Multiple cracking in carbon/epoxy laminates and pre-stressing of fibers

The multiple cracking of laminates with brittle plies can be suppressed by prestraining in tension of the fibers in the ductile plies. Experiments with tensile loading, acoustic emission, and crack counting demonstrate that such multiple cracking can be delayed and thus higher working strains can be allowed (without multiple cracking) for such laminates. In [0°/±65°/0°] laminates the strain for crack initiation can be increased from about 9.9% (for no prestrain) to above 1.4% (for 0.8% prestrain).Presented at the Ninth International Conference on the Mechanics of Composite Materials, Riga. October, 1995.Materials Department, Risøe National Laboratory, Roskilde, Denmark. Published in Mekhanika Kompozitnykh Materialov, Vol. 32, No. 3, pp. 350–362, May–June, 1996.     

Stress distribution caused by two neighboring out-of-plane locally cophasally curved fibers in a composite material

In the present paper, within the framework of a piecewise homogenous body model, with the use of the exact three-dimensional equations of elasticity theory, a method proposed earlier is developed for investigating the stress distribution caused by two neighboring out-of-plane locally cophasally curved fibers located along two parallel planes in an infinite elastic body. The body is loaded at infinity by uniformly distributed normal forces in the direction of fiber location. The self-equilibrated normal and shear stresses caused by the curved fibers are analyzed, and the influences of interaction between the fibers and of the geometric nonlinearity on the distribution of these stresses are studied. Numerical results for this interaction are obtained.     

Morphological characteristics of carbon fibers

Scanning electron microscopy has been used to study the surface, before and after thermochemical treatment, and the fracture sites of PAN carbon fibers heat-treated at 2100°C. The fractographs are analyzed in an attempt to estimate the effect of various defects on the strength of PAN carbon fibers.All-Union Scientific-Research and Design-Technological Institute of Electro-Carbon Products, Moscow Region. Translated from Mekhanika Polimerov, No. 1, pp. 158–160, January–February, 1976.     

Quantitative evaluation of the brittleness of carbon fibers

A simple method is proposed for the rapid determination of the brittleness of fibers. Measurement data are given for glass and carbon fibers. It is shown that the conditions of heat processing for carbon fibers may fundamentally alter their brittleness.A. F. Ioffe Physical-Engineering Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 5, pp. 950–952, September–October, 1973.     

Estimation in truncated Poisson distribution

Bayes’ estimator of truncated Poisson distribution (TPD) has been obtained by using gamma prior. Furthermore, recurrence relations for the estimator of the parameter are obtained. R-software has been used for comparing the estimates with the corresponding maximum likelihood estimator (MLE).     

Estimation of distribution density

The article investigates the asymptotic properties of the estimators of the density P(x) derived using a sample X₁,...,X _n when the distance of the estimator from p(x) is measured in the metricL _p,2p2.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Institute im. V. A. Steklova AN SSSR, Vol. 98, pp. 61–85, 1980.     

Investigation of the modulus of elasticity of carbon fibers

A simplified analysis of the dependence of the elastic properties and electrical conductivity of a carbon fiber on its orientation index is presented. The experimentally confirmed inverse correlation between the electrical resistivity and the speed of sound makes it possible to calculate the modulus of elasticity of carbon fibers from data on the bulk resistivity.Moscow Aviation Technological Institute. Translated from Mekhanika Polimerov, No. 5, pp. 846–850, September–October, 1971.     

Method suited for constructing deformation diagrams of composite materials on the basis of the statistical distribution of the strength of the reinforcing fibers

Starting from an analysis of the statistical accumulation of the defects during rupturing of the separate fibers in a composite material, a theoretical method suited for constructing deformation diagrams of composite materials and based on averaging of the stresses in the defect volumes of the material is proposed. The effect of two statistical distribution (Waybul's and uniform) laws of the strength of the original reinforcing fibers on the shape of the deformation diagrams of composite materials is analyzed.     

Interlaminar fracture and low-velocity impact of carbon/epoxy composite materials

The interlaminar fracture and the low-velocity impact behavior of carbon/epoxy composite materials have been studied using width-tapered double cantilever beam (WTDCB), end-notched flexure (ENF), and Boeing impact specimens. The objectives of this research are to determine the essential parameters governing interlaminar fracture and damage of realistic laminated composites and to characterize a correlation between the critical strain energy release rates measured by interlaminar fracture and by low-velocity impact tests. The geometry and the lay-up sequence of specimens are designed to probe various conditions such as the skewness parameter, beam volume, and test fixture. The effect of interfacial ply orientations and crack propagation directions on interlaminar fracture toughness and the effect of ply orientations and thickness on impact behavior are examined. The critical strain energy release rate was calculated from the respective tests: in the interlaminar fracture test, the compliance method and linear beam theory are used; the residual energy calculated from the impact test and the total delamination area estimated by ultrasonic inspection are used in the low-velocity impact test. Results show that the critical strain energy release rate is affected mainly by ply orientations. The critical strain energy release rate measured by the low-velocity impact test lies between the mode I and mode II critical strain energy release rates obtained by the interlaminar fracture test. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000). Published in Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 195–214, March–April, 2000.     

Estimation in a mixture normal distribution

By Stochastic simulations we discuss the fitness of a mixture normal distribution to observations from general mixture distributions using the MLE method and the EM algorithm. We calculate the probability of misclassifying objects and estimate the optimal number of mixture components with mutual information measure.     

Effect of parameters of the distribution of the length and orientation of short fibers on characteristics of the dynamic viscoelasticity of a polymer composite

Conclusion An algorithm for calculating the dynamic viscoelastic characteristics of a composite reinforced with short fibers was developed and realized in the form of a computer program. An analysis was made of the dependence of the characteristics of the composite on the volume content and length of its fibers, as well as on statistical distributions of fiber length and orientation in the material. It was shown that a change in the parameters of the statistical distributions has a significant effect on both the elastic and the dissi-pative properties of the composite. It was found that ignoring the statistical fiber-length distribution might lead to overestimation of the real component of the complex modulus and underestimation of the mechanical loss tangent.Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 13–17, January–February, 1990.     

Estimation risk and stability of optimal portfolio composition

The mean-variance portfolio models indicate that for optimal investment decisions, the ‘true’ ex-ante values of the model parameters should be used. Instead, in practice, ex-post parameter estimates are used. If in the estimation process, the probability distribution of estimators is not known, there is a problem of estimation risk. This paper investigates the impact of estimation risk on the composition of optimal portfolios. As the multivariance distribution of the vector of optimal portfolio weights allocated to risky assets is analytically intractable, a use of the Monte Carlo simulation experimental is made. This study suggests that the composition of optimal portfolio is relatively more stable when the estimates of model parameters are obtained from longer series of historical observations or the expected portfolio return is low.