Mathematical simulation of failure processes of composite materials reinforced with brittle fibers

Conclusions 1. It is concluded on the basis of an analysis of experimental data and also from theoretical investigations with respect to stress redistribution upon the breaking of fibers that the successive breaking of a number of fibers, caused by the overload from the breaking of individual fibers, is one of the principal mechanisms according to which the complete failure of a material reinforced with brittle fibers takes place.2. A discrete model of a composite material has been worked out. A random fiber strength distribution over the surfaces of the cross sections of the composite material is produced on the computer by the application of Monte Carlo methods.3. A program was written for the computer which simulates the testing of composite materials, permitting the investigation of the statistical accumulation of damage in failure processes as well as the avalanchetype processes of the complete failure of a material.4. The effect of the statistical distribution of the strength of the reinforcing fibers, the ratio of properties, and the volume fractions of composites on the failure processes of composite materials is investigated. Deformation diagrams of a D-16 aluminum alloy-boron fiber composite material, constructed on the basis of an anlysis of the simulated process of fiber breaking in a composite, agree well with the experimental relations.5. The opinion is expressed that the development of cybernetic simulation of failure processes will permit giving an answer to a number of actual questions in the study of materials and the mechanics of failure.Baikov Institute of Metallurgy, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 5, pp. 800–808, September–October, 1976.     

An approach to numerical modeling of the dynamics of reacting gases in nozzles

An approach is proposed to computer simulation of gas-dynamic processes in chemically nonequilibrium flows in supersonic nozzles. An algorithm for the solution of the problem is developed. Convergence of iterative processes and stability of the linearized problem are investigated.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 58, pp. 89–95, 1986.     

Structural damage accumulation and stable postcritical deformation of composite materials

The macroscopic failure of composite materials is preceded by complex multilevel processes accompanied by accumulation and localization of damaged centers and formation of a failure cluster. Therefore, the study of these mechanisms is one of the basic problems for the mechanics of modern composite materials used in aerospace engineering. The formation of a theory of the stable postcritical deformation of the work-softening media is considered. The pseudo-plastic deformation affected by structural damage of granular composites is investigated within the framework of the considered two-level structurally phenomenological model of heterogeneous media. The stable evolution of the interconnected processes is accompanied by stress redistributions, partial or complete unloading, and strain or damage localization that are one of the main causes of implementation of the postcritical deformation stage. The numerical calculation results of inelastic deformation and failure of the periodic unidirectional fiber-reinforced composites are presented under conditions of the displacement-controlled transverse proportional loading mode. The main mechanisms of the work-softening behavior for the indicated type of materials are described in the macro-homogeneous stress-strain states. Macroscopically, the failure of heterogeneous media as a result of postcritical deformation and the loss of stability of damage accumulation depends on the stiffness of the loading system. When a deformable body is fixed on the closed surface with sufficiently but not infinitely large coefficients of stiffness, it is possible to observe the equilibrium development of the localized volumes of work-softening and damage. The constitutive equations for the work-softening isotropic, transverse isotropic, and orthotropic media are presented. The effect of the loading system on the stability of deformation, damage accumulation, and failure under monotone and nonmonotone triaxial loading was studied. The growth of failure strains with increase in stiffness of the loading system and unequal resistance of heterogeneous body are registered and investigated. A preventive unloading method is offered for the mathematical modeling of the damage accumulation during the testing of the materials on the servo-controlled systems. The displacement-controlled mode is simulated by a series of soft loading and unloading cycles. The detected phenomenon of failure where the unloading leads to stress-strain diagrams with a negative slope of the descending branch was not found either in the displacement or stress-controlled monotone loading mode.Submitted to the 10th International Conference on Mechanics of Composite Materials, April 20–23, 1998, Riga, Latvia.Perm' State Technical University, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 2, pp. 234–250, March–April, 1998.     

