Simulation of phase transformations in the field of internal stresses

• Autorzy: Vlasov N. , Fedik I.

Warianty tytułu

PL

Modelowanie przemian fazowych w polu naprężeń wewnętrznych

• Konferencja: 14th KomPlasTech Conference, Zakopane, January 14-17, 2007
• Języki publikacji: EN

Abstrakty

EN

The main types of the internal stresses are the thermal and residual ones and fields of structural defects as well. These stresses have an essential effect on the phase transformations in metals. The kinetics of the process is described by a parabolic equation under corresponding initial and boundary conditions [1,2]. In general, the internal stresses fields have complex dependence on coordinates. Therefore, essential mathematical difficulties occur when solving a diffusion equation taking into account the stresses. A pleasant exclusion from a general rule is the internal stresses with a logarithmic coordinate dependence. Such dependence allows the exact solution of the diffusion kinetics task to be obtained. In this report preference is given to just such coordinate dependences of internal stresses field. The aim of this report is simulating the phase transformations in the field of internal stresses with a logarithmic coordinate dependence. Triple grain boundaries are considered as structural defects. They serve as stress concentrators under dynamic or temperature loadings. This is caused by the orientation dependence of elastic and thermophysical characteristics of the contiguous grain material. The dilatation field of considered defects depends logarithmic on the radial coordinate. The hydride phases formation within the alloys on the base of zirconium is enough to be mentioned as an illustration. This material is used for claddings of fuel elements of nuclear reactors. Elastic interaction of a hydrogen atom with the triple grain boundaries is defined by known relation , where ?ll is the first invariant of the tensor of structural defect stresses and ?? is the change in crystal volume when placing a hydrogen atom. Analytical relations for the field of atomic hydrogen concentration near the triple grain boundaries are given. If the concentration of hydrogen atoms exceeds the solubility limit at a given temperature, hydride phases are formed in zirconium. The further growth of hydrides is limited by the diffusion supply of hydrogen atoms. The influence of a stress field is that, in addition to the concentration gradient, the hydrogen atoms migrate due to the stress field gradient of the triple grain boundaries. Because of this, the velocity of the hydride phase boundary increases. Numeral simulation of the material phase transformations process taking into account the internal stresses field includes a definite sequence of the mathematical operations. These operations define the algorithm of the material phase transformations calculation: definition of the first invariant of the internal stresses tensor, mathematical formulation of the task of impurity atoms diffusion followed by the new phase formation. The exact analytical solution task of phase transformations in the area of the triple grain boundaries is the test example for a complex field of internal stresses.

PL

Głównymi typami naprężeń wewnętrznych są naprężenia termiczne i rezydualne, a także obszary defektów materiało­wych. Naprężenia te posiadają znaczący wpływ na przemiany fazowe w materiale. Kinetyka takich zjawisk opisana jest poprzez równanie paraboliczne z odpowiednimi warunkami początkowymi i brzegowymi. Celem niniejszego artykułu jest symulacja przemian fazowych w obszarze naprężeń wewnętrznych z logarytmiczną zależnością współrzędnych. Zależność taka umożliwia otrzymanie dokładnego rozwiązania zagadnienia kinetyki dyfuzji. Natomiast potrójna granica pomiędzy ziarnami brana jest pod uwagę jako defekt materiału i jest miejscem koncentracji naprężeń. Jako przykład pokazano strukturę stopów na bazie cyrkonu charakteryzującą się formowaniem faz hybry­dowych. Dokładne rozwiązanie analityczne zagadnienia trans­formacji fazowych w obszarze potrójnych granic ziaren stanowi przykład testowy dla analizy kompleksowego pola naprężeń wewnętrznych.

Słowa kluczowe

EN

internal stresses; diffusion kinetics; phase transformations

• Wydawca: Wydawnictwa AGH
• Czasopismo: Computer Methods in Materials Science
• Rocznik: 2007
• Tom: Vol. 7, No. 1
• Strony: 78--82
• Opis fizyczny: Bibliogr. 10 poz., rys.

Twórcy

autor

Vlasov N.

autor

Fedik I.

• Scientific Research Institute Scientific Industrial Association "Luch", Zheleznodorozhnaya, 24, Podolsk, Moscow region Russia 142100,

Bibliografia

• Melan, E., Parkus, H., 1953, Wärmespannungen infolge stationärer Temperaturfelder, Springer-Verlag, Wien.
• Parkus, H., 1959, Instationäre Wärmespannungen, Springer-Verlag, Wien.
• Smith, E., 1997. The stress in a zirconium alloy due to the hydride precipitation misfit strains, J. Mater. Sci., 32, 1127-1131.
• Teodosiu, C., 1982, Elastic models of crystal defects, Springer, Heidelberg.
• Timoshenko, S.P., Gudier, G., 1979, Theory of Elasticity, Translation from English, Nauka, Moscow.
• Yarias, A.G., Massih, A.R., 2000. Simulation of hydrogen em-brittlement in zirconium alloys under stress and temperature gradients, J. Nuclear Materials, 279, 273-285.
• Vlasov, N.M., Gontar, A.S., Zaznoba, Y.A., 2001. Decomposition of Solid Solution in an Alloy under High Plastic Strain, Technical Physics, 46, 569-572.
• Vlasov, N.M., Fedik, I.I., 2002. Hydrogen segregation in the of three fold junctions of grain boundaries, Int. J. Hydrogen Energy, 22, 921-926.
• Vlasov, N.M., Fedik, I.I., 2006, Structural and impurity traps for hydrogen atoms, Int. J. Hydrogen Energy, 31, 265-267.
• Wappling, D., Massih, A.R., Stahle, P., 1997. A model for hydride-induced embrittlement in zirconium - based alloys, J. Nuclear Materials, 249, 231-238.