êîýôôèöèåíòîâ êîíöåíòðàöèè ïî íàïðÿæåíèÿì K � è äåôîðìàöèÿì K � â óïðóãî-
ïëàñòè÷åñêîé îáëàñòè èñõîäÿ èç èçâåñòíûõ çíà÷åíèé òåîðåòè÷åñêîãî êîýôôèöèåíòà
êîíöåíòðàöèè íàïðÿæåíèé �� â óïðóãîé îáëàñòè [6–9].
Öåëüþ äàííîé ðàáîòû ÿâëÿåòñÿ îïðåäåëåíèå äîñòîâåðíîñòè èñïîëüçîâàíèÿ ñîâðå-
ìåííûõ èíæåíåðíûõ ìåòîäîâ îöåíêè ýôôåêòèâíûõ êîýôôèöèåíòîâ êîíöåíòðàöèè
íàïðÿæåíèé è äåôîðìàöèé, à òàêæå âîçìîæíîñòü óòî÷íåíèÿ ðàñ÷åòîâ ïóòåì ââåäåíèÿ
ïàðàìåòðîâ ïîâðåæäåííîñòè.
Ìåòîäû îïðåäåëåíèÿ ýôôåêòèâíûõ êîýôôèöèåíòîâ êîíöåíòðàöèè. Äëÿ
îäíîãî âèäà êîíöåíòðàòîðà íàïðÿæåíèé ñðàâíèì ðåçóëüòàòû ðàñ÷åòà K � è K � ïî
íàèáîëåå ÷àñòî ïðèìåíÿåìûì â íàñòîÿùåå âðåìÿ óðàâíåíèÿì.
Ñîãëàñíî óðàâíåíèþ Íîéáåðà, èìååì [6]
K K� � ��� 2 ; (1)
K
i
i
�
�
�
� max
;
í
K
i
i
�
�
�
� max
,
í
(2)
ãäå � i max , � i max , � ií , � ií – èíòåíñèâíîñòè ìàêñèìàëüíûõ è íîìèíàëüíûõ íàïðÿ-
æåíèé è äåôîðìàöèé ñîîòâåòñòâåííî.
Äëÿ ìåòàëëè÷åñêèõ ìàòåðèàëîâ ñîãëàñíî (1) ïîëó÷åíû çàâûøåííûå çíà÷åíèÿ
K � è K � , îñîáåííî ïî äåôîðìàöèÿì [5, 7].
Ìåòîä Ãëèíêè áàçèðóåòñÿ íà ïðåäïîëîæåíèè, ÷òî óäåëüíàÿ ýíåðãèÿ äåôîðìàöèè
â îñíîâå êîíöåíòðàòîðà W� ðàâíà íîìèíàëüíîé óäåëüíîé ýíåðãèè Wí [8]:
W W� ��� 2
í , (3)
ãäå
W di i i
i
�
�
� � �� � ( ) ;
0
W di i i
i
í í í í�� � � �
�
( ) .
0
Ìîäèôèêàöèÿ Ìàõóòîâûì óðàâíåíèÿ Íîéáåðà ïðåäóñìàòðèâàåò ó÷åò âèäà äèà-
ãðàììû äåôîðìèðîâàíèÿ, â òîì ÷èñëå è öèêëè÷åñêîé. Äëÿ ñòàòè÷åñêîãî íàãðóæåíèÿ
îíà çàïèñûâàåòñÿ òàê [9]:
Í. È. Áîáûðü, Â. Â. Êîâàëü
22 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2017, ¹ 3
K K
n m
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( )
,
( )
í
í
(4)
ãäå � � �í í ïö� – îòíîñèòåëüíîå íîìèíàëüíîå íàïðÿæåíèå; n – ïîñòîÿííàÿ, îïðå-
äåëÿåìàÿ èç ðàñ÷åòà èëè ýêñïåðèìåíòà äëÿ çàäàííûõ �� è � í ; m – êîýôôèöèåíò
óïðî÷íåíèÿ.
Ïðàâàÿ ÷àñòü âûðàæåíèÿ (4) äëÿ ïðåäåëüíîãî óïðóãîãî ñîñòîÿíèÿ ðàâíà åäèíèöå.
Ïðè óâåëè÷åíèè óïðóãîïëàñòè÷åñêèõ äåôîðìàöèé äàííîå çíà÷åíèå óìåíüøàåòñÿ äî
îïðåäåëåííîãî ìèíèìóìà, ÷òî ñîîòâåòñòâóåò ïîòåðå óñòîé÷èâîñòè ïëàñòè÷åñêîé äå-
ôîðìàöèè â çîíå êîíöåíòðàòîðà.
