Predicting the transverse strength of unidirectional composites under combination loading

This article presents a mathematical model for predicting the transverse strength of unidirectional fiber composites subjected to combination transverse loading under different conditions. The behavior of the matrix is described by nonlinear physical equations consistent with the strain theory of plasticity for the active loading section. The fibers are assumed to be isotropic and elastic. The boundary-value problem of micromechanics that is formulated includes strength criteria for the matrix and fibers that mark the beginning of their possible failure. The modeling of the fracture process is taken farther through the use of a scheme that reduces the stiffness of the matrix and fibers in the failed regions in relation to the sign of the first invariant of the stress tensor. The method of local approximation is used together with the finite-element method to calculate the stress and strain fields in unidirectional composites with cylindrical fibers in a tetragonal layup. The model is used to study the behavior of an epoxy-based organic-fiber-reinforced plastic subjected to transverse loading in different simple paths — including simultaneous compressive and tensile loads, as well as transverse shear.Paper to be presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October 1995).Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 4, pp. 473–481, July–August, 1995.     

冲击压缩下陶瓷材料中的破坏波模型

从多晶陶瓷材料细观结构非均匀性及其导致的应力奇异性分析出发,建立了陶瓷材料在冲击压缩下的本构关系,以及以表征材料损伤和破坏的非弹性体积应变为传播特征的破坏波控制方程,破坏层的非弹性体积应变包括由微裂纹成核、扩展引起的膨胀体积应变和由气孔塌陷引起的压缩体积应变两部分．结合92.93%氧化铝陶瓷板碰撞试验,数值模拟了冲击压缩下陶瓷材料中破坏波的传播过程,并对跨越破坏波阵面应力历程和剪切强度的变化规律进行了分析．     

Longitudinal shear of unidirectionally reinforced plastics

The deformation and strength properties of undirectionally reinforced plastics in longitudinal shear are investigated. A law of shear deformation that takes into account the nonlinear properties of the matrix is established. Two modes of failure of the reinforced plastic are examined. The dependence of the shear strength of the plastic on the volume reinforcement content and the strength properties of the matrix is investigated.     

Effect of viscosity of a thermoplastic prepreg and matrix upon winding of rings

The problem of compression of a unidirectional layer and shear of a polymer interlayer during winding of rings is considered. The equations determining the dependence of the layer thickness and stresses on the parameters entering into the power flow law for a prepreg and polymer matrix and on the basic parameters of the winding process—the initial tension of the prepreg, its placement rate, and the radius of a mandrel—are derived. The ring thickness measurements obtained at various temperatures and initial tension forces of plies confirm the adequacy of the model offered. It is found that the viscous properties of the prepreg and matrix upon winding affect the relative change in the layer thickness to a greater extent than the stresses in these layers. With increase in temperature and tension force upon winding, the effect of viscous deformations of the prepreg and matrix increases. A decrease in viscosity and an increase in the tension force of the tape lead to a higher strength of the ring in tension and interlaminar shear; however, the growing percolation of the polymer melt leads to a greater inhomogeneity of the structure of the composite in the ring and to a lower reinforcing effect of the factors mentioned. Presented at the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000). Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 3, pp. 419–428, 2000.     

Experimental Evaluation of the Effect of the Structure of Composite Rings on Their Properties in the Radial Direction

Based on the results of bending tests on cut glass-fiber-reinforced plastic rings with a longitudinal-circumferential reinforcement, their radial peel strength is evaluated. The effect of the fiber layout on the properties of the rings in the radial direction is investigated. It is shown that their radial tensile strength only slightly depends on the fiber layout but is basically determined by the properties of the polymer interlayer between the fibers. In radial tension, the presence of fibers in the polymer layer leads to a strain concentration, which results in a premature failure of the polymer phase of the composite. The strain-concentration factor cannot be used for an accurate prediction of the breaking stresses or strains of the composite, because of different failure modes of the pure resin and the composite.     

The Effect of Surface Treatment of F-12 Aramid Fibers with Rare Earths on the Interlaminar Shear Strength of Aramid/Epoxy Composites

Solutions of a rare-earth modifier (RES) and the epoxy chloropropane (ECP) grafting modification method are used for the surface treatment of F-12 aramid fibers. The effects of RES concentration on the interlaminar shear strength (ILSS) of F-12 aramid fiber/epoxy composites are investigated in detail, and the fracture surfaces of ILSS specimens are analyzed by SEM. It is shown that the RES surface treatment is superior to the ECP grafting treatment in promoting the interfacial adhesion between aramid fibers and the epoxy matrix. However, the tensile strength of single fibers is almost unaffected by the RES treatment. The optimum ILSS is obtained at a 0.5 wt.% content of rare-earth elements.__________Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 41, No. 2, pp. 265–272, March–April, 2005.     

