Theoretical and experimental investigation of anisotropic damage in textile-reinforced composite structures

In the present work, a phenomenological plane-stress damage-mechanics-based model for textile-reinforced composites is presented and its predictive capability is evaluated by carrying out a series of experimental tests. Damage variables are introduced to describe the evolution of the damage state and, as a subsequence, the degradation of material stiffness. For calculating the nonlinear stress and strain distribution of complexly loaded composites with a textile reinforcement, a special emphasis has to be placed on the interaction between the fiber failure due to the stress in the fiber direction and the matrix failure due to the transverse and shear stresses. This demands the formulation of realistic failure criteria taking into account the microstructural material behavior and different fracture modes. The new failure criteria, like the fracture mode concepts, consider these fracture modes, as well as further fracture types, in the reinforcement plane. The failure criteria are based on equations for failure surfaces in the stress space and damage thresholds in determining the stiffness degradation of the composite. The model proposed was used to characterize the strength and the failure behavior of carbon-fiber-reinforced composites. For this purpose, several unidirectional and bidirectional tests were performed to determine the specific properties of the material. The specimens were investigated by using acoustic emission techniques and strain-controlled tension and torsion tests.Russian translated published in Mekhanika Kompozitnykh Materialov, Vol. 40, No. 6, pp. 791–810, November–December, 2004.     

Flexible composites, strength, deformation, and fracture processes. 1. Reinforcement structures and tensile strength

Fiber-reinforced flexible composites are extensively used for different kinds of applications, for example, tubes, drive belts, tires, and coated fabrics. Typical for these materials are matrix materials allowing large strain deformation and reinforcement structures allowing bending. Apart from the tensile strength and limited bending stiffness, damage resistance and ductile-brittle transition characteristics are discussed. The tensile strength usually follows the rule of mixture. The mode of fracture and damage resistance, however, strongly depend on penetration of the matrix into the fiber bundles, textile structure, and internal friction. Models for the work of fracture and the ductile-to-brittle fracture transition are discussed.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Published in Mekhanika Kompozitnykh Materialov, Vol. 34, No. 6, pp. 747–760, November–December, 1998.     

Fracture toughness characteristics of laminated composites

Parameters characterizing the resistance of laminated composites to interlaminar fracture are discussed. The properties of the specific interlaminar fracture work, i.e., the amount of work spent on the formation of a unit of new surface of interlaminar crack, were examined. Taking account of the anisotropy of the material, this work may be characterized using a matrix. Upon change in the direction of crack growth, the matrix elements are transformed similarly to the components of a symmetrical second rank tensor. An interpretation is offered for the matrix elements. The proposed theoretical model was in accord with our experimental results.Moscow Engineering Institute. Technical University, Russia. Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 21–31, January–February, 1996.     

Resistance of bony tissue to tensile fracture

The tensile fracture resistance of compact bony tissue is considered. The relation between specific strain energy and stress level is established. A strength criterion characterizing the degree of deformation is proposed on the basis of a model, according to which compact bony tissue may be regarded as a composite material. The mode of variation of the proposed resistance parameter over the various zones of the cross section of the diaphysis of a human tibia has been experimentally established.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 6, pp. 1084–1091, November–December, 1971.     

Microstress fields and the mechanical properties of disordered fiber composites

Conclusion The effective elastic moduli and Poisson's ratios and the mean characteristics of the stress fields in the components of unidirectional fiber composites with a stochastic structure are nearly the same as the corresponding values calculated for a regular model of the composite. Relatively small increase (up to 6%) is seen in the transverse shear moduli with the transition from a regular structure to a stochastic structure. In the latter, there is a substantial increase in the stress concentration factor. Here, the difference between the stochastic structure and the regular structure increases with an increase in fiber stiffness and is particularly great (with a difference of two to three orders of magnitude) in the case of shear loading. The probability of the occurrence of microscopic fracture in the binder of the investigated materials is higher in transverse tension, but the difference from the results obtained for the regular models is more significant in the case of shear loading. Microscopic fracture nuclei will be formed in the matrix of the composite with the stochastic structure at considerably lower macroscopic stresses than are required for the regular structure.Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 860–865, September–October, 1990.     