Ìîäèôèêàöèÿ Áèðãåðîì óðàâíåíèÿ Íîéáåðà ïðåäóñìàòðèâàåò, ÷òî äåéñòâèòåëü-
íàÿ äåôîðìàöèÿ â çîíå êîíöåíòðàòîðà èìååò âèä
� � �i i i� �
1
2
( );max min � � ��i imin ;� í �
�
��
�
i i
K
max .�
2
í (5)
Ïîñëå ïîäñòàíîâêè âåëè÷èíû K � èç (2) â (5) è ïîñëåäóþùåãî ïðåîáðàçîâà-
íèÿ ïîëó÷èì çàâèñèìîñòü [10]
K K
K
� �
� �
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2
2
1 . (6)
Äëÿ ïðîâåðêè äîñòîâåðíîñòè ïðåäåëîâ ïðèìåíèìîñòè óðàâíåíèé (1), (3), (4) è
(6) ïðîâåäåì ðàñ÷åò ÍÄÑ öèëèíäðè÷åñêîãî îáðàçöà äèàìåòðîì 30 ìì ñ êîëüöåâîé
âûòî÷êîé ðàäèóñîì R� 3 ìì èç àëþìèíèåâîãî ñïëàâà ÀÌã5Ì ïðè ñòàòè÷åñêîì íàãðó-
æåíèè. Òåîðåòè÷åñêèé êîýôôèöèåíò êîíöåíòðàöèè íàïðÿæåíèé �� � 2,77. Îáðàçåö
íàãðóæàëè îñåâîé ñèëîé ñ íàïðÿæåíèåì â çîíå âûòî÷êè � í � 95 ÌÏà. Ðàñ÷åò ÍÄÑ â
çîíå êîíöåíòðàòîðà âûïîëíåí ñ èñïîëüçîâàíèåì ïðîãðàììíîãî ïàêåòà Femap with NX
Nastran. Àíàëèòè÷åñêèå çíà÷åíèÿ èíòåíñèâíîñòåé ìàêñèìàëüíûõ íàïðÿæåíèé è äå-
ôîðìàöèé ðàññ÷èòûâàëè ïî (2) ñ ó÷åòîì óðàâíåíèé (1), (3), (4) è (6).
Àíàëèç ïðèìåíèìîñòè ðàçëè÷íûõ ïðèáëèæåííûõ ìåòîäîâ îöåíêè êîíöåíòðàöèè
íàïðÿæåíèé ïîêàçûâàåò, ÷òî íàèáîëåå ïðèåìëåìûìè äëÿ èíæåíåðíûõ ðàñ÷åòîâ ÿâëÿ-
þòñÿ ìåòîäû Áèðãåðà è Ìàõóòîâà. Ñðåäíÿÿ ïîãðåøíîñòü ïî ýòèì ìåòîäàì ïî ñðàâ-
íåíèþ ñ êîíå÷íîýëåìåíòíûì ðàñ÷åòîì ñîñòàâëÿåò 4,6 è 3,3% ñîîòâåòñòâåííî.
 ðàìêàõ îáùåãî òåðìîäèíàìè÷åñêîãî ïîäõîäà ê îïèñàíèþ âíóòðåííèõ íåîáðà-
òèìûõ ïðîöåññîâ â òâåðäîì äåôîðìèðóåìîì òåëå â ðàáîòå [10] ïðåäëîæåíà ôåíîìå-
íîëîãè÷åñêàÿ ìîäåëü êèíåòèêè íàêîïëåíèÿ ðàññåÿííûõ ïîâðåæäåíèé:
dD
dt EB
Q
i
i
� � � �
�
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��
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1
2
2
2
2
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1 1 3 1 2( ) ( ) ( )
�
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�
��
�
�
�
��
c
i
p� ( )
, (7)
ãäå B, c – ïàðàìåòðû ìàòåðèàëà; � – êîýôôèöèåíò Ïóàññîíà; Q� – ïàðàìåòð
æåñòêîñòè íàãðóæåíèÿ, Q i� � �� 0 ; � i
p( )
– èíòåíñèâíîñòü ñêîðîñòè ïëàñòè÷åñêîé
äåôîðìàöèè, � � �i
p
ij
p
ij
p( ) ( ) ( )�
2
3
.
Ôàêòîð ïîâðåæäåííîñòè â îöåíêå íàïðÿæåííî-äåôîðìèðîâàííîãî ñîñòîÿíèÿ ...
