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Traditionally, it is assumed that a deformable body yields under load at the moment when the stress-state or the stored energy parameters at the most critical points in the body reach the maximum allowable values and that the moment of failure is uniquely determined by the strength constants of the material. However, there is experimental evidence that-the rigidity of the loading system also affects the resistance to failure. Here the loading system includes both the loading device (the testing machine, the structural elements which transmit the load, the working fluid or gas, etc.) and area of the deformable body around the failure zone [1, 2].If the load is "soft," i.e., if the loading forces are independent of the resistance of a body in a homogeneous stress state, then failure really does correspond to the maximum stresses. In the other limiting case (a "rigid" load), the boundary points are displaced by a given amount, and damage can accumulate in an equilibrium process, which is reflected by a descending section in the stress-strain diagram [3][4][5][6][7][8][9]. If the loading system has finite rigidity, the moment that load-carrying capability is lost can correspond to one point or another on the descending part of the stress-strain diagram. The material state corresponding to the highest point on the stress-strain diagram is the critical point, but -to be more precise -failure is the final rapid non-equilibrium stage of this process, and can be viewed as the result of the loss of stability of accumulated damage at a supercritical strain stage. Also, the concept of a supercritical strain stage allows the reserves of load-carrying capacity to be used in optimizing structure design.A more precise calculation that uses the total strain diagram requires the formulation and solution of boundary-value problems that consider material yield [10][11][12][13], and also possible stability losses in the weakened zones [4, 13, 14]. Here we present new boundary conditions that consider the rigidity of the loading system, formulate the defining equations, introduce supercritical strain conditions, obtain stability criteria for damage accumulation at the supercritical strain stage for an elementary material particle, and give a formulation of boundary-value problems that considers these effects within the framework of the mechanics of deformable solids.1. Equation of State. For a material with microdamage, the stress tensor a is related to the strain tensor e in terms of a fourth-order damage-vulnerability tensor fl by a defining equation in the form [15] ( 1.1) where C is the elastic modulus tensor; the Iklra n = (1/2)(~/on~tn + ~/m) are the components of the unit tensor, and ~ is the Kronecker delta.In this model, all processes that change the material state are described by the damage-vulnerability tensor operator 0, whose components are uniquely defined by the strain (loading) process. If the stresses can be defined by knowing the strains only at the current moment of time, then fl is a function. When experimental...

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An engineering micromechanical model for carbon/carbon composites with a pyrocarbon (PC) matrix is presented. The model of the matrix plays an essential role in modelling of the material. This model takes into account the structural heterogeneity of the PC matrix and the anisotropy of the carbon fibres. The PC matrix is considered as a polycrystalline aggregate of anisotropic PC grains (or crystallites) with random shapes and orientations. The carbon fibres are homogeneous and anisotropic. The mathematical foundation for the model is a homogenization procedure for a multicomponent heterogeneous medium with a stochastic structure, anisotropic components and variable volume fractions of the components. The stochastic structure of the matrix generates fields of fluctuating microstresses and stochastic fractures of individual PC grains. Due to the anisotropy, the PC grains can fracture or become partially damaged via several fracture modes with different probabilities depending on the macrostress state of the material. The model allows calculation of the full stress-strain diagram for the carbon/carbon composite with arbitrary multiaxial loads and to forecast the appropriate strength limits. As an application of the model, numerical results are presented for a three-point bending of a short beam made of unidirectional materials. The calculated interlaminar shear strength matches the available experimental data.

The introduction of lightweight composite materials (CM) to the design of aircraft gas-turbine plants is one trend in the improvement of their parameters. Above all, it is most expedient to use CM in fabricating the following casing parts: soundproofmg panels, fa~ housings, nozzle fairings, and the engine-reversing unit, which operate under comparatively light loadings. When the subassemblies in question are effectively processed, it is possible to build even more heavily loaded components from composites: power housings, force linkages, fan blades, etc. These measures make it poss~le to reduce the weight of a single engine by 100-150 kg and increase the commercial payload of the aircraft by 200-600 kg. In designing lightweight fan housings, nozzle fairings, and the reversing unit from polymeric composite materials for new aircraft, it has been established that a significant gain can he achieved in terms of weight only when traditional mechanical flange fastening assemblies are rejected and replaced by flanges also built of CM.By virtue of the fact that it is precisely the flange connections that are the most loaded components of the structures in question, the calculation of their stress-strain state (SSS) and strength assessment are decisive in confirming the serviceability of housings and failings on the whole.Flange blanks are produced by the successive facing of layers of glass-cloth-and epoxy-resin-base I~DT-69N-S prepregs and 1 lt~ unidirectional carbon-fiber prepregs on a metallic mandrel in the axial and circumferential directions. A circular subwinding with a unidirectional glass prepreg was also used in certain structural variants. After facing, the flanges are mated with the blank of the basic section of the housing or fairing, polymerized in an autoclave under a vacuum bag at a pressure of 0.5 MPa for 7 h, and allowed to cool to ambient temperature for 10 h. Degree of polymerization of the finished articles is 95-98%, and the binder content is 30-40% in the prepreg layers.In our study, we present results of SSS calculation, and estimates of the factors of safety and fatigue lives of basic typical strnctural variants of the polymerie-CM flanges shown in Fig. 1. The radius of the inner surface of the flanges was 0.88-1.01 m, the thickness of a single glass-prepreg layer 0.25 ram, and the thickness of a single carbon prepreg layer 0.125 ram. Systems of external forces acting on a housing or fairing resulted in an equivalent load distributed over the mating surface S t of the jacketed flange (see Fig. le). Free-support conditions were assigned to segment S u, which corresponds to the region of the bolted connection.The mathematical statement of the axisymmetric problem of the theory of elasticity in a variational formulation consists of a search for the minimum of the Lagrange functional, the variation of which in the absence of mass forces assumes the form Perm' State Technical University.