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§ 7.1. Стандартноk= 7; испытание<= /span>

Пр= 086;цедура испытаний н = 72; вязкость разрушения при плоской деформации стандартизl= 6;вана (см. [1, 2]) Американскl= 0;м обществом испытания материалов ASTM. На первый взгляд, необходимоl= 9;ть в стандартноl= 4; испытании кажется стр = 72;нной. Вследствие универсальl= 5;ости концепции, связанной с коэффициенm= 0;ом K, для таких испытаний подходит любой образ = 77;ц с трещиной, для которог = 86; может быть вычислен коэффициенm= 0; K. Однако для того, чтобы при вершине трещины пол = 91;чить плоскую деформацию, необходимо = 74;ыполнить несколько требований. Эти критери = 80; определяет стандарт ASTM. Кроме того, существуют стандарты для других механическl= 0;х испытаний, например дл = 03; испытания н = 72; растяжение. Эти стандарты необходимы = 74; том случае, когда нужно производитn= 0; материал с заданными с = 87;ецифически&#= 1084;и свойствами.

Бо= 083;ьшая работа по установленl= 0;ю стандарта н = 72; испытание для определениn= 3; KIc была проведена Сроули и Брауном [3, 4]. Дл= 103; получения критериев, гарантируюm= 7;их согласованl= 5;ость результатоk= 4; испытаний, понадобилаl= 9;ь большая программа испытаний. Б= 099;ли рекомендовk= 2;ны образец для трехточечнl= 6;го изгиба и компактный образец для растяжения, показанные на рис. 7.1. Приведем выражения коэффициенm= 0;ов К:

дл= 103; образца, работающегl= 6; на изгиб (обозначени = 03; приведены н = 72; рис. 7.1),

(7.1)

дл= 103; компактногl= 6; образца, работающегl= 6; на растяжен = 80;е,

(7.2)

Ри&#= 1089;. 7.1. Стандартныk= 7; образцы, работающие: = а — = на изгиб: б — на растяжение

Об= 088;азцы должны имет = 00; усталостныk= 7; трещины, а для обеспечениn= 3; образованиn= 3; трещины в ну= 078;ном месте — стартовые выточки. В элементах конструкциl= 1;, имеющих большую толщину, уст= 072;лостные трещины чащ = 77; всего образуются = 74; углу (рис. 7.2, а). Это приводи = 90; к тому, что трещина имеет невос = 87;роизводимы&#= 1081; изогнутый фронт, непригодныl= 1; для стандартноk= 5;о испытания. Этого можно избежать, делая в образцах ше = 74;ронную выточку (рис. 7= .2, б). Наличие такой выточки приводит к образованиn= 2; трещины в центре образца, что повышает вероятностn= 0; образованиn= 3; сравнительl= 5;о прямого фронта трещины. Образцы с выточкой имеют дополнителn= 0;ное преимущестk= 4;о, заключающеk= 7;ся в почти немедленноl= 4; образованиl= 0; трещины при приложении циклическиm= 3; нагрузок.=

По= 089;ле испытания можно легко определить = 88;азмер и форму усталостноl= 1; трещины. Область усталостноk= 5;о разрушения = 80; область око = 85;чательного разрушения имеют различную форму поверхностl= 0;, а поэтому по-разному отражают падающий свет, что дел&#= 1072;ет их легко различимымl= 0;, как видно из рис. 7.3. Стандарт определяет длину трещины (рис. 7= .2, б) по формуле а= =3D (а1 + а2 + а3)/3, и если а1, а= 2, или а3 отлl= 0;чаются от а более чем на 5 %, то испытание считается непригодныl= 4;. Испытание также считается непригодныl= 4;, если размер трещины на поверхностl= 0; отличается от a более чем на 10 % (иногда трещина отстает от с= 076;виговых губ) и если любая часть фронта трещ = 80;ны находится о = 90; выточки бли = 78;е, чем наименьшая из величин 0,05= 072; или 1,3 мм.

Ри&#= 1089;. 7.2. Стартовые выточки: а — &= #1085;ормальная краевая; б — шевронная<= span style=3D'font-size:8.5pt;font-family:Arial;color:#330066'>

Ри&#= 1089;. 7.3. Образцы для определениn= 3; вязкости ра = 79;рушения при плоской деформации:

по&#= 1074;ерхности разрушения работающих на изгиб образцов, выполненныm= 3; из титановы = 93; сплавов (а, k= 4;, г)

и и&= #1079; алюминиевоk= 5;о сплава (б); N — <= b>ше&#= 1074;ронная ниточка; P — <= b>зо&#= 1085;а усталостноk= 5;о разрушения;

К — = зо&#= 1085;а окончательl= 5;ого разрушения; = S — <= b>гу&#= 1073;ы сдвига

Дл= 103; того чтобы усталостнаn= 3; трещина был = 72; острой, предъявляюm= 0;ся требования также к цикл= 080;ческой нагрузке. Наиболее важное из ни= 093; заключаетсn= 3; в том, чтобы максимальнk= 2;я интенсивноl= 9;ть напряжений за время цик= 083;а не превышал = 72; 60 % от величины= ; KIc; как видно из рис. 7.4, только при достаточно острой вершине трещины получаются согласованl= 5;ые значения KIc (см. [5]). Большая величина K в процессе образованиn= 3; усталостноl= 1; трещины могла бы привести к слишком большому ее притуплениn= 2;, а отсюда — к неверным оценкам значений KIc.

Ри&#= 1089;. 7.4. Вл&#= 1080;яние уровня напряжения при усталостноl= 4; разрушении на измеренное значение KIc

в алюминиевоl= 4; сплаве 7075—7651 [4] (п = 86; данным ASTM)            =             &nb= sp;            =             &nb= sp;            =             &nb= sp;   

        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;       

 

 

§ 7.2. Требования к размерам образцов<= /h2>

К размеру образца предъявляюm= 0;ся строгие тре = 73;ования. Это вызвано необходимоl= 9;тью соблюдения условия плоского деформировk= 2;ния материала при вершине трещины. В гл. V было показано, чт= 086; толщину образца следует выб = 80;рать большей размера зон = 99; пластичносm= 0;и, иначе образуется плоское напряженноk= 7; состояние. Н= 072; поверхностl= 0; образца всегда обра = 79;уется область плоского напряженноk= 5;о состояния, поэтому, для того чтобы плоская деф = 86;рмация играла главную рол = 00;, область пло = 89;кого напряженноk= 5;о состояния должна быть = 086;тносительн&= #1086; малой.

Не= 086;бходимо, чтобы толщина образца был = 72; намного больше размера зон = 99; пластичносm= 0;и. Поскольку этот размер пропорционk= 2;лен это требование означает, чт= 086; толщина B должна удовлетворn= 3;ть неравенствm= 1; Согласно рис. 7.5, согласованl= 5;ые значения КIc получаются, если а>≈2,5; это значени = 77; а принято в ка= 095;естве требования ASTM. При меньших значениях а<= /i> области плоского напряженноk= 5;о состояния н = 72; поверхностl= 0; образца сравнительl= 5;о велики и имеют большое влияние на процесс рас = 87;ространени&#= 1103; трещины; это приводит к тому, что наблюдаемаn= 3; величина вязкости разрушения = 87;ревышает действителn= 0;ное значение KIc для плоской деформации.

Ри&#= 1089;. 7.5. Влияние толщины образца на измеренное значение KIc дл&#= 1103; легированнl= 6;й стали [4]

По= 076;обное условие предъявляеm= 0;ся и к размеру трещины: зон= 072; пластичносm= 0;и должна быть = 084;ала по сравнени = 02; с длиной трещины. Это накладываеm= 0; ограничениk= 7; на относительl= 5;ую длину трещины. Существует также друга = 03; важная сторона этого вопроса, накладываюm= 7;ая ограничениk= 7; на абсолютный размер трещины. Из соотношениn= 3; между напряжениеl= 4; разрушения = 80; размером трещины следует, что при малы= 093; значениях a величина σ = 89; становится бесконечноl= 1;. В действителn= 0;ности этого не происходит, поскольку при а =3D 0 величина σ = 89; =3D σu как показано на рис. 7.6. Если размер трещины мен = 00;ше, чем аmin (рис. 7.6), то разрушение произойдет при меньшем напряжении, чем напряжение, вычисленноk= 7; из коэффициенm= 0;а KIc. Разрушение = 74; точке A привело бы к тому, что за величину KIc была бы принята величина, равная Если бы разрушение могло произойти в точке B (рис. 7.6), то результа = 90; был бы Это означает, чт= 086; наблюдаемоk= 7; значение KIc для такого образца меньше, чем действителn= 0;ное значение KIc; испытание такого образца привело бы к ошибочному = 88;езультату.

Ри&#= 1089;. 7.6. Минимальныl= 1; размер трещины

Ри= 089;. 7.7 показывает, что для обеспечениn= 3; получения согласованl= 5;ых значений KIc необходимо, чтобы разме = 88; трещины а б= 099;л больше или равен Полученн= ые при испытании образцов с маленькими трещинами данные о значениях KIc превышают действителn= 0;ное значение KIc, что противоречl= 0;т рис. 7.6. Расхождениk= 7; произошло из-за того, что относительl= 5;ый размер трещ = 80;ны (по сравнени= 102; с размером зоны пласти = 95;ности) был слишком мал; при этом абсолютный размер трещины мог быть достаточныl= 4;.

Ри= 089;. 7.7. Влияние размера трещины на измеренное значение КIc для легированнl= 6;й стали [4]

Со= 074;ершенно очевидно, чт= 086; обе величин = 99;, B и a, должны быть больше, чем Если размер зоны плоской деформации принять равным (см. гл.= IV) то отсюда следует, что величины a и <= i>B должны быть по крайней мере в 25 раз больше шири = 85;ы зоны пластичносm= 0;и. Соответствm= 1;ющим образом выбираются = 80; другие размеры обр = 72;зца, а именно W =3D 2а= , причем 2B < W < 4B. Длина образ = 94;а, работающегl= 6; на изгиб, равна 4W, а длина компактногl= 6; образца, предназначk= 7;нного для растяжения, равна 1,2W.

В этих требованияm= 3; предполагаk= 7;тся, что для получения требуемых размеров образца нео = 73;ходимо оценить ожидаемое значение KIc до испытани = 03;. Затем прово = 76;ится испытание и = 089; помощью уравнений (7.1) l= 0; (7.2) определяетl= 9;я значение K. Это значени = 77; K обозначают через KQ; он= 086; является предполагаk= 7;мой величиной в = 03;зкости разрушения. После этого размеры а и В сравнивают = 89; величиной Если эти размеры достаточно велики, то KQ= есть определяемk= 2;я величина КIc при условии, что удовлетворk= 7;ны все остальн = 99;е условия; есл= 080; нет — результат неверен.            =             &nb= sp;            =             &nb= sp;            =             &nb= sp;            =             &nb= sp;      

        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;      

 

 

§ 7.3. Нелинейносm= 0;ь

Во время испытания н = 72; вязкость разрушения на графопострl= 6;ителе строится график зави = 89;имости раскрытия трещины от приложенноl= 1; нагрузки. Раскрытие трещины измеряется = 89; помощью изм = 77;рительного устройства, снабженногl= 6; электротенk= 9;одатчиками. Измеритель поперечногl= 6; разрыва устанавливk= 2;ется в специальн = 86; проделанныk= 7; в шевронной выемке пазы (&#= 1088;ис. 7.8). При увеличении раскрытия трещины во в= 088;емя нагружения пружины распрямляюm= 0;ся и их концы сл&#= 1077;дуют за движение = 84; берегов трещины.

Ди= 072;граммы «нагрузка — РТ» (раскрытие трещины), как показано на рис. 7.9, могут иметь разли = 95;ные формы. Вначале с увеличениеl= 4; P раскрытие растет линейно. В этом идеальном случае (а) общее разрушение происходит при достиже = 85;ии величины KIc. Если пластическl= 0;е деформации невелики, ли= 085;ия P — РТ остается прямой. Во многих случаях (б) при нагрузк = 77; PQ происходит внезапное раскрытие трещины. Это раскрытие трещины, часто связанное с = 86; слышным щелчком, называется хлопком. В записи испы = 90;ания это проявляетсn= 3; как скачкообраk= 9;ное возрастаниk= 7; величины РТ. Рост трещин = 99; останавливk= 2;ется либо за счет небольшого = 91;меньшения нагрузки, либо за счет увеличения сопротивлеl= 5;ия росту трещины (см. гл. V, IX). После хлопка можн = 86; производитn= 0; дальнейшее = 91;величение нагрузки, пока при РF не произойдет разрушение. Иногда происходят последоватk= 7;льные хлопки. В принципе дл = 03; вычисления величины KQ следует использоваm= 0;ь нагрузку РQ, при которой происходит хлопок.

Дл= 103; материалов средней вязкости разрушения обычно прои = 89;ходит постепенноk= 7; увеличение нелинейносm= 0;и диаграммы «нагрузка — РТ» (в). Эта нелинейносm= 0;ь является результатоl= 4; действия двух факторов: пластическl= 6;го деформировk= 2;ния и постепенноk= 5;о разрушения = 89;колом, предшествуn= 2;щего полному разрушению. Если бы нелинейносm= 0;ь была вызван = 72; только ростом трещины, то диаграмма этого типа была бы боле= 077; или менее эк= 074;ивалентна случаю б. При этом величину РQ можно было б= 099; определить как нагрузк = 91;, при которой, например, произошло удлинение н = 72; 2 %. В случае, когда одновременl= 5;о происходят пластическl= 6;е деформировk= 2;ние и раскрытие трещины, проблема разрешаетсn= 3; следующим образом. Есл= 080; пластичносm= 0;ь отсутствуеm= 0;, то диаграмма «нагрузка — РТ» имеет ви= 076; прямой лини = 80;. В упругом случае РТ пропорционk= 2;льно размеру трещины (см. гл. III):

        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;          (7.3)<= /o:p>

гд= 077; С1 — константа.

Ри&#= 1089;. 7.8. Измеритель поперечногl= 6; раскрытия:=

а <= /i>— ус&#= 1090;ановленный на шевронно = 81; выточке;

б — установленl= 5;ый на образце, предназначk= 7;нном для определениn= 3; вязкости разрушения при изгибе;

1= — <= b>те&#= 1085;зодатчики; 2 — пружины

Ри&#= 1089;. 7.9. Эксперименm= 0;альные диаграммы 1 — <= b>ра&#= 1079;рушение; 2 — хлопок

Ле= 075;ко видеть, что наклон С1a/E линии P — РТ пропорционk= 2;лен размеру трещины. Для того чтобы найти точку двухпроценm= 0;ного увеличения длины трещины, достаточно на рис. 7.10, а провести линию OB, наклон которой на 2 % меньше. Пересечениk= 7; линии OВ с OAC определяет нагрузку PQ. В действителn= 0;ности нелинейносm= 0;ь происходит частично из-за пластическl= 6;го деформировk= 2;ния. Стандарт ASTM предъявляеm= 0; требование, согласно которому пр = 80; двухпроценm= 0;ном расширении трещины нелинейносm= 0;ь за счет пластическl= 6;го деформировk= 2;ния должна быть больше, чем нелинейносm= 0;ь, происходящk= 2;я из-за роста трещины. Прямые лини = 80; на рис. 7.10, а ис&#= 1082;ривляются тогда, когда возникают пластическl= 0;е деформации, как на рис. 7.10, б= ;. Форму этих кривых можно аппроксимиl= 8;овать (см. [5, 6, 7]). В предыдущих главах показано, чт= 086; пластическl= 0;е деформации можно учест = 00;, используя эффективныl= 1; размер трещины aэф&#= 1092; =3D a+r*p. Подставляя это соотношениk= 7; в уравнение (7.= 3), получаем

        (7.4)

Ри&#= 1089;. 7.10. Нелинейные диаграммы, полученные во время испытаний:
а — упругая; = б — <= b>уп&#= 1088;угопластич= еская

Соглас= но уравнению (7.4), нелинейносm= 0;ь за счет пластичносm= 0;и растет как третья степ = 77;нь P, в то время как нелинейносm= 0;ь, происходящk= 2;я за счет рост= 072; трещины, остается пропорционk= 2;льной размеру трещины. Пусть причиной не = 83;инейности xQ являетсn= 3; пластичносm= 0;ь, а распростраl= 5;ение трещины вызывает отклонение линии на вел= 080;чину yQ, как показано на рис. 7.11. Далее предположиl= 4;, что при нагрузке Р1, при которой величина у = 074;се еще равна нулю, x =3D x1, т. е. при нагрузке P1 трещина все еще не растет. Тогда, согласно ур = 72;внению (7.4),

        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;  (7.5)

Ри&#= 1089;. 7.11. Критерий нелинейносm= 0;и: 1 — = упругость; 2 — = упругопласm= 0;ичность

Станда= рт предъявляеm= 0; к испытанию = 076;ополнитель&= #1085;ое требование R= 12; чтобы при Р1 =3D 0,8РQ трещина не росла. Из уравнения (7.5) следует, что xQ ≈ 2x1. Так как предъявленl= 6; требование, согласно ко = 90;орому xQ ≈ уQ, необходимо, чтобы

        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;  (7.6)

Ур= 072;внение (7.6) утверждает= ;, что это требование, предъявляеl= 4;ое к испытанию, равносильнl= 6; условию, по которому нелинейносm= 0;ь при P =3D 0,8РQ н= 077; должна превышать 25 % отклонения от прямой линии при нагрузке РQ.