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2017, ¹ 3 23
Ïîñêîëüêó ââåäåíèå â çàâèñèìîñòü (7) ýêâèâàëåíòíîãî íàïðÿæåíèÿ òèïà Ïèñà-
ðåíêo–Ëåáåäåâà ( ( ) )� �� � �ýêâ � � �i 1 1 [11] ïîçâîëÿåò ó÷èòûâàòü äâà ìåõàíèçìà
ðàçðóøåíèÿ: îòðûâ è ñðåç, åå ìîæíî ïðåîáðàçîâàòü ñëåäóþùèì îáðàçîì:
dD
dt EB
R
i
c
i
p�
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�
��
2
2
( )
, (8)
ãäå R� – ôóíêöèÿ âèäà íàïðÿæåííîãî ñîñòîÿíèÿ,
R Q
i
� �� � �
�
�
�� � � �
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�
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� � �
2
3
1 1 3 1 2
1
2
2( ) ( ) ( ) .
Äàííàÿ ôóíêöèÿ ìîæåò ïðèíèìàòü òàêèå çíà÷åíèÿ: R� �1 (ïðè ðàñòÿæåíèè);
R� � � �� � � �
2
3
1
1
3
1 22 ( ) ( ) (ïðè ñæàòèè) è R� � � �� � � �
2
9
1 1 3 2( )( ) (ïðè êðó÷å-
íèè).
Ïàðàìåòðû B è c îïðåäåëÿþòñÿ ïðè èñïûòàíèè íà ðàñòÿæåíèå îáðàçöîâ.
Çàâèñèìîñòü (8) äëÿ ñòåïåííîãî çàêîíà óïðî÷íåíèÿ � �i i
p mA� ( )
( )
ïîñëå èíòå-
ãðèðîâàíèÿ ïðèíèìàåò âèä
D
A
EB S
c
p S
m
p S�
�
�
�
�
�
� �
2
2
1
[( ) ( ) ],
) ( )� ��
(9)
ãäå S – ïàðàìåòð ìàòåðèàëà, S mc� �2 1; � ( )p è � ò
( )p – òåêóùåå è ïîðîãîâîå (íà
óðîâíå ïðåäåëà òåêó÷åñòè) çíà÷åíèå ïëàñòè÷åñêîé äåôîðìàöèè ñîîòâåòñòâåííî.
Óðàâíåíèÿ (8) è (9) çàïèñàíû äëÿ ðåøåíèÿ çàäà÷ òåîðèè ïëàñòè÷íîñòè. Äëÿ
ðåøåíèÿ çàäà÷ ïðîãíîçèðîâàíèÿ ðåñóðñà ýëåìåíòîâ êîíñòðóêöèé íåîáõîäèìî ó÷èòû-
âàòü, ÷òî ëîêàëüíàÿ ïëàñòè÷åñêàÿ äåôîðìàöèÿ âîçíèêàåò â ðåïðåçåíòàòèâíîì ýëåìåí-
òå åùå íà óðîâíå ïðåäåëà âûíîñëèâîñòè ìàòåðèàëà [12]. Ýòî âèäíî èç ðèñ. 1, ãäå
ïîêàçàí íà÷àëüíûé ó÷àñòîê êðèâîé íàêîïëåíèÿ ðàññåÿííûõ ïîâðåæäåíèé â ìàòå-
ðèàëå, êîòîðûé ïîëó÷åí ñîãëàñíî ìåòîäèêå [13]. Èññëåäîâàíèå ïðîâîäèëè ïðè òåìïå-
ðàòóðå T� 293 Ê.
Ñ ó÷åòîì êèíåòèêè íàêîïëåíèÿ ðàññåÿííûõ ïîâðåæäåíèé íà íà÷àëüíîì ó÷àñòêå
óðàâíåíèå (9) ïðèíèìàåò âèä
D D
A
EB S
R
c p S
� �
�
�
�
�
�
�ò
2
2
( )
,
( )�
(10)
ãäå D ò – ïðåäåëüíàÿ ïîâðåæäåííîñòü ìàòåðèàëà íà óðîâíå ïðåäåëà ïðîïîðöèîíàëü-
íîñòè (òåêó÷åñòè).
Çàâèñèìîñòü D ò îò óðîâíÿ ïðåäåëüíîé ïëàñòè÷íîñòè ìàòåðèàëà ïîêàçàíà íà
ðèñ. 2.
Ïîëó÷åííûå ýêñïåðèìåíòàëüíûå ðåçóëüòàòû îïèñûâàþòñÿ ñëåäóþùåé çàâèñè-
ìîñòüþ:
D K K
R R
ò �
�
�
�
�
�
�
�
1
2
2
!
!
, (11)
24 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2017, ¹ 3
Í. È. Áîáûðü, Â. Â. Êîâàëü
ãäå ! – îòíîñèòåëüíîå óäëèíåíèå; R – îòíîñèòåëüíîå ñóæåíèå ïîñëå ðàçðûâà; K1 è
K 2 – êîýôôèöèåíòû, K1
419 10� " � , K 2
431 10� " � .
