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The modelling of splitting destruction of barriers from anisotropic materials in 3D

Depending on kinematic or geometric parameters of the stressing of barriers, their deterioration may happen as a result of cratering, fuse blowing, formation of a spalling plate, etc. For the purposes of modelling simulation of various types of deterioration, it is important to use different criteria of deterioration. This work offers an approach to the modelling of slabbing deterioration of barriers allowing for the anisotropy of elastic and plastic properties of barrier materials. The equations of continuum mechanics are means of modelling the kinetics of formation, development, and fusion of micropores in waves of tension. The presented computation model of the deterioration of anisotropic materials in waves of tension consists of two parts, which are 1) equations describing the law of development of discontinuity flaws (pores of spherical shape) and 2) equations defining the behaviour of the elastoplastic material, taking into account changes in mechanical properties (elastic and plastic ones) due to the formation and development of a great number of pores right up to the deterioration of the material. Introduction Even normal impact loading causes three-dimensional stress state in the obstruction. Spallation fracture in engineering materials with zonal, structural and crystallographic heterogeneity depends on the quality of the material. Spallation fracture velocity depends on applied stress and is proportional to concentration of fracture nuclei and their average growth rate. Zonal heterogeneity is determined by ingot technology and pressure shaping. Ingot manufacturing is accompanied by heterogeneous distribution of alloying agents and inevitable impurities in cast zones (surface, central, upper and bottom) and inside crystallites. An additional problem is original porosity and contraction cavities which make several percents in casting blocks. When these materials are rolled, some pores are sealed, while the rest of them are transformed into the system of flat cracks along rolling direction and vertical to estimated loading. Thus it leads to significant anisotropy in mechanical properties in the plane and through the thickness of the cast. Spallation strength evaluation makes it possible to determine the performance level of the structure made of such materials. But all experimental techniques used to research spallation fracture phenomena provide only indirect information about fractures process and stresses. Computer simulation of dynamic deformation and spallation fracture of engineering elastoplastic materials makes it possible to get the spallation fracture model independent from material deformation model. The research uses spallation fracture criterion modified by critical level of deformation by Johnson G.N. [1] Heterogeneous porous anisotropic medium is viewed as a two-component material, consisting of the matrix and inclusions, i.e. pores. Forgetting surface energy of pores and gas pressure in them, we see that porous material pressure is determined though matrix pressure and porosity. The equation to describe porosity variance in the material is obtained from the solution of a single pore deformation under hydrostatic tension in dynamic approximation [2]. It is supposed that departures from spherical shapes of pores in an anisotropic material can be ignored. This sets certain limits for model validity: the model is can be applied to calculate fracture of porous materials with low anisotropy of plastic properties, such as that of metals and alloys. The continual-kinetic approach is used to simulate fracture as a continuous process of damage accumulation by means of aggregate parameters. Material fracture under tension is the process of formation, merging and growth of micropores. The net effect of micropores on stress state of the medium consists in lower values of mechanical properties due to smaller effective cross-section plane in the porous material though which the loading is transmitted. The peculiarity of plastic deformation of porous solids is that it is accompanied by irreverible change in volume, besides, plastic deformation depends on hydrosatic stress component, i.e. even hydrostatic stress component can cause plasticity. In case of high concentration of micorpores in the cell the distance between neighboring mocroppores becomes proportionate to their size. Besides, due to the chaotic distribution of micropores it is possible for the neigboring micorpores to be closer to each other. It leads to assumption of micropores interaction when they reach critical concentration followed by their merge and, in the long run, by aperture of continuity between pores in the cell. The cell gets a fracture with the size equal to characteristic cell size. In the statement of the problem simulation of deformation and fracture in isotropic and anisptropic materials differs only in connection between stresses and deformation. Mathematic simulation is performed within continuum mechanics. The set of equations to describe the motion of compressible medium includes the following equations: continuity equation, motion equation and energy equation [3]. The model is used based on one of the first porous medium models. From Carroll-Hault model we use the equation of state for porous materials taken as   ) , / ( E V f P  , (1) which makes it possible to take into account smaller effective cross-section area through which the load in a porous material is transmitted [4]. Here P is hydrostatic pressure, V is volume,  is porosity, E specific internal energy. The damage is measured by means of porosity factor originally proposed by Herrman [5]. This is the relation of specific volume of porous medium ( ) m p V V V   to the specific volume of the solid material matrix (basic material):