По= 089;кольку величина уQ (за счет роста трещины) может составлять 2 %, то отсюда следует, что сумма xQ + уQ= ) может составлять 4 % (а x1 может составлять 1 %) от упругого РТ при P =3D РQ. Однако из-за конечности размеров образца вел = 80;чины нелинейносm= 0;ей являются функцией а/= W. Оказываетсn= 3; (см [5]), для стандартныm= 3; образцов, служащих дл = 03; определениn= 3; КIc, для которых = а/W ≈ 0,5, величина &#= 1091;Q + xQ составляет примерно 5 % от упругого РТ при P =3D РQ. Следователn= 0;но, для определениn= 3; РQ необходимо провести линию, накло= 085; которой на 5 % меньше, чем наклон линейной части диаграммы Р<= /i> — РТ. В точке пересечениn= 3; этой линии с диаграммой находим величину РQ. Затем можно проверить выполнение соотношениn= 3; (7.6) при P =3D 0,8РQ. Если это условие не удовлетворn= 3;ется, то испытани = 77; недействитk= 7;льно. В случае, когда соотношениk= 7; (7.6) удовлетворk= 7;но, величину РQ можно использоваm= 0;ь для вычисления K= Q и выполнить другие проверки достоверноl= 9;ти результатоk= 4; испытания.=

Измере= ние отклонения линии диаграммы о = 90; прямой при P =3D 0,8РQ является не очень точны = 84;. Поэтому в бу= 076;ущем это требование, предъявляеl= 4;ое к испытанию, вероятно, будет изменено. Разумеется, оно будет преобразовk= 2;но в условие, по которому величина РQ должна быть не меньше 90 % оm= 0; нагрузки, пр= 080; которой происходит окончательl= 5;ое разрушение.        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;      

        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;       

 

 

§ 7.4. Применимосm= 0;ь критериев<= /span>

Во= 079;никает вопрос, действителn= 0;но ли критерии обоснованнl= 6;сти испытаний п = 86; определениn= 2; KIc имеют на практике столь важно = 77; значение. В э&#= 1090;ом вопросе до сих пор мног= 086; путаницы. Величина KIc, определеннk= 2;я в условиях строгого выполнения этих критериев, есть (в определеннm= 9;х пределах) константа материала. Если критер = 80;и применяютсn= 3; произвольнl= 6;, то согласов = 72;нных значений этой константы н = 77; получается. Если материалы необходимо охарактериk= 9;овать их вязкость = 02; (как они характеризm= 1;ются прочностью на растяжен = 80;е и пределом текучести), то при этом могут быть использоваl= 5;ы только обоснованнm= 9;е данные по определениn= 2; KIc. Материалы, обладающие определеннl= 6;й вязкостью, должны быть снабжены паспортом с проставленl= 5;ым в нем обоснованнm= 9;м значением величины KIc. Классификаm= 4;ия материалов = 74; соответствl= 0;и с их вязкостью разрушения, вообще говоря, долж= 085;а быть основана на обоснованнm= 9;х данных.

Ес= 083;и критерии обоснованнl= 6;сти не выполняю = 90;ся, то измеренное = 79;начение вязкости KQ не является константой материала. Величина KIc, зависит от геометрии образца (см. гл. VIII). Когда размер образца слишком мал (или трещина слишком мала), измерение величины KQ приносит мало пользы. К этому заключению = 84;ожно прийти, расс= 084;атривая рис. 7.6. При слишком малой толщине обр = 72;зца B значение KQ может быть все-таки весьма полезным: эт= 086; значение является мерой вязкости пластины да = 85;ной толщины.

По= 089;кольку на практике деформация элементов конструкциl= 1; не является плоской из-з= 072; недостаточl= 5;ой толщины эти = 93; элементов, и= 093; сопротивлеl= 5;ие росту трещи = 85; не определяетl= 9;я коэффициенm= 0;ом KIc. В таких случаях действителn= 0;ная вязкость об = 99;чно больше, чем K<= sub>Ic; это означае = 90;, что использоваl= 5;ие коэффициенm= 0;а KIc приводи = 90; к заниженны = 84; оценкам допустимой длины трещи = 85;ы и остаточно = 81; прочности такой конст = 88;укции. Эти оценки могут быть гораздо бол = 77;е заниженнымl= 0;, особенно в тех случаях, когда интенсивноl= 9;ть напряжений, при которой = 087;роисходит разрушение, значительнl= 6; выше, чем при хлопке (см. гл. VIII). Хотя обоснованнm= 9;е значения коэффициенm= 0;а KIc, несомненно, очень полезны, следует иметь в виду, что для каждого приложения следует исп = 86;льзовать то значение вязкости, которое соответствm= 1;ет данной геометрии и толщине (см. [8]), и не следует строго придерживаm= 0;ься обоснованнl= 6;го значения KIc, если оно мал= 086; подходит дл = 03; данного случая.

В элементах конструкциl= 1;, толщина которых так = 86;ва, что в них преимущестk= 4;енно устанавливk= 2;ется плоская деформация, часто образ = 91;ются трещины, имеющие форму полуэллипсk= 2;. Как показано в гл. III, интенсивноl= 9;ть напряжений вдоль фронт = 72; такой трещины мен = 03;ется. Интенсивноl= 9;ть напряжений максимал= ьна на конце малой оси (которая обы= 095;но является наиболее глубокой то = 95;кой поверхностl= 5;ой выемки). Если <= i>а и с — полуоси эллипса, то

        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;      (7.7)

гд= 077; — интенсивноl= 9;ть напряжений на конце гла= 074;ной оси. Обычно предполагаk= 7;тся, что разруше = 85;ие происходит, когда Однако в этот момен= 090; это означает, чт= 086; на конце главной оси трещина распростраl= 5;яться не может. На самом деле разрушение произойдет при т. е. действителn= 0;ное поведение материала п = 88;и разрушении зависит от формы выемк = 80; и еще больше —- от анизотропнm= 9;х свойств материала. Этот вопрос рассмотрен = 74; гл. XI.

Ве= 083;ичина KIc для структурныm= 3; материалов может прини = 84;ать различные значения, поскольку вязкость разрушения зависит от направлениn= 3; распростраl= 5;ения трещины (анизотропи = 03;), термообрабl= 6;тки (предел текучести), температурm= 9; и многих других параметров (вопрос о влиянии эти = 93; переменных на величину вязкости рассмотрен = 74; гл. XI). Поэтому при использоваl= 5;ии значений KIc следует указывать условия, в которых нах = 86;дился материал, и обстоятельl= 9;тва, при которых были получены эт = 80; данные. В табл. 7.1 привед= ;ены некоторые данные вязкости разрушения ряда сплаво = 74;, что позволяет о = 94;енить величину коэффициенm= 0;а KIc для некоторых строительнm= 9;х материалов.

Зн= 072;чения вязкости разрушения для плоской деформации высокопрочl= 5;ых материалов = 83;ежат в пределах о= 090; 50 до 350 кгс/мм3/2 (15 – 100 ). В табл. 7.1 указаны требуемые толщины образцов. В зависимостl= 0; от предела текучести материала требуемая толщина, как правило, име= 077;т порядок от 2 до 20 мм. Для практическl= 0;х целей образцы с толщиной, меньшей 10 мм, используютl= 9;я редко. Материалы с низким пред = 77;лом текучести имеют ударную вязкость пр = 80; плоской деформации порядка 500 кгс/мм3/2 или более, однак= 086; такие значения вязкости то = 95;но измерить нельзя. Высокая вязкость пр = 80; низком пределе текучести приводит к чрезвычайнl= 6; высоким значениям (KIc/σуs)2, так что требуемая для стандартноk= 5;о испытания толщина может достигать величины по = 88;ядка 1 м и более. Совершенно очевидно, чт= 086; на практике испытания н = 72; определениk= 7; KIc материалов такой высокой вязкости неосуществl= 0;мы. Характерисm= 0;ика материала с точки зрени = 03; его сопротивлеl= 5;ия росту трещи = 85; должна быть основана на различных механическl= 0;х концепциях разрушения типа РТ (см. гл. IX) или, где это возможно, J –интеграла (гл. VI).

Пр= 086;ведение испытаний н = 72; определениk= 7; величины KIc для этих материалов непрактичнl= 6; и, более того, бесполезно. Материалы вряд ли буду= 090; использоваm= 0;ься даже при толщинах порядка 1 м. Здесь видно одно из ограничениl= 1; ЛУМР (линейн= 086;й упругой механики разрушения), применимых только к материалам, для которых отношение модуля упругости к пределу текучести при комнатной температурk= 7; меньше (в грубом приближениl= 0;), чем 200–250. При низких температурk= 2;х металлы могут проявлять существеннl= 6; больше хрупких свойств (например, хрупкое раз = 88;ушение в сталях). Таким образом, ЛУМ= 056; для температурm= 9; вязкохрупкl= 6;го перехода ил = 80; ниже применима даже к низкопрочнm= 9;м сталям (см. гл. XI).

Таблица 7.1 Типичные значения КIc пр&#= 1080; комнатной температурk= 7;

 &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;             =

        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;     

 

Ма&= #1090;ериал

Ус&= #1083;овия

σy= s

KIc=

Не&= #1086;бходимая минимальна= 103; толщина B

 

кг&= #1089;/мм2

кс&= #1080;

кг&= #1089;/мм3/2

мм<= o:p>

Дю&= #1081;м

Стали=

 

 

 

 

 

 

 

Легирl= 6;ванные

 

300

900°F, 3 ч

200<= /span>

285<= /span>

182<= /span>

52

2,1<= /span>

0,09=

300

850°F, 3 ч

170<= /span>

242<= /span>

300<= /span>

85

7,8<= /span>

0,31=

250

900°F, 3 ч

181<= /span>

259<= /span>

238<= /span>

68

4,3<= /span>

0,18=

Сталь Д6АС

Те&= #1088;мообработк= ;а

152<= /span>

217<= /span>

210<= /span>

60

4,8<= /span>

0,20=

 

Те&= #1088;мообработк= ;а

150<= /span>

214<= /span>

311<= /span>

89

10,7=

0,44=

 

По&= #1082;овка

150<= /span>

214<= /span>

178–280

51–80

–

–

Сталь 4340=

Уп&= #1088;очнение

185<= /span>

265<= /span>

150<= /span>

43

1,7<= /span>

0,07=

А 533 В

Ре&= #1072;кторная сталь

35

50

630<= /span>

180<= /span>

810,0

33,00

Углерl= 6;дистая сталь

Ни&= #1079;копрочная<= /o:p>

24

35

>700

>200

2150,0

82,00

Титанl= 6;вые

сплавm= 9;:

 

 

 

 

 

 

 

6Al–4V

(α+β)= STA

112<= /span>

160<= /span>

122<= /span>

35

3,0<= /span>

0,12=

13V–11Cr–3Al

STA<= /span>

115<= /span>

164<= /span>

89

25

1,5<= /span>

0,07=

6Al–2Sn–4Zr–6Mo

(α+β)= STA

120<= /span>

171<= /span>

85

24

1,3<= /span>

0,05=

6Al–6V–2Sn=

(α+β)= STA

110<= /span>

157<= /span>

120<= /span>

34

3,0<= /span>

0,12=

4Al–4Mo–2Sn–0,5Si=

(α+β)= STA

96

137<= /span>

224<= /span>

64

13,6=

0,55=

Алюмиl= 5;иевые

сплавm= 9;:

 

 

 

 

 

 

 

7075

T651=

55

79

94

27

7,3<= /span>

0,30=

7079

T651=

47

68

105<= /span>

30

12,5=

0,49=

DTD5024

По&= #1082;овка:

 

 

 

 

 

 

 

в продольном направлени= 080;

50

72

126<= /span>

36

15,9=

0,65=

 

в коротком поперечном направлени= 080;

49

70

53

15

3,0<= /span>

0,12=

2014

T4

46

65

90

26

9,6<= /span>

0,40=

2024

T3

40

57

110<= /span>

31

19,0=

0,75=

Оргстk= 7;кло

–

–

–

5,3<= /span>

1,5<= /span>

–

–

 

§ 8.1. Введение

Об= 097;епринятого метода испытания материалов на вязкость при плоском напряженноl= 4; состоянии и представлеl= 5;ия результатоk= 4; этого испыт = 72;ния не существует, поскольку в этой област = 80; при объяснении наблюдаемыm= 3; явлений воз = 85;икает ряд трудностей. Однако многие конс = 90;рукции, особенно в авиации, строят из тонких листов, и, сле&= #1076;овательно, задача о плоском напряженноl= 4; состоянии имеет огромное практическl= 6;е значение. Задача о плоском напряженноl= 4; состоянии имеет полезное с техническоl= 1; точки зрени = 03; решение. Остаточную прочность армированнl= 6;го листа с трещиной можно вычислить, з= 085;ая остаточную прочность неармироваl= 5;ной панели (см. гл. XVI).

Не совсем еще ясен вопрос = 086; представлеl= 5;ии данных, касающихся неармироваl= 5;ных панелей, однако этот вопрос може = 90; быть исследован техническиl= 4;и методами, хотя он и нуждается в дальнейшей разработке. Представлеl= 5;ие, связанное с коэффициенm= 0;ом K1с, как оказываетсn= 3;, имеет ряд преимущестk= 4;. Коэффициенm= 0; K1с здесь будет использоваl= 5; для описани = 03; вязкости разрушения при плоском напряженноl= 4; состоянии материала с трещиной ти = 87;а «разрыв» (ти= 087; I) по аналогии с коэффицие = 85;том KIc — вязкостью разрушения при плоской деформации.

После краткого описания процесса разрушения при плоском напряженноl= 4; состоянии в = 085;астоящей главе приведены методы вычисления коэффициенm= 0;а K1с. Затем рассматривk= 2;ется концепция, связанная с понятием R – кривой. Заключителn= 0;ная часть главы посвящена некоторым специальныl= 4; вопросам ис = 87;ытаний материалов при плоском напряженноl= 4; состоянии.      

        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;      

 

 

§ 8.2. Плоское напряженноk= 7; состояние с инженерной точки зрени = 03;

Ра= 089;смотрим нагруженныl= 1; номинальныl= 4; растягиваюm= 7;им напряжениеl= 4; σ тонкий лис = 90; с центральн = 86;й поперечной трещиной, имеющей раз = 84;ер 2a0 (рис. 8.1). Это напряжение можно увеличить д = 86; значения σi, при котором трещина начнет медленно расти (см. [1]). Этот медленный рост трещин = 99; стабилен: он моментальнl= 6; прекращаетl= 9;я, как только н= 072;грузка становится постоянной. Несмотря на то, что трещина теперь длиннее, для поддержаниn= 3; процесса ее распростраl= 5;ения требуется большее напряжение. Наконец, при определеннl= 6;м критическоl= 4; напряжении `= 3;c трещина достигает критическоl= 1; длины 2ac; при этом рос= 090; трещины становится нестабильнm= 9;м, в результат = 77; чего происходит внезапное общее разрушение пластины. Если началь = 85;ая трещина длиннее, то рост трещин = 99; начинается при меньшем напряжении. Разрушающеk= 7; напряжение такой пластины (остаточная прочность) т= 072;кже более низко = 77;, однако рост трещины про = 80;сходит медленнее (рис. 8.1).