基于坐标平移法的正常固结非饱和土三剪弹塑性本构模型

采用单应力变量法和双应力变量法建立了非饱和土的三剪统一强度准则,在此基础上用坐标平移法分别推导了相应的破坏应力比.将所得破坏应力比与非饱和土修正Cambridge模型进行结合,分别建立了单应力变量及双应力变量下的正常固结非饱和土三剪弹塑性本构模型,并对其做了ABAQUS二次开发.以南昌非饱和重塑红土为研究对象,分别对其...     

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.     

Interaction of a polymer matrix and short reinforcing fibers

A model of a glass-reinforced plastic with short unidirectional fibers is proposed. The distribution of tensile stresses in the polymer matrix and the fibers and the shear stress distribution at the interface in uniaxial tension are investigated in the elastic formulation.Riga Polytechnic Institute. Translated from Mekhanika Polimerov, No. 6, pp. 1030–1035, November–December, 1971.     

A circular inhomogeneity with a mixed-type imperfect interface in anti-plane shear

We present a rigorous study of the problem associated with a circular inhomogeneity embedded in an infinite matrix subjected to anti-plane shear deformations. The inhomogeneity and the matrix are each endowed with separate and distinct surface elasticities and are bonded together through a soft spring-type imperfect interphase layer. This combination is referred to in the literature as a ‘mixed-type imperfect interface’ due to the fact that the soft interphase layer (described by the spring model) is bounded by two stiff interfaces arising from the separate surface elasticities of the inhomogeneity and the matrix. The entire composite is subjected to remote shear stresses and we allow for the presence of a screw dislocation in either the inhomogeneity or the matrix. The corresponding boundary value problem is reduced to two coupled second-order differential equations for the two analytic functions defined in the two phases (as well as their analytical continuations) leading to solutions in either series or closed-form. The analysis indicates that the stress field in the composite and the image force acting on the screw dislocation can be described completely in terms of three size-dependent parameters and a size-independent mismatch parameter. Interestingly, in the absence of the screw dislocation, the size-dependent stress field inside the inhomogeneity is uniform. Several numerical examples are presented to demonstrate the solution for a screw dislocation located inside the matrix. The results show that it is permissible for the dislocation to have multiple equilibrium positions.     

Effect of Coulomb friction on the fiber/matrix debonding and matrix cracking in unidirectional fiber-reinforced brittle-matrix composites

A model for a macroscopic crack transverse to bridging fibers is developed based upon the Coulomb friction law, instead of the hypothesis of a constant frictional shear stress usually assumed in fiber/matrix debonding and matrix cracking analyses. The Lamé formulation, together with the Coulomb friction law, is adopted to determine the elastic states of fiber/matrix stress transfer through a frictionally constrained interface in the debonded region, and a modified shear lag model is used to evaluate the elastic responses in the bonded region. By treating the debonding process as a particular problem of crack propagation along the interface, the fracture mechanics approach is adopted to formulate a debonding criterion allowing one to determine the debonding length. By using the energy balance approach, the critical stress for propagating a semi-infinite fiber-bridged crack in a unidirectional fiber-reinforced composite is formulated in terms of friction coefficient and debonding toughness. The critical stress for matrix cracking and the corresponding stress distributions calculated by the present Coulomb friction model is compared with those predicted by the models of constant frictional shear stress. The effect of Poisson contraction caused by the stress re distribution between the fiber and matrix on the matrix cracking mechanics is shown and discussed in the present analysis. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 2, pp. 171–190, March–April, 2007.     

Effect of stress ratio on the fatigue strength of organic plastics

Conclusions Experimental fatigue curves of a unidirectional organic plastic are obtained for a number of asymmetry factors and diagrams of the limiting cycle stresses are constructed for a load in the direction of the fibers and across the fibers, and for in-plane shear of a layer. The simplest methods of approximating the calculated diagrams are tested. It is shown that the method of layer-by-layer analysis of fatigue failure makes it possible to construct limiting-stress diagrams for a laminar oblique-ply composite with an accuracy acceptable for engineering calculations, proceeding from the same analysis as for an individual layer.Translated from Mekhanika Kompozitnykh Materialov, No. 3, pp. 421–429, May–June, 1991.     

Shear strength of webs with holes

In lightweight design the webs of beams which are loaded by bending are often provided with holes. Aim of this article is to present a method to calculate the shear strength of webs with certain holes. The semi-analytical method is derived with respect to the results of geometrically and physically non-linear numerical simulations in which the shear strength of the web is calculated. The method consists of a plastic failure approach for rather thick webs and a framework analogy to model the failure of a solid web after onset of buckling. To take the influence of the holes into account the shear strength of the solid web is reduced as a function of geometry parameters. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stress distribution in an infinite elastic body with a covered periodically curved fiber

Within the frame work of a piecewise homogeneous body model, with the use of the three-dimensional geometrically nonlinear exact equations of elasticity theory, a method is developed for determining the stress distribution in unidirectional fibrous composites with periodically curved fibers. The distribution of the normal and shear stresses acting on interfaces for the case where there exists a bond covering cylinder of constant thickness between the fiber and matrix is considered. The concentration of fibers in the composite is assumed to be low, and the interaction between them is neglected. Numerous numerical results related to the stress distribution in the body considered are obtained, and the influence of geometrical nonlinearity on this distribution is analyzed. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 45, No. 2, pp. 269-288, March-April, 2009.     

