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Complex investigations of mechanical behavior of metal matrix composites, coated materials and nature composites were carried out in the frame of the hierarchical numerical simulation approach. Relaxation constitutive equation taking into account the dislocation nature of plastic flow was developed. Non-homogeneous deformation mechanisms in the composites, including slow flows such as Luders front propagation, were investigated with an account for interfaces of different scales. An explicit introducing the material microstructure with clearly expressed curvilinear interfaces is shown to account for the scale factor. The use of different constitutive models for different microstructure components (plastic metals and alloys, brittle or viscous- brittle ceramics) provides the interconnection and interplay of different physical processes. Using the "metal matrix - ceramic reinforcing particle" composite as an example, the following hierarchy of characteristic scales can be explicitly introduced into the model formulation: macro – representative clusters of reinforcing particles (average size of 1 mm.), meso II – single reinforcing particle (average size - 20 mm. ), meso I – the radius of curvature of the interface (average size - 2 microns), micro – local fracture region (size - 200 nm). The simulated processes of plastic flow in the matrix and of particle cracking develop simultaneously and influence each other, and a homogenized response of the composite to an external loading depends on the properties of the constituent materials. Local regions exposed to tensile stresses was found to arise even under compression of the composite material, with the stress values being close to the magnitude of the external compressive load. It is these regions where the fracture of composites occurs. Considering a three-dimensional local volume with a single reinforcing particle, the interface curvature is shown to influence the fracture mechanisms: the particle cracking or debonding. The change in the cracking mechanism is found to appear in a certain depth of the rock formation and to be due to a change in the local stress-strain conditions near interfaces dependently on the rock pressure. A study of deformation and fracture of two-phase plastic substrate - brittle coating microstructures was carried out in two-dimensional formulation. The influence of the coating thickness and strain rate on the strength of the composites in investigated.
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