Fibre stability in anisotropic matrix at small strains

As acknowledged in almost all monographs on the fracture of composite materials, one of the major fracture mechanism in unidirectional fibrous composites under uniaxial compression along the reinforcing elements is the stability loss of the material structure (the structural instability). According to this mechanism, theoretical investigations of the fracture along the fibres are reduced to those of the stability loss in the material structure, and the value of external critical forces is accepted as the value of failure forces. At present, numerous theoretical investigations have been carried out in this field with the use of the three-dimensional linearized theory of stability in the framework of the piecewise-homogeneous body model. However, in all the investigations it is assumed that the matrix and the fibre material are isotropic. It is evident that in many cases it is necessary to take into account the anisotropy of the matrix material when investigating the stability loss of fibres. In view of the above, in the framework of the piecewise-homogeneous body model using the three-dimensional linearized theory of stability, the present paper considers the stability loss of the fibre in the anisotropic (transversally isotropic) matrix. The effect of the properties of the matrix material on the critical values of the external loading is examined.Submitted to the 10th International Conference of Mechanics of Composite Materials (Riga, April 20–23, 1998).Published in Mekhanika Kompozitnykh Materialov, Vol. 33, No. 5, pp. 603–611. September–October, 1997.     

Prediction of changes in the strength of filled thermoplastics upon aging in an oxidizing atmosphere

Problems related to analyzing specimens with damaged surface layers have been examined using polyamide, trioxane—dioxolane copolymer, and polycarbonate as source materials. A model was developed for the brittle fracture of block specimens with damaged surface layers, which provides an estimate of the restraints to plastic deformation in these layers. Three segments are seen in the strength—time curves featuring 1) increasing strength, 2) decreased strength with brittle fracture, and 3) constant low strength. The strength of filled specimens of a specific period permits us to evaluate the effect of the filler on the fracture resistance of the matrix. A method was proposed for predicting the strength of filled samples using the matrix aging data.Translated from Mekhanika Kompozitnykh Materialov, Vol. 29, No. 3, pp. 375–380, May–June, 1993.     

Effect of fiber length on the strength and fracture properties of a fiber-filled silicone composite

The mechanism by which fillers strengthen polymers is discussed, and the effect of fiber length on static and impact bending strength and on the area of the fracture surface is studied with reference to the example of a silicone composite. A correlation is established between the strength properties and the area of the fracture surface. On the basis of the data obtained it is shown that, as the fiber length increases, the fracture mechanism changes from extraction of the ends of the fibers along the fracture path to breakage of the fibers.Moscow Lomonosov Institute of Fine Chemical Technology. Ter-Gazaryan State Scientific-Research Planning Institute of Polymer Adhesives, Kirovakan. Translated from Mekhanika Polimerov, No. 3, pp. 445–449, May–June, 1971.     

Fracture in Ceramic-Matrix Composites Reinforced with Strongly Bonded Metal Particles

The resistance of a ceramic matrix composite to the cleavage cracking across a field of strongly bonded, uniformly distributed metal particles is studied. The crack trapping and bridging effects of the metal particles are analyzed by means of calculating the strain energy and the traction work. An explicit expression for the critical energy release rate as a function of particle volume fraction has been obtained. The fracture resistance is independent of elastic properties of the matrix and the sample geometry and is predominantly determined by the size/spacing ratio of the particles. It is shown that the theoretical curves agree with experimental data quite well. The methodology developed in this article can be used in studying the fracture resistances of composites with high filler contents and irregular filler geometries.__________Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 41, No. 3, pp. 303–318, May–June, 2005.     

Effect of surface treatment of carbon fibers on the strength properties of carbon fiber plastics

Conclusions The strength characteristics of composites based on carbon fibers having a coating of silicon carbide are in direct dependence on the coating thickness and on the porosity, which makes it possible to assume the possibility of increasing the degree of realization of the strength characteristics of fibers having a coating in a composite by increasing the degree of impregnation of the carbon cord with the binder. The latter finds confirmation also in the fact that at a small coating thickness on the carbon fiber (of the order of 5 nm) the porosity of the composite obtained is equal to the porosity of the material based on the carbon fiber without coating. Moreover, as is evident from Fig. 3c, the casing of silicon carbide does not form a continuous coatting over the whole perimeter of the cord. The presence of these prerequisites, and also the high resistance of carbon fibers having a silicon carbide coating to oxidation [9], open up wide prospects for creating new composite materials based on them.Translated from Mekhanika Kompozitnykh Materialov, No. 4, pp. 603–606, July–August, 1979.     