Markov model of connection between the distribution of static strength and fatigue life of a fibrous composite

Within the framework of a unified mathematical model based on the Markov chain theory, an attempt is made to describe the distribution of static strength, the fatigue curve, and the accumulation of fatigue damages. It is assumed that the fatigue failure of a test specimen occurs after the destruction of some its critical microvolume consisting of two — elastic (brittle fibers) and plastic (matrix) — parts. In the second part, plastic strains accumulate as soon as the cyclic load exceeds some level. Numerical examples are presented. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 5, pp. 615–630, September–October, 2006.     

基于有限元的金属基短纤维复合材料MMC的一种统计蠕变模型

在有限元分析的基础上建立了一个单向应力状态下金属基短纤维复合材料(MMC)的统计蠕变模型.首先建立细胞模型并进行有限元分析,得到了单向应力状态下材料细观尺寸及载荷方向对宏观蠕变响应的影响规律.通过在细胞模型中增加一界面层(考虑材料特性和厚度)来研究基体和纤维的界面对MMC宏观蠕变响应的影响.基于细胞模型的数值结果,提出了一适用于纤维平面随机分布的随机统计模型,该模型考虑了纤维的断裂.通过试验获得纤维的统计分布规律.分析结果表明随机统计模型可以满意地描述试验结果.进一步讨论了材料细观尺寸,纤维的断裂特性以及界面层的材料特性和厚度对MMC宏观蠕变响应的影响.     

Fatigue strength of glass fiber/epoxy angle-ply laminates with different matrix ductility

Conclusion Angle ply laminates made up of glass fiber/epoxy plies have a good static strength for laminate angles up to about 45 °. This is due to the limitation of transverse strain in the plies due to constraints exerted by neighboring plies. At laminate angles of 50 ° and above the transverse and shear strains in the plies are not sufficiently constrained and cause failure in the matrix material. The constraint effect is present in fatigue but since the polymeric matrix material is sensitive to fatigue loading fatigue failure will occur at much lower strain levels than in static loading. This effect cannot be offset by increasing the ductility of the matrix material. Thus, strain to failure under fatigue loading will be only a small fraction of the static strain to failure for angle ply laminates with ply angles up to around 45 ° where the static strength is due to the constraint effect.Published in Mekhanika Kompozitnykh Materialov, No. 5, pp. 632–638, September–October, 1992.     

A comparative study of fiber-matrix interactions by using micromechanical models

The purpose of this study is to describe the interfacial interactions in terms of stress distributions on short fibers in fiber-matrix unit-cell models. The fiber and matrix are subjected to tensile loading. The study consists of three main parts. First, fiber-matrix cell segments are modeled using a 3D finite-element analysis (FEA) with ANSYS. Three different finite-element geometrical unit-cell models are generated in order to simulate the Cox analytical model: a fiber-matrix combination, a single fiber, and a single matrix element. The second part contains the results of 3D FE analyses, which are applied to the Cox formulations by using a computer program developed. In the last part, the analytical solutions for distributions of normal and shear stresses are investigated. Cox 2D linear elasticity solutions, together with finite-element ones, are presented in detail in graphs. The interfacial interactions between the fibers and matrix are also discussed considering the relative changes in the distributions of normal and shear stresses. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 4, pp. 505–520, July–August, 2008.     

Multifractal Parametrization of the Structure of Deformed Carbon Fibers

Deformed carbon fibers are investigated, and their failure model is proposed based on the Sierpinski set and the hypothesis of two — brittle and viscous — fracture modes, whose existence is confirmed by examples of a correlation between the mechanical strength and elastic modulus of the fibers. For the first time, a multifractal diagram is obtained, which allows one to justify the classification of carbon fibers into brittle and inelastic ones.     

Measuring the stresses in fibers of a loaded composite material by the method of infrared spectroscopy

Conclusions 1. Actual stresses in reinforcement fibers of a loaded composite have been measured by infrared spectroscopy.2. It has been shown that the plain rule of mixtures, not accounting for changes in mechanical properties of the matrix during processing of a composite, does not apply to a hot molded polyethylene-polypropylene composite.3. It is suggested that around the reinforcement fibers there exists an ordered layer of the matrix material capable of carrying a heavy load. A method is proposed, furthermore, for calculating the mechanical characteristics of the composite with such a layer. The volume fraction and the thickness of this hardened layer have been estimated from experimental data.Paper presented at the Third All-Union Conference on Polymer Mechanics in Riga, 1976.A. F. Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 5, pp. 832–837, September–October, 1977.