Ри&#= 1089;. 8.1. Параметры остаточной прочности при плоском напряженноl= 4; состоянии<= span style=3D'font-size:8.5pt;font-family:Arial;color:#330066'>

В первом приближениl= 0; можно предположиm= 0;ь, что все события, происходящl= 0;е в процессе р= 072;спростране&= #1085;ия трещины и разрушения при плоском напряженноl= 4; состоянии, происходят при определ = 77;нном значении коэффициенm= 0;а интенсивноl= 9;ти напряжений, заданного одним из сле= 076;ующих выражений:=

  (8.1)

где α — коэффициенm= 0;, зависящий о = 90; геометрии п = 72;нели и ее размера. В этих выражениях вместо дейс = 90;вительного размера трещины a можно использоваm= 0;ь эффективныl= 1; размер трещ = 80;ны a+r*p (r*p — коррекция н = 72; зону пластичносm= 0;и), однако, как оказываетсn= 3;, в техническиm= 3; приложенияm= 3; коррекция н = 72; зону пластичносm= 0;и не нужна.

Ис= 087;ытания (см. [1, 2, 3]) показали, чт= 086; величины K1i= , K1с и К1е l= 5;е являются константамl= 0; материала, такими, как K<= sub>Ic. Однако в первом приближениl= 0; они являютс = 03; константам&= #1080; для данной толщины, для ограниченнl= 6;го диапазона изменения длин трещин = 080; для данного размера панели. Измеренное значение K1 = 89; зависит от размера панели W, как показано на рис. 8.2. Оказываетсn= 3;, величина K1 = 89; меньше для более узких панелей. С увеличениеl= 4; размера панели K1с постепенно увеличиваеm= 0;ся, принимая постоянное значение, когда этот р= 072;змер превышает определеннl= 6;е значение. Эт= 086; постоянное значение K1 = 89; для больших панелей и является действителn= 0;ным значением K1с для материала данной толщины. Далее приво = 76;ится объяснение зависимостl= 0; величины K1 = 89; от размера панели.

Ри&#= 1089;. 8.2. Наблюдаемыk= 7; значения K1с<= /sub> и <= /b>К1е<= /sub>

ка&#= 1082; функции ширины панели для двух алюмин = 80;евых сплавов [1, 3, 4]=

Пр= 080; проектировk= 2;нии конструкциl= 1;, состоящих и = 79; тонких листов, необходимо иметь данны = 77; о величинах = K1с для различных толщин. Феддерсеноl= 4; [5] был предлож= ен метод анализа и представлеl= 5;ия этих данных, который особенно полезен при проектировk= 2;нии (см [6]). Для панелей, достаточно = 96;ироких, чтобы при их испытании получить действителn= 0;ное значение K1 = 89;, соотношениk= 7; между остаточной прочностью = 80; длиной трещины можно представитn= 0; кривой, изображеннl= 6;й на рис. 8.3. На рисунке также показ = 72;на прямая лини = 03;, представляn= 2;щая собой пластическl= 0;е деформации = 80;стинного сечения пластины: во всех точках этой прямой истинные напряжения = 74; той части образца, через которую не проходит тр = 77;щина, превышают предел текучести. Заштриховаl= 5;ные области указывают размеры трещин, при которых, для того чтобы вызвать разрушение = 87;ри данной величине K1 = 89;, необходимо было бы приложить к истинному с = 77;чению напряжения, превышающиk= 7; предел теку = 95;ести. Поскольку в материале н = 77; могут возни = 82;нуть напряжения выше предел = 72; текучести, разрушение для таких длин трещин произойдет при напряженияm= 3;, меньших напряжения, вычисленноk= 5;о с помощью ко= 101;ффициента K1с, т. е. измеренное значение вязкости такого обра = 79;ца будет меньш = 77;, чем K1с.

Об= 098;яснению этого противоречl= 0;я было посвящ = 77;но много теоретичесl= 2;их разработок, которые, однако, не смогли собрать все данные воед = 80;но и составить цельную картину для всех размеров трещин. Таки= 084; образом, на данном этап = 77; остается свести все данные к простой общей форме, пригодной для инженерных приложений. Феддерсен [5] утверждает: для того что= 073;ы провести гладкую и непрерывнуn= 2; кривую остаточной прочности, можно воспользовk= 2;ться двумя касательныl= 4;и к идеализироk= 4;анной K – кривой (штриховая линия на рис. 8= .3). В подтвержд = 77;ние этого предположеl= 5;ия он приводит = 086;бширные эксперименm= 0;альные данные. Одна касательнаn= 3; к K – кривой проведена о = 90; точки σ =3D σys<= /sub>, где σys – предел текучести, а другая – от точки 2a =3D W, гд&= #1077; W – ширина образца.

Ри&#= 1089;. 8.3. Анализ Феддерсена [5]<= /span>

Уг= 086;л наклона касательноl= 1; к K – кривой в произвольнl= 6;й точке определяетl= 9;я выражением=

        &= nbsp;           &nbs= p;      (8.2)

Отсюда для касательноl= 1;, проходящей через точку (&#= 963;ys, 0), получаем (рис. 8.3)

        &= nbsp;  (8.3)

Это означает, чт= 086; независимо от величины = K левая точка касания всегда находится н = 72; расстоянии 2/3 предела текучести о = 90; оси абсцисс. Для касател = 00;ной, проходящей через точку (0,= W), из выражени = 03; (8.2) следует, чт = 86;

        &= nbsp;      (8.4)

Ур= 072;внение (8.4) показывает= ;, что правая точка касан = 80;я определяетl= 9;я общей длино = 81; трещины, равной 1/3 ш= ;ирины образца. Такие построения применимы к = 86; всем случая = 84; процесса образованиn= 3; трещин при плоском напряженноl= 4; состоянии, т. е. к величинам K1c, а также K1i и K1e, как показано на рис. 8.4.

Эт= 086;т метод анализа очень хорош = 86; подтверждаk= 7;тся эксперименm= 0;альными данными, что видно из рис. 8= .5. Легко видет = 00;, что величин = 99; K1i, K1e и K1c следует определять из тех результатоk= 4; испытаний, для которых = 63;c < 2/3σys и 2a = < W/3, иначе будут получены неверные значения К. Рассмотренl= 5;ые ранее две касательныk= 7; к K – кривой не имеют серьезного физическогl= 6; обоснованиn= 3;, однако они весьма поле = 79;ны при инженерных расчетах (см. [= 6]). Величины K1e и K1c, как оказываетсn= 3;, приблизитеl= 3;ьно постоянны только для ограниченнl= 6;го диапазона и = 79;менения размеров трещин. Но это как раз тот диапазо = 85; изменения длин трещин, который представляk= 7;т наибольший практическl= 0;й интерес. Коррекция н = 72; зону пластичносm= 0;и, примененнаn= 3; к длине трещины в случае пост = 86;янных значений K1c (см. [5]), на самом деле не улучшает ситуацию, а т&#= 1086;лько излишне усл = 86;жняет метод расчета.

Ги= 073;кость метода Феддерсена состоит в том, что он допускает простое представлеl= 5;ие данных эксперименm= 0;а. Простое представлеl= 5;ие значений K1 = 77; и K1с позволяет построить полную диаграмму о = 89;таточной прочности для любого размера пан = 77;ли, как показан = 86; на рис. 8.6, а. Эт&#= 1072; кривая определяетl= 9;я выражением для K1c. Касательныk= 7; к этой криво= 081; проведены о = 90; точки (0, σуs) – точка касания лежит на уровне 2/3σ<= i>ys – от точки (2a =3D <= i>W, 0), где W – ширина панели (точк= 072; касания лежит на уро= 074;не W/3). Существует определеннm= 9;й минимальныl= 1; размер панели Wmin, при котором обе точки касания совпадают. Д= 083;я панелей с меньшими размерами остаточная прочность определяетl= 9;я условием текучести истинного сечения. Следователn= 0;но, для того чтобы при испытании панели получить истинные значения K1e и K1с, эта панель должна имет = 00; определеннm= 9;й минимальныl= 1; размер. Из соотношениn= 3; следует, что левая точка касания определяетl= 9;я выражением=

        (8.5)

Ри&#= 1089;. 8.4. Метод Феддерсена [5]<= /span>

Ри&#= 1089;. 8.5. Анализ Феддерсена результатоk= 4; испытаний [8—11] (по данным ASTM)=

Ус= 083;овие совпадения двух точек касания пол = 91;чаем в виде (1/3) Wmin =3D 2a1 или, подставляя сюда уравнение (8.5),=

        &= nbsp;           &nbs= p;            &= nbsp;     (8.6)

Из этих рассуждениl= 1; вытекают требования, = 087;редъявляем&= #1099;е к испытанию на вязкость разрушения при плоском = 085;апряженном состоянии. Н= 072; самом деле, единые требования предъявляюm= 0;ся к длине трещ= 080;ны и к величине напряжения, = 072; именно:

        &= nbsp;           &nbs= p;            &= nbsp;          (8.7)

Послед= нее из этих двух требований можно удовлетворl= 0;ть, выбрав подх = 86;дящим образом отношение а<= /i>/W. Если в испытании разрушение происходит = 87;ри напряжении, меньшем 2/3 σys, то с помощью полученных = 74; нем данных можно вычислить истинное значение K1c. Если σc >2/3σys, то даже для трещин, размер которых 2a =3D W/3, панель слишком мал = 72;. Если для такого испы = 90;ания вычислить величину K, то результа = 90; окажется меньшим, чем действителn= 0;ное значение K1c (штриховая линия, проходящая через точку = A, на рис. 8.6, a). Это объясняет вид зависимостl= 0; полученных из эксперименm= 0;а значений K1c от размера панели (см. рис. 8.2). Отметьте: если бы в уравнение (8.6) было подставленl= 6; это слишком маленькое значение K1c, то было бы получено слишком маленькое значение Wmin и результат испытания мог бы ошибочно сч = 80;таться верным. Требование = 82; размеру панели закл = 02;чено в соотношениn= 3;х (8.7), и таким образом ура = 74;нение (8.6) не являетсn= 3; выборочным критерием.=

Ри&#= 1089;. 8.6. Остаточная прочность для различных размеров панелей:

1= — <= b>бо&#= 1083;ьшие значения К1c, ма&#= 1083;ые значения аys; 2= — <= b>ма&#= 1083;ые значения К1с, бо&#= 1083;ьшие значения аys

Зн= 072;я истинные значения K1c для сплавов, представлеl= 5;ных на рис. 8.2, с пом= 086;щью уравнения (8.6) можно вычислить с = 86;ответствую&#= 1097;ие минимальныk= 7; размеры пан = 77;лей. Эти минимальныk= 7; размеры равны прибл = 80;зительно 520 мм для сплава 2024 и соответствk= 7;нно 135 и 110 мм для сплава 7075. Кривые на рис. 8.2 показывают, что размер панели, равный 110 мм, для материала и = 79; сплава 7075 слиш= ;ком мал. Причина этого состоит в том, что точн&#= 1086;е определениk= 7; величины K1c представляk= 7;т собой сложную проблему, по= 089;кольку измерить критическуn= 2; длину трещи = 85;ы сложно. При приближениl= 0; к критическоl= 4;у условию разрушения скорость роста трещи = 85;ы постепенно увеличиваеm= 0;ся. Следователn= 0;но, однозначноk= 7; определениk= 7; критическоl= 1; длины трещины затруднено = 80; измерения критическоl= 1; длины носят = 089;убъективны&= #1081; характер, имея в основном ма = 83;ую точность. Поэтому величина K1c определяетl= 9;я с большей достоверноl= 9;тью, чем K1e.

Эт= 086; может показ = 72;ться до некоторо = 81; степени неожиданныl= 4;, но на самом деле для практики не имеет больш = 86;го значения. Дл= 103; неармироваl= 5;ной панели остаточную прочность следовало б = 99; определять = 89; помощью коэффициенm= 0;а K1e, поскольку объектом обнаружениn= 3; является начальная усталостнаn= 3; трещина. С техническоl= 1; точки зрени = 03; этот медленный рост трещин = 99; до размера 2a<= sub>c перед разрушениеl= 4; несуществеl= 5;; имеет значе = 85;ие только величина нагрузки, вызывающей разрушение при данном размере усталостноl= 1; трещины.

Из приведенноk= 5;о ранее анализа следует сде = 83;ать заключение, что материалы с высокой вязкостью могут быть более чувствителn= 0;ны к образованиn= 2; трещин, чем материалы с = 084;алой вязкостью, а именно в случае, когд= 072; ширина панелей меньше, чем W<= sub>min. Это отражен = 86; на рис. 8.6, б. Материал с пределом текучести в точке B обладает большей вязкостью, чем материа = 83; с пределом текучести в точке С, следователn= 0;но, в больших панелях первый мате = 88;иал обладает большим сопротивлеl= 5;ием росту трещины. Однако для панелей, размер кото = 88;ых меньше или равен W6, этот материал обладает меньшим сопротивлеl= 5;ием росту трещины, пос= 082;ольку остаточная прочность его определ = 03;ется текучестью истинного сечения (спл= 086;шная линия B — W6 &= #1083;ежит ниже штриховой линии C =3D W6). Это хорошо известный эффект (см. [7]); его подтвер = 78;дает пересечениk= 7; K – кривых на рис. 8.2, полученных при испытании сплавов 2024 и 7075. Следователn= 0;но, в узких панелях или конструкциn= 3;х (например, стрингерах) лучше приме = 85;ять материалы с низкой вязкостью, чем материа = 83;ы с высокой вязкостью. Однако посл = 77;дние могут обладать более низкими скоростями распростраl= 5;ения трещин и тог= 076;а применение их окажется все-таки предпочтитk= 7;льнее. Величины K1c и K1e, как было показано в гл. IV, зависят от толщины о= 073;разца. Недостаточl= 5;о представитn= 0; единственнm= 9;й набор значений K1i= , K1e и K1c для образцов определеннl= 6;й толщины. Предпочтитk= 7;льнее было бы прив= 077;сти график, подобный тому, что показан на рис. 8.7. Более толстые пластины обладают ме = 85;ьшими значениями K= 1e и K1c, и при больших толщинах соответствm= 1;ющие им две кривы= 077; сливаются (там, где K1c уменьшаетсn= 3; до вязкости разрушения K= Ic, соответствm= 1;ющей плоской деформации).

Ри&#= 1089;. 8.7. Влияние толщины на ударную вязкость пр = 80; плоском напряженноl= 4; состоянии:=

а — сп&#= 1083;ав Al – = Cu – Mg [9]; б<= /i> — <= b>сп&#= 1083;ав Al – = Zn – Mg [4] (п = 86; данным ASTM)            =             &nb= sp;            =             &nb= sp;        

        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;

 

 

§ 8.3. Концепция R - кривой

Дл= 103; анализа данных о плоском напряженноl= 4; состоянии было предложено много други = 93; методов. Некоторые и = 79; них являютс = 03; инженернымl= 0; концепциямl= 0;, например анализ проч = 85;ости детали с вырезом Кун = 72; и Фигга [12], ана = 83;из прочности детали с трещиной, развитый Куном [13], концепция эффективноl= 1; ширины (см. гл. XVI), предложеннk= 2;я Криклоу [14] и Кl= 8;истенсеном [15]. Наиболее предпочтитk= 7;лен инженерный метод Феддерсена, поскольку и = 89;пользовани&#= 1077; коэффициенm= 0;а К дает непосредстk= 4;енную связь с концепциямl= 0; механики разрушения = 80; поскольку н = 80; один из других методов не позволяет получать лу = 95;шие результаты (см. [16, 17]). Наиболее существеннm= 9;м недостаткоl= 4; всех инженерных методов является то, что в них не учитываетсn= 3; процесс медленного стабильногl= 6; роста трещины, являющегосn= 3; существеннl= 6;й частью процесса разрушения при плоском напряженноl= 4; состоянии.=

Ма= 082; Клинток [18] рассмотрел задачу о медленном стабильном росте трещины на основе анализа плоского напряженноk= 5;о состояния. Этот подход ограничен рассмотренl= 0;ем трещины тип = 72; III. В случае неупрочняюm= 7;ихся материалов напряжение = 74; пластическl= 6;й зоне при плоском напряженноl= 4; состоянии равно пределу текучести. Поскольку н = 72;пряжение постоянно, процесс разрушения не может зависеть от напряжения. Мак Клинток предполагаk= 7;т, что процесс разрушения = 86;пределяетс&#= 1103; величиной деформаций. Распростраl= 5;ение трещины происходит, когда дефор = 84;ация на некоторо = 84; расстоянии c= от вершины трещины превышает критическоk= 7; значение.=

Ма= 082; Клинток получил выражение для пластич = 77;ской деформации перед трещиной типа III. Если эта деформация превышает критическоk= 7; значение, то трещина продвигаетl= 9;я на da. В результате величина деформации увеличиваеm= 0;ся на (∂r/∂a)∂σ. Для того чтобы увеличить деформацию на расстоян = 80;и р от новой вершины трещины до критическоk= 5;о значения, этого увеличения недостаточl= 5;о. Поэтому процесс роста трещины стабилен; да= 083;ьнейший рост трещин = 99; может произойти только за счет увеличения напряжения, которое приведет к дополнителn= 0;ному увеличению деформации на величину (∂r/∂a)∂σ. Расчеты, проведенныk= 7; по этому критерию, до= 074;ольно хорошо совпали с результатаl= 4;и испытаний н = 72; распростраl= 5;ение трещин типа III= (см. [18]).

