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V.N. Leitsin, M.A. Dmitrieva
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Powder systems Concentration inhomogeneity Different condition of synthesis Different structure of product Layered systems Homogeneity High reproducibility of experimental results
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b a Reactive cell
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Stage I Plastic deformation Wk=W-WDWk=W-WD Stage II Fracture of layers (texture formation)
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b a v1v1 v2v2 R(c)=0,
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Boundary conditions ω is an amplitude deflections of the plate, p is a frequency
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l i =c iR /p ij Irwin equation Rayleigh wave c iR - Rayleigh wave velocity, p ij – natural frequency A * - work to increase the area of cracks per unit, K IC - fracture toughness of the material, E - Young's modulus, ν - Poisson's ratio
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σ В – is the breaking point of a powder component K Ic – is the fracture toughness and с is the velocity of elastic waves Further development of material fracture is defined by the incubation period [2]: A criterion for complete fracture of material The kinetic equation of material damage The instantaneous damage ω0 as a function of applied pressure р can be written [1] in the form: [1] Kashtanov, A.V. and Petrov, Yu.V., Tech. Phys., 2006, vol. 51, no. 5, pp. 604–614. [2] Glebovskii, P.A. and Petrov, Yu.V., Phys. Solid State, 2004, vol. 46, no 6, pp. 1051–1054.
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1. Plastic deformation: 2. Fracture of layers: v imp =c R,
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Pre-exponent Change in the reactivity Condition of reactive equivalence The kinetic function φ(z)=0,5z -1
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1. Determination of Rayleigh velocity of components; 2. Determination of the velocity of applied load; 3. Determination of natural frequencies of the elements; 4. Estimation of possible characteristic size of the texture of damaged material; 5. Estimation of energy balance during the process of shock modification, taking into account the incubation time of damage; 6. Estimation of local parameters of the kinetics of chemical reactions; 7. Estimation of chemical transformations conditions.
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A.A. Denisaev, A.S. Shteinberg, A.A. Berlin // Russian Journal of Physical Chemistry B, 2008. vol 2, No 3, pp 491-497 4Al+3(-C 2 F 4 -)=4AlF 3 +6C+8678 kJ/kg
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l 1Ft, mml 1Al, mm 7,171,590,960,65 9,822,181,320,90 6,091,520,890,64 8,352,091,220,87 5,601,500,860,62 7,672,051,180,85 3,841,490,830,58 5,262,051,140,79 3,311,330,780,54 4,541,821,070,74 2,711,140,780,53 3,711,571,070,72 2,621,140,710,50 3,581,570,970,69 2,361,090,680,44 3,231,500,930,60 2,151,000,670,43 2,951,370,920,59 1,830,970,670,37 2,501,340,920,50
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Dependence of the relative volume of the material δ, which reached the state of resonance on amplitude of the dynamic loading P The results indicate the presence of a critical value of the amplitude of the shock pulse, the overcoming of which leads to a resonant mode at first in teflon (P = 40 MPa) and then in aluminum (P = 880 MPa).
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The studies have shown the promise of the developed approach of modeling the conditions of shock-induced reaction in layered reactive systems. Development of the theory of multicomponent chemically reacting systems under dynamic loading for layered reacting systems lets us to consider a concentration-deterministic multi-component reactive system to ensure good reproducibility of experimental results, on the one hand, and significantly reduce the required amount of parametric studies - on the other hand. Thank You for Your attention
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