Damage and Fracture Composites and WearCutting and Drilling Damage and Fracture Composites and WearCutting and DrillingA mathematical model of damage evolution and fracture is developed on the basis of the kinetic theory of strength and percolation model of microcrack coalescence. Formulas for the time to failure of cracked and non-cracked specimen are derived. It is shown that the fractal dimension of fracture surface is different at different stages of crack growth. The concept of two regimes of crack formation, one being caused by the microcrack coalescence and similar to the percolation, and the second, similar to the fractal aggregation, is formulated. Interrelations between the damage evolution law and crack growth law are also considered.
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A crack velocity versus crack length relation is derived on the basis of a fractal model of crack growth. The propagation of a crack is supposed to be caused by joining of randomly distributed microcracks to the crack. The fractal dimension of fracture surface is calculated on the basis of a probabilistic description of the joining of a microcrack to the crack. The effect of fractal dimension of a crack on the time to failure of a cracked body is discussed as well.
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Theoretical investigations of damage and fracture which are based on concepts of the theory of complex systems are reviewed and analyzed.
The models of fracture which have been developed with the use of the methods of following theories,
are considered: theory of phase transitions and statistical
physics, percolation and fractals theories, theories of
dynamical systems, bifurcations and self-organization.
The main
achievements, perspectives and limitations of the application of
these methods in modelling of fracture are analyzed.
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A mathematical model of damage evolution in heterogeneous materials is developed using the methods of the theory of fuzzy sets. The fuzzy concept of damage is formulated and some applications of this concept are considered. The influence of the material heterogeneity on the damage as well as the heterogenization of the material due to the damage evolution are studied. On the basis of the fuzzy concept of damage, it is shown that the greater the heterogeneity of material, the closer is the material to failure under loading.
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A mathematical model of damage evolution and localization in heterogeneous materials is developed on the basis of the theory of stochastic equations. The kinetic differential equation for time-dependent probability distribution of a damage parameter, which is similar to the Fokker-Planck equation, formulas for the time-to-failure and probability of failure are derived theoretically. By solving the stochastic damage evolution equation together with the wave propagation equations in damaged heterogeneous materials, it was shown numerically that the correlation coefficient between values of the damage parameter in neighbouring points of a material (this coefficient characterizes the degree of the damage localization in the material) increases with increasing the averaged damage parameter.
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The mechanisms which occur during damage initiation, evolution and
crack growth in AlSi cast alloys are studied by in-situ tensile testing
in a scanning electron microscope. It is shown that microcracks in
AlSi7Mg0,3 alloys are predominantly formed in the Si eutectic. Shear
bands are seen to precede the breaking of the Si particles and the
dislocation pile-up mechanism can thus be confirmed as the dominant
damage initiating process. Both micro- and macrocrack coalescence have
been observed in the course of the experiments. The effect of the
microstructure of the AlSi cast alloys on damage nucleation, crack
formation and softening is analyzed.
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Mechanisms of deformation, damage and fracture in AlSi7Mg0,3 cast alloys, with lamellar and Sb-modified globular structure of the Si-eutectic were investigated experimentally and numerically. A numerical technique was developed and verified
to simulate the deformation of material, taking into accout its real structure.
Crack initiation and subsequent crack propagation in the real microstructure of the alloys were simulated using the method of multiphase elements and the automatic element elimination technique.
A new 3D method of multiphase finite elements which permits the simulation of the elasto-plastic deformation behaviour of specimens with real microstructures has been developed. In contrast to conventional ``single-phase elements'', the Gaussian points of a ``multiphase element'' may be assigned to different phases in the material, and the interface may run across the finite element. This makes it possible to use a simple FE mesh to simulate the deformation by complex microstructures, local properties of which can be assigned to the Gaussian points of the mesh automatically.
The 3D-multiphase elements were applied to the simulation of the deformation behaviour of CT specimen, as well as to some simpler models. The 3D-multiphase element was verified by comparison with 2D simulation, single-phase FE simulation as well as with the experimental observations of the deformation of CT-specimens. It was shown that 3D-multiphase elements are a very reliable and efficient technique in simulating the deformation of specimens with real microstructures.
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The formation and growth of a crack in a two-phase material is simulated
using the method of multiphase finite elements (MPFE) and element
elimination technique (EET). The MPFE method uses finite elements, the
Gaussian points of
which may be assigned to different phases of the heterogeneous material
with different physical properties. The efficiency of these techniques for
different materials and different levels of simulation was studied.