Ñîãëàñíî ðèñ. 3 ïðåäåëüíîå çíà÷åíèå ïàðàìåòðà ïîâðåæäåííîñòè DR ëèíåéíî
çàâèñèò îò ïëàñòè÷åñêèõ ñâîéñòâ ìåòàëëè÷åñêèõ ìàòåðèàëîâ, DR R� 0 0078, .
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2017, ¹ 3 25
Ðèñ. 1. Çàêîíîìåðíîñòè íàêîïëåíèÿ ïîâðåæäåíèé íà íà÷àëüíîì ó÷àñòêå äèàãðàììû äåôîð-
ìèðîâàíèÿ ïðè îäíîîñíîì ðàñòÿæåíèè îáðàçöîâ èç ñòàëåé 18Õ2Í4ÂÀ (1), 15ÕÑÍÄ (3),
12Õ18Í10Ò (4) è ñïëàâà Ä16Ò (2).
Ðèñ. 2. Çàâèñèìîñòü ïàðàìåòðà ïîâðåæäåííîñòè íà óðîâíå ïðåäåëà òåêó÷åñòè îò ïëàñòè÷åñêèõ
ñâîéñòâ ìåòàëëè÷åñêèõ ìàòåðèàëîâ.
Ôàêòîð ïîâðåæäåííîñòè â îöåíêå íàïðÿæåííî-äåôîðìèðîâàííîãî ñîñòîÿíèÿ ...
Êîíêðåòèçàöèÿ ïàðàìåòðà ïîâðåæäåííîñòè ïîçâîëÿåò èñïîëüçîâàòü ïîíÿòèå
ýôôåêòèâíûõ íàïðÿæåíèé � ýô â äèàãðàììå äåôîðìèðîâàíèÿ ìàòåðèàëà. Ñîãëàñíî
ýòîìó ïîäõîäó ïðèíèìàåòñÿ ãèïîòåçà îá èíâàðèàíòíîñòè äåôîðìàöèé â ïîâðåæ-
äåííîì è íåïîâðåæäåííîì ìàòåðèàëå, à ýôôåêòèâíûå íàïðÿæåíèÿ îïðåäåëÿþòñÿ
÷åðåç äåéñòâèòåëüíîå çíà÷åíèå íàïðÿæåíèé � ä è ñîîòâåòñòâóþùåå åìó çíà÷åíèå
ïîâðåæäåíèÿ D( ):�
�
�
�ýô
ä�
�1 D( )
. (12)
Äëÿ ñòåïåííîé àïïðîêñèìàöèè äèàãðàììû äåôîðìèðîâàíèÿ â îòíîñèòåëüíûõ
âåëè÷èíàõ èìååì
�
� � �
� � �
�
#
�
�
�
m äëÿ >
äëÿ
ò
ò
;
,
(13)
ãäå �, � – îòíîñèòåëüíûå íàïðÿæåíèÿ è äåôîðìàöèè ñîîòâåòñòâåííî, � � �� ò ,
� � �� ò ; � ò è � ò – ïðåäåë òåêó÷åñòè (ïðîïîðöèîíàëüíîñòè) ïî íàïðÿæåíèÿì è
äåôîðìàöèÿì ñîîòâåòñòâåííî.
Åñëè äåéñòâèòåëüíóþ è ýôôåêòèâíóþ äèàãðàììû äåôîðìèðîâàíèÿ â óïðóãî-
ïëàñòè÷åñêîé îáëàñòè îïèñàòü çàâèñèìîñòüþ òèïà (13), òî ñ ó÷åòîì óðàâíåíèÿ (12)
ïîëó÷èì çàâèñèìîñòü êîýôôèöèåíòà óïðî÷íåíèÿ äëÿ ýôôåêòèâíîé äèàãðàììû mýô
îò ñîîòâåòñòâóþùåãî êîýôôèöèåíòà äëÿ äåéñòâèòåëüíîé mä :
m m
D
D
ýô ä
ò� �
�
�
�
�
�
log
( )
.� �
1
1
(14)
Òàêèì îáðàçîì, îöåíêà ïàðàìåòðà ïîâðåæäåííîñòè è ýôôåêòèâíîãî êîýôôè-
öèåíòà óïðî÷íåíèÿ äèàãðàììû äåôîðìèðîâàíèÿ ñîãëàñíî (10)–(12), (14) ïîçâîëÿåò
ìîäåðíèçèðîâàòü ðàñ÷åòíûé ìåòîä Ìàõóòîâà ïóòåì óòî÷íåíèÿ ïðàâîé ÷àñòè çàâèñè-
ìîñòè (4).
