Lode-Nadai Coefficient Research Articles

Hierarchical modeling of deformation and damage of metal matrix composite under uniaxial loading conditions

A three-dimensional model for deformation of metal matrix composite with aluminum matrix and silicon carbide reinforcement particles is developed. The model accounts for an internal structure of the composite, as well as rheology of its constituents. The model is further used in numerical simulations in order to study the evolution of stress-strain state parameters in a randomly-chosen composite microstructure fragment under uniaxial tension and compression loading on micro- and macroscale. The parameters include the stress stiffness coefficient, the Lode-Nadai coefficient and equivalent (von Mises) strain. It is found that local deformation regions and internal tensile stress concentration regions appear in the material of composite matrix. Adhering to a phenomenological damage theory, a damage development is computed in the matrix metal. We present damage fields and damage distributions for uniaxial tension and compression.

Patterns of stress drop in earthquakes of the Northern Tien Shan

Source parameters of local earthquakes that occurred between 1998 and 2012 within the Kyrgyz seismological network (KNET) are used to study the patterns of stress drop in the Northern Tien Shan. The dynamic parameters of source radius r, the seismic moment M0, and the stress drop Ao are estimated for eighty seven M = 3.0-5.5 (K = 9.5-13.7) events, which make up 86% of earthquakes with this magnitude (99) for the period of observations. Earthquake mechanisms are determined either from P-wave arrivals (66 events) or by inversion (14 events). The distribution of earthquake mechanisms with the maximum (14 events) and minimum (14 events) stress drop shows that the amount of released stress correlates with slip geometry and revere-slip events contribute the most to the stress drop in the area. The spatial distribution of events with Ao > 0.9 MPa is compared with maps of kinematic parameters (Lode-Nadai coefficient or stress ratio, qo, and strain angle, o, based on average strain tensors according to the complete earthquake catalog for the Northern Tien Shan (1056 events for 1998-2012). The two sets of source parameters (r, M0, Ao and jio, o) correlate within the eastern Kyrgyz Range and the Karamoinok and Syndyk Ranges. © 2016, V.S. Sobolev IGM, Siberian Branch of the RAS. Published by Elsevier B.V. All rights reserved.

A fracture locus for a 50 volume-percent Al/SiC metal matrix composite at high temperature

The effect of the stress state on the fracture locus function of the 50 vol.% Al/SiC metal matrix composite at high temperature is studied. The value of fracture locus function is quantitatively characterized by the amount of shear strain accumulated prior to the moment of failure. Nondimensional invariant parameters are used as characteristics of the stress state, namely, the stress triaxiality k and the Lode-Nadai coefficient μ σ showing the form of the stress state. Besides conventional testing for tension, compression and torsion of smooth cylindrical specimens, the complex of mechanical tests includes a new type of testing, namely, that for bell-shaped specimens. These kinds of testing enable one to study fracture strain under monotonic deformation in the ranges μ σ = 0 … + 1 and k = − 1.08...0 without using high-pressure technologies. The stress–strain state during specimen testing is here evaluated from the finite element simulation of testing in ANSYS. The tests were performed at a temperature of 300 °C and shear strain rate intensity Η = 0.1; 0.3; 0.5 1/s. The test results have offered a fracture locus, which can be used in models of damage mechanics to predict fracture of the material in die forging processes.

The structure of the Tuapse shear zone according to the field tectonophysical data

The results of field structural studies of the Tuapse shear zone in the Northwest Caucasus are presented. This zone is characterized by shear displacements of various scales with a dominant horizontal shear, viz., a geodynamic type of the stress state, which leads to the formation of faults with mostly lateral displacement of wings, i.e., along the strike of the fault surface. The quantitative characteristics of the local stress conditions in the shear zone (the positions of principal axes and the Lode–Nadai coefficient) are determined on the basis of cataclastic analysis and geological indicators of the paleostresses. The differences between these characteristics are considered for the large tectonic zones. Significant spatial (areal) variations in orientations of the axes of major normal stresses in the shear zone and their local weak gentle variations are evidence of a consistent general stress direction during the formation of faults during the Late Eocene–Miocene deformation epoch.