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.     

Two interfacial shear strength calculations based on the single fiber composite test

The fragmentation of a single fiber embedded in a polymer matrix upon stretching (SFC test) provides valuable information on the fiber-matrix bond strength (), which determines stress transfer through the interface and, thus, significantly affects the mechanical properties of the composite material. However, the calculated bond strength appears to depend on data interpretation, i.e., on the applied theoretical model, since the direct result of the SFC test is the fiber fragment length distribution rather than the value. Two approaches are used in SFC testing for calculation of the bond strength: 1) the Kelly-Tyson model, in which the matrix is assumed to be totally elastic and 2) the Cox model using the elastic constants of the fiber and the matrix. In this paper, an attempt has been made to compare these two approaches employing theory as well as the experimental data of several authors. The dependence of the tensile stress in the fiber and the interfacial shear stress on various factors has been analyzed. For both models, the mean interfacial shear stress in the fragment of critical length (l_c) was shown to satisfy the same formula () = (_cD)/2l_c, where D is the fiber diameter and _c is the tensile strength of a fiber at gauge length equal to l_c. However, the critical lengths from the Kelly-Tyson approach and Cox model are differently related to the fragment length distribution parameters such as the mean fragment length. This discrepancy results in different () values for the same experimental data set. While the main parameter in the Kelly-Tyson model assumed constant for a given fiber-matrix pair is the interfacial shear strength, the ultimate (local) bond strength _ult may be seen as the corresponding parameter in the Cox model. Various _ult values were obtained for carbon fiber-epoxy matrix systems by analyzing the data of continuously monitored single fiber composite tests. Whereas the mean value of the interfacial shear stress calculated in the Cox approach was comparable to the interfacial shear strength from the Kelly-Tyson model, its ultimate value characterizing the true adhesional bond strength appeared to be three or four times greater.To be presented at the Ninth International Conference on the Mechanics of Composite Materials in Riga, Latvia, October, 1995.Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 4, pp. 446–461, July–August, 1995.     

Effect of small additives of oligomer on the viscoelastic properties of carbon fiber plastics

The viscoelastic properties of carbon fiber composites whose phenol-formaldehyde matrix is modified by thermodynamically incompatible isocyanate derivatives have been investigated. Data are given on fiber wetting (Table 11), internal stress (Table 2), viscoelastic properties (Fig. 1), and tensile strength (Fig. 2). The modified composites are strengthened by the addition of 0.5–4% oligomer additive. This process involves the formation of a two-phase structure, in which the additive phase microparticles act as a polymer filler. Due to selective interactions, the intermediate layer formed at the fiber-binder interface leads to changes in the viscoelastic properties and tensile strength of the matrix and improved maintenance characteristics for the material as a whole.Translated from Mekhanika Kompozitnykh Materialov, Vol. 29, No. 4, pp. 440–445, July–August, 1993.     

Deformation and Damaging of Composites with Transversally-isotropic Components under Compressive Loading

In the present paper, the problem of deformation and damage of composites with a porous isotropic matrix and transversally-isotropic unidirectional fibers under compressive loading is considered when microdamages are accumulated in the fiber. Fractured micro-volumes are modelled by a system of randomly distributed quasi spherical pores. The Shleicher-Nadai fracture criterion is used as a condition for the origin of micro-pores (micro-damage) based on the assumption of a rigid material. The limit value of the strength of the material is assumed as a stochastic function of coordinates. By using a numerical procedure, the solution of the above problem is found. The nonlinear stress-strain diagrams for a transversally-isotropic composite are obtained for the case of uniaxial compression-tension along the fibers. The nonlinearity of the deformations of the composite is caused by accumulation of micro-damages in the matrix. The influence of the physical-mechanical properties of materials, of the volume concentration, of the porosity of components, of the geometrical parameters of the structure, and of the character of the scatter of the strength in the material on the micro-damage of the material and, as a consequence, the influence on the macro-stress-macro-strain diagram is analyzed. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

The effect of interphase on residual thermal stresses. 2. Unidirectional fiber composite materials

In real composite materials an additional phase may exist between the fiber and the matrix. This phase, commonly known as the interphase, is a local region that results from the matrix bonds with the fiber surface or the fiber sizing. The differing thermal expansions or contractions of the fiber and matrix cause thermally induced stresses in composite materials. In the present study, a four-cylinder model is proposed for the determination of residual thermal stresses in unidirectional composite materials. The elastic modulus of the interphase is a function of the interphase radius and thickness. The governing equations in terms of displacements are solved in the form of expansion into a series [1]. The effective elastic characteristics are obtained using the finite element approach. The effect of the interphase thickness and different distributions of the interphase Young's modulus on the thermal residual stress field in unidirectional composite materials is investigated.For Pt. 1, see [1].Published in Mekhanika Kompozitnykh Materialov, Vol. 33, No. 2, pp. 200–214, March–April, 1997.     