Др= 091;гим методом анализа процесса разрушения сколом является концепция, основанная на балансе энергии. Энергетичеl= 9;кая концепция может объяснить некоторые типичные явления, которые будут рассмотренm= 9; в последних параграфах главы. Согласно энергетичеl= 9;кой концепции (см. гл. V), во время медленного стабильногl= 6; роста трещины существует непрерывныl= 1; баланс межд = 91; выделяемой = 80; потребляемl= 6;й энергией. Если этот баланс нарушится, т= 086; либо прекра = 90;ится рост трещин = 99;, либо этот процесс роста стане = 90; неустойчивm= 9;м. Следователn= 0;но, в процессе медленного стабильногl= 6; увеличения длины трещины интенсивноl= 9;ть выделения энергии будет равна сопротивлеl= 5;ию роста трещины:

        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;   (8.8)

Ве= 083;ичину G во время роста трещины можно измерить, и, к&= #1072;к оказываетсn= 3;, для поддержаниn= 3; процесса ме = 76;ленного роста трещины необходимо постоянное увеличение G= . Совершенно очевидно, чт= 086; с продвижениk= 7;м трещины потреблениk= 7; энергии возрастает. = 057;огласно уравнению (8.8), мгновенные значения G во время роста трещины покажут, как R зависит от размера трещины. Оказываетсn= 3;, величина R в процессе медленного роста трещины уве = 83;ичивается (рис. 8.8). На рис. 8.8 также показаны ли = 85;ии, отражающие зависимостn= 0; величины G от размера трещины и величины приложенноk= 5;о напряжения.

Ри&#= 1089;. 8.8. Энергетичеl= 9;кий подход в задаче о пло= 089;ком напряженноl= 4; состоянии<= span style=3D'font-size:8.5pt;font-family:Arial;color:#330066'>

Во время медленного роста трещины вел = 80;чины G и R в соответствl= 0;и с уравнение = 84; (8.8) изменяются= ; вдоль линии ABC. Посл= ;е увеличения длины трещины LM размер трещины ста = 83; равным 2ac. &#= 1058;очка C на рис. 8.8 является точкой нестабильнl= 6;сти, предшествуn= 2;щей разрушению, потому что начиная с этого момента вел = 80;чина G изменяетс= 103; вдоль линии = CD и становитс = 03; больше, чем R. Условие разрушения определяетl= 9;я точкой каса = 85;ия этих кривых:

        &= nbsp;           &nbs= p;            &= nbsp;  (8.9)

Ур= 072;внения (8.9) являются полезным критерием разрушения, = 077;сли кроме соотношениn= 3; G=3Dps2a/E известно аналитичесl= 2;ое выражение для R. Иначе эти уравнения использоваm= 0;ь для количес = 90;венных оценок нельзя. Радж= 091; [19] и Внук [20] пред= приняли попытку вывести такое выраж = 77;ние на основе те= 086;рии пластичносm= 0;и, вычисляя интенсивноl= 9;ть потреблениn= 3; энергии пластическl= 0;х деформаций = 74; пластическl= 6;й зоне перед трещиной.=

Кр= 072;ффтом и др. [21] было высказано предположеl= 5;ие о том, что величина R является только функцией Da и не зависит от a0. В этом случа= 077; R – кривая инвариантнk= 2; и имеет одинаковый = 74;ид для любой начальной длины трещины. Это предположеl= 5;ие было использоваl= 5;о автором [1, 22] дл= 103; вывода полуэмпириm= 5;еского решения ура = 74;нений (8.9). Во многих испытаниях критическаn= 3; длина трещины пропорционk= 2;льна начальной длине трещины, т. е.

        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;          (8.10)

Эт= 086; означает, чт= 086; между отрезками KM и LM (рис. 8.8) существует определеннl= 6;е соотношениk= 7;, которое одинаково для всех касательныm= 3;. В этом случа= 077; уравнение (8.8) l= 7;озволяет получить функцию R в явном виде. Рассмотрим рис. 8.9 (имеющиl= 1; тот же вид, что и рис. 8.8), на котором оси для удобств = 72; обозначены через x и у. Касательнаn= 3; к точке (xi, yi) задана соотношениk= 7;м

        &= nbsp;           &nbs= p;            &= nbsp; (8.11)

Ри&#= 1089;. 8.9. Вывод уравнения R – <= b>кр&#= 1080;вой

Эт= 080;м показано, чт= 086; при у =3D 0 величина x =3D x<= /i>0, следователn= 0;но,

        &= nbsp;           &nbs= p;    (8.12)

Из уравнения (8.10) следует, что

        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;           (8.13= )

Об= 098;единяя уравнения (8.12) = 80; (8.13), получаем=

        &= nbsp;           &nbs= p;            &= nbsp;   (8.14)

Из уравнения (8.10) следует, что это соотношениk= 7; должно выполнятьсn= 3; для любой точки = i; таким образом, уравнение (8.14) есть дифференциk= 2;льное уравнение кривой, изображеннl= 6;й на рис. 8.9. Его решение имеет вид=

        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;             = (8.15)

ил= 080; в обозначениn= 3;х рис. 8.8

        &= nbsp;           &nbs= p;            &= nbsp;           (8= .16)

гд= 077; β – констант = 72;. Далее известно, чт= 086;

        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;             = (8.17)

Ур= 072;внения (8.16) и (8.17) позволяют численно разрешить критерий разрушения, определяемm= 9;й системой уравнений (8.9). Результатоl= 4; этого решен = 80;я являются следующие соотношениn= 3;:

        &= nbsp;    (8.18)

Вт= 086;рое уравнение системы (8.18) вытекает непосредстk= 4;енно из первого, если подставить = 74; него соотношениk= 7; ac =3D αa0; оба уравнения получены по = 76;становкой уравнений (8.16) = 80; (8.17) в систему двух уравне = 85;ий (8.9). Таким образом, уравнения (8.18) показывают, что на самом деле получе = 85; результат ac =3D αa0 и что уравнения (8.18) являются отражением предположеl= 5;ия о том, что ac = =3D αa0.

Дл= 103; α =3D 1 эти соотнl= 6;шения приводятся = 82; виду σca1/2 =3D <= i>c, которое имеет тот же вид, что и в концепции, с= 074;язанной с понятием коэффициенm= 0;а K. Для случая σ =3D 1 сопротивлеl= 5;ие росту трещи = 85;ы R =3D β (равняется константе G1c) и процесс медленного роста трещины не возникает [уравнение (8.10)], т. е. α =3D 1 для хрупких материалов. Уравнения (8.18) = 84;ожно обобщить (см. [= 23]) на случай панели коне = 95;ных размеров.=

Далее будет отмечено, чт= 086; эксперименm= 0;ально R – кривую можно определить двумя различными путями. Прежде всег = 86; вид R – кривой можн = 86; определить = 74; одном-единс = 90;венном испытании, з= 085;ая последоватk= 7;льные значения величины G, которые она принимает в = 86; время медленного роста трещины, и используя соотношениk= 7; R =3D G =3D ps2a/E. Обычно результаты испытания записывают = 85;а ленту, с помощью которой кривую медл = 77;нного роста можно определить довольно то = 95;но, R – кривую можно также получить, определяя т = 86;чки нестабильнl= 6;сти в ряде испытаний. Совокупносm= 0;ь этих точек нестабильнl= 6;сти задает вид R – кривой через соотношениk= 7;

Пр= 086;верить пригодностn= 0; уравнений (8.10), (8.= 16) и (8.18) можно, анализируя данные испытаний. Один и тот же набор данны = 93; испытаний должен удовлетворn= 3;ть трем уравнениям для одного и того же значения α. Н= 072; рис. 8.10 и 8.11 представлеl= 5;ы четыре набора данн = 99;х испытаний для четырех различных толщин листов, выполненныm= 3; из сплава Al – Zn = 211; Mg (см. [24]). Данные для σc и R нанесены в логарифмичk= 7;ском масштабе; пр= 080; этом получаются прямые лини = 80;, наклон кото = 88;ых определяетl= 9;я коэффициенm= 0;ом α. R – кривые на рис. 8.11 были определены как геометр = 80;ческие места точек нестабильнl= 6;сти (второй из рассмотренl= 5;ых ранее методов). Малый разброс значений α показывает, что подход, связанный с понятием R – кривой, непригоден. Использоваl= 5;ие этой концепции определяетl= 9;я главным образом тем фактом, что с ее помощью м= 086;жно объяснить некоторые особенностl= 0; процесса разрушения при плоском напряженноl= 4; состоянии, как станет ясно в последующиm= 3; параграфах. Однако для инженерных приложений метод Федде = 88;сена является более удобным и более прямы = 84;.

Ри&#= 1089;. 8.10. Остаточная прочность алюминиевоk= 5;о сплава [24]:

а <= /i>— за&#= 1074;исимость σc от 2a0 в логарифмичk= 7;ском масштабе по обеим осям;

б — <= b>со&#= 1086;тношение между критическиl= 4; и начальным размерами трещины

Ри&#= 1089;. 8.11. R – кривые для алюминиевоk= 5;о сплава 7075-Т6

За последнее время интерес к R – кривым снов = 72; возрос. Исследоватn= 0; R – кривые и установить стандартныk= 7; методы испы = 90;аний на определениk= 7; их вида — задача, стоя= 097;ая перед специальныl= 4; комитетом ASTM. h= 2; последние годы появилось несколько публикаций (например, [25]), посвященныm= 3; этому предмету. Результаты, = 087;олученные Хейером и Ма= 082; Кэйбом [26, 27], указывают н = 72; то, что предпочтитk= 7;льнее использоваm= 0;ь образцы в виде клиновидноl= 1; консольной = 73;алки. Поскольку из-за уменьшения G= нестабильнl= 6;сть не наступае = 90;, можно опред = 77;лить R –кривую для гораздо больших дли = 85; трещин. Тем не менее значение R – кривой до конца еще не ясно.

Ги= 087;отеза Краффта и др. [= 21] о том, что R – кривая инвариантнk= 2;, т. е. не зависит от начального размера трещины, пок= 072; еще не получ= 080;ла общего признания. Некоторые эксперименm= 0;альные данные подтверждаn= 2;т полезность этой гипотезы, и в ее пользу мо= 078;но привести некоторые аргументы (см. [21, 28]). Если процесс медленного роста трещины про = 80;сходит при постоянном уровне значений K, то зона пластичносm= 0;и в начале процесса ро = 89;та трещины всегда одинакова, поскольку Сначала для продвижениn= 3; трещины на определеннl= 6;е расстояние требуется одна и та же э&= #1085;ергия пластическl= 0;х деформаций, т. е. начальная часть R – кривой инвариантнk= 2;. Однако это все еще стро= 075;о не доказано.

До сих пор не существует аналитичесl= 2;ого представлеl= 5;ия формы R – кривой. Показано, чт= 086; она возрастает, но это лишь результат предположеl= 5;ия о ее инвариа= 085;тности. Установленl= 6;, что действителn= 0;ная работа разрушения пренебрежиl= 4;о мала по сравнению с энергией, заключенноl= 1; в зоне пластичносm= 0;и. Действителn= 0;ная работа разрушения совершаетсn= 3; за счет энергии пластическl= 0;х деформаций, содержащейl= 9;я в чрезвычайнl= 6; малом объем = 77; материала, непосредстk= 4;енно перед фронтом трещины. Это работа, необходимаn= 3; для образованиn= 3; и слияния микропустоm= 0;. Процессы образованиn= 3; и слияния микропустоm= 0; определяютl= 9;я местным критерием: для образованиn= 3; пустот долж = 85;ы возникнуть достаточно большие нап = 88;яжения и деформаци = 80;. Однако в момент выполнения этого местн = 86;го критерия образуется уже большая = 079;она пластичносm= 0;и. Энергия это = 81; зоны пласти = 95;ности гораздо больше действителn= 0;ной работы разрушения. Поэтому последней можно пренебречь; таким образом, сопротивлеl= 5;ие росту трещи = 85;ы определяетl= 9;я энергией, содержащейl= 9;я в зоне пластичносm= 0;и. Следователn= 0;но, если бы трещина расширяласn= 0; при нулевом напряжении, то для формированl= 0;я зоны пластичносm= 0;и не потребовалl= 6;сь бы никакой энергии. Дру= 075;ими словами, R – кривая должна начинаться = 74; нулевой точке. Расширение трещины не может произ = 86;йти, пока напряжения = 80; деформации при вершине трещины не достигли критическоl= 1; величины. Если такое критическоk= 7; условие вып = 86;лнено, то к этому моменту уже образовалаl= 9;ь большая зон = 72; пластичносm= 0;и и величина R существеннl= 6; отлична от нуля. В этих условиях возможностn= 0; распростраl= 5;ения трещины определяетl= 9;я наличием достаточноl= 1; энергии для = 092;ормировани&= #1103; новой зоны пластичносm= 0;и вокруг продвигающk= 7;йся трещины (см. гл. V).    =             &nb= sp;            =             &nb= sp;            =             &nb= sp;            =             &nb= sp;            =             &nb= sp;            =             &nb= sp;            =             &nb= sp;       

        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;

 

 

§ 8.4. Влияние толщины

Ка= 082; уже было показано на рис. 8.7 и в гл. IV, значения величин К1l= 9; и К1e зависят от толщины. При увеличении толщины пластины К1с постепенно уменьшаетсn= 3; до КIс. Это явление широко освещено в литературе, однако систематичk= 7;ских данных пока немного.

Вл= 080;яние толщины связано с непрерывныl= 4; переходом о = 90; плоской деформации = 82; плоскому на = 87;ряженному состоянию. Когда в толстых пан = 77;лях приповерхнl= 6;стные области, в которых преобладаеm= 0; плоское напряженноk= 7; состояние, становятся сравнительl= 5;о малыми, их влиянием мо = 78;но пренебречь = 80; процесс разрушения становится не зависимы = 84; от толщины. В тонких пане = 83;ях область плоского напряженноk= 5;о состояния н = 77; мала по сравнению с областью пл = 86;ской деформации, = 080; с увеличениеl= 4; отношения размеров областей плоского напряженноk= 5;о состояния и плоской деформации номинальноk= 7; напряжение разрушения возрастает. = 057; этим отноше = 85;ием связан переход от плоской поверхностl= 0; разрушения = 82; поверхностl= 0;, повернутой на 45° (см. ри = 89;. 4.17).

Сл= 077;дует отметить, чт= 086; влияние предела текучести н = 72; величину вязкости в переходной области гораздо больше, чем п&#= 1088;и плоском напряженноl= 4; состоянии или плоской деформации, как показан = 86; на рис. 8.12. Если &#= 1073;ы предел текучести н = 77; оказывал никакого вл = 80;яния на максимальнl= 6;е значение K1c= max (плоское напряженноk= 7; состояние) и на КIc, то величина ег = 86; все-таки влияла бы на процесс разрушения = 74; переходной области. Про= 094;есс разрушения зависит от отношения количества материала в зоне плоского напряженноk= 5;о состояния к количеству материала в = 079;оне плоской деф = 86;рмации. В свою очередь это отношение з = 72;висит от размера зоны пластичносm= 0;и, а поэтому — от предела текучести. Чем больше предел текучести, тем меньше зона пластичносm= 0;и; в зоне плоской деформации находится б = 86;льшее количество материала и вязкость ст = 72;новится меньше (рис. 8.12, а). В действителn= 0;ности K1cmax и КIc также зависят от предела текучести (рис. 8.12, б), что приводит к увеличению влияния предела текучести н = 72; процесс разрушения = 74; переходной области.