An estimation of reliability of unidirectional composites by catastrophe theory

In the present work, interest is centered on the theory of fracture and practical approaches to reliability estimation of unidirectional composite materials which are based on it. Fracture mechanics is considered not as a theory of macrocracks but as mechanics of fracture mechanisms of the composites with allowance made for probability estimation. A model of composite material with fibers eliminated from the carrying scheme and parameters specific to the stress-strain-damage state (SSDS) was considered. According to the model, during loading, self-accelerated energy rise is accounted for by structural damages growth — the catastrophe takes place. The model allows us to calculate the critical stress. The composites redistribute forces from overloading zones to neighboring ones by microstructural deformations and damages. It is the effect of reservation of carrying ability. Due to this effect, low-value probability of fracture is sufficiently less for the composite than for homogeneous materials. The approach allows us to evaluate the reliability function for both static loading and fatigue.Presented at the Ninth International Conference on the Mechanics of Composite Materials, Riga, October, 1995.Computing Center of the Russian Academy of Sciences, Krasnoyarsk, Russia. Published in Mekhanika Kompozitnykh Materialov, Vol. 32, No. 4, pp. 539–548, July–August, 1996.     

Statistical analysis of the bearing capacity of rim-spoke flywheels made of reinforced plastics

Conclusion The suggested numerical method makes it possible to plot the distribution functions of the bearing capacity of RSF at the structural level of their design elements (rim, spokes) with a view to the scatter of the strength and strain properties of the used materials and the geometry of arrangement of the structure. This involves taking into account the random nature of the radial distribution in the rim material of both strain and strength properties, which makes it possible to investigate more fully the processes of failure really occurring in RSF. The suggested method is the basis for stipulating a scientifically substantiated safety factor (the theoretical bearing capacity) in dependence on the required reliability; this makes it possible to use a differentiated approach to problems of devising RSF for actual purposes. Our investigations may serve as the basis for solving problems of optimal planning of RSF according to the conditions of the required reliability.Translated from Mekhanika Kompozitnykh Materialov, No. 6, pp. 1041–1047, November–December, 1987.     

Elastic characteristics of ferrocement reinforced by hexagonal grids

The methods of the structural mechanics of composite materials are used to develop a method for predicting the elastic modulus and shear modulus of ferrocement reinforced with hexagonal woven and stamped grids. The method takes into account the elastic properties of the components and the geometry of the reinforcement.Riga Technical University, LV-1047 Latvia. Translated from Mekhanika Kompozitnykh Materialov, No. 2, pp. 182–186, March–April, 1997.     

Elastic characteristics of ferrocement reinforced with woven meshes

Applying structural mechanics methods for composite materials, we have worked out a procedure for predicting the elasticity modulus, the shear modulus, and Poisson's ratio for ferrocement taking into account the elastic properties of the components, the wire diameter, the mesh size, and the distance between the meshes. The results make it possible to exploit the potential of such reinforcement to the fullest.Translated from Mekhanika Kompozitnykh Materialov, Vol. 30, No. 4, pp. 526–530, July–August, 1994.     

Failure of oriented materials under tension

A model of failure in oriented materials is proposed which takes account of orientation and failure proceeding simultaneously. The model offered enables a number of anomalous properties observed in the materials under consideration to be explained.Institute of Polymer Mechanics, Riga. Translated from Mekhanika Polimerov, Vol. 9, No. 3, pp. 460–467, May–June, 1973.     

Thermoelasticity problems in the mechanics of composite materials with large-scale deformation of the filler

A problem is posed and a method of solution developed for a class of thermoelasticity problems in the mechanics of composite materials with large-scale structural deformations, in which in the continuum approximation the composite material is modelled by a homogeneous orthotropic body with curvilinear orthotropy. As an application the authors establish the foundations of a theory of buckling for planar structural elements subjected to constant thermal fields.Translated from Matematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 29, pp. 16–25, 1989.     

General structural equilibrium solutions of boundary-value problems in the mechanics of composites

Based on the theory of R-functions, we have constructed general structural equilibrium solutions for stresses identically satisfying both the differential equilibrium equations and the contact conditions at the three-identically boundaries of inhomogeneities of arbitrary shape. These solutions can be used in developing the next generation of numerical and analytical methods in the mechanics of inhomogeneous bodies and the micromechanics of composite materials.Kharkov State Technical University of Construction and Architecture, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 4, pp. 474–481, July–August, 1997.     