Paleostress reconstructions and structure of the Tuapse strike-slip fault

The results of the field structural studies of Northwest Caucasus Tuapse Shear Zone are presented. There are strike-slip displacements of different scale and the domination of horizontal shear conditions (type of geodynamic stress state that cause the formation of faults with mainly lateral movement of the wings along strike fault surface) within this zone. Using the method of cataclastic analysis of the collected geological paleostresses indicators the quantitative characteristics of the local stress states within the shear zone - position of the principal stresses axes and the Lode-Nadai coefficient - are identified. Differences of these characteristics considered for large tectonic zones. Significant spatial (territorial) variations of the orientations of the principal normal stresses axes identified within the shear zone, and their small smooth variations within local areas, which indicate on consistency of the general stress direction in the formation of studied fault structures in the Late Eocene-Miocene deformation period.

Influence of the stressed state on the limiting plasticity of M00K copper rolled wire

A fracture locus of copper rolled wire depending on the stressed-state coefficient (k) and Lode–Nadai coefficient (μσ) is constructed. The region of using this fracture locus to calculate the damage is limited by values k < 1,4 and –1 < μσ < 0. To construct the fracture locus, we performed twisting tests of cylindrical samples and tension tests of cylindrical and plane samples in air and in a chamber with a controlled liquid pressure, which was varied from 49 to 375 MPa. The constructed fracture locus will be further used for the calculations of damage of copper rolled wire in drawing processes, by the results of which, recommendations for lowering the wire breakage during drawing will be elaborated.

ВЛИЯНИЕ НАПРЯЖЕННОГО СОСТОЯНИЯ НА ПРЕДЕЛЬНУЮ ПЛАСТИЧНОСТЬ ТРУБНОЙ СТАЛИ ГРУППЫ ПРОЧНОСТИ Х80

The dependence of ultimate plasticity on the triaxiality parameter and the Lode-Nadai coefficient is obtained for steel X80. The fracture locus allows the plasticity of the investigated materials to be evaluated for the whole range of the Lode-Nadai coefficient. Cylindrical specimen tension, bell-type specimen tension and compression and membrane extrusion are used for fracture locus calibration. The results can be used for plasticity resource estimation for steels under a complex stress-strain state in main pipelines subject to extreme loads.

Deformation of the Earth’s crust in the Northern Tien Shan according to the earthquake focal data and satellite geodesy

For evaluating the deformations of the Earth’s crust in the Northern Tien Shan, we calculated the mode and intensity of the seismotectonic deformations (STD) for this region. The input for these calculations were the catalog data on the focal mechanisms of earthquakes, obtained by wave inversion of the signals recorded at the Kyrgyz seismic network (KNET) for the period 1994–2006. In the construction of STD maps, a modern approach to the classification of seismotectonic deformations was applied. This approach distinguishes eleven typical patterns of deformation. The areal distributions of the Lode-Nadai coefficient, as well as of the vertical component and the aspect angle of the deformed state were obtained. At the same time, based on the GPS measurements in the Northern Tien Shan during 1994–2006, the rates of dilatation and shear deformation of the Earth’s crust were estimated. A comparison between the directions of strain axes derived from the GPS data and from the earthquake focal data is carried out.

Seismotectonic deformations and recent tectonics of the Tien Shan

Seismotectonic strains (STSs) are calculated on the basis of the catalog of focal mechanisms of earthquakes including more than 5000 events compiled at the Institute of Seismology, National Academy of Sciences of the Kyrgyz Republic, in order to investigate deformation processes in the Tien Shan (38°–44°N, 68°–80°E). A modern approach to STS classification based on the identification of 11 deformation settings (including four main, two extreme, and five transitional settings) is applied for constructing STS maps. Areal distributions of the Lode-Nadai coefficient, vertical component, and angle of the stress-state type are obtained. The results of the calculations are verified by comparing them with STS calculations using focal mechanisms of 116 strong earthquakes from the centroid moment tensor catalog of Harvard University that occurred in the studied region in 1976–2003.