The simulation of damage and crack growth was conducted for several groups of
composites: WC-Co hard alloys, Al/Si and Al/SiC composites, and both on
macro-, meso- and microlevel. On the
macrolevel, the initiation and propagation of a crack in a quasi-homogeneous
composite material with averaged properties is simulated.
For the simulation of damage in ductile matrix of composites on microlevel, a
improved criterion of damage based on Rice-Tracey and crystal plasticity
approach was developed.
It is shown that the used modern techniques of numerical simulation (MPFE and
EET) is very
efficient in simulation of deformation and damage evolution in
heterogeneous materials with inclusions.
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The damage initiation and growth in
ductile materials is simulated with the use of
the Rice and Tracey's damage parameter and the element elimination
techniques, and also with the use of the cohesive surface concept. The
force-displacement curves for the deformed specimens are determined.
The effect of the critical level of the damage
parameter on the force-displacement curve and critical load is studied.
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The formation and failure of hard skeleton of sintered composites with a high content of high melting point filler are studied theoretically. On the basis of a probabilistic analysis of the joining of filler particles in sintering, the characteristics of the structure of composite (i.e., connectivity and contiguity of the hard skeleton) are calculated. Conditions of the failure of the skeleton in a loaded specimen from sintered composite are determined on the basis of the theories of percolation and reliability. It is shown that the compressive strength of the composites is proportional to the square root of the contiguity of skeleton. The developed model allows to analyze the interrelations between conditions of sintering, structure and strength of the composite.
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The local rate of wear of a tool made from matrix composite is calculated on the basis of a model of tool wear as a fatigue failure of hard grains on the contact surface. The effect of tool wear on the tool shape and the reverse effects are studied with the use of a model of the dulling and wear of a tool based on the dynamical system theory. The tool is modeled as a dynamical control system with feedbacks. The effect of temporal variations of cutting forces and tool-to-workpiece vibrations on the tool wear are investigated.
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The effect of regimes of grinding by CBN grinding wheels
on the parameters of surface roughness (Ra, Rz, Rm, Sm, etc)
of specimens from high-speed steels are studied experimentally. The (nonlinear) regression equations which relate the surface roughness parameters with the grinding rate and feed are obtained.
The correlation coefficients between the roughness
parameters, between the parameters and regimes of grinding as well as coefficients of sensitivity of the surface
roughness parameters to the grinding regimes are calculated.
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A mathematical model for the formation of fractal interfaces in liquid-phase sintering of composites is developed and the
influence of the fractality of interface on the damage initiation in matrix is investigated.
It is shown that conditions of the diffusion mass transfer in the liquid phase sintering influence the interface structure and strength of composites: the greater is the rate of mass transfer of the filler material in sintering, the greater the fractal dimension of filler/ matrix interface and the more intensive the damage initiation in composite matrix under loading of the sintered composite.
An informational approach to the drilling tool design
is suggested. On a basis of a model of tool/rock
interaction, relation between an informational characteristic
of drilling tool and the damage in loaded rock is obtained.
A general principle of tool improvement
is stated as follows: the tool effectiveness is the more,
the greater is an informational entropy of distribution
of local characteristics of tool. To test an applicability
of this approach technical solutions and patents in the
area of mining tool design are analyzed.
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Experimental investigations of cutting of brittle materials are presented. Mechanisms of brittle material cutting and the effects of tool shape and orientation of work surface are studied.It is shown that the efficiency of drilling by multicutter tools may be improved if one uses the effect of an interaction of cracks formed under neighbouring cuts. Equations for cutting forces and recommendations for the optimal placement of cutters on a complex tool are presented.
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Experimental and theoretical investigations of physical mechanisms of rock fragmentation under mechanical loading are reviewed. Mechanisms of the formation of zone of crushed material, subsurface cracks, chipping as well as the effect of tool shape and rate of loading on the fragmentation of rock are considered. The analysis allows to fomulate possible ways of drilling tool improvement .
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Methods of the theory of information are applied to model the stress state in disordered materials and the contact interaction of two bodies made from disordered materials. The stress distribution in loaded disordered material is described with the use of a probability function of local stress components which is determined with the use of the maximum entropy method. Possibilities of a practical application of developed model are demonstrated by investigating of the indexing effect. It is shown that the location of cutters or teeth on a multicutter tool in groups or in pairs ensures higher intensity of work material destruction and can be recommended for the tool improvement.
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