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.
Abstract-The study is directed to conclusion and approbation of the new defining relations that describe arousal and change of stress fields in isotropic material during crystallization, taking into account temperature strains and structural shrinkage. The statement of the crystallization problem and numerical realization of the process by the example of linear and plane statements have been made. The problem of crystallization of a beam of isotropic material under nonuniform cooling with phase transitions has been considered. The authors removed the defining relations describing the occurrence and change of stress fields in an isotropic material during crystallization, taking into account temperature deformations and structural shrinkage. The numerical realization of the problem of crystallization of a beam was made by two methods: a finite difference method and a finite element method. The tendency of accumulation of an error of the finite difference method has been established. The verification of defining relations by the example of the problem of plate nonuniform controlled cooling from temperature above melting point has been made at the second stage of the study. Displacement, stress and strain fields that satisfy the physics of the process and boundary conditions have been obtained.
We investigate the tensely-strained state of three-dimensional construction at the measured settlements of the foundation. The numerical model of the construction is developed within the limits of the theory of the plates bending and rectilinear rods, it allows to reveal dangerous places in the strength members particularly in the interfloor plate. The three-dimensional model of the dangerous area is developed, which allows to define the level of damaging the plates material. Settlements levels leading to first cracks and full destruction of the investigated area of the construction are defined.
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