Elastoplastic Strain Invariant of Metals

Abstract

Л.Б. ЗУЕВ, С.А. БАРАННИКОВА, А.Г. ЛУНЕВ Èíñòèòóò ôèçèêè ïðî÷íîñòè è ìàòåðèàëîâåäåíèÿ ÑÎ ÐÀÍ, ïðîñï. Àêàäåìè÷åñêèé, 2/4; 634055 Òîìñê, Ðîññèÿ УПРУГОПЛАСТИЧЕСКИЙ ИНВАРИАНТ ДЕФОРМАЦИИ МЕТАЛЛОВÐàññìàòðèâàåòñÿ îñíîâíàÿ õàðàêòåðèñòèêà ðàçâèòèÿ ëîêàëèçîâàííîãî ïëàñòè÷åñêîãî òå÷åíèÿ, -óïðóãîïëàñòè÷åñêèé èíâàðèàíò äåôîðìàöèè, -íà ïðèìåðå äå ôîðìàöèè äåâÿòíàäöàòè ðàçëè÷íûõ ìåòàëëîâ. Ïîêàçàíî, ÷òî ðàñïðåäåëåíèå ýêñïåðèìåíòàëüíî ïîëó÷àåìûõ çíà÷åíèé èíâàðèàíòà ïîä÷èíÿåòñÿ íîðìàëüíîìó çàêîíó ðàñïðåäåëåíèÿ. Ðàññìàòðèâàåòñÿ ïðèðîäà èíâàðèàíòà è å¸ ñëåäñòâèÿ, êîòîðûå îïèñûâàþò íàèáîëåå âàaeíûå çàêîíîìåðíîñòè ðàçâèòèÿ ëîêàëèçîâàííîãî ïëàñòè÷åñêîãî òå÷åíèÿ. Óñòàíîâëåíî, ÷òî èç óðàâíåíèÿ èíâàðèàíòà ìîãóò áûòü ïîëó÷åíû îñíîâíûå õàðàêòåðèñòèêè àâòîâîëíîâûõ ïðîöåññîâ ðàçâèòèÿ ëîêàëèçîâàííîé ïëàñòè÷íîñòè, íàïðèìåð, ñêîðîñòü è äèñïåðñèÿ àâòîâîëí. Ìîãóò áûòü ðàññ÷èòàíû ñîîòíîøåíèÿ ìåaeäó ìàñøòàáàìè ðàçâèòèÿ ëîêàëèçîâàííîé ïëàñòè÷íîñòè, à òàêaeå çàâèñèìîñòü äëèíû àâòîâîëíû îò ñòðóêòóðíûõ ïàðàìåòðîâ ìàòåðèàëà. Óñòàíîâëåíà ñâÿçü èçìåðÿåìîé âåëè÷èíû èíâàðèàíòà ñ ïîëîaeåíèåì èññëåäóåìîãî ìåòàëëà â Ïåðèîäè÷åñêîé ñèñòåìå ýëåìåíòîâ (Ìåíäåëååâà).Êëþ÷åâûå ñëîâà: ìåòàëë, äåôîðìàöèÿ, ïëàñòè÷íîñòü, ñòðóêòóðà, ëîêàëèçàöèÿ, óïðî÷íåíèå, àâòîâîëíû, äèñëîêàöèè. Введение: автоволны локализации деформацииÐàçâèòèþ ôèçè÷åñêîé òåîðèè ïëàñòè÷íîñòè òîëüêî çà ïîñëåäíèå ñòî ëåò áûëè ïîñâÿùåíû òûñÿ÷è ñòàòåé. Òåì íå ìåíåå, ýòà ïðîáëåìà äî ñèõ ïîð îñòà¸òñÿ äàë¸êîé îò ïîëíîé ÿñíîñòè. Ïðè÷èíà òàêîãî ïîëîaeåíèÿ ñîñòîèò, ïðåaeäå âñåãî, â ÷ðåçâû÷àéíîé ñëîae íîñòè ïðîöåññîâ, ëåaeàùèõ â îñíîâå ïëàñòè÷åñêîãî ôîðìîèçìåíåíèÿ, è çäåñü îñîáåííî âàaeíà ïðèíöèïèàëüíàÿ íåëèíåéíîñòü ñâÿçè íàïðÿaeåíèÿ òå÷åíèÿ ñ äåôîðìàöèåé äàaeå ïðè óìåðåííûõ çíà÷åíèÿõ ïîñëåäíåé. Êðîìå òîãî, ñóùåñòâåííà òàêaeå ñïîñîáíîñòü ìàòåðèàëà «ïîìíèòü» îáî âñåõ èñïûòàííûõ âîçäåéñòâèÿõ, êîòîðûå èñïûòàëà äåôîðìèðóåìàÿ ñðåäà. Òàêàÿ ïàìÿòü îáåñïå÷èâàåòñÿ çà ñ÷¸ò íåîáðàòèìîãî ñîçäàíèÿ â ìàòåðèàëå äåôåêòíîé ñòðóêòóðû è ñóáñòðóêòóðû.The principal characteristic of localized plastic-flow development, known as the elastoplastic invariant of deformation, is investigated for nineteen various metals. As shown, the distribution of the experimentally obtained values of the invariant can be described by the normal distribution low. The origin of the invariant and the consequences, which describe the most important features of localized plastic flow, are discussed. As established, the principal characteristics of autowave processes of localized plasticity development, for instance, the rate and dispersion, can be calculated. It is possible to calculate the relations between the scales of localized plasticity development as well as the dependence of autowave length on the structure characteristics of metals. The relationship between the measurable invariant value and the position of metal in the (Mendeleev) Periodic table is established.

Estimates of Metal Deformability

“…In the case of tension test, the deformation work is numerically equal to the surface area under stress-strain curve, and is the sum of the work of elastic and plastic deformation. Experimental evidence of the localized plastic flow was obtained using a double-exposure speckle photography method specially adapted for the study of deformation in photographic or digital versions [6][7][8]. This technique enables to reconstruct the field of displacement vectors r(x,y), that occurs when the strain increases δε ≈ 10 -3 on the sample surface, and to calculate all components of the plastic distortion tensor:…”

“…The velocity of the zones of localized plastic flow is determined by the strain hardening coefficient of the material [6][7][8] = + Ξ/~1/…”

“…In all cases the observed values of the velocities of the zones of localized plastic flow and the spatial period are 10 -5  Vaw  10 -4 m/s and ~ 5 ... 10 mm respectively. The product of Vaw (complex parameter of plasticity) characterizes the process of plastic flow [6][7][8] and has dimension of kinematic viscosity m 2 /s.…”

“…It is likely that at the intermediate stages, the deformation also proceeds in the form of a localization, and inadequate data is caused by the features of the experimental techniques used for the study. At deformation localization, an initially homogeneous medium is spontaneously divided into deformable and non-deformable volumes, the boundaries of which can be movable [6]. It is obvious that in localization zones and between them, plastic deformation develops in different ways.…”

“…In recent years, many authors experimentally observed patterns of localized plastic flow during deformation. In [1][2][3][4][5][6][7][8], laser interferometry, digital image correlation method, and thermal imaging systems were used for this.…”