Resistance of three-layered structures to static and cyclic bending

Conclusions The above studies of two types of three-layer structural elements showed that the types have different resistances to static deformation in bending. Regardless of the materials, the use of structures which are symmetrical in regard to stiffness makes it possible to obtain a stiffness and strength for the structure which are 10–15% lower than the stiffness and strength of the external plates if the thickness of the latter does not account for more than 25% of the thickness of the structure. This finding, in turn, permits a substantial reduction in the weight of the structure by the use of a lower-density material for the internal layer. Resistance to static bending is determined mainly by the resistance of the structure to shear stresses. The mechanism of fatigue fracture differs appreciably from the fracture mechanism in static deformation. Regardless of the thickness of the structural elements, fatigue fracture for both types of structure occurs as a result of the acting normal compressive stresses. The endurance limit of the hybrid structure is determined by the fatigue resistance of the external layers, and its value is nearly equal to the resistance of the pure materials.Presented at the Sixth All-Union Conference on the Mechanics of Polymer and Composite Materials (Riga, November, 1986).Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 878–882, September–October, 1986.     

Creep of Heat-Resistant Composites of an Oxide-Fiber/Ni-Matrix Family

A creep model of a composite with a creeping matrix and initially continuous elastic brittle fibers is developed. The model accounts for the fiber fragmentation in the stage of unsteady creep of the composite, which ends with a steady-state creep, where a minimum possible average length of the fiber is achieved. The model makes it possible to analyze the creep rate of the composite in relation to such parameters of its structure as the statistic characteristics of the fiber strength, the creep characteristics of the matrix, and the strength of the fiber-matrix interface, the latter being of fundamental importance. A comparison between the calculation results and the experimental ones obtained on composites with a Ni-matrix and monocrystalline and eutectic oxide fibers as well as on sapphire fiber/TiAl-matrix composites shows that the model is applicable to the computer simulation of the creep behavior of heat-resistant composites and to the optimization of the structure of such composites. By combining the experimental data with calculation results, it is possible to evaluate the heat resistance of composites and the potential of oxide-fiber/Ni-matrix composites. The composite specimens obtained and tested to date reveal their high creep resistance up to a temperature of 1150°C. The maximum operating temperature of the composites can be considerably raised by strengthening the fiber-matrix interface.     

Computational modeling of shape memory fibers in conforming and non-conforming compound structures

In this work a material model for shape memory alloy (SMA) fibers is presented. A constitutive model is provided which aims for computational use. The presented model incorporates all relevant material nonlinear phenomena. It takes pseudoplasticity into account as well as pseudoelasticity and further the shape memory effect (SME). The constrained SME (CSME) and the two-way SME are covered by the presented material model. The constitutive model is implemented in a one-dimensional truss formulation and in a 3D-rebar element. Both formulations are used to model fiber composite structures. Those are described by the use of a non-conforming and a conforming mesh on the mesoscale. The numerical examples show the capability of the formulation. Different meshing strategies for the fiber–matrix compound are discussed. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Experimental study of fracture toughness and energy in composite materials

The paper presents an experimental investigation of fracture characteristics of composite materials. The post-peak response of the load-crack opening displacement of notched specimens is used to evaluate the fracture energy associated with progressive matrix damage and crack growth. Effects of fiber orientation and other geometric characteristics on fracture parameters are studied. The load versus crack opening displacement as well as crack length, fracture toughness, and energy versus the number of loading cycles are obtained for different specimens. Based on the experimental results of this study, concepts of the fracture mechanics are applied to evaluate the evolution of fracture toughness and energy.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Department of Mechanical & Industrial Engineering, University of Manitoba, Winnipeg, Manitoba, Canada, R3T 2N2. Published in Mekhanika Kompozitnykh Materialov, Vol. 34, No. 3, pp. 323–332, May–June, 1998.