The mechanismoftempered glass fracture is analyzed. Calculationmethods are proposed for determining the degree of tempering required to ensure the safe character of glass fragmentation, the number of glass fragments resulting from fracture, and their average size.The fracture of tempered glass is the self-supporting fracture ofa fragile body, and one can talk of the appearance ofa fracture wave [9]. Consider a plate of thickness h that is situated in a uniform field of main tensile stresses cr m • The stationary character of propagation of the fracture wave is possible only when its velocity is equal to the velocity of propagation of longitudinal elastic waves Co which can be determined by formula [10] where 0 is the thickness of the glass.It would be correct to make the calculation relating the number ofthe fragments N to the stresses in the central (mid. dIe) layer cr c in the case ofunifonn strain of the plate across the entire thickness h. However, in tempered glass the stresses across the plate thickness vary. Let us introduce the average stress value over the plate thickness [8] for industrially tempered glassThe purpose of the present paper is to elucidate the interrelation between the degree of tempering of glass and the number of the fragments resulting from fracture, and to determine the minimum degree of tempering required to ensure the safe character of fragmentation of tempered glass.In fracture of tempered glass, cracks propagate in its middle layer, which is in a state of strain [6]. Let us represent this layer as a separate plate, whose thickness for glass temperedThe nature of fracture of tempered glass determines its degree of safety, The minimum number of fragments oftempered glass for a prescribed area of 5 x 5 ern? is limited by GOST 5727-88. It is known that the number of fragments is proportional to the degree of tempering of the glass, i.e., to the tensile stresses in the middle layer of the tempered glass. However, in spite of the fact that standards similar to the one quoted here exist in all industrial countries, the problem of the minimally required degree of tempering which ensures the safety of glass of different thickness or composition remains unanswered.The reason for that is probably as follows. Although the problem of the interrelation between the degree of tempering and the number of the fragments resulting from fragmentation ofa specific glass was first studied by P. Acloque in 1956 [1], that paper, as well as some later works, were based on the experimental investigations. Owing to the difference in the experimental methods used and the glass compositions investigated, the data obtained by J. Barsom, K. Akeioshi and E. Kanai, do not provide an answer to the question mentioned above.In [5], the method for predicting the number of fragments makes it possible to account for the physical properties ofdifferent glass compositions (namely, the modulus of elasticity of the glass). However, the calculations were based on the Rittinger law of comminution (the law of surfaces). Theref...

The structure of high-porosity materials whose structure has a complicated organization, containing macroand micropores, amorphous and crystalline phases, and other heterogeneous inclusions, is modeled.Foam glass is one of the most effective heat-insulating building materials, which has a unique set of properties and a wide range of applications. However, despite this, only foam glass made by foreign producers is offered in the market for building materials. In our country, the production of foam glass is in the beginning stages. This is primarily because the technological regimes have not been adequately worked out. Although the production of foam glass is a relatively simple process, there are problems associated with the complicated heat treatment of the specially selected batch.Analysis of heat treatment of foam glass batch shows that two main stages can be identified according to structure formation. At the beginning of heat treatment, the material possesses a finely dispersed structure, whose particles sinter and then foam up as a result of intense release of gases by the foaming agent. At the final stage of foaming, the pores in the material reach their maximum size, and from this moment the structure of the article no longer changes substantially throughout the entire next stage of production. Foam glass has a high temperature and is in an easily deformable plastic state, which requires a structure to be fixed as rapidly as possible. For this, the article is subjected first to rapid cooling and then the temperature is stabilized over the cross-section of the material. At the final stage of heat treatment of foam glass annealing is necessary to remove residual stresses.These two stages can be studied separately, independently of one another.The present article is focused mainly on the production stage for foam glass -with a formed structure. Aside from macropores the foam glass at this stage contains micropores and crystalline inclusions. Thus the system is quite complicated. Empirical data alone and the simplest loading regimes (stretching, compression, shear, and so on) are not sufficient to study the system. Detailed modeling of the interaction of the structural elements is necessary.There are two main approaches to modeling the structure of porous materials -discrete and homogeneous. In the homogeneous method it is necessary to determine the thermophysical characteristics of a homogenized insulation system (thermal conductivity, specific heat, and so on). In view of the complex organization of the structure, this approach is undesirable and will not produce significant results of practical value. This situation is unacceptable. In addition, in this case the final goal of mathematical modeling is to determine the stresses formed during heat treatment of foam glass, and for a homogenized model it is difficult to take account of the characteristic features of their distribution in the porous body. For foam glass it is necessary to determine the maximum admissible stresses and the elastic modulus, which ar...

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