Fiber-reinforced Lamina Research Articles

Mechanical characterization and asymptotic homogenization of 3D-printed continuous carbon fiber-reinforced thermoplastic

The present work investigates the mechanical properties of continuous carbon fiber-reinforced thermoplastic by testing composite specimens which were manufactured using an innovative process based on the fused filament fabrication (FFF, analogous to FDM®). The adopted testing procedures and their results are presented, as well as an introduction to the manufacturing process, which is patented by Markforged Inc. The experimental mechanical properties (stiffness and strength) of the composite specimens, measured in tensile (longitudinal and transverse), compression (longitudinal) and in-plane shear are reported. The asymptotic homogenization technique is applied in order to predict the elastic mechanical properties of the carbon fiber-reinforced lamina. In contrast to recent studies, this investigation has revealed that considering Nylon as the thermoplastic matrix embedding the continuous fiber consistently underpredicts the transverse and in-plane shear elastic properties of the reinforced laminae. These results suggest that the composition of the thermoplastic resin is not exactly the same for the unreinforced and reinforced filaments. Additionally, cross-sectional micrographs of specimens are analyzed in detail and considerable insight has been gained concerning the thermoplastic resin of reinforced filaments.

Unidirectional fiber-reinforced composite laminae: Homogenization and localization

An algorithm for the computation of the homogenized material properties of unidirectional fiber-reinforced laminae is described. The method of extraction is such that superconvergence is realized. It is shown that the homogenized material properties are substantially independent of the number of RVEs. An algorithm for the determination of the micromechanical solution over an RVE (localization) is described and the conditions that predictors of failure initiation must satisfy are stated.

Finite Element Formulation for Active Composite Laminates

Smart structures are characterized by a synergistic integration of active materials into a passive structure connected by a control system to enable an automatic adaptation to changing environmental conditions. Piezoelectric materials are widely used as distributed sensors and actuators in smart structures, where especially hybrid composites - a combination of fiber-reinforced and piezoelectric laminae - are very powerful smart material systems. First, a brief review of the developed shell type finite element for smart composite structures is presented. It is a degenerated shell element based on the Reissner-Mindlin kinematical assumptions for modeling thin and moderately thick structures made of multilayered material including piezoelectric active layers polarized in the thickness direction. The main focus of the paper is put on the test examples originally proposed by other authors. The finite element results were compared with the reference solutions obtained by Ritz type approximations. The considered test cases investigate the effects of shell shallowness, bending/twisting coupling and the influence of the piezoelectric layer thickness on the deformation of the laminated structure.

A numerical approach for predicting the failure locus of fiber reinforced composites under combined transverse compression and axial tension

A computational model based on the finite element method is presented for the estimation of strength of a fiber-reinforced lamina subjected to a combination of the transverse compression and axial tension. A complex damage mechanism including fiber breakage, fiber/matrix debonding and matrix plastic deformation is reproduced in the proposed model by using appropriate constitutive equations. The numerical simulation of mechanical response of the unidirectional lamina under biaxial loading is used to obtained the failure locus. Subsequently, the model is verified against an analytical solution and experimental data. It was found that the numerical calculations agree better with experimental results than analytical predictions.

A two-scale homogenization framework for nonlinear effective thermal conductivity of laminated composites

In this study, we formulate the effective temperature-dependent thermal conductivity of laminated composites. The studied laminated composites consist of laminas (plies) made of unidirectional fiber-reinforced matrix with various fiber orientations. The effective thermal conductivity is obtained through a two-scale homogenization scheme. A simplified micromechanical model of a unidirectional fiber-reinforced lamina is formulated at the lower scale. Thermal conductivities of fiber and matrix constituents are allowed to change with temperature. The upper scale uses a sublaminate model to homogenize temperature-dependent thermal conductivities of only a representative lamina stacking sequence in laminated composites. The effective thermal conductivity of each lamina, in the sublaminate model, is obtained using the simplified micromechanical model. The thermal conductivities from the micromechanical and sublaminate models represent average nonlinear properties of fictitiously homogeneous composite media. Interface conditions between fiber and matrix constituents and within laminas are assumed to be perfect. Experimental data available in the literature are used to verify the proposed multi-scale framework. We then analyze transient heat conduction in the homogenized composites. Temperature profiles, during transient heat conduction, in the homogenized composites are compared to the ones in heterogeneous composites. The heterogeneous composites, having different fiber arrangements and sizes, are modeled using finite element (FE) method.

