Theory Of Composite Materials Research Articles

Fiber waviness in textile composites and its stochastic modeling

A generic stochastic theory of composite materials with continuous, randomly curved (imperfect) fiber reinforcements, recently developed by the present authors, enables one to quantify the effect of fiber deviations from the assumed “perfect” paths. The theory of random functions and stochastic extension of the orientational averaging approach are utilized to evaluate the mean values and standard deviations of the full set of anisotropic stiffness characteristics. The major advantage of this novel stochastic approach is its applicability to practically any fiber reinforcement architecture, from unidirectional to multidirectional, 3-D woven, and braided composites. Importantly, the approach does not ask for exact quantification of the reinforcement imperfections, but needs only a limited knowledge of the mean path of the reinforcement and standard deviation of the local tangent. Numerical examples illustrating applications of the stochastic theory developed consider three types of composites having (i) unidirectional, (ii) biaxial, 2-D braided, and (iii) 3-D orthogonally woven reinforcements. The first example concerns validation of the model. The second example is selected due to the commonly observed significant randomness of the fiber architecture in biaxially braided composite shell elements. The third example illustrates the effect of Z-yarn waviness (illustrated by optical microscopy) in orthogonally woven composites on their elastic characteristics.

Plasticity Theory for Particulate Composite Materials with Imperfect Interfaces

Plasticity Theory for Particulate Composite Materials with Imperfect Interfaces

On the presence of liquid in Earth's inner core

Seismological studies indicate that the inner core of Earth is anisotropic for compressional waves (P waves), and has low shear wave (S wave) velocity, and high seismic attenuation. Using an effective medium theory for composite materials, we show that the presence of a volume fraction of 3 to 10% liquid in the form of oblate spheroidal inclusions aligned in the equatorial plane between iron crystals is sufficient to explain the aforementioned seismic phenomena. Variation of S-wave velocity between the polar axis and equatorial plane is more sensitive to the addition of liquid than that of P waves. The liquid could arise from the presence of dendrites or a mixture of elements other than iron that exist in liquid form under inner-core conditions.

A coupled anisotropic damage model for the inelastic response of composite materials

A coupled incremental damage and plasticity theory for rate-independent and rate-dependent composite materials is introduced here. This allows damage to be path-dependent either on the stress history or thermodynamic force conjugate to damage. This is achieved through the use of an incremental damage tensor. Damage and inelastic deformations are incorporated in the proposed model that is used for the analysis of fiber-reinforced metal–matrix composite materials. The damage is described kinematically in both the elastic and inelastic domains using the fourth-order damage effect tensor which is a function of the second-order damage tensor. A physical interpretation of the second-order damage tensor is given in this work which relates to the microcrack porosity within the unit cell. The inelastic deformation behavior with damage is viewed here within the framework of thermodynamics with internal state variables. Computational aspects of both the rate-independent and rate-dependent models are discussed in this work. The Newton–Rapson iterative scheme is used for the overall laminate system. The constitute equations of both the rate-independent and the rate-dependent plasticity coupled with damage models are additively decomposed into the elastic, inelastic and damage deformations by using the three-step split operator algorithm [J.W. Ju, Internat. J. Solids Struc. 25 (1989) 803–833]. The main framework return maping algorithm [M. Ortiz, C. Simo, Internat. J. Numer. Meth. Eng. 23 (1986) 353–366] is used for the correction of the elasto-plastic and viscoplastic states. However, for the case of the damage model these algorithms are redefined according to the governed damage constitutive relations. In order to test the validity of the model, a series of laminated systems (0 (8s)), (90 (8s)), (0/90) (4s), (−45/45) (2s) are investigated at both room and elevated temperatures of 538°C and 649°C. The results obtained from the special purpose developed computer program, DVP-CALSET (Damage and Viscoplastic Coupled Analysis of Laminate Systems at Elevated Temperatures), are then compared with the available experimental results and other existing theoretical material models obtained from the work of B.S. Majumdar, G.M. Newaz [CR-189095, NASA, 1992] and G.Z. Voyiadjis, A.R. Venson [Internat. J. Damage Mech. 4 (4) (1995) 338–361].