Effect of synergism in the mechanics of multilayer designs. 2. synthesis of optimal acoustic systems

Conclusion Use of the synergism effect in the mechanics of inhomogeneous systems, and algorithms constructed on the basis of the theory of optimal control makes it possible to synthesize multilayer designs that are optimum in terms of weight capacity, thermal stability, sound conduction, and sound insulation. The proposed approach to solution of the problem of the optimal design of multilayer acoustic systems makes it possible firstly to develop a rather effective method on the basis of this approach; this method reduces to a solution that is optimal in terms of the physical parameters of the layer materials, the layer thicknesses, and the number of layers; and, secondly, to establish a number of qualitative attributes of the parameters of optimal multilayer structures. This approach is also promising for the development of methods for the optimization of multilayer foundations and systems that dampen vibrational loadings, earthquake-resistant designs, and armor protection.Presented at the Fifth All-Union Conference on the Mechanics of Polymer and Composite Materials (Riga October, 1983).See [1] for Report 1.Translated from Mekhanika Kompozitnykh Materialov, No. 4, pp. 686–691, July–August, 1984.     

Equilibrium failure processes of granular composites

The macroscopic failure of inhomogeneous media results from damage accumulation on different structural levels. During rigid loading, when given displacements of boundary points are ensured, irrespective of the body's resistance, structural-failure processes of composite materials take place in an equilibrium regime and result in the manifestation of such nonlinear-behavior effects as a descending branch on the strain diagram. the structural elements of a granular composite are homogeneous and firmly connected along the interface. Their geometry and mutual arrangement are given and do not change during deformation and failure of the medium, and the medium itself is macrohomogenous. The strength of isotropic structural elementsis estimated by comparing the second invariant of the stress tensor with its critical value. Nonfulfillment of the indicated strength criterion is associated with loss of ability to resist changes in form; at this point, the positive value of the first invariant corresponds to loss of such ability to resist and increase in volume. The deformation and structural failure of the medium are investigated as a single process that can be described under quasi-static loading by a boundary problem consisting of a closed system of Eqs. (1) and (2) and boundary conditions providing for a macrohomogeneous strain state. A principal feature of the boundary problem under consideration is the possibility of considering in constitutive relationships the states of the inhomogeneous medium, which correspond to partial or complete loss of bearing capacity of the structural elements. The random structural strength constants correspond to three-parameter Weibull distribution (6). The representative volume of a granular composite, which fills a domain in the form of a cube, is modeled by a set of istropic elastobrittle strain diagrams containing a descending branch are obtained as a result of the mathematical modeling of deformation processes and structural failure to realized a representative volume containing 384 structural elements with different strength and similar elastic constants.Presented at the Ninth International Conference on the Mechanics of Composite Materials, Riga, October, 1995.Perm'State Mechanical University, Russia. Translated From Mekhanika Kompozitnykh Materialov, Vol. 32, No. 6, pp. 808–817, November–December, 1996.     

Finite element simulation for material accumulation and welding processes including a free melt surface

A modeling and simulation approach for problems with solid-liquid-solid phase transitions and a free surface, feasible for material accumulation processes based on laser-based free form heading and welding processes for joining different metallic materials is presented. Both named processes are modeled within the framework of continuum mechanics by coupling the Stefan problem with the Navier-Stokes equations including a free capillary surface. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Cracking resistance and long-term strength of dispersion-hardened composites

Conclusions The previously proposed relationships were used to develop a method of predicting the endurance of dispersion-hardened composites on the basis of results of tensile tests on the material at a constant strain rate. It is shown that stress raisers in the form of cut out or defects which weaken the working cross section, greatly reduce the endurance of the material. The proposed method of evaluating the effect of stress raisers on the endurance of polymer materials is based on the assumption on the initiation of a crack-like defect and its propagation in accordance with the loss of linear fracture mechanics.Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 869–877, September–October, 1989.     