Çíà÷åíèÿ ïðåäåëîâ òåêó÷åñòè � ò è ïðåäåëîâ ïðî÷íîñòè � â äëÿ äèàãðàìì
äåôîðìèðîâàíèÿ íåêîòîðûõ ìåòàëëè÷åñêèõ ìàòåðèàëîâ, à òàêæå âåëè÷èíû ïàðàìåò-
ðîâ ðàññåÿííûõ ïîâðåæäåíèé ïðèâåäåíû â òàáëèöå.
26 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2017, ¹ 3
Ðèñ. 3. Çàâèñèìîñòü ïðåäåëüíîãî çíà÷åíèÿ ïàðàìåòðà ïîâðåæäåííîñòè îò âåëè÷èíû ìàêñè-
ìàëüíîãî îòíîñèòåëüíîãî ïîïåðå÷íîãî ñóæåíèÿ ìåòàëëè÷åñêèõ ìàòåðèàëîâ.
Í. È. Áîáûðü, Â. Â. Êîâàëü
Îòíîñèòåëüíî íåçíà÷èòåëüíîå âëèÿíèå ðàññåÿííûõ ïîâðåæäåíèé íà âåëè÷èíó
ïðåäåëà òåêó÷åñòè ïðè ñòàòè÷åñêîì íàãðóæåíèè äàåò ñóùåñòâåííûé ðåçóëüòàò ïðè
ðàñ÷åòå ðåñóðñà íà ìàëî- è ìíîãîöèêëîâóþ óñòàëîñòü ïðè èñïîëüçîâàíèè äåôîð-
ìàöèîííûõ èëè ýíåðãåòè÷åñêèõ êðèòåðèåâ.
Ðàññìîòðèì âëèÿíèå ïîâðåæäåííîñòè íà íàïðÿæåííî-äåôîðìèðîâàííîå ñîñòîÿ-
íèå â óñëîâèÿõ êîíöåíòðàöèè íàïðÿæåíèé íà ïðèìåðå ïëàñòèíû ñ îòâåðñòèåì.
Ýêñïåðèìåíòàëüíàÿ äèàãðàììà äåôîðìèðîâàíèÿ êîíñòðóêöèîííûõ ìàòåðèàëîâ â
÷èñëåííûõ ðàñ÷åòàõ çàäàâàëàñü ñ ïîìîùüþ ôóíêöèè Multilinear Isotropic Herdening.
Êîíå÷íîýëåìåíòíàÿ ñåòêà ìîäåëèðîâàëàñü ïóòåì ðàçáèåíèÿ ïëàñòèíû íà îòäåëüíûå
çîíû. Â çîíå êîíöåíòðàöèè íàïðÿæåíèé ñåòêà ñîîòâåòñòâóþùèì îáðàçîì ñãóùàëàñü
äëÿ ïîâûøåíèÿ òî÷íîñòè îöåíêè ÍÄÑ. Ýòà ïðîöåäóðà âûïîëíÿëàñü äî òåõ ïîð, ïîêà
ðàçíèöà ìåæäó äâóìÿ ïîñëåäîâàòåëüíûìè ðåøåíèÿìè íå ñîñòàâëÿëà ìåíåå 2%. Âåëè-
÷èíà òåîðåòè÷åñêîãî êîýôôèöèåíòà êîíöåíòðàöèè íàïðÿæåíèé �� îïðåäåëÿëàñü èç
óïðóãîãî ðåøåíèÿ. Óðîâåíü ïîâðåæäåíèé ïðè óïðóãîïëàñòè÷åñêîì äåôîðìèðîâàíèè
ïëàñòèíû îïðåäåëÿëñÿ â ñîîòâåòñòâèè ñ (10).
Ïðè ðàñ÷åòå ÍÄÑ ñ ïîìîùüþ ïàêåòà ANSYS èñïîëüçîâàëèñü êîíå÷íûå ýëåìåí-
òû òèïà PLANE 82, ïîñêîëüêó îíè îáåñïå÷èâàþò áîëåå òî÷íóþ àïïðîêñèìàöèþ
ãåîìåòðèè êîíöåíòðàòîðà. Ìîäåëü ïîâðåæäåííîñòè ââîäèëàñü â êà÷åñòâå ïîäïðîãðàì-
ìû ïîëüçîâàòåëÿ. Ýòî ïîçâîëÿåò ïîëó÷àòü ïîëÿ ðàñïðåäåëåíèÿ ðàññåÿííûõ ïîâðåæ-
äåíèé â çîíå êîíöåíòðàöèè íàïðÿæåíèé, à òàêæå îöåíèòü ïðåäåëüíîå ñîñòîÿíèå
êîíñòðóêòèâíîãî ýëåìåíòà.