Ри&#= 1089;. 8.12. Влияние предела текучести н = 72; вязкость:

а — = ги&#= 1087;отетически= й случай; б — <= b>ре&#= 1072;льный случай

Не= 089;мотря на то что имеется определеннl= 6;е качественнl= 6;е понимание эффекта влияния тол = 97;ины, общепринятl= 6;й количествеl= 5;ной модели до си= 093; пор не сущес= 090;вует. Далее будут введены и рассмотренm= 9; несколько моделей. Бламмом [29] была выдвинута количествеl= 5;ная модель, основанная на двух предположеl= 5;иях:

1.      =   Размер гу= 073; сдвига при разрушении не зависит о= 090; толщины, т. е. переход от плоской деформации во внутренних областях к плоскому напряженноl= 4;у состоянию п = 88;и поверхностl= 0; всегда происходит = 74; одном и том же объеме материала. Это означае = 90;, что размер губ сдвига равен половине толщины, на которой развиваетсn= 3; плоская деформация.

2.      =   Явление плоского разрушения является поверхностl= 5;ым, в то время как образованиk= 7; губ сдвига п= 086; своей природе объемно. Предполагаk= 7;тся, что энергия плоского разрушения пропорционk= 2;льна размеру плоских частей пове = 88;хности разрушения (= В–В0). Предполагаk= 7;тся также, что эн&#= 1077;ргия разрушения = 89; образованиk= 7;м губ сдвига пропорционk= 2;льна (В/2)2 до В0 и равна (В0/2)2 = 087;осле В0, где В0 — максимальнk= 2;я толщина, при которой может полно = 89;тью развиться плоское напряженноk= 7; состояние.=

В этом случае энергия, необходимаn= 3; для разруше = 85;ия, равна:

         = (8.19)

предпо= лагается, что k и q – константы материала. Поскольку критическаn= 3; интенсивноl= 9;ть выделения энергии рав = 85;а G1c =3D dW/Bda, то отсюда след = 91;ет, что

(8.20)

Получа= ющаяся в результат = 77; зависимостn= 0; от толщины показана на рис. 8.13. Значения k и <= /span>q определяют из эксперименm= 0;а.

Оч= 077;нь похожий результат получается из модели, предложеннl= 6;й Броеком и Влигером [24], кl= 6;торая является обобщением модели, разработанl= 5;ой Ишервудом и Вильямсом [30] для плоског = 86; напряженноk= 5;о состояния. Несколько упрощающих предположеl= 5;ий относительl= 5;о зоны пластичносm= 0;и приводят к следующему соотношениn= 2;:

        &= nbsp;           &nbs= p;            &= nbsp;            (8.21)

где ef – истинная деформация, при которой происходит разрушение материала, а величина В0 имеет то же значение, чт= 086; и в модели Бламма. Согл= 072;сно уравнению (8.21), для больших значений В = 074;еличина K1c постепенно приближаетl= 9;я к KIc. В случае, когд= 072; толщина равна велич = 80;не определя= емой условиями ASTM, измеренное значение KIc еще не равно истинному значению KIc. Соответств&= #1091;ющая разность зависит от свойств материала.=

Ри&#= 1089;. 8. 13. Модель Бламма, учитывающаn= 3; влияние тол = 97;ины [29]

В г&#= 1083;. IV отмечено, что плоское напряженноk= 7; состояние может полностью развиться, если размер зоны пластичносm= 0;и имеет тот же порядок, что и толщина пластины. Эт= 086; означает, чт= 086; В0 должно быть равно размеру зон = 99; пластичносm= 0;и при плоской деформации. Этот размер, в свою очередь, равен удвоенной коррекции н = 72; зону пластичносm= 0;и. Следователn= 0;но,

        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;  (8.22)

Ес= 083;и толщина B достаточна для того, чтобы удовлетворl= 0;ть условию ASTM, то из уравнени = 03; (8.22) следует, чт= 086; В0/В =3D 0,425. Для материала с параметрамl= 0; ef =3D 0,3, σys =3D 50 кгс/мм2 и Е =3D= 7000 кгс/мм2 из уравнения (8.21) получаем, чт= 086; K1c/KIc =3D 1,038. Величина вязкости разрушения, полученная = 74; результате измерений в обоснованнl= 6;м испытании при плоской деформации, превышала б = 99; истинное значение KIc примерно на 4 %. Для материалов = 89; большим значением σys эта разност = 00; была бы еще меньше. Для стали с параметрамl= 0; ef =3D 0,1, σys =3D 200 кгс/мм2 и Е =3D= 21000 кгс/мм2 измk= 7;ренное значение вязкости превышало б = 99; истинное значение KIc всего лишь н= 072; 1 %.

Ур= 072;внение (8.21) эквиваленm= 0;но уравнениям (8.2= 0), полученным из модели Бламма. Отметим, что во втором из уравнений (8.20) величина Полагая в этом уравнении B0/B>0, получаем, чт= 086; Подстано= вка этого равенства в уравнения (8.20) = 89; учетом соотношениn= 3; приводит к следующем = 91; соотношениn= 2;:

        &= nbsp;           &nbs= p;         (8.23)=

которо= е эквивалентl= 5;о уравнению (8.21). Это уравнен = 80;е говорит о том, что, зная коэффициенm= 0; KIc, можно рассчитать процесс разрушения при плоском напряженноl= 4; состоянии и = 074; переходном случае.

Ан= 076;ерсон [31] провел анализ имеющихся данных, касающихся влияния толщины на процесс раз = 88;ушения. Он пришел к выводу, что для этих дан= 085;ых линейное уменьшение величины K1c с увеличениеl= 4; толщины является приемлемой аппроксимаm= 4;ией (рис. 8.14). Зная два «основн = 99;х» значения вязкости K1c= max и KIc, можно построить диаграмму вязкости разрушения, изображеннm= 1;ю на рис. 8.14. Точк= 091; A можно получить из = 091;словия а точка C получается из условия получения плоской деф = 86;рмации ASTM:

В работе Си и Хатранфта [32] приведено другое объя = 89;нение эффекта влияния толщины. Авт= 086;рами было отмечено, чт= 086; количество выделяемой энергии, приходящейl= 9;я на единицу длины
фронта трещины, является функцией толщины, а не константой. Энергия, выделяющаяl= 9;я при распрос = 90;ранении трещины на единицу длины, равна где символом обозначе= на средняя интенсивноl= 9;ть выделения энергии. С увеличениеl= 4; толщины величина увеличив= ается.

Ри&#= 1089;. 8.14. Влияние толщины по Андерсону [31]=

Вм= 077;сто того чтобы использоваm= 0;ь можно воспользовk= 2;ться величиной средней интенсивноl= 9;ти напряжений По версии Си и Хатранфта, интенсивноl= 9;ть напряжений вдоль фронт = 72; трещины меняется. Пр= 080; одном и том же заданном напряжении = 80;нтенсивнос&#= 1090;ь напряжении при плоском напряженноl= 4; состоянии меньше, чем при плоской деформации; т. е. чем больше част = 00; толщины, кот= 086;рая находится в плоском напряженноl= 4; состоянии, тем меньше средняя интенсивноl= 9;ть напряжений Отсюда следует, что в смешанном напряженно- = 76;еформирова&#= 1085;ном состоянии средний коэ = 92;фициент интенсивноl= 9;ти напряжений меньше, чем «наблюдаемm= 9;й» коэффициенm= 0; интенсивноl= 9;ти напряжений, определяемm= 9;й выражением В случае плоской деформации Можно предположиm= 0;ь, что разрушение происходит всегда, когд= 072; средняя интенсивноl= 9;ть напряжений равна KIc. Это означае = 90;, что «истинная» вязкость ра = 79;рушения предполагаk= 7;тся не зависяще = 81; от толщины и что эта «истинная» вязкость есть KIc. В этом случае наблюдаемаn= 3; зависимостn= 0; вязкости от толщины объясняетсn= 3; тем фактом, что величин = 72; K1c определяетl= 9;я равенством а по Си и Хатранфту, эта величин = 72; есть наблюд = 72;емое, а не действителn= 0;ное значение интенсивноl= 9;ти напряжений. Тогда критерий разрушения имеет вид Наблюдае= мое значение вязкости определяетl= 9;я по формуле=

        &= nbsp;           &nbs= p;            &= nbsp;        (8.24)

Та= 082; как есть функция толщины, то уравнение (8.24) показывает, как K1c зависит от толщины. Численные значения можно получить из кривых, представлеl= 5;ных Си и Хатранфтом.

Ср= 072;внение данных испытаний с различными = 84;оделями, учитывающиl= 4;и влияние толщины, выполнено н = 72; рис. 8.15 и 8.16. Данные испы = 90;аний не согласуютсn= 3; с этими моделями, если соотве = 90;ствующие кривые получаются выбором соответствm= 1;ющих значений σys и ef. Однако если уравнения (8.21) = 80; (8.23) обобщить и привести к виду

        &= nbsp;           &nbs= p;            &= nbsp;    (8.25)

то, подбирая коэффициенm= 0; q, можно получить лучшее согласие. Этот коэффи = 94;иент зависит от того, что принято за размер зоны пластичносm= 0;и, и от критери= 103; образованиn= 3; плоского напряженноk= 5;о состояния. Так как эти предположеl= 5;ия более или менее произ = 74;ольны, то нельзя ничего возразить против их подгонки, чт= 086; и было сделано на рис. 8.15 и 8.16, а.=

На рис. 8.16, б приведено сравнение тех же самых данных испы = 90;аний с моделью Си и Хатранфта. Величина является функцией не только толщины В, но и размера трещины а. Поэтому вдоль оси абсцисс отложена величина В/= а. Кроме того, зависит от параметр = 72; q, который, как видно из рис. 8= .16, б, может принимать различные значения. Рассматривk= 2;я эксперименm= 0;альные данные для о= 076;ной толщины (небольшие изменения K1c), можно заключить, что либо зависимостn= 0; от размера трещины, вычисленнаn= 3; по модели Си и Хатранфта, слишком сильная, либ= 086; предположеl= 5;ие о том, что «истинная» вязкость материала н = 77; зависит от напряженно- = 76;еформирова&#= 1085;ного состояния, неверно.

Мы пришли к заключению, что ни одна из моделей н= 077; дает удовлетворl= 0;тельного согласия с данными испытаний. В настоящее время для ин= 078;енерной оценки эффекта влияния толщины наилучшим, возможно, является приближеннm= 9;й метод Андер = 89;она.

Ри&#= 1089;. 8.15. Модели Бламма, а также Броек = 72; и Влигера

Ка= 082; влияет толщина на вид R – кривой, до сих пор как следует не установленl= 6;, однако этот вопрос стои = 90; рассмотретn= 0;. Если предположиm= 0;ь, что уравнение (8.16) достаточно хорошо описывает вид R – кривой, то возникает вопрос, буде= 090; ли толщина влиять на коэффициенm= 0; β или α, или на обе эти величины сразу. Снача= 083;а рассмотрим случай, когд= 072; толщина влияет толь = 82;о на α. Этот случай изображен н = 72; рис. 8.17. Предпо = 83;ожим, что в случае плоской деформации величина α уменьшаетсn= 3; до единицы. Это имело бы следующие следствия:=

Дл= 103; плоской деформации ^= 5; =3D 1 означает, что при β =3D GIc значение R =3D β. Следователn= 0;но, R – кривая становится горизонталn= 0;ной линией, проходящей через GIc. В этом случае немедленноk= 7; разрушение произошло б = 99; в самом начале процесса роста трещи = 85;ы. Идеальный процесс раз = 88;ушения при плоской деформации можно было б= 099; определить из диаграмм = 99; «нагрузка — РТ».

Пр= 080; малых значениях α (например, α =3D 1,1, толстая пла = 89;тина, но не идеально плоская деформация) расширение трещины началось бы при GIc, при этом процес = 89; медленного роста трещины не возник бы: G – линия прошл = 72; бы над R – кривой (точк= 072; С5 на рис. 8.17). Диаграмма «нагрузка — РТ» была бы т&#= 1086;й же самой, что и в случае α =3D 1.

Пр= 080; промежуточl= 5;ых значениях α произошел б = 99; хлопок (AB), после чего последовалl= 6; бы небольшо = 77; возрастаниk= 7; нагрузки до соответствm= 1;ющей точки C (при котором произошло б = 99; разрушение).

Пр= 080; больших значениях α для возникновеl= 5;ия нестабильнl= 6;сти, предшествуn= 2;щей разрушению, потребовалl= 6;сь бы большее возрастаниk= 7; нагрузки, ка= 082; показано на соответствm= 1;ющих диаграммах «нагрузка — РТ». Это следует из того факта, что точка нестабильнl= 6;сти C поднимаетсn= 3; (выше GIc).

Ув= 077;личение α означает, что происходит более стабильный рост трещин = 99; (ac =3D αa0), что находит сво = 77; отражение в перемещениl= 0; точек касания C вправо.

Ри&#= 1089;. 8.16. Сравнение моделей, учитывающиm= 3; влияние толщины:

a= — <= b>мо&#= 1076;ель Андерсона [31]; &#= 1073; — <= b>мо&#= 1076;ель Си и Хатранфта [32]=

(да&= #1085;ные взяты из различных источников; для всех мат= 077;риалов у= ys<= /b> = =3D 50 кгс/мм2)

Ри&#= 1089;. 8.17. R – кривые для случая, когда увеличению толщины соответствm= 1;ет уменьшение ^= 5;

С другой стороны, влияние толщины мож = 85;о также объяснить изменением ^= 6;, считая α величиной, н= 077; зависящей о = 90; толщины. Это= 090; случай отображен н = 72; рис. 8.18. Следуе = 90; сделать пре = 76;положение о том, что критерий роста трещи = 85;ы не зависит о= 090; энергии, заключенноl= 1; в зоне пластичносm= 0;и и что он задан точко = 81; A. Эта модель имеет следующие следствия:=

Ре= 079;кое начальное возрастаниk= 7; R – кривых для &#= 946;3 и β2 имело бы своим следствием процесс разрушения без хлопка, как показан = 86; на соответс = 90;вующей диаграмме «нагрузка — РТ».

Ум= 077;ньшение β привело бы = 082; появлению хлопка (β1, β= 4). Большие хлопки происходилl= 0; бы при меньш= 080;х значениях β. Обратите внимание, например, на большой хлопок от A к = B4 для β4 и сравните ег = 86; с хлопком от А к В3 для β1.

Пр= 080; малых значениях β = 74; начало процесса ро = 89;та трещины произошло б = 99; немедленноk= 7; разрушение: линия ОА пр= 086;ходит выше точки С= 5. Соответствm= 1;ющая диаграмма «нагрузка — = 056;Т» была бы идеальной для случая плоской деф = 86;рмации.

За счет подъем = 72; точек C большие значения β приводят к большему по = 76;ъему диаграмм «нагрузка — РТ». Все точки C лежат на одной верти = 82;альной линии: значение α н = 77; меняется. Сл= 077;довательно, медленный рост трещин = 99; всегда происходит на одно и то же расстояние (хотя он и происходит при меньшем напряжении), пока при малом значении β этот процес = 89; медленного роста трещины не исчезает совсем (C5 л= 077;жит ниже линии OA)= .

От= 099;скать физические аргументы для решения вопроса о том, влияет ли толщина н= 072; α или на β, пока не представляk= 7;тся возможным. Эксперименm= 0;ы (см. [24]) показал= 080; сравнительl= 5;о высокую плотность значений α (см. рис. 8.10) и уменьшение ^= 6;. Прежде чем станет возможным количествеl= 5;ное определениk= 7; зависимостl= 0; R – кривой от толщины, необходимо проделать б = 86;льшую работу.

Кр= 086;ме теоретичесl= 2;ого подхода существуют также эксперименm= 0;альные методы определениn= 3; R – кривых, число которых пок = 72; невелико. Измерения R, проведенныk= 7; на основе определениn= 3; интенсивноl= 9;ти выделения энергии, в испытаниях = 89; медленным ростом трещины можно дополнить более прямы = 84; методом, который заключаетсn= 3; в установленl= 0;и количества энергии, рас= 093;одуемой на образованиk= 7; пластическl= 0;х деформаций посредствоl= 4; измерения этих деформаций. = 053;екоторая предваритеl= 3;ьная работа в это= 084; направлениl= 0; была выполнена Руком и Брэдшоу [33], которые получили R – кривую, подобную те = 84;, что были определены = 76;ругими методами.=

Ри&#= 1089;. 8.18. R – кривые для случая, когда увеличению толщины соответствm= 1;ют

постоя= нное значение α<= span style=3D'font-size:8.5pt;font-family:Arial;color:#330066'> и уменьшение ^= 6;            =             &nb= sp;            =             &nb= sp;            =             &nb= sp;            =             &nb= sp;            =          

        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;

 

 

§ 8.5. Испытание при плоском напряженноl= 4; состоянии<= /span>

Дл= 103; испытаний при плоском напряженноl= 4; состоянии необходимы большие образцы. До сих пор для таких испытаний н = 77; были предложены стандартныk= 7; образцы. Совершенно очевидно, чт= 086; образцы, работающие на изгиб, и компактные образцы на растяжение для тонких листов непригодны. Большинствl= 6; исследоватk= 7;лей используют панели с центральноl= 1; трещиной. Пример такого образца представлеl= 5; на рис. 8.19. Для того чтобы иметь запис = 00; медленного роста трещины во время каждо = 75;о испытания, обычно используют киносъемку. Если испытания предназначk= 7;ны для получен = 80;я полезных значений К1c или К1e, то в них должны быть выполнены выборочные = 82;ритерии 2a < W/3 и σс < (2/3) σys.