Analysis of the fracture of fiber composites on the basis of the statistical theory of branching processes

A statistical theory of branching processes is used to examine models of the localized and delocalized fracture of fiber composites. It is shown that despite the differences between the two types of models, both can be reduced to the same generalized Markov process. A new fracture criterion to be used for all types of models is proposed. The use of this criterion makes it possible to theoretically describe a new structural effect — the dependence of the breaking stress of a composite specimen on its cross-sectional area. In the limiting case of an infinitely large cross-sectional area, the breaking stress calculated on the basis of the proposed approach turns out to be equal to that calculated using previous models. The breaking stress for specimens of finite dimensions turns out to be lower than for specimens of infinite size. This result is due to the nonlinear dependence of the probability of fiber rupture on the additional overstresses that develop in the composite during local microscopic fractures. The results that are obtained should be taken into account in the calculation of the strength of structurally reinforced composites and small structural elements made of composite materials.Kompozit Research Center, St. Petersburg, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 6, pp. 795–807, November–December, 1996.     

Prediction of the creep of polyester resin in the presence of randomly acting temperature and humidity factors

The possibility of using the theory of random processes to predict the temperature and moisture creep of polymeric materials in the presence of randomly acting temperature and humidity factors is considered. A procedure for estimating the long-term deformation under such conditions is described with reference to the uniaxial creep of PN-3 polyester resin using time—temperature and time—moisture superposition. The possible correlation of the ambient temperature and humidity is taken into account. The results of a computer calculation show that the theoretical and experimental data are in satisfactory agreement.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 219–226, March–April, 1973.     

Effect of stability of the structural parameters of laminated reinforced plastics on their strength properties

Conclusion As a result of the completed analysis, we estimated the effect of scatter of the strength properties of the layers, instability of the layers' strain properties, and instability of the geometry of the structure on the strength properties of multidirectional LRP's in a plane stress state. It was established that instability of the structural parameters produces two negative tendencies: a reduction in the mean values of LRP strength and an increase in their scatter. From the viewpoint of ensuring the reliability of structures (structural elements) made of such materials, these tendencies reinforce one another and are thus even more dangerous. It follows from this that the production method employed should not only (or not even mainly) solve the problem of increasing the values of the parameters of the materials (and their semifinished structural elements), it should also address the problem of alleviating their instability — improving the quality of production.The numerical analysis established the limits at which it is necessary to account for instability of structural parameters in engineering calculations: for the strain properties of the layers — a coefficient of variation of the elastic modulus greater than 10%; for the scatter of the angles of orientation of the layers — a standard deviation greater than 5 °. These numerical results and the computer program developed may prove useful in evaluating the actual properties of structural parameters determined in indirect tests of LRP's, as well as in more adequately comparing empirical data with corresponding calculations based on structural theories. The development of such an approach to analyzing the strength properties of multidirectional LRP's in bending also holds promise.Translated from Mekhanika Kompozitnykh Materialov, No. 4, pp. 659–666, July–August, 1990.     

Structural evaluation of materials by artificial neural networks

It is shown that due to the complexity of interaction of the excitation field with a material in determining its physical characteristics, as well as sophisticated correlation relationships between the physical characteristics and structure of a real material, in many cases, relization of the structural evaluation of materials on the basis of idealized mathematical models of the underlying physical processes is of limited use. As an alternative, it is proposed to use an artificial neural network for the extraction of quantitative information of interest from measurements of the physical characteristics. A general overview of artificial neural networks is given. A methodology of the use of a multilayer perceptron for determining various structural parameters from the dielectric spectra is described. As an example, determination of the moisture content and density of sawdust from the dielectric modulusis considered by the neural-network technique. The noise performance of the neural network is analyzed by applying an additive and multiplicative noise to the input data.Institute of Polymer Mechanics, University of Latvia, Riga, LV-1006 Latvia. Published in Mekhanika Kompozitnykh Materialov, Vol. 35, No. 1, pp. 109–124, January–February, 1999.     

Structure and properties of polymers

The history of the development of the structural mechanics of polymers is reviewed and the more important of its future tasks are noted.Institute of Heteroorganic Compounds, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 3, pp. 387–394, May–June, 1972.