Ïðèìåð ðåçóëüòàòîâ ÷èñëåííîãî ðàñ÷åòà ïîëåé ðàñïðåäåëåíèÿ ïîâðåæäåíèé â
çîíå îòâåðñòèÿ ïðè îäíîîñíîì àêòèâíîì ðàñòÿæåíèè ïëàñòèíû ïðè âåëè÷èíå âíåø-
íåé ðàñòÿãèâàþùåé íàãðóçêè 200 ÌÏà ïðèâåäåí íà ðèñ. 4.
Âèäíî, ÷òî ñ óâåëè÷åíèåì äèàìåòðà îòâåðñòèÿ ðàñòóò çîíà ïîâðåæäåíèé â
îáëàñòè êîíöåíòðàòîðà è ìàêñèìàëüíîå çíà÷åíèå ïîâðåæäåííîñòè.
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2017, ¹ 3 27
Ìåõàíè÷åñêèå ñâîéñòâà ìàòåðèàëîâ è ïàðàìåòðû ðàññåÿííûõ ïîâðåæäåíèé
Ìàòåðèàë � ò , ÌÏà � â, ÌÏà Ïîâðåæäåíèå
D ò DR
Ä16Ò 398
399
(402) 532
558
(582) 0,0075 0,12
18Õ2Í4ÂÀ 960
1014
(1056) 1343
1516
(1649) 0,043 0,575
15ÕÑÍÄ 349
352
(359) 515
600
(633) 0,012 0,50
12Õ18Í10Ò 248
249
(252) 627
1061
(1171) 0,006 0,52
ÂÒ22 1236
1253
(1264) 1414
1590
(1672) 0,011 0,065
07Õ16Í6 710
736
(740) 951
1298
(1534) 0,004 0,295
Ïðèìå÷àíèå. Íàä ÷åðòîé ïðèâåäåíû çíà÷åíèÿ äëÿ óñëîâíîé äèàãðàììû, ïîä ÷åðòîé – äëÿ
äåéñòâèòåëüíîé, â ñêîáêàõ – äëÿ ýôôåêòèâíîé.
Ôàêòîð ïîâðåæäåííîñòè â îöåíêå íàïðÿæåííî-äåôîðìèðîâàííîãî ñîñòîÿíèÿ ...
 û â î ä û
1. Àíàëèç ïðåäåëîâ ïðèìåíèìîñòè ñîâðåìåííûõ èíæåíåðíûõ ìåòîäîâ îöåíêè
ýôôåêòèâíûõ êîýôôèöèåíòîâ êîíöåíòðàöèè íàïðÿæåíèé è äåôîðìàöèé â óïðóãî-
ïëàñòè÷åñêîé îáëàñòè ïîêàçûâàåò ïðåèìóùåñòâà èñïîëüçîâàíèÿ óðàâíåíèÿ Ìàõóòîâà
äëÿ ýëåìåíòîâ ñ êîíöåíòðàòîðàìè íàïðÿæåíèé (äåôîðìàöèé).
2. Ýêñïåðèìåíòàëüíî ïîäòâåðæäåíî, ÷òî ââåäåíèå ïàðàìåòðà ïîâðåæäåííîñòè â
ñèñòåìó îïðåäåëÿþùèõ óðàâíåíèé ñóùåñòâåííî óòî÷íÿåò ðàñ÷åò ÍÄÑ ýëåìåíòîâ
êîíñòðóêöèé ïðè óïðóãîïëàñòè÷åñêîì äåôîðìèðîâàíèè. Ïðè ðåøåíèè çàäà÷ òåîðèè
ïëàñòè÷íîñòè çà ïîðîãîâîå çíà÷åíèå ïàðàìåòðà ïîâðåæäåííîñòè íåîáõîäèìî ïðèíè-
ìàòü ïðåäåë ïðîïîðöèîíàëüíîñòè, à ïðè îöåíêå ðåñóðñà – ïðåäåë âûíîñëèâîñòè
êîíñòðóêöèîííîãî ìàòåðèàëà.
3. Ïîêàçàíî, ÷òî èñïîëüçîâàíèå â èíæåíåðíûõ ðàñ÷åòàõ ïîêàçàòåëÿ ïðåäåëüíîãî
çíà÷åíèÿ ðàññåÿííîãî ïîâðåæäåíèÿ DR �1 çàâûøàåò ðåàëüíóþ íåñóùóþ ñïîñîá-
íîñòü ìåòàëëè÷åñêèõ ìàòåðèàëîâ íà óðîâíå ïðåäåëà ïðî÷íîñòè.