Об= 088;азцы для испытаний при плоском напряженноl= 4; состоянии в противополl= 6;жность образцам дл = 03; испытаний при плоской деформации не обязательнl= 6; должны всег = 76;а иметь усталостнуn= 2; трещину. Когда вязко = 89;ть достаточно велика, для того чтобы п= 088;и медленном росте трещина продвигалаl= 9;ь на значительнl= 6;е расстояние, усталостнуn= 2; трещину можно заменить острым пропилом. Пропил незначителn= 0;но увеличит напряжение = 74; начале проц = 77;сса роста трещины, но с началом этого проце = 89;са пропил превратитсn= 3; в действителn= 0;ную трещину и остаточная прочность образца буд = 77;т той же, что и в случае усталостноl= 1; трещины той же начально = 81; длины. Все это было показано в эксперименm= 0;ах (см. [34]). Если разрушению тонкого листа не предшествуk= 7;т медленный рост трещин = 99;, то имитация трещины пропилом недопустимk= 2;. В этом случа= 077; малая острота пропила может быть достаточноl= 1; для того, чтобы сделать напряжение образованиn= 3; трещины σi больше, чем разрушающеk= 7; напряжение `= 3;c.

Пр= 086;цесс разрушения = 74; этом случае можно объяс = 85;ить с помощью концепции баланса эне = 88;гии, как это сделано на рис. 8.20. Рост острой трещ = 80;ны начинается при напряжении `= 3;i, а разрушени = 77; происходит при напряжении `= 3;c. В случае, когда трещина имитируетсn= 3; пропилом, напряжение, необходимоk= 7; для образов = 72;ния трещины, может увеличитьсn= 3; до σ2. Баланl= 9; энергии теперь буде = 90; достигнут в = 090;очке B, а разрушение, как и в описанном ранее случа = 77;, произойдет при напряжении `= 3;c. Пропилы можно сделать настолько тупыми, что образованиn= 3; трещины не произойдет до тех пор, пока не буде= 090; достигнуто напряжение `= 3;3, большее σc. h= 2; этом случае не может быт= 100; достигнуто никакого баланса энергии, и немедленно, без предвар = 80;тельного медленного роста трещины, воз= 085;икает нестабильнl= 6;сть, предшествуn= 2;щая разрушению. Допустимый радиус кривизны пр = 86;пила зависит от свойств материала. Для материа = 83;ов с более низкой вязкостью разрушения требуются более остры = 77; трещины: для стали Н-11 увел= ичение остаточной прочности наблюдалосn= 0; уже при радиусе кривизны пропила порядка 20 мкм (см. [35]). Величина допустимогl= 6; радиуса кри = 74;изны определяетl= 9;я из эксперименm= 0;а.

Ри&#= 1089;. 8. 19. Испытание на разрушение при плоском = 085;апряженном состоянии<= span style=3D'font-size:8.5pt;font-family:Arial;color:#330066'>

с цифровым печатным и телетайпныl= 4; выводом величин, нагрузки РТ = 080; податливосm= 0;и.

Об&#= 1088;атите внимание на противопроk= 5;ибочные направляющl= 0;е и на кинокамеру для съемок=

ме&#= 1076;ленного роста трещины

Ри&#= 1089;. 8.20. Притупленнm= 9;е вершины трещины

в испытаниях при плоском напряженноl= 4; состоянии [1,34]

(по данным Мак Милана)

Не= 089;ингулярный член σ в уравнениях, описывающиm= 3; поле напряж = 77;ний для пластин = 99; с трещиной, находящейсn= 3; под действием одноосного напряжения, указывает н = 72; то, что напряжение `= 3;x, действующеk= 7; вдоль краев трещины, является сжимающим и имеет порядок приложенноk= 5;о извне продо = 83;ьного растягиваюm= 7;его напряжения. Это сжимающ = 77;е напряжение может вызвать, особенно в тонких листах, прогиб участка пластины, на= 093;одящегося в непосредстk= 4;енной близости от трещины (рис. 8.21). Такой прогиб можн = 86; легко продемонстl= 8;ировать вручную, растягивая листок бумаги с центральныl= 4; поперечным прорезом. Та= 082; как прогиб может оказывать влияние на процесс медленного роста трещины и на остаточную прочность, этому явлению был = 86; посвящено несколько исследованl= 0;й (см. [2, 36—39]).

Ка= 088;лсон и др. [38] исследовалl= 0; явление прогиба формально, рассматривk= 2;я его как зада= 095;у об устойчивосm= 0;и пластины. Однако обыч = 85;о используетl= 9;я простая формула прогиба стержня (см. [12, 36, 37]). Поскольку поперечное растягиваюm= 7;ее напряжение, действующеk= 7; вдоль краев трещины, равно номинальноl= 4;у значению однородногl= 6; напряжения `= 3;, прогиб начн = 77;тся, когда σ =3D σb, где

        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;          (8.26)=

Ур= 072;внение (8.26) является формулой дл = 03; прогиба шарнирно опертого стержня, тол= 097;ина которого В, модуль упругости Е<= /i>, а эффективнаn= 3; длина le. Длина стержня le будет связана с длиной трещины а соотношениk= 7;м

        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p; (8.27)

Ри&#= 1089;. 8.21. Прогиб трещины и противопроk= 5;ибочные направляющl= 0;е

Им= 077;ются различные точки зрени = 03; относительl= 5;о наиболее реального значения α, которое имеет порядок 0,5 (см. [36]= ), но скорее всего эта величина зависит от толщины листа (см. [2, 38]).

Дл= 103; длинных трещин прогиб возникает задолго до разрушения образца и поэтому может влият = 00; на величину остаточной прочности. П= 086; этой причин = 77; в опытах на определениk= 7; остаточной = 87;рочности прогиба стараются избежать, на= 082;ладывая на пластину жесткие брусья (см. ри&= #1089;. 8.19 и 8.21), которые известны ка = 82; противопроk= 5;ибочные направляющl= 0;е. Исследованl= 0;я методом фотоупругоl= 9;ти, проведенныk= 7; Диксоном и С= 090;рэннигэном [36], показали, что максимальнl= 6;е напряжение при вершине прорези в модели, не ограниченнl= 6;й направляющl= 0;ми, было пример = 85;о на 30 % больше, чем в случае, когда к ней были приложены противопроk= 5;ибочные направляющl= 0;е. Эти направляющl= 0;е, несомненно, оказывают влияние на остаточную прочность. О= 073; уменьшении остаточной прочности примерно на 10 % сообщалось = 74; работах Уолкера [2] и Тротмэна [39] и до 40 % — в работ = 77; Формзна [37]. Этl= 6; уменьшение, конечно, должно зависеть от длины трещи = 85;ы. Для иллюстрациl= 0; влияния прогиба на процесс стабильногl= 6; медленного роста трещины и на величину остаточной прочности некоторые и = 79; большого количества данных Уолкера [2] представлеl= 5;ы на рис. 8.22.

Хо= 090;я противопроk= 5;ибочные направляющl= 0;е и считают предпосылкl= 6;й для проведения полезного испытания н = 72; определениk= 7; остаточной прочности, вопрос о том, всегда ли он= 080; необходимы, = 077;ще не решен. На практике прогиб в конструкциn= 3;х, состоящих и = 79; тонких листов, не всегда впол = 85;е ограничен. Даже в армированнm= 9;х конструкциn= 3;х прогиб може = 90; иногда быть ограничен плоской изгибной жесткостью стрингеров. Образованиk= 7; прогиба полностью исключаетсn= 3; только внеплоской изгибной жесткостью стрингера, когда этот стрингер проходит поперек трещины. Вычисление остаточной = 87;рочности оболочечноl= 1; конструкциl= 0;, состоящей и = 79; тонких листов, прогиб которых не о= 075;раничен, безусловно должно основыватьl= 9;я на испытани = 03;х этих листов без направляющl= 0;х, поскольку наличие эти = 93; направляющl= 0;х приводит к у= 084;еньшению величины K1c. На рис. 8.19 показано применение противопроk= 5;ибочных направляющl= 0;х в реальном эксперименm= 0;е.

Ри&#= 1089;. 8.22. Влияние прогиба на медленный рост трещин = 99; и остаточну = 02; прочность [2]<= /b>

Ин= 086;гда возникает вопрос: допустимо л = 80; устанавливk= 2;ть критическиl= 1; размер трещины, дел= 072;я разрез в образце, находящемсn= 3; под постоянной = 85;агрузкой? Опыты показали (см. [28]), что при это= 084; была бы получена неверная информация. = 042; этих опытах образцы с центральныl= 4; разрезом на = 75;ружались до нагрузки, чуть меньше = 81; той, при которой должен был б= 099; начаться ме = 76;ленный рост трещин = 99;. Нагрузка с этого момен = 90;а поддерживаl= 3;ась постоянной, = 072; одновременl= 5;ое распростраl= 5;ение двух концов трещины поддерживаl= 3;ось вплоть до разрушения = 89; помощью дву = 93; алмазных пи = 83;. Некоторые р = 77;зультаты этих испытаний представлеl= 5;ы на рис. 8.23.

На первый взгляд, следовало б = 99; ожидать, что разрушение во время пропиливанl= 0;я произойдет, когда будет достигнута критическаn= 3; длина трещины (соответств = 91;ющая приложенноl= 4;у напряжению). Однако пропиливанl= 0;е может быть продолжено намного дальше. Можн= 086; показать, чт= 086; это расхождениk= 7; происходит из-за малой остроты пропила по сравнению с остротой ве = 88;шины усталостноl= 1; трещины, поскольку верхняя кривая справедливk= 2; для медленн = 86; распростраl= 5;яющейся действителn= 0;ной трещины. Одн= 072;ко полученные из эксперименm= 0;а точки наход = 03;тся на таком большом расстоянии = 74; вертикальнl= 6;м направлениl= 0; от этой кривой, что малая остро = 90;а пропила не может быть единственнl= 6;й причиной расхождениn= 3;.

Ес= 083;и эти результаты рассматривk= 2;ть с позиций концепции R – кривой (рис. 8.24, а), то они оказываютсn= 3; более разумными. Н= 072; рис. 8.24, б показана диаграмма остаточной прочности. Трещина с начальной длиной а0 l= 4;ожет быть нагружена д = 86; напряжения `= 3;i (точка А), при котором начинается медленный рост трещин = 99;. К моменту, когда напряжение увеличено д = 86; σc, размер трещины увеличиваеm= 0;ся до ac, при этом возникает нестабильнl= 6;сть, предшествуn= 2;щая разрушению. На рис. 8.24, а показана соответствm= 1;ющая диаграмма баланса энергии, выраженная через интенсивноl= 9;ть выделения энергии G и сопротивлеl= 5;ие росту трещины R. Медленный рост трещин = 99; начинается, когда напряжение увеличиваеm= 0;ся до σi. В это = 84; случае величина представ= лена точкой A. При дальнейшем увеличении напряжения изменение G происходит = 74;доль R – кривой. Наконец, когда напряжение достигнет величины σc и размер трещины увеличится до ac (точка B), распростраl= 5;ение трещины может продолжатьl= 9;я при постоянном напряжении. Величина G возрастает, оставаясь больше, чем R, и возникает нестабильнl= 6;сть, предшествуn= 2;щая разрушению.

Ри&#= 1089;. 8.23. Искусственl= 5;о созданный медленный р = 86;ст трещины

пр&#= 1080; постоянном напряжении [28] (по данным Пергамона)=

Ра= 089;смотрим теперь трещину, имеющую начальную длину а0 и нагруженнуn= 2; до напряжения `= 3;i. Распростраl= 5;ение трещины осуществляk= 7;тся искусственl= 5;о за счет пропиливанl= 0;я, в то время как напряжение поддерживаk= 7;тся постоянным = 80; равным σi. Интенсивноl= 9;ть высвобождаn= 2;щейся энергии G в соответствl= 0;и с равенство = 84; будет увеличиватn= 0;ся пропорционk= 2;льно а, и изменение этой величины будет происходитn= 0; вдоль прямо = 81; линии AD. Наконец, в то&#= 1095;ке C выполняетсn= 3; условие G > R и возникает нестабильнl= 6;сть, предшествуn= 2;щая разрушению (точка C на рис. 8.25, б). Если бы разрушение произошло в = D, как предполагаl= 3;ось сначала, то во время про= 087;иливания R – кривая переместилk= 2;сь бы на место линии DF, изображеннl= 6;й на рис. 8.24, а штрихами, пр= 080; этом разрушение произошло б = 99; в точке D. Перемещениk= 7; R – кривой во время испытания маловероятl= 5;о (см. [28]). Если в описываемоl= 4; опыте пропиливанl= 0;е прекратить = 74; точке H, непрерывно увеличивая после этого нагрузку, то разрушение должно произойти в точке K. На рис. 8.24, б отмечены эквивалентl= 5;ые точки. Подобный хо = 76; процесса разрушения подтверждаk= 7;тся испытаниямl= 0; (см. [28]).

Ит= 072;к, можно констатироk= 4;ать, что проведение испытания н = 72; надежность, проводимое посредствоl= 4; расширения трещины за счет пропиливанl= 0;я ее под нагрузкой, п= 088;иводит к завышенно = 81; оценке критическоl= 1; длины трещины.

Рис. 8.24. R – <= b>кр&#= 1080;вая (а) и искусственl= 5;ый медленный рост трещин = 99; (б) [28] (по данным Пергамона)=   

        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;

 

 

§ 8.6. Заключение=

Задачи о плоском напряженноl= 4; состоянии б = 86;лее сложны, чем задачи о плоской деформации, = 074; особенностl= 0; потому, что процессы разрушения при плоском = 085;апряженном состоянии недостаточl= 5;о изучены. В данной глав = 77; были рассмотренm= 9; различные методы решения задач о процессах образованиn= 3; и развития трещин при плоском нап = 88;яженном состоянии и = 074; переходном случае. Методы, связ= 072;нные с понятием R - кривой, наглядны и зачастую дают возможностn= 0; дать количествеl= 5;ные оценки параметров разрушения. Однако последние работы Си и Хатранфта, п= 086; всей вероятностl= 0;, указывают н = 72; то, что для решения эти = 93; задач требуется совершенно новый подхо = 76;. С техническоl= 1; точки зрени = 03;, концепция, п= 088;едложенная Феддерсеноl= 4;, и модель Андерсона, описывающаn= 3; эффект влияния толщины, явл= 103;ются наиболее удачными подходами.        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;

        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;      

 

 

§ 9.1. Разрушение после образованиn= 3; общей текуч = 77;сти

Ме= 093;аника разрушения, основанная на линейной теории упругости (ЛУМР), может быть плодот = 74;орно использоваl= 5;а только в том случае, если зона пластичносm= 0;и мала по сравнению с размером трещины. Обычно это условие вып = 86;лняется в материала = 93;, в которых разрушение происходит при напряженияm= 3;, существеннl= 6; меньших предела текучести при плоской = 076;еформации. В этих условиях разрушение можно охарактериk= 9;овать величиной К<= /i>Ic или GIc. Зона пластичносm= 0;и в случае, когда преобладаеm= 0; плоское напряженноk= 7; состояние, больше, чем при плоской деформации. Если разрушение при этом все-таки происходит при напряженияm= 3;, которые мал = 99; по сравнени = 02; с пределом текучести, т= 086; задача, так или иначе, решается от = 85;осительно простыми методами. Однако если = 079;она пластичносm= 0;и велика по сравнению с размером трещины (разрушение происходит при больших напряженияm= 3; или велико сопротивлеl= 5;ие росту трещины), то в этом случае линейная механика разрушения неприменимk= 2;.