Linear theory for the bending and extension of a thin, residually stressed, fiber-reinforced lamina

The Euler equations of a thickness-wise expansion of the potential energy of a thin body, truncated at a specified order in thickness, furnish a model for the bending and stretching of plates and shells. However, truncated expansions of the energy typically do not lead to well-posed minimization problems. This is related to the fact that the truncations may fail to satisfy the relevant Legendre–Hadamard condition, which is necessary for the existence of minimizers. This lack of well-posedness is thus entirely consistent with well-posedness in the exact theory. However, it is an inconvenience from the viewpoint of analysis. What is desired is an accurate, well-posed truncation that preserves the structure of classical plate theory. The present work is concerned with the development of such a model for a uniform fiber-reinforced lamina.

Control of the transient deformation of a piezoelastic beam with a closed-loop controlsystem subjected to mechanical disturbance considering the effect of damping

In this paper, control of the transient deformation of a piezoelastic beam with a closed-loopcontrol system subjected to dynamic change in the mechanical environment is studiedconsidering the effect of damping. The analytical model is a symmetric cross-ply laminatedbeam composed of fiber-reinforced laminae and two piezoelectric layers. The beam issimply-supported at both edges, and is subjected to mechanical disturbance. To suppressthe dynamic deformation due to the disturbance, the beam is subjected to the closed-loopcontrol procedure in which one of the piezoelectric layers serves as a sensor to detect thedeformation due to the disturbance and the other serves as an actuator to suppress it. Theanalytical solution of the transient deflection is formulated based on the classical laminatetheory and the equation of motion considering the effect of damping. Using numericalexamples, suppression of the deflection due to mechanical disturbance by a series of pulsesof electrical voltage is examined. Appropriate parameters, such as the gain, thesensing time and the duration and number of pulses, of the control procedureto suppress the deflection are found. Moreover, the optimized combination ofthe initial time and duration of a pulse under a fixed gain is obtained by directexploration.

Three-dimensional microscopic interlaminar analysis of cross-ply laminates based on a homogenization theory

In this study, a method for three-dimensional microscopic interlaminar analysis of cross-ply laminates is developed based on a homogenization theory to analyze microscopic interactions between unidirectional long fiber-reinforced laminae. For this, a unit cell of a cross-ply laminate, which includes interlaminar areas, is defined under the assumption that each lamina in the laminate has a transversely square fiber array. Then, showing that the laminate has a point-symmetric internal structure, the symmetry is utilized to introduce half of the unit cell as the domain of analysis. Moreover, the domain of analysis is divided into substructures using a substructure method combined with the homogenization theory, significantly reducing the computational costs. The present method is then applied to the analysis of interlaminar stress distributions in a carbon fiber/epoxy cross-ply laminate subjected to in-plane uniaxial tension. It is shown that microscopic shear stress noticeably occurs at the interface between the 0°- and 90°-plies. It is also shown that the microscopic interaction between the two plies is observed only in the vicinity of the interface.

Non-linear dynamic behaviour of a piezothermoelastic laminate

Non-linear dynamic behaviour of a piezothermoelastic laminate including the dynamic deflection deviated arbitrarily from the equilibrium state is analysed. As an analytical model, we consider a rectangular laminate composed of fiber-reinforced laminae and piezoelectric layers subjected to mechanical, thermal, and electrical loads. Non-linear large deformation of the laminate is analysed based on the von Kármán strains and the first-order shear deformation theory. Equations of motion of the laminate are analysed using the Galerkin method. As a result, it is found that the dynamic deflection of the laminate is governed by the equation for a polynomial oscillator, and the following quantities are obtained: (1) the buckling temperature due to in-plane thermal load; (2) the static large deflection due to combined in-plane and anti-plane loads; (3) the natural frequency of the oscillation in the vicinity of the static equilibrium state; (4) the dynamic large deflection deviated arbitrarily from the state. Moreover, numerical examples are shown to investigate the methods to rise the buckling temperature and to linearize thermal deflection and the natural frequency by applying the electrical voltage to the piezoelectric actuators. As a result, it is found that appropriate application of the electrical voltage serves as structural stabilization of the laminate.