4. Ðàçðàáîòàííàÿ ìåòîäèêà â âèäå ïîäïðîãðàììû ïîëüçîâàòåëÿ ïîçâîëÿåò îïðå-
äåëÿòü ïîëÿ íàêîïëåííûõ ðàññåÿííûõ ïîâðåæäåíèé è êîíêðåòèçèðîâàòü çîíû âåðîÿò-
íîãî âîçíèêíîâåíèÿ ìàêðîòðåùèíû â ýëåìåíòàõ êîíñòðóêöèé ñ ó÷åòîì îñíîâíûõ
òåðìîñèëîâûõ ïàðàìåòðîâ íàãðóæåíèÿ.
Ð å ç þ ì å
Íàâåäåíî ³ ïðîàíàë³çîâàíî ³íæåíåðí³ ìåòîäè ðîçðàõóíêó íàïðóæåíü ³ äåôîðìàö³é ó
çîíàõ êîíöåíòðàö³¿ ïðè ïðóæíî-ïëàñòè÷íîìó äåôîðìóâàíí³ êîíñòðóêòèâíèõ åëåìåí-
ò³â. Ïîêàçàíî, ùî äëÿ îö³íêè ê³íåòèêè åôåêòèâíèõ êîåô³ö³ºíò³â êîíöåíòðàö³¿ íàïðó-
28 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2017, ¹ 3
Ðèñ. 4. Ïîëÿ ïîâðåæäåííîñòè äëÿ ïëàñòèíû ñ îòâåðñòèåì ðàçíîãî äèàìåòðà èç ñïëàâà Ä16Ò.
Í. È. Áîáûðü, Â. Â. Êîâàëü
æåíü ³ äåôîðìàö³é íàéá³ëüø ïðèéíÿòíîþ çà òî÷í³ñòþ º ìîäèô³êàö³ÿ Ìàõóòîâèì
ð³âíÿííÿ Íîéáåðà. Ââåäåíî ïîíÿòòÿ ðîçñ³ÿíî¿ ïîøêîäæåíîñò³. Óñòàíîâëåíî åôåêòèâ-
í³ñòü âèêîðèñòàííÿ ïàðàìåòðà ïîøêîäæåíîñò³ äëÿ îö³íêè â³ðîã³äíîñò³ ìåõàí³÷íèõ
âëàñòèâîñòåé ðÿäà ìåòàë³÷íèõ ìàòåð³àë³â. Âïëèâ ðîçñ³ÿíèõ ïîøêîäæåíü íà îö³íêó
íàïðóæåíî-äåôîðìîâàíîãî ñòàíó êîíñòðóêòèâíèõ åëåìåíò³â ïîêàçàíî íà ïðèêëàä³
ïðóæíî-ïëàñòè÷íîãî äåôîðìóâàííÿ ïëàñòèíè ç îòâîðîì.
1. Kachanov L. M. Introduction to Continuum Damage Mechanics. – Boston; Dordrecht:
Martinus Nijhoff, 1986. – 148 p.
2. Ðàáîòíîâ Þ. Í. Ââåäåíèå â ìåõàíèêó ðàçðóøåíèÿ. – Ì.: Íàóêà, 1987. – 80 ñ.
3. Lemaitre J. and Desmorat R. Engineering Damage Mechanics. – Berlin; Heidelberg:
Springer, 2005. – 380 p.
4. Bobyr’ N. I., Grabovskii A. P., Timoshenko A. V., and Khalimon A. P. Procedure for
the evaluation of the accumulation of defects in metallic structural materials under
complex elastoplastic loading // Strength Mater. – 2006. – 38, No. 1. – P. 92–98.
5. Ñåðåíñîí Ñ. Â., Øíåéäåðîâè÷ Ð. Ì., Ìàõóòîâ Í. À. è äð. Ïîëÿ äåôîðìàöèé ïðè
ìàëîöèêëîâîì íàãðóæåíèè. – Ì.: Íàóêà, 1979. – 278 ñ.
6. Neuber H. Theory of stress concentration for shear-strained prismatical bodies with
arbitrary nonlinear stress-strain law // J. Appl. Mech. – 1961. – 28. – P. 544–550.
7. Áèðãåð È. À. Ïðîãíîçèðîâàíèå ðåñóðñà ïðè ìàëîöèêëîâîé óñòàëîñòè // Ïðîáë.
ïðî÷íîñòè. – 1985. – ¹ 10. – Ñ. 39–44.
8. Glinka G. Energy density approach to calculation of inelastic strain-stress near
notches and cracks // Eng. Fract. Mech. – 1985. – 22, No. 3. – P. 485–508.