Эт= 072; проблема имеет две стороны. Во-первых, та&#= 1082;ой случай реал = 80;зуется в материала = 93; с низкой вязкостью разрушения = 80; с очень короткими трещинами. Напряжение, при котором происходит разрушение = 74; таких материалах, при стремлении размера трещины к нулю прибли = 78;ается к бесконечноl= 9;ти (рис. 9.1). Поскольку это невозможно, то напряжение разрушения при размере трещины (a/W)1= определяеm= 0;ся точкой B, которая находится ниже точки A, вычисленноl= 1; из коэффициенm= 0;а КIc. Соверш = 77;нно очевидно, чт= 086; это напряжение средствами ЛУМР (линейной механики разрушения) определить нельзя (в гл. XIII было показано, чт= 086; для решения такой задач = 80; иногда можн = 86; применять инженерные методы). Вообще говоря, если &#= 1085;апряжение в истинном сечении равно преде = 83;у текучести, т= 086; зона пластичносm= 0;и станет большой и распростраl= 5;ится на все сечен= 080;е, через которое проходит трещина:

 =

        &= nbsp;           &nbs= p;          (9.1)<= /o:p>

 =

где σnet в сечении с трещиной получается делением нагрузки на площадь сечения оставшейся неразрушенl= 5;ой части материала. В случае мало = 81; трещины σnet ≈ σ. Следователn= 0;но, можно ожидать, что величину КIc можно использоваm= 0;ь, пока σc не приблизитсn= 3; к пределу текучести. Н= 072; практике дл = 03; применения ЛУМР σc должно быть меньше, чем 66 % от предела текучести (критерий истинности значения К1c Феддерсена). Второй случай, когд= 072; линейная ме = 93;аника разрушения неприменимk= 2;, реализуетсn= 3; в материала = 93; с высокой вязкостью р = 72;зрушения (рис. 9.1). Уравне= 085;ие (9.1), описывающеk= 7; условие текучести и = 89;тинного сечения, можно переписать = 74; виде

 

        &= nbsp;           &nbs= p;            &= nbsp;            (9.2)

 

Уравне= ние (9.2) представляk= 7;т собой уравнение прямой лини = 80;, проходящей от σys к точке a/W =3D 1, как показан = 86; на рис. 9.1 штриховой линией. Если материал обладает высокой вязкостью то напряжение разрушения, вычисленноk= 7; методами линейной механики разрушения, всегда выше, чем напряжение, при котором возникает течение истинного сечения. Это означает, чт= 086; величину нельзя измерить: общее течение возникает в точке C, а точка D никогда не может быть достигнута.

В этих условиях возникновеl= 5;ию пластическl= 6;го течения более ничто не препятствуk= 7;т (рис. 9.2) и зона пластичносm= 0;и распростраl= 5;яется на внутреннюю часть сечения с трещиной; пр= 080; вершине трещины сво = 73;одно возникает пластическk= 2;я деформация. Следует ожидать, что трещина начнет расп = 88;остранятьс&#= 1103;, если пластическk= 2;я деформация при вершине трещины превысит критическоk= 7; значение (в гл. II и XI рассмотрен случай, когд= 072; существует критическаn= 3; комбинация напряжения = 80; деформации, необходимаn= 3; для разруше = 85;ия). Пренебрегаn= 3; эффектом механическl= 6;го упрочнения, можно считать, что, после того как возникл = 86; общее течение и достигнуто условие разрушения, напряжение не увеличит = 89;я. Мерой пластическl= 6;й деформации при вершине = 090;рещины является критическоk= 7; раскрытие т = 88;ещины при ее вершине (КРТ). Ясно, что разрушение возникает после того, как превышено к = 88;итическое значение КР = 58;. Этот критерий вп = 77;рвые был предложен Уэлсом [1, 2].

 

Ри&#= 1089;. 9.1. Разрушение после возникновеl= 5;ия общей текучести<= span style=3D'font-size:8.5pt;font-family:Arial;color:#330066'>

 =

Рис. 9.2. Общая текучесть<= span style=3D'font-size:8.5pt;font-family:Arial;color:#330066'>            =             &nb= sp;            =             &nb= sp;            =             &nb= sp;            =             &nb= sp;            =             &nb= sp;            =          

        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;       

 

 

§ 9.2. Раскрытие трещины при ее вершине=

Дл= 103; начала проверим, не противоречl= 0;т ли критерий Уэлса линейной механике разрушения. = 042; рассматривk= 2;емом здесь случа = 77; можно воспользовk= 2;ться формулой дл = 03; расчета раскрытия т = 88;ещины (РТ), полученной методами линейной ме = 93;аники разрушения. Относительl= 5;ое перемещениk= 7; поверхностk= 7;й трещины (рис. 9= .3) было задано = 074; гл. III формулой= ;

 =

        &= nbsp;           &nbs= p;      (9.3)

 =

Примен= яя коррекцию н = 72; зону пластичносm= 0;и, получаем<= /p>

 

        &= nbsp;           &nbs= p; (9.4)

 

где (a + r*p) – эффективныl= 1; размер трещины, а начало сист = 77;мы координат находится в центре трещины. Раскрытие материальнl= 6;й трещины при ее вершине получается подстановкl= 6;й в эту формул= 091; значения x =3D a<= /i>. Поскольку r*p= <<a оказываетсn= 3;, что

 

        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;   (9.5)

 

Переме= щая начало системы координат в вершину трещины, получаем общее выражение д = 83;я раскрытия трещины:

 

        &= nbsp;           &nbs= p;            &= nbsp;   (9.6)

Ри&#= 1089;. 9.3. Относительl= 5;ое перемещениk= 7; краев трещи = 85;ы

 =

В этом случае величина КР = 58; получается подстановкl= 6;й в (9.6) значений r= =3D r*p и aэфф≈<= i>a что приводи = 90; к уравнению (9.= 5).

По= 076;становка приводит к следующем = 91; выражению:=

 =

        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;     (9.7)

 =

Уравне= ние (9.7) не выходит за рамки области при = 84;енения линейной механики разрушения: = 088;азрушение происходит при KI =3D KIc согласно уравнению (9.7), это условие выполняетсn= 3; при постоянном значении КР = 58;, причем оказываетсn= 3;, что критери = 81; Уэлса применим в линейной механике разрушения.

Чт= 086;бы использоваm= 0;ь этот критерий в линейной механике разрушения, потребовалl= 6;сь бы измерить величину КР = 58;. Непосредстk= 4;енное измерение КРТ затруднитеl= 3;ьно, а в обычных испытаниях R= 12; фактически невозможно. Получить значение КР = 58; можно косвенно, измеряя величину K и используя уравнение (9.7). Это означал = 86; бы принятие допущения относительl= 5;о коэффициенm= 0;а 4/π, введенного при использоваl= 5;ии коррекции н = 72; зону пластичносm= 0;и, однако остается неясным, как измерить величину этой коррек = 94;ии. Данную проблему можно обойт = 80;, подставляя = 74; уравнение (9.4) уравнение (9.5), откуда (прен= 077;брегая членом (r*p)2)

 =

        &= nbsp;  (9.8)

 =

Соглас= но уравнению (9.7), величину КР = 58; можно опред = 77;лять косвенно, измеряя РТ (например, пр&#= 1080; x =3D 0 в центре пластины), не делая никаких предположеl= 5;ий относительl= 5;о размера коррекции н = 72; зону пласти = 95;ности. РТ можно легко измерить с помощью измерителя деформации (см. гл. VII).

С другой стороны, часто используют уравнения, описывающиk= 7; раскрытие трещины при ее вершине, которые следуют из подхода Дагдейла (см. гл. IV). В этом случае (см. [3]) для КРТ полу= 095;ается следующее выражение:=

 =

        &= nbsp;           &nbs= p;           (9.9)=

 

Ра= 089;кладывая эту функцию = 074; ряд, имеем

 =

   (9.10)

 

Та= 082; как σ мало по сравнению с = 63;ys, то

 =

        &= nbsp;           &nbs= p;            &= nbsp;         (9.11)

 

Уравне= ние (9.11) имеет тот ж= 077; вид, что и (9.7), если не считать коэффициенm= 0;а 4/π, который, ка= к было показано, зависит от выбора коррекции н = 72; зону пластичносm= 0;и. Вообще говоря,

 

        &= nbsp;           &nbs= p;        (9.12)

 

В случа= ;е плоского напряженноk= 5;о состояния коэффициенm= 0;ом (1 – ν2) в уравнении (9.12) можно пренебречь.

В литературе можно встретить различные з = 85;ачения λ. Они завися= 090; от места, в котором опр = 77;деляют величину КР = 58;, т. е. от того, какое место принимают з = 72; вершину трещины. В результате описанных ранее квазиупругl= 6;пластическ= 080;х расчетов были получены зн = 72;чения коэффициенm= 0;а λ, равные 1 и 4/π. Интегрировk= 2;ние перемещениl= 1; вокруг зоны пластичносm= 0;и (см. [1, 4]) также приводит к значению 4/π. Для материала, н= 077; подверженнl= 6;го механическl= 6;му упрочнению, Рис [5] получил значение λ =3D 1,48, &= #1072; в работе Раиса и Джонсона [6] получено значение λ =3D 1,27. Расчеты, проведенныk= 7; методом кон = 77;чных элементов (см. гл. XIII) Леви и др. [7], а также С= 072;мптером и др. [8], привел = 80; соответствk= 7;нно к значениям 2,14 и 1,155.

Резуль= тат расчета зависит в определеннl= 6;й степени от сделанных предположеl= 5;ий. Поэтому прямые измерения λ могут оказаться б = 86;лее надежными. Эти измерения можно выпол = 85;ять различными путями. Использоваl= 5;ие оптических методов сводилось к непосредстk= 4;енному измерению КРТ с фотографий или косвенн = 86;му — с помощью реплик с поверхностl= 0; образца вокруг вершины трещины (см. [9]). При этом получаются значения λ порядка единицы (см. [9, 10]), которые относятся к плоскому напряженноl= 4;у состоянию (н= 072; поверхностl= 0; образца). С помощью металлограm= 2;ического секционироk= 4;ания Боулзом [11] были измерены значения КР = 58; во внутренних слоях образца (в этих эксперименm= 0;ах для предотвращk= 7;ния разгрузки трещины заполнялисn= 0; пластмассоl= 1;). Он также получил значение λ ≈ 1. Тщательно выполненныk= 7; измерения Робинсона и Тетельмана [12]= , возможно, наиболее достоверны. Они пропита = 83;и трещину затвердеваn= 2;щей силиконовоl= 1; резиной, а отливки, для того чтобы облегчить и = 93; наблюдение = 74; сканирующиl= 1; электронныl= 1; микроскоп, позолотили. Робинсон и Тетельман п = 86;лучили значение λ, равное единице.            =             &nb= sp;            =             &nb= sp;            =             &nb= sp;            =             &nb= sp;            =             &nb= sp;            =             &nb= sp;    

        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;       

 

 

§ 9.3. Возможные пути использоваl= 5;ия критерия КР = 58;

 =

В предыдущем параграфе было показано, чт= 086; критерий разрушения КРТ эквивалентk= 7;н критерию разрушения, полученномm= 1; методами ли = 85;ейной механики разрушения, = 074; том случае, к&#= 1086;гда последняя применима. Для обобщения н = 72; случай, когд= 072; разрушение наступает после возникновеl= 5;ия общего течения, следует сде = 83;ать существеннl= 6;е предположеl= 5;ие о том, что справедливl= 6;сть этого критерия сохраняетсn= 3; вплоть до напряжений порядка предела тек = 91;чести. В пользу такого предположеl= 5;ия говорят рассуждениn= 3;, приведенныk= 7; в § 9.2 и 9.6.

Ес= 083;и критерий КР = 58; можно обобщить, то отсюда следует, что можно также установить критическоk= 7; значение КРТ как константу материала. В этом случае возможно применение данного кри = 90;ерия по двум направлениn= 3;м:

Ра= 089;сматривая рис. 9.1, мы види = 84;, что разрушение образца с размером трещины (a/W)1= в точке В про= 080;сходит при том же критическоl= 4; значении КР = 58;, что и разрушение образца с размером трещины (a/W)2= в точке E. Друг&= #1080;ми словами, для измерения критическоk= 5;о значения КР = 58;Ic можно использоваm= 0;ь образец с маленькой т = 88;ещиной. Уравнения с (9.= 3) по (9.12) к этому образцу неп = 88;именимы, однако они применимы к образцу с ра= 079;мером трещины (a/W)2= . Поскольку последний разрушаетсn= 3; при том же значении КР = 58;Ic, то для определениn= 3; KIc можно использоваm= 0;ь уравнение (9.12). Это означае = 90;, что ударную вязкость можно определить (см. [12]), измеряя КРТ в малом образце с маленькой трещиной; пр= 080; этом не было бы необходимоl= 9;ти в больших образцах дл = 03; определениn= 3; KIc, размеры которых определяет стандарт ASTM.

Не= 082;оторые материалы обладают столь высок = 86;й вязкостью, что величин = 91; KIc в них нельзя определить. Эти материалы можно охарактериk= 9;овать их критичес = 82;ими значениями КРТ (материа= 083; высокой вязкости на рис. 9.1). Поскольку уравнения с (9.= 3) по (9.12) в этом случае не применяют, то, зная крит&#= 1080;ческое значение КР = 58;, нельзя вычислить р = 72;зрушающее напряжение или критическиl= 1; размер трещины. Кроме того, значения КР = 58;С можно использоваm= 0;ь для сравнения способностl= 0; материалов = 89; высокой вязкостью сопротивляm= 0;ься разрушению; большее значение КР = 58;С означает, чт= 086; материал сильнее сопротивляk= 7;тся росту трещины.

Примен= ение п. б, очевидно, наиболее интересно, поскольку дает возможностn= 0; распростраl= 5;ить механику ра = 79;рушения на очень вязкие материалы, хотя количе = 89;твенные оценки при этом сделат = 00; нельзя. Именно этом = 91; приложению = 82; вязким мате = 88;иалам в литератур = 77; уделено наибольшее = 74;нимание.        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;     

        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;      

 

 

§ 9.4. Эксперименm= 0;альное определениk= 7; КРТ

 

Не= 087;осредствен&= #1085;ое эксперименm= 0;альное определениk= 7; КРТ возможн = 86;, пока применима линейная механика разрушения. = 042; этом случае = 084;огут быть использоваl= 5;ы уравнения, выведенные = 74; предыдущих параграфах главы. С помощью ура = 74;нения (9.8) можно установить критическоk= 7; значение КР = 58; для пластин = 99; с центральноl= 1; трещиной, измеряя РТ в центре трещины или = 074; каком-либо другом мест = 77;. Эти измерения были выполн = 77;ны Броеком и Влигером [13] для больших пластин из алюминиевоk= 5;о сплава, находящихсn= 3; в плоском напряженноl= 4; состоянии. Некоторые и = 79; полученных ими результатоk= 4; представлеl= 5;ы на рис. 9.4. Из рисунка видно, что для данной толщины пластины было получено бо = 83;ее или менее постоянное значение КР = 58;с, которое, как оказалось, находится в определеннl= 6;м согласии с коэффициенm= 0;ом К1с (при λ=3D1).<= /o:p>

 =

Ри&#= 1089;. 9.4. Величина КРТ при разрушении больших пан = 77;лей с центральн = 86;й трещиной [13]

 =

Из= 084;ерения КРТ обычно проводят на трехточечнm= 9;х образцах, предназначk= 7;нных для изгиба, подобных те = 84;, на которых определяют &= #1050;Iс. Полное описание испытания н = 72; определениk= 7; РТ зафиксировk= 2;но в литератур = 77; [14, 15], а специаль&= #1085;ая группа в Вел= 080;кобритании установила рекомендуеl= 4;ый порядок проведения испытания н = 72; определениk= 7; РТ (см. [16]). Эти образцы предназначk= 7;ны для испытан = 80;я таких вязки = 93; материалов, = 074; которых разрушение происходит после наступлениn= 3; общей текучести. Это приводи = 90; к усложнени = 02; косвенных измерений КРТ, поскольку н = 77; существует формул, связывающиm= 3; КРТ с измеренным = 79;начением РТ. Для испытания, проводимогl= 6; посредствоl= 4; изгиба трехточечнl= 6;го образца, проблема, ка= 082; будет показано далее, разре= 096;ается довольно просто.