Quasifractional Approximants in the Theory of Composite Materials

We study the effective heat conductivity of regular arrays of perfectly conducting spheres embedded in a matrix with unit conductivity. Quasifractional approximants allow us to derive an approximate analytical solution, valid for all values of the spheres volume fraction ϕ [0, ϕmax] (ϕmax is the maximum volume fraction of a spheres). As a starting point we use a perturbation approach for ϕ → 0 and an asymptotic solution for ϕ → ϕmax. Three different spatial arrangements of the spheres, simple cubic, body centred and face centred cubic arrays, are considered. Results obtained give a good agreement with numerical data.

Composite Materials and Structures: Science, Technology and Applications - A Compendium of Books, Review Papers, and Other Sources of Information

A fast growing volume of literature in various fields of composite materials and structures has inspired the authors to attempt to assemble all major books and review papers in a concise compendium presented here. This could give researchers, engineers, designers, and graduate students a rapid access to the vast volume of references on any specific topic in the field of composites and thereby satisfy their research requirements. The compendium includes encyclopedias, handbooks, design guides, textbooks, reference books, review papers and also a few collections of papers. The topics span theory, modeling and analysis of composite materials, processing and manufacturing, properties and characterization, theory and analysis of composite structures, joints and connections, designing with composites, and composites applications. The compendium includes over 400 references, which are arranged in alphabetical order within each topic under consideration. Additionally, the reader can find, in this compendium, the lists of major conferences, journals, and ASTM STP publications on composites. The major objective of this work is not critically reviewing or discussing specific research approaches and results. The authors have rather intended to provide extensive bibliographic information that may help the reader to get familiar with the primary literature and, if necessary, undertake further literature search on any particular problem of interest.

Modeling Chloride Penetration in Saturated Concrete

A mathematical model is established for chloride penetration in saturated concrete. The model takes into account various influential parameters such as water-to-cement ratio, curing time, types of cement, and aggregate content. Two material models are developed for binding capacity and chloride diffusivity, which have a dominant effect on the chloride diffusion process. The chloride binding capacity is modeled by means of the chloride adsorption isotherm. The chloride diffusivity is modeled by a composite material theory in which concrete is considered as a two-phase material with the cement paste as one phase and the aggregate as another. To take into account the effect of aggregate content, the three-phase model for diffusivity of a two-phase composite developed by Christensen is used. The diffusivity for cement paste is characterized by the Kozeny-Carman model as modified by Martys et al. The influences of temperature and chloride ion concentration are also handled in the model. The model prediction agrees quite well with available test results.

A constitutive theory for porous composite materials

A phenomenological model for porous layered materials has been developed. The phenomenological approach for layered materials is combined with a poroelastic constitutive model. Explicit expressions for effective elastic moduli, thermal expansion coefficients, and poroelastic moduli are obtained. The obtained results reduce to those of layered materials when there are no pores. The obtained model is applied to failure analysis of thermochemically decomposing composites subjected to high temperature and high heating rates. A separate analysis of carbon fiber and phenolic resin responses explains why carbon fiber shrinkage causes more delamination failure.

ACTIVE CONTROL OF VIBRATIONS AND NOISE OF DOUBLE WALL CYLINDRICAL SHELLS

Active control of vibrations and noise transmissions of double wall composite cylindrical shells using pairs of spatially discrete piezoelectric actuators is investigated. The velocity feedback and sound pressure rate feedback control procedures are developed. The inner and outer shells which are separated by a soft core are modelled by Love's thin shell theory for laminate composite materials and the inputs are taken as stationary random pressures and/or random point forces. A galerkin-like procedure is used to obtain solutions of the governing structural-acoustic equations. Parametric studies are performed to demonstrate the effect of actuator placement, actuator size, control gains, spillover, structural and acoustic damping characteristics

Stochastic theory of composite materials with random waviness of the reinforcements

A general stochastic theory of the elastic properties of composite materials with continuous randomly curved spatial reinforcement is developed. The theory of random functions is utilized to evaluate the probabilistic characteristics of the local waviness of the reinforcement. A probabilistic extension of the orientation averaging model is developed to evaluate the elastic response of composites with multidirectional reinforcement having stochastic waviness. One fundamental advantage of the developed theory, compared to existing analytical approaches, is that an exact description of the reinforcement waviness is not required for predicting elastic properties. The only essential characteristics used as input data are the mean reinforcement paths and standard deviation of the local tangent, which is a random value characterizing the reinforcement path deflection from the “perfect” one. It is shown that existing approaches for evaluating elastic response of the composite with imperfect continuous fiber reinforcement can be obtained from the developed theory as particular cases. The theory is illustrated with examples of a unidirectional composite and a helically wound composite with randomly curved reinforcements. Numerical examples show that even small local waviness of the reinforcement paths may significantly affect the elastic response of composites considered.

Effective transverse response of fiber composites with nonlinear interface

This paper presents a framework for the analysis of the constitutive response of composites in which nonlinear behavior originates solely from the force-separation response of the interfaces. The direct method of composite materials theory is employed to pass from local nonlinear behavior of a solitary inclusion problem to nonlinear aggregate response. The resulting model, which involves no adjustable parameters, falls within the conceptual framework of continuum damage mechanics with “damage” variables that have geometrical meaning on the microscale. They are shown to be the expansion coefficients arising in the eigenfunction representation of the displacement jump at a representative inclusion—matrix interface. Detailed calculations of stress—strain response are carried out for the case of transverse shear and plane dilatation of unidirectional fiber composites in dilute concentration. Bifurcation of equilibrium separation in the solitary inclusion problem is shown to precipitate instability in composite response. Interfaces are assumed smooth and such that normal separations are governed by the nonlinear force law of Ferrante et al. (1982) . Comments on the extension of the formulation to include the effects of finite concentration are provided as well.

A general constitutive theory for linear and nonlinear particulate media with microstructure evolution

This work is concerned with the development of a constitutive theory for composite materials with particulate microstructures, which is capable of predicting, approximately, the evolution of the microstructure and its influence on the effective response of composites under general three-dimensional finitestrain loading conditions, such as those present in metal-forming operations. In its present form, the theory is general enough to be used for linearly viscous, nonlinearly viscous and perfectly plastic composites with randomly oriented and distributed ellipsoidal inclusions (or pores), which, in the most general case, can change size, shape and orientation. In addition, the “shape” and “orientation” of their center-to-center statistical distribution functions can also evolve with the deformation. To illustrate the key features of the new theory in the context of a simple example, an application is carried out for plane-strain loading of two-phase systems consisting of random distributions of aligned rigid particles in a power-law matrix phase. The results show that the evolution of the relevant microstructural variables, as well as the effective response, depend in a complex fashion on the initial state of the microstructure, as well as on the specific boundary conditions. In particular, it is found that the changes in orientation of the particles provide a mechanism analogous to “geometric softening” in ductile single crystals, which can lead to significant changes in the instantaneous hardening rate of the composite. This is shown to have important consequences for the possible onset of shear localization in the composite.

Homogenization procedure and Pade approximations in the theory of composite materials with parallelepiped inclusions

An analytical solution, describing homogenized coefficients for composite materials with periodic cylindrical inclusions of square section domain, has been obtained by asymptotic methods and Pade approximants for any size of inclusions and its conductivity.

Molecular Rigidity in Dry and Hydrated Onion Cell Walls.

Solid-state nuclear magnetic resonance relaxation experiments can provide information on the rigidity of individual molecules within a complex structure such as a cell wall, and thus show how each polymer can potentially contribute to the rigidity of the whole structure. We measured the proton magnetic relaxation parameters T2 (spin-spin) and T1p (spin-lattice) through the 13C-nuclear magnetic resonance spectra of dry and hydrated cell walls from onion (Allium cepa L.) bulbs. Dry cell walls behaved as rigid solids. The form of their T2 decay curves varied on a continuum between Gaussian, as in crystalline solids, and exponential, as in more mobile materials. The degree of molecular mobility that could be inferred from the T2 and T1p decay patterns was consistent with a crystalline state for cellulose and a glassy state for dry pectins. The theory of composite materials may be applied to explain the rigidity of dry onion cell walls in terms of their components. Hydration made little difference to the rigidity of cellulose and most of the xyloglucan shared this rigidity, but the pectic fraction became much more mobile. Therefore, the cellulose/xyloglucan microfibrils behaved as solid rods, and the most significant physical distinction within the hydrated cell wall was between the microfibrils and the predominantly pectic matrix. A minor xyloglucan fraction was much more mobile than the microfibrils and probably corresponded to cross-links between them. Away from the microfibrils, pectins expanded upon hydration into a nonhomogeneous, but much softer, almost-liquid gel. These data are consistent with a model for the stress-bearing hydrated cell wall in which pectins provide limited stiffness across the thickness of the wall, whereas the cross-linked microfibril network provides much greater rigidity in other directions.

