The role of the collective behavior of defect ensembles at the crack tip and the laws of fatigue crack propagation in aluminum-magnesium alloy AMg6 have been studied under conditions of symmetric tension-compression gigacycle loading at 20 kHz using ultrasonic fatigue testing machine Shimadzu USF2000. 3D New View 5010 interferometer profiler high resolution data of defect induced roughness in the crack process zone under fatigue crack path revealed the existence of two characteristic scales: the scale of the process zone and the correlation length that is the scale when the correlated behavior of defect induced roughness has started. A mathematical model allowing the assessment of fatigue resistance of functional metal material on the basis of the analysis of loading parameters and the resulting fracture surface is developed. Analyzing the image by means of the wavelet-analysis, the basis parameters of a destruction surface are allocated. Based on the analysis of the destruction surface characteristics and the corresponding loading parameters, the fatigue life of the functional material is evaluated. For the solution of the problem, the elements of the fuzzy sets theory are used.
Институт гидродинамики им. М.А. Лаврентьева СО РАН, Новосибирск, Россия Новосибирский национальный исследовательский государственный университет, Новосибирск, РоссияРассматривается система из четырех квазилинейных дифференциальных уравнений первого порядка, описывающая плоское пластическое течение материала вне выпуклого отверстия с учетом эффекта инерции. Показано, что система имеет два семейства кратных вещественных характеристик, каждому из которых соответствует один собственный и один присоединенный векторы. В силу этого данная модель не является гиперболической в классическом смысле. Система уравнений преобразуется к эволюционному виду, и на ее основе выполнены численные расчеты, иллюстрирующие влияние сил инерции на основные параметры течения.Ключевые слова: пластическое течение, силы инерции, криволинейные координаты, кратные характеристики, разностная схема
EVOLUTIONARY MODEL OF THE PLANE PLASTIC FLOW OF A MATERIAL WITH ALLOWANCE FOR INERTIAL FORCES
B.D. Annin, V.V. Ostapenko and A.A. Chesnokov
Lavrentyev Institute of Hydrodynamics SB RAS, Novosibirsk, Russia Novosibirsk National Research State University, Novosibirsk, RussiaWe consider a system of four quasi-linear first-order differential equations describing the planar plastic flow of a material outside of a convex hole taking into account the effect of inertia. It is shown that the system has two sets of multiple real characteristics, for each one eigenvector and one adjoined vector are appropriate. For this reason, this model is not hyperbolic in the classical sense. The system of equations is transformed into a set of evolutionary equations, which is used for numerical calculations illustrating the effect of inertia forces on the main parameters of the flow.
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