Та= 082; как сечение образца, свя= 079;ывающее обе его части, разделенныk= 7; трещиной, полностью находится з = 72; пределом те = 82;учести, его можно рассматривk= 2;ть как пластич = 77;ский шарнир (рис. 9.5, = а) с центром вращения, находящимсn= 3; на расстоян = 80;и r (W – a) от вершины трещины. Предполагаk= 7;тся, что края тре= 097;ины остаются прямыми. Коэффициенm= 0; вращения r следует определить эксперименm= 0;ально. В этом случа= 077; относительl= 5;ое перемещениk= 7; краев трещины при ее вершине связано с РТ на открытом конце трещины линейным соотношениk= 7;м (рис. 9.5, б)

 =

        &= nbsp;           &nbs= p;            &= nbsp;     (9.13)

 =

или

 =

        &= nbsp;           &nbs= p;            &= nbsp;      (9.14)

 =

Ри&#= 1089;. 9.5. Пластическl= 0;й шарнир

 =

Экспер= именты (см. [17, 18]) показали, чт= 086; коэффициенm= 0; вращения пр = 80; нагружении увеличиваеm= 0;ся почти от нул= 103; (весь материал образца обл = 72;дает упругими свойствами, за исключениеl= 4; зоны пластическl= 6;го течения при вершине трещины) до более или ме= 085;ее постоянногl= 6; значения 1/= 3 (связка полностью находится в зоне пласти = 95;ности), которое часто используют при вычисле = 85;иях. Робинсон и Тетельман [12] эксперименm= 0;ально установили, что коэффициенm= 0; вращения r зависит от КРТ, как показано на рис. 9.6. Проводn= 3; кривую чере = 79; эти эксперименm= 0;альные точки, они пришли к следующему выражению для r:

 

      (9.15)=

 =

где КРТ выражено в тысячных долях дюйма. Подставляя выражение (9.15) = 74; (9.14), приходим к уравнению, которое легко решит = 00; с помощью стандартноl= 1; вычислителn= 0;ной программы.=

 =

Ри&#= 1089;. 9.6. Зависимостn= 0; коэффициенm= 0;а вращения от КРТ [12].

Ра&#= 1079;личные условные знаки относятся к ра&#= 1079;ным материалам (Fe,= Al, Ti)

 =

Из= 103;щное решение задачи об изменении коэффициенm= 0;а вращения было получено Виерманом и Мюллером [19]. Они использоваl= 3;и образец, в котором усталостнаn= 3; трещина зарождаласn= 0; в довольно глубоком механическl= 6;м вырезе, который можно было приспособиm= 0;ь для двойног = 86; измерителя поперечногl= 6; разрыва (рис. 9= .7). В этом случа= 077; не нужно знать коэффициенm= 0; вращения, поскольку величину КР = 58; можно получить, измеряя РТ в двух точках:

 =

   (9.16)

 =

Ри&#= 1089;. 9.7. Применение двойного измерителя поперечногl= 6; разрыва:

а – схема измерителя; = 073; – разрез; в – пе&#= 1088;емещения

 =

Коэффи= циент вращения можно также определить из двух диаграмм измерения Р = 58;, сделанных с помощью двойного измерителя. Виерман и Мюллер получили, чт= 086; его значени = 77; меняется от 0,1= 95 в упругом случае до приблизитеl= 3;ьно постоянногl= 6; значения 0,47 в случае образованиn= 3; пластическl= 6;го шарнира. Последнее значение до = 74;ольно хорошо согласуетсn= 3; с результат = 72;ми Робинсона и Тетельмана, показаннымl= 0; на рис. 9.6.&= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;  

        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;       

 

 

§ 9.5. Параметры, влияющие на критическоk= 7; значение КР = 58;

Пр= 080; испытании н = 72; определениk= 7; РТ строится = 076;иаграмма в координатаm= 3; «нагрузка — РТ» точно так же, как и в испытании н = 72; определениk= 7; KIc. Поскольку испытание н = 72; определениk= 7; KIc является существеннl= 6; упругим, соответствm= 1;ющая диаграмма представляk= 7;т собой пряму = 02; линию; при этом допускаютсn= 3; лишь неболь = 96;ие отклонения от нее (см. гл. VII). Испытание н = 72; определениk= 7; РТ является, в свою очередь, существеннl= 6; пластическl= 0;м, и полученна = 03; диаграмма «нагрузка — РТ» имеет вид, показанный на рис. 9.8. В рекомендацl= 0;ях по проведению испытания н = 72; определениk= 7; РТ (см. [16]) специально отмечается, = 095;то величину КР = 58;С следует определять = 74; момент разрушения. = 054;днако разрушению может предшествоk= 4;ать процесс медленного стабильногl= 6; расширения трещины. Зафиксировk= 2;ть медленный рост трещин = 99;, предшествуn= 2;щий разрушению, чрезвычайнl= 6; сложно, поэтому величину КРТС обычно определяют = 74; точке максимальнl= 6;й нагрузки.=

Ри&#= 1089;. 9.8. Диаграмма испытания н = 72; определениk= 7; РТ

На результаты испытания п = 86; определениn= 2; РТ могут ока= 079;ывать влияние различные геометричеl= 9;кие параметры: размер трещины a/W (см. [3, 17, 20, 21]); толщина полученных = 74; результате испытания обломков [см. [= 12, 22])} глубина связки (см. [23]); о&= #1089;трота выреза (см. [20, 22]); жесткость испытательl= 5;ой машины (см. [22]). Некоторые результаты испытаний представлеl= 5;ы на рис. 9.9. Критическаn= 3; величина КР = 58; достигает своего постоянногl= 6; значения пр = 80; a/W>0,2.

Ри&#= 1089;. 9.9. Влияние различных геометричеl= 9;ких параметров на величину КРТ:

а – размера образца (бойлерная сталь) [3]; б – ра= 079;мера трещины [20] (по данным Чэпмена и Холла)

Ес= 083;и бы испытани = 77; предназначk= 2;лось для косвенн = 86;го определениn= 3; KIc, то необходимо было бы измерить зн = 72;чение КРТ в начале процесса медленного = 88;оста трещины. Существеннl= 6; также, чтобы вершина трещины находилась = 74; плоском напряженноl= 4; состоянии. В стандартноl= 4; испытании в = 99;полнить точные измерения начала проц = 77;сса роста трещины сложно. Определить начало рост = 72; трещины можно с помощью методики измерения э = 83;ектрическо&#= 1075;о потенциала (см. [24]). Электричесl= 2;ий потенциал, измеренный по обе стороны выр = 77;за, позволяет определить размер трещ = 80;ны. Существуют = 80; другие методы, однако в бол= 100;шинстве случаев они недостаточl= 5;о чувствителn= 0;ны.

Оп= 099;ты по определениn= 2; КРТ в начале процесса образованиn= 3; трещины был = 80; выполнены Робинсоном = 80; Тетельманоl= 4; [12]. Пропитывая трещину затвердеваn= 2;щей силиконовоl= 1; резиной, они получали реплику вершины трещины. Эта процедура позволила также определить поперечную деформацию, что было необходимо для проверк = 80; выполнения условия плоского де = 92;ормировани&#= 1103;. Полученные ими результаты = 87;оказали, что минимальнаn= 3; толщина, необходимаn= 3; для обеспечениn= 3; выполнения условия пло = 89;кого деформировk= 2;ния, задана соотношениk= 7;м

        &= nbsp; (9.17)

По= 089;кольку эти опыты выполнялисn= 0; для определ = 77;ния KIc в материалах = 89; низкой вязкостью, ударную вяз = 82;ость в них можно определить из уравнени = 03; (9.12). Это означает, чт= 086; величину Bmin можно выразить следующим образом:

        &= nbsp;           &nbs= p;  (9.18)

Для стали E =3D 21 000 кгс/мм2, а предел текучести равен 95 кгс/мм= 2. Для таких па= 088;аметров из соотношениn= 3; (9.18) следует, чт= 086; Bmin>0,1(КIc/σys)2. Совершенно очевидно, чт= 086; в этих условиях по = 85;адобились бы существеннl= 6; меньшие обр = 72;зцы, чем в опытах на определениk= 7; КIc, в которых Bmin<= /sub>>2,5(КIc/σys)2<= /sup>. Точность такого косвенного измерения KIc можно оценить из рис. 9.10. На этом рисунке зна = 95;ения вязкости были определены = 89; помощью ура = 74;нения (9.12). Полученны = 77; в этих измерениях = 88;езультаты обнадеживаn= 2;т, однако данный мето = 76; измерения применять нельзя, пока не получены достаточныk= 7; данные о характере в = 83;ияния геометрии образца и пока не разр= 072;ботана удовлетворl= 0;тельная методика оп = 88;еделения момента зарождения трещины.

Рис. 9.10. Значения КIc, определеннm= 9;е косвенным и прямым методами дл = 03; стали 4340 [12]&nbs= p;   

        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;       

 

 

§ 9.6. Ограничениn= 3;. Разрушение при общей текучести<= /span>

 =

Ес= 083;и на геометри = 02; образца наложить некоторые ограничениn= 3; (см [12, 21]), то связку трехточечнl= 6;го образца, предназначk= 7;нного для изгиба, действителn= 0;но можно рассматривk= 2;ть как пластическl= 0;й шарнир. Форм= 091; зоны пластичносm= 0;и в сталях, в которых содержание азота превышает 0,005 = %, можно выяви = 90;ь методом травления (с= 084; [25]). Результатm= 9;, полученные этим методо = 84; (см. [12]), приведе&#= 1085;ы на рис. 9.11. При определеннm= 9;х условиях зона пластичносm= 0;и может распростраl= 5;иться на удаленны = 77; части поверхностl= 0; образца: либ= 086; сразу после начала пластическl= 6;го течения (рис. 9= .11, а), либо позже в процессе испытания (рис. 9.11, б) (см. [21]). В этих случая = 93; раскрытие трещины зависит не только от уг= 083;а поворота пластическl= 6;го шарнира в св= 103;зке образца и рассуждениn= 3;, приведенныk= 7; в предыдуще = 84; параграфе, более не справедливm= 9;. Такое поведение образца позволяет частично объяснить влияние геометрии о = 73;разца на критическоk= 7; значение КР = 58;. Тем не менее необходимо дальнейшее исследованl= 0;е данной проблемы.=

 =

Ри&#= 1089;. 9.11. Пластическl= 0;й шарнир

 =

До сих пор не существует единого мнения отно = 89;ительно важности КР = 58; (см. [26—30]). В самой вершине трещины перемещениk= 7; действителn= 0;но равно нулю. Рассматривk= 2;ется эффективноk= 7; значение КРТ, которое является относительl= 5;ым перемещениk= 7;м краев фиктивной трещиной, имеющей размер a + r*p на расстоянии &= #1072; от ее центра (рис. 9.3). Как показано на рис. 9.3, это зна = 95;ение КРТ являетс = 03; эффективныl= 4;. КРТ для дейс= 090;вительной вершины трещины равно нулю, что подтверждаk= 7;тся экстраполяm= 4;ией измеренных значений РТ на рис. 9.12. Кром= 077; того, это подтверждаk= 7;тся вычисленияl= 4;и, проведенныl= 4;и методом кон = 77;чных элементов (см. § 13.3). Последние вычисления наводят на мысль о том (см. [26—30]), что, возможно, более подходящимl= 0; параметрамl= 0; для определ = 77;ния напряженно R= 12; деформировk= 2;нного состояния при вершине = 090;рещины являются радиус вершины трещины или величина КР = 58; на пересечениl= 0; границы зон = 99; пластичносm= 0;и и краев трещины (рис. 9.13). При этом остается неясным, как провести эксперименm= 0;ы, в результат = 77; которых можно было б= 099; определить значения этих параметров.

До= 087;олнительна&= #1103; неопределеl= 5;ность заключаетсn= 3; в том, что перед разрушениеl= 4; возникает процесс медленного стабильногl= 6; роста трещи = 85;ы. С практическl= 6;й точки зрени = 03; представляk= 7;т интерес только максимальнl= 6;е сопротивлеl= 5;ие росту трещи = 85;ы, а не начало ее роста (если не рассматривk= 2;ть KIc). Однако остается вопрос, является ли точка максимальнl= 6;й нагрузки в испытании н = 72; определениk= 7; РТ наиболее важной в технике. Как &#= 1087;оказано в гл. VIII, расстояние, на которое распростраl= 5;яется трещина в процессе своего медленного стабильногl= 6; роста, зависит от размера трещины. Это означает, чт= 086; величина КР = 58; в момент разрушения, которое произошло после медленного роста трещи = 85;ы, не обязательнl= 6; является единственнl= 6;й характерисm= 0;икой сопротивляk= 7;мости материала разрушению. Поведение образца, предназначk= 7;нного для определениn= 3; РТ во время медленного роста трещины, может также зависеть от жесткости испытательl= 5;ой машины.

Ис= 087;ытания на определениk= 7; РТ несомненно = 87;ерспективн&#= 1099;, однако необходимы дальнейшие исследованl= 0;я для развити = 03; данного подхода до такого уровня, при котором материалы с высокой вязкостью р = 72;зрушения можно было б= 099; охарактериk= 9;овать одним параметром. Необходимо также дальн = 77;йшее развитие метода для косвенного определениn= 3; KIc в материала = 93; малой вязкости.=

Ри&#= 1089;. 9.12. Зависимостn= 0; величины РТ от места, в ко&= #1090;ором проводилисn= 0; измерения [30]:

1 – эффективноk= 7; значение КР = 58;; 2 – движущийся = 94;ентр вращения

 =

Ри&#= 1089;. 9.13. Величина КРТ, определеннk= 2;я на пересече = 85;ии границы зон = 99; пластичносm= 0;и и краев трещ= 080;ны

 =

Пр= 072;ктическое использоваl= 5;ие критическиm= 3; значений КР = 58; сильно огра = 85;ичено в том смысле, что они не дают возмож = 85;ость предсказатn= 0; сопротивлеl= 5;ие разрушению реальной конструкциl= 0; и вычислить разрушающеk= 7; напряжение или критическиl= 1; размер трещины. С другой стороны, величину КР = 58;С можно использоваm= 0;ь для классификаm= 4;ии материалов = 87;о их сопротивляk= 7;мости разрушению, на основе которой можно проводить селекцию материалов = 80; их заготовк = 91;. Рассматривk= 2;я еще раз рис. 9.1, приходим к выводу, что выход, возможно, заключаетсn= 3; в том, чтобы сопротивлеl= 5;ие разрушению материалов высокой вязкости вы = 95;ислять исходя из условия текучести истинного сечения. После возникновеl= 5;ия пластическl= 6;го течения истинного сечения способностn= 0; материала выдерживатn= 0; дальнейшее увеличение нагрузки весьма ограничена. = 057;ледователь&= #1085;о, разрушающеk= 7; напряжение = 80; критически&= #1081; размер трещины в этом случае определялиl= 9;ь бы из услови= 103;:

 =

        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;    (9.19)

 

Уравне= ние (9.19) означает, что сопротивлеl= 5;ие материала разрушению характеризm= 1;ется пределом текучести, т.е. отпадает необходимоl= 9;ть знать значение РТ. Согласно некоторым д = 72;нным Робинсона и Тетельмана [12], представлеl= 5;ным на рис. 9.10, величина КР = 58; в начале процесса зарождения трещины пропорционk= 2;льна пределу текучести. Это означае = 90;, что уравнен = 80;е (9.19) в некоторы = 93; случаях справедливl= 6;. Дальнейшее подтверждеl= 5;ие этой идеи можно найти = 074; работе Хана = 080; др. [31], в которо= 081; уравнения (9.9) l= 0; (9.12) объединенm= 9; и приведены = 082; виду

 

        &= nbsp;           &nbs= p;            (9.20)

 

Это уравнение, описывающеk= 7; величину K, можно записать в каноническl= 6;м виде:

 

   (9.21)

 

где φ представляk= 7;т собой коэффициенm= 0; коррекции н = 72; зону пласти = 95;ности. Графическаn= 3; зависимостn= 0; этого корректироk= 4;очного коэффициенm= 0;а от σ/σys представлеl= 5;а на рис. 9.14. Для больших значений σ/σys коэффициенm= 0; φ можно аппроксимиl= 8;овать ступенчатоl= 1; функцией. В этом случае критерий разрушения принимает вид

 

        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;      (9.22)

 =

что эквивалентl= 5;о уравнению (9.19), если пренеб = 88;ечь коррекцией на размер. Разрушение трубопровоk= 6;ов и емкостей высокого давления, построенныm= 3; из материал = 86;в с высокой вязкостью разрушения, как оказываетсn= 3;, можно предсказывk= 2;ть (см. [31]) с помощь&#= 1102; уравнения (9.22). Эти результаты рассмотренm= 9; в гл. XV.

 =

Рис. 9. 14. Коррекция н = 72; зону пластичносm= 0;и, предложеннk= 2;я Ханом и др. [31]: 1 – ступенчатаn= 3; функция         

        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;       

 

 

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