Parametric study of the conditions of supershear crack propagation in brittle materials

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in AIP Conference Proceedings 1683, 020209 (2015) and may be found at https://doi.org/10.1063/1.4932899.The paper is devoted to the numerical analysis of the conditions of acceleration of dynamically propagating longitudinal shear cracks from sub-Rayleigh to intersonic/supershear velocities. We showed that an ability of the initial crack to propagate in supershear regime can be predicted with use of the empirically derived dependence of the geometrical criterion of sub-Raleigh-to-intersonic transition on material and crack parameters

Key role of elastic vortices in the initiation of intersonic shear cracks

Using the particle-based method of movable cellular automata, we analyze the initiation and propagation of intersonic mode II cracks along a weak interface. We show that the stress concentration in front of the crack tip, which is believed to be the mechanism of acceleration of the crack beyond the speed of shear waves, is due to the formation of an elastic vortex. The vortex develops in front of the crack during the short initial period of crack propagation. It expands and moves away from the crack tip and finally detaches from it. Maximum stress concentration in the vortex is achieved at the moment of detachment of the vortex. The crack can accelerate towards the longitudinal wave speed if the magnitude of shear stresses in the elastic vortex reaches the material shear strength before vortex detachment. We have found that for given material parameters, the condition for the unstable accelerated crack propagation depends only on the ratio of the initial crack length to its width (e.g., due to surface roughness)

On the role of scales in contact mechanics and friction between elastomers and randomly rough self-affine surfaces

The paper is devoted to a qualitative analysis of friction of elastomers from the point of view of scales contributing to the force of friction. We argue that – contrary to widespread opinion – friction between a randomly rough self-affine fractal surface and an elastomer is not a multiscale phenomenon, but is governed mostly by the interplay of only two scales – as a rule the largest and the smallest scales of roughness of the contacting bodies. The hypothesis of two-scale character of elastomer friction is illustrated by computer simulations in the framework of the paradigm of Greenwood, Tabor and Grosch using a simplified one-dimensional model

Gravity with Higher Derivatives in D-Dimensions

The aim of this review is to discuss the ways to obtain results based on gravity with higher derivatives in D-dimensional world. We considered the following ways: (1) reduction to scalar tensor gravity, (2) direct solution of the equations of motion, (3) derivation of approximate equations in the presence of a small parameter in the system, and (4) the method of test functions. Some applications are presented to illustrate each method. The unification of two necessary elements of a future theory is also kept in mind - the extra dimensions and the extended form of the gravity.Comment: 22 pages, 9 figures, this article belongs to the Special Issue Selected Papers from the 17th Russian Gravitational Conference - International Conference on Gravity, Cosmology and Astrophysics (RUSGRAV-17

Sub-Planckian scale and limits for f(R)f(R) models

We study the Universe evolution starting from the sub-Planckian scale to present times. The requirement for an exponential expansion of the space with the observed metric as a final stage leads to significant restrictions on the parameter values of a $f(R)$-function. An initial metric of the Universe is supposed to be maximally symmetric with the positive curvature

Inhomogeneous compact extra dimensions and de Sitter cosmology

In the framework of multidimensional $f(R)$ gravity, we study the metrics of compact extra dimensions assuming that our 4D space has the de Sitter metric. Manifolds described by such metrics could be formed at the inflationary and even higher energy scales. It is shown that in the presence of a scalar field, varying in the extra factor space $\mathbb{M}_2$, it is possible to obtain a variety of inhomogeneous metrics in $\mathbb{M}_2$. Each of these metrics leads to a certain value of the 4D cosmological constant $\Lambda_4$, and in particular, it is possible to obtain $\Lambda_4 =0$, as is confirmed by numerically obtained solutions. A nontrivial scalar field distribution in the extra dimensions is an important feature of this family of models.Comment: 15 pages, 9 figure

Numerical analysis of the geometrical and material criteria of acceleration of shear crack to supershear velocity in brittle nanoporous solids

The paper is devoted to the study of dynamic propagation of mode II cracks in porous brittle materials with nanoscale pore size. We compared static (shear strength) and dynamic parameters of crack growth in dry and fluid saturated nanoporous brittle materials at different degrees of confinement. We have shown that pore fluid in nanoporous brittle materials influences mainly the dynamics of crack propagation. This leads in particular to pronounced peculiarities of the dependence of the critical value of dimensionless geometrical parameter of the initial crack (it majorizes the interval of the ratios of length to thickness for the cracks that are capable to accelerate to intersonic velocity) on applied crack normal stress. The results of the study are relevant for understanding the conditions of supershear regime of propagation of mode II cracks as well as for assessment of the ability of mode II cracks in brittle materials (including nanoporous fluid-saturated solids) to develop in supershear regime

An influence of normal stress and pore pressure on the conditions and dynamics of shear crack propagation in brittle solids

The paper is devoted to the study of the influence of crack-normal stress on the shear strength of the brittle material with initial crack and the geometrical condition of acceleration of dynamically growing crack towards the longitudinal wave speed. We considered elastic-brittle permeable materials with nanoscale pore size. We have shown that pore fluid in nanoporous brittle materials influences mainly the condition of shear crack propagation transition from conventional sub-Rayleigh regime to supershear one. The results of the study make it possible to assess the ability of initial cracks in brittle materials to develop in supershear regime under the condition of confined longitudinal shear

An important role of elastic vortices in unsteady propagation of longitudinal shear cracks in brittle materials

The paper is devoted to the numerical study of some fundamental aspects of longitudinal shear crack propagation in sub-Rayleigh and supershear regimes. The simulation was carried out with use of particle-based movable cellular automaton method. It is shown that a well-known phenomenon of shear crack acceleration towards longitudinal wave speed is explained by the formation and development of elastic vortex traveling ahead of the crack tip at a shear wave velocity. The stress concentration area ahead of the crack tip revealed by different authors is connected with the elastic vortex. Shear crack accelerates towards the longitudinal wave speed through the formation of a daughter crack by the mechanism of shearing (the daughter crack is formed in the center of elastic vortex). Analysis of sub-Raleigh-to-intersonic transition showed that the condition of this transition can be expressed in terms of dimensionless geometrical crack parameter