9. Ìàõóòîâ Í. À. Äåôîðìàöèîííûå êðèòåðèè ðàçðóøåíèÿ è ðàñ÷åò ýëåìåíòîâ
êîíñòðóêöèé íà ïðî÷íîñòü. – Ì.: Ìàøèíîñòðîåíèå, 1981. – 271 ñ.
10. Áîáûðü Í. È., Áàáåíêî À. Å., Õàëèìîí À. Ï. Êîíòèíóàëüíàÿ ìåõàíèêà ïîâðåæ-
äåííîñòè è åå èñïîëüçîâàíèå â çàäà÷àõ ñëîæíîãî ìàëîöèêëîâîãî íàãðóæåíèÿ //
Òåõí. äèàãíîñòèêà è íåðàçðóøàþùèé êîíòðîëü. – 2008. – ¹ 4. – Ñ. 25–34.
11. Ïèñàðåíêî Ã. Ñ., Ëåáåäåâ À. À. Äåôîðìèðîâàíèå è ïðî÷íîñòü ìàòåðèàëîâ ïðè
ñëîæíîì íàïðÿæåííîì ñîñòîÿíèè. – Êèåâ: Íàóê. äóìêà, 1976. – 416 ñ.
12. Òðîùåíêî Â. Ò. Äåôîðìèðîâàíèå è ðàçðóøåíèå ìåòàëëîâ ïðè ìíîãîöèêëîâîì
íàãðóæåíèè. – Êèåâ: Íàóê. äóìêà, 1981. – 340 ñ.
13. Òèìîøåíêî Î. Â., Êîâàëü Â. Â., Êðàâ÷óê Ð. Â. Âïëèâ âèäó íàïðóæåíîãî ñòàíó íà
êðèòè÷íå çíà÷åííÿ ïîøêîäæóâàíîñò³ äëÿ êîíñòðóêö³éíèõ ìàòåð³àë³â ïðè ïðóæíî-
ïëàñòè÷íîìó äåôîðìóâàíí³ // ³ñí. ÍÒÓÓ “Êϲ”. Ñåð. Ìàøèíîáóäóâàííÿ. –
2011. – ¹ 63. – Ñ. 103–107.
Ïîñòóïèëà 10. 04. 2017
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2017, ¹ 3 29
Ôàêòîð ïîâðåæäåííîñòè â îöåíêå íàïðÿæåííî-äåôîðìèðîâàííîãî ñîñòîÿíèÿ ...
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/NLD (Gebruik deze instellingen om Adobe PDF-documenten te maken die zijn geoptimaliseerd voor prepress-afdrukken van hoge kwaliteit. De gemaakte PDF-documenten kunnen worden geopend met Acrobat en Adobe Reader 5.0 en hoger.)
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/UKR <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>
/ENU (Use these settings to create Adobe PDF documents best suited for high-quality prepress printing. Created PDF documents can be opened with Acrobat and Adobe Reader 5.0 and later.)
/RUS <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>
>>
/Namespace [
(Adobe)
(Common)
(1.0)
]
/OtherNamespaces [
<<
/AsReaderSpreads false
/CropImagesToFrames true
/ErrorControl /WarnAndContinue
/FlattenerIgnoreSpreadOverrides false
/IncludeGuidesGrids false
/IncludeNonPrinting false
/IncludeSlug false
/Namespace [
(Adobe)
(InDesign)
(4.0)
]
/OmitPlacedBitmaps false
/OmitPlacedEPS false
/OmitPlacedPDF false
/SimulateOverprint /Legacy
>>
<<
/AddBleedMarks false
/AddColorBars false
/AddCropMarks false
/AddPageInfo false
/AddRegMarks false
/ConvertColors /ConvertToCMYK
/DestinationProfileName ()
/DestinationProfileSelector /DocumentCMYK
/Downsample16BitImages true
/FlattenerPreset <<
/PresetSelector /MediumResolution
>>
/FormElements false
/GenerateStructure false
/IncludeBookmarks false
/IncludeHyperlinks false
/IncludeInteractive false
/IncludeLayers false
/IncludeProfiles false
/MultimediaHandling /UseObjectSettings
/Namespace [
(Adobe)
(CreativeSuite)
(2.0)
]
/PDFXOutputIntentProfileSelector /DocumentCMYK
/PreserveEditing true
/UntaggedCMYKHandling /LeaveUntagged
/UntaggedRGBHandling /UseDocumentProfile
/UseDocumentBleed false
>>
]
>> setdistillerparams
<<
/HWResolution [2400 2400]
/PageSize [612.000 792.000]
>> setpagedevice
|