Mechanics of Brittle Fracture

Abstract

Development of steeply dipping coal seam deposits of the Prokop'ev-Kiselov coal-bearing region of the Kuznets Basin introduces an important problem, i.e., calculation of the stressstrain state of a sloping-bedded rock mass. As has been demonstrated in a number of works, e.g., in [I], in many mechanics problems the rock mass may be modeled by an elastic uniform and isotropic material.The authors in [2] use these assumptions in order to analyze the stability horizontal workings in a slopping-bedded rock mass.In [3] it is assumed that the stress-strain state in each layer may be assumed to be uniform, and in the rock mass as a whole close to the working it may be assumed to be symmetrical relative to the working axis. On the basis for using the theory for complex variable functions, calculation of the stress field around a working in seams whose thickness is quite small and whose elasticity moduli are identical or similar, is carried out. However, mining is often carried out in rock masses of complex structure with layers of different thickness and with diffeent deformation properties.In order to determine the stress-strain state of these rock masses, analytical methods are not always suitable, and therefore it is necessary to turn to numerical methods, one of which is an effective method for solving rock mechanics problems, i.e., the finite element method [4][5][6][7][8].It will be used subsequently in order to find the stress-strain state of a sloping-bedded rock mass.

Dynamic Propagation Problems of Mode Iii Semi-Infinite Crack

“…where, C 44 , C 55 are the elastic constants, ρ is the mass density and W is the displacement component along Z (Cherepanov, 1979;Sih, 1968;Sih and MacDonald, 1964;Freund, 1998;Nian-Chun et al, 2004;2005;2006;Atkinson, 1975;1965). Using Atkinson transform (Nian-Chun et al, 2004;2005;2006;Atkinson, 1975;1965), it is found that Equation 2:…”

“…When T(η) = i (C -ρη ) C , in order to represent expediently, therefore the positive root is taken. Here exists (Cherepanov, 1979;Nian-Chun et al, 2004;2005;2006;Atkinson, 1975):…”

“…The considered problems are confined in the anti-plane. The anti-plane equation of motion for an orthotropic anisotropic body is given by (Eringer, 1975;Sih, 1977a;Erdogan, 1968;Cherepanov, 1979;Kostrov, 1964;Freund, 1998):…”

“…Dynamic problem is an important research field in modern fracture mechanics. Due to the interaction of the stress waves under complex dynamic loading cases, the theory of dynamic fracture mechanics is still innovated and developed (Cherepanov, 1979;Sih, 1968;Freund, 1998). However, a lot of engineering structures are under the conditions of dynamic loadings and the static theory can't effectually III resolve a series of dynamic queries, so it is indispensable to study the fracture dynamics problems (Sih, 1968;Kostrov, 1964;Freund, 1998;Sih and MacDonald, 1974;Srolovitz and Source, 1997).…”

“…The considered problems are confined in the anti-plane. The anti-plane equation of motion for an orthotropic anisotropic body is given by (Eringer, 1975;Sih, 1977a;Erdogan, 1968;Cherepanov, 1979;Kostrov, 1964;Freund, 1998): Statics problems of anti-plane shear loading were researched very much (Eringer, 1975;Sih, 1977a;Erdogan, 1968) in the past of several decades. Dynamic problem is an important research field in modern fracture mechanics.…”