Ensemble Of Cracks Research Articles

Ориентационная природа эффекта деформационной памяти при трехосном циклическом неравнокомпонентном сжатии песчаника

Для описания механизмов и условий проявления эффекта деформационной памяти (эффекта Кайзера) в горных породах, подвергающихся трехмерному непропорциональному циклическому нагружению с изменением ориентации и формы эллипсоида Ламе, проведены эксперименты с кубическими образцами из полимиктового песчаника на Испытательной системе трехосного независимого нагружения с непрерывной записью сигналов акустической эмиссии. Результаты непропорционального трехосного сжатия по разработанной 9-цикловой программе нагружения показали, что доминирующим механизмом проявления эффекта памяти повреждений в каждом определенно ориентированном ансамбле дефектов является развитие микротрещин нормального отрыва, ориентированных субнормально к направлению минимального главного напряжения. Было обнаружено, что проявление эффекта Кайзера определяется не столько фактом раскрытия существующих «благоприятно» ориентированных микротрещин, сколько их дискретным ростом и появлением новых дефектов. Полученные экспериментальные результаты могут рассматриваться в качестве триггера для развития моделей деформирования и разрушения горных пород, учитывающих анизотропную природу и ориентационные эффекты развития поврежденности при различных сложных напряженно-деформированных состояниях и реальных условиях трехосного непропорционального нагружения, которые наблюдаются в природных и антропогенных системах.

Рост объемных эпитаксиальных пленок AlN полуполярной ориентации на подложках Si (001) и гибридных подложках SiC/Si (001)

Abstract The possibility of growing bulk (more than 7 μm thick) epitaxial semipolar AlN films on Si(001) and hybrid SiC/Si(001) substrates without cracks has been investigated. It is found that an AlN layer grown on the Si substrate is extended, whereas an AlN layer grown on the hybrid SiC/Si substrate is compressed. The limiting (critical) thickness of the semipolar AlN layer on the Si(001) substrate is determined to be ~7.5 μm. When the film thickness exceeds this value, an ensemble of cracks is formed in the film, leading to its total cracking and exfoliation from the substrate. The semipolar epitaxial AlN films with a thickness of more than 40 μm are grown on hybrid SiC/Si substrates without cracking and exfoliation from the substrate.

Kinetic genesis of some statistic regularities of fracture

The statistics of strength and longevity of solids has been the subject of investigation for many years. Some common regularities in fracture statistics have been experimentally revealed. These are Jhurkov's exponential and power-type longevity equations, Weibull's statistics of strength, and different types of size effect. However, the present notions on the nature of the observed statistic regularities are far from being complete. Here the object is to examine fracture statistics on the basis of a previously suggested kinetic approach. We consider the evolution of the statistical ensemble of cracks under static and steady-rate loading of a solid. The growth of an individual crack is therewith treated as a spasmodic stochastic process and presented by a time-dependent distribution density of a crack size. That function is used to construct the conditional longevity distribution with respect to the growth of an individual crack with the prescribed initial size. The final longevity distribution is found as the distribution of a minimum of conditional longevities. That procedure has been realized for both brittle and quasi-brittle cases. The obtained longevity and strength distributions were found to be in qualitative agreement with the observed statistic regularities. However, the conventional `weak link concept' and proposals for the statistics of dangerous defects are in conflict with the obtained results. It is moreover shown that, within the limits of the wide-spread concept, Jhurkov's longevity equation and Weibull's statistics of strength are mutually exclusive. Although the results were obtained from simple models, there is a good probability of kinetic origin for the basic statistic regularities of fracture.

Crack dynamics via Lagrange's equations and generalized coordinates

Cracks that are subjected to a sudden, sufficiently large, increase in stress respond with a combination of opening and unstable growth. This behavior is idealized here by representing the opening and growth as two generalized coordinates and determining the corresponding Lagrangean. Then the equation of motion are established for an arbitrary time-dependent driving pressure. Lagrange's equations are especially appropriate for systems involving dissipation, nonholonomic constraints, and other such processes that can not be accounted for in a Hamiltonian formulation. It is shown that the standard results for crack opening and stability are consequences of the Lagrange formulation, as is an algebraic expression for crack speed. Of course, the solution for the crack dynamics is approximate, but solving the full PDEs for the unstable cracks in a brittle structure (∼10,000 cracks/cc) is not practical, nor would it be appropriate since the details of the cracks vary between samples. Thus, the Lagrange formulation makes it possible to analyze brittle materials containing an ensemble of cracks in an efficient manner. In an example the ODEs are integrated numerically and it is shown that the results are consistent with analytic results. In that work the surface energy is considered constant, but when the stresses are modest, crack growth is governed by creep processes. It is shown that this slow growth can be accounted for by letting the surface energy depend on the stress-intensity factor in a manner that is based on crack-speed data.

Constructive statistical cracks mechanics

Abstract Physical postulates for the construction of non-equilibrium statistical mechanics for an ensemble of cracks are suggested. The kinetics of crack configurations is described by the hopping random Markov process, by which cracks appear and disappear by jumps. The Gibbs distribution is a stationary measure of this process. The rheology of a body with cracks can be described as time-dependent thermo-visco-elasticity. It is proved that the second law of thermodynamics is true for the model. Constitutive relations and expressions of energy balance and energy dissipation are given.

Ground motion in the near field of a fluid‐driven crack and its interpretation in the study of shallow volcanic tremor

We present a study of the motion of the ground in the near field of a fluid‐driven tensile crack embedded in a layered half space. The source that we consider is the jerky opening of a channel connecting two fluid‐filled cracks, and the cause of this opening is the excess pressure of fluid in one of the cracks. We make a complete representation of the three components of ground motion in the space, time, and frequency domains and analyze the effects of fluid compressibility, source depth, and medium structure on the ground response. The calculations show the presence of a dominant frequency of motion which depends not only on the source geometry and bulk modulus of the fluid but also on medium characteristics, receiver position, and the component of motion being considered. Using this source model, we view an episode of volcanic tremor as a continuous sequence produced by numerous jerky openings of channels occurring randomly in time along a chain of cracks. Our results are applied to the October 5–6, 1963, east rift eruption of Kilauea volcano, Hawaii, and found to be compatible with available seismic data, suggesting that magma is transported through an ensemble of cracks with the area of 1 × 1 km, each pair of cracks constituting an individual dike segment which opens in discrete increments at a rate of 1/s. We obtain the following parameters for each dike‐segment opening: increase in cavity volume, 40 m3; stress drop, 0.004 bar; seismic moment, 1019 dyn cm; and force applied by the fluid to open the dike, 1014 dyn. The total moment integrated over the entire duration of tremor for the eruption is 0.5 · 1024 dyn cm, roughly equivalent to a single magnitude M = 5 earthquake. The seismic source parameters and other field observations offer constraints on the process of mass transport and are compatible with the excess pressure and viscosity of magma of about 40 bars and 102 P, respectively.