Adiabatic phase transformations in confinement

The phase diagram of small one-component particles has been analyzed under conditions of thermal insulation, i.e., conservation of energy. In large isolated systems the absolute stability belongs to heterogeneous states with phase separation. However, for small particles the global stability analysis shows a considerable extension of the single-phase regions into a two-phase zone of the phase diagram. Moreover, for very fine particles with sizes only 5-20 times exceeding interfacial thickness, phase separation does not occur at all and the equilibrium is achieved on homogeneous transition states that can never be obtained in bulk samples because of their absolute instability. The thermodynamic and dynamical explanations are presented. This type of a small-particle phase diagram may be relevant to the theory of amorphization, magnetocaloric effect, and nanophase composite materials where small particles or thin whiskers, capable of undergoing a transition, are immersed into a poorly conducting matrix. In case of small particles of solid solution, where mass conservation replaces the conservation of energy, present results predict the appearance of new stable phases with compositions deeply inside the miscibility gap.

Prediction of viscosity in the two-phase range of a ternary glass-forming system

In order to predict the viscosity of liquid and correlation between equilibrium and the glass state, the theory for composite materials and suspensions was applied to an appropriate composition range of a ternary glass-forming system where one liquid and one crystal are in a state of equilibrium. According to the results the theoretical calculation showed good agreement with the measurement within the validity of the theory. The viscosity behaviour of both results was discussed from the viewpoint of the physicochemical structure of liquid and it was suggested that glass reflects latently some characteristics of the state of equilibrium.

A Thermoviscoplastic Theory for Composite Materials by Using a Matrix—Partitioned Unmixing-Mixing Scheme

A thermo-elasto-viscoplastic constitutive theory for fiber-reinforced composite materials is suggested by extending the existing unmixing-mixing scheme which is based upon some micromechanical observations. A new technique, which is called the "matrix-partition method,' is introduced in the model development. By this method, deformation states in the matrix phase can be represented with a set of mechanical variables for the respective parts of the partitioned matrix. As material parameters, which explain the three-dimensional microstructural effects resulting from kinematic compatibilities in the boundaries of the fibers and the matrix, the stress variation factors and the strain contribution factors are defined. The strain component of thermal expansion due to temperature changes is also included for the mathematical formulation. To verify the derived constitutive equations, the representative volume element of a unidirectionally fiber-reinforced lamina is discretized and analyzed by the developed finite element code. The overall stress-strain curves are obtained through the finite element analyses subject to various loading conditions, and compared with the predicted curves by the constitutive equations based on the matrix-partioned unmixing-mixing model. The numerical results illustrate the validity and the usefulness of the proposed theory on composite thermoviscoplasticity.

Correction to the Fukuda-Kawata Young's modulus theory and the Fukuda-Chou strength theory for short fibre-reinforced composite materials

The theories for modulus and strength of short fibre-reinforced composite materials are based on the calculation of the force sustained by fibres crossing an arbitrary line perpendicular to the applied load, called the scan line, in a thin, rectangular specimen. The widely referenced Fukuda-Kawata modulus theory and the Fukuda-Chou strength theory are based on an apparently incorrect procedure for the calculation of the force sustained by the fibres crossing the scan line. The error is explained in detail by comparing the Fukuda-Kawata modulus theory and the Cox modulus theory. The magnitude of this error is calculated for specific cases.

Theory and synthesis of advanced thermal-protective composite materials

We present the results of synthesis of an advanced performance thermal protective material based on silicon-organic materials. This material compares favourably with the existing traditional thermal-protective materials based on phenolic resins. The characteristics of the material developed closely resemble the characteristics of thermal-protective glass-plastics in airodynamic gas flow, although its density is more than three times lower. Covering technology for the material developed makes use of the method of pneumatic spraying, which is essentially simpler and more inexpensive than the manufacturing technology for glass-plastics. The mathematical design method developed especially for this material is presented.

Wave triplets in two-phase composites

The possibility of an appearance of wave triplets in composites is studied. It is shown that a resonant interaction in industrial composites is possible. It is stated graphically only in two classic examples of layered and fiber reinforced composites that dispersion curves of the materials allow a resonant wave interaction. The quadratic nonlinear theory of two-phase mixtures is built as the variant of a microstructure theory of composite materials. Triplets of harmonic waves are studied in the framework of this theory.