Control of mechanical deformation of a laminate by piezoelectric actuator taking into account the transverse shear

The control of dynamic deformation of a laminate plate is conducted by applying electrical load to a piezoelectric actuator integrated into the laminate. The dynamic behavior of the laminate is analyzed in the paper taking into account the effect of transverse shear. The analytical model of the laminate is composed of fiber-reinforced laminae and piezoelectric layers constituting a symmetric cross-ply laminate rectangular plate with simply-supported egdes. It is subjected to mechanical and electrical loads acting on the piezoelectric actuator in order to compensate the effect of the mechanical loads. The behavior of the laminate is analyzed based on the first-order shear deformation theory. Closed-form solutions are obtained for the following quantities: (1) natural frequencies of the laminate plate, (2) weight functions for the deflections and rotations and (3) transient deflections due to loads varying arbitrarily with time. Illustrative examples are shown for the control of deflections caused by the mechanical loads by means of electrical voltage applied to the piezoelectric actuators.

Nonlinear dynamic behavior of a piezothermoelastic laminated plate with anisotropic material properties

In this paper, we analyze the nonlinear dynamic behavior of a piezothermoelastic laminated plate with anisotropic material properties. The analytical model is a rectangular laminate composed of fiber-reinforced laminae and piezoelectric layers. The model is assumed to be a symmetric cross-ply laminate with all egdes simply-supported and to be subjected to mechanical, thermal and electrical loads as intended control procedures or as disturbances. The von Karman strains are introduced to treat non-linear deformation. The behavior of the laminate is analyzed by using the Galerkin Method. We discuss the following quantities: (i) the buckling temperature due to in-plane thermal load; (ii) the large static deflection due to combined in-plane and anti-plane loads; (iii) the natural frequency of infinitesimal oscillation around the static equilibrium state; (iv) the natural frequency of the oscillation with finite amplitude around the static equilibrium state. Moreover, numerical examples are shown to investigate the methods to rise the buckling temperature, to linearize the thermal deflection and the natural frequencies by applying the electrical voltage to the piezoelectric actuators.

Effect of damping on dynamic behavior of a piezothermoelastic laminate considering the effects of transverse shear

In this paper, we analyze dynamic behavior of a piezothermoelastic laminate considering the effect of damping due to interlaminar shear and the effect of transverse shear. The analytical model is a rectangular laminate composed of fiber-reinforced laminae and piezoelectric layers. The model is assumed to be a symmetric cross-ply laminate with all egdes simply supported and to be subjected to mechanical, thermal and electrical loads varying arbitrarily with time. Behavior of the laminate is analyzed based on the first-order shear deformation theory. The effect of damping due to interlaminar shear is incorporated into our analysis by introducing the interlaminar shear stresses which satisfy the Newton’s law of viscosity. Solutions of the following quantities are obtained: (1) natural frequencies of the laminate, (2) weight functions for the deflection and rotations and (3) unsteady deflection due to loads varying arbitrarily with time. Moreover, numerical examples of the solutions are shown to examine the effects of damping and transverse shear on dynamic behavior of the laminate and how the voltage applied to the laminate decreases the deflection due to mechanical or thermal loads.

Control of mechanical deformation of a laminate by electrical load to piezoelectric actuator considering the effects of damping and transverse shear

In this paper, we treat the control of dynamic deformation of a laminate by applying electrical load to piezoelectric actuators. Dynamic behavior of the laminate is analyzed considering the effect of damping due to interlaminar shear and the effect of transverse shear. The analytical model is a rectangular laminate composed of fiber-reinforced laminae and piezoelectric layers. The model is assumed to be a symmetric cross-ply laminate with all edges simply supported and to be subjected to unavoidable mechanical load and to electrical loads to piezoelectric actuators. Behavior of the laminate is analyzed based on the first-order shear deformation theory. The effect of damping due to interlaminar shear is incorporated into our analysis by introducing the interlaminar shear stresses which satisfy the Newton’s law of viscosity. The following quantities are obtained: (1) natural frequencies of the laminate, (2) weight functions for the deflection and rotations and (3) transient deflection due to loads varying arbitrarily with time. Moreover, the methods to control the deflection due to mechanical load by applying electrical voltage to the piezoelectric actuator are shown.

Determination of the Elastic Constants of a Transversely Isotropic Lamina Using Laminate Coefficients of Thermal Expansion

Three-dimensional elastic constants for a fiber-reinforced lamina are often difficult to obtain from traditional mechanical tests. The relationships developed in thiswork enable the determination of any three of the five independent elastic constants, of a transversely isotropic lamina, from measurements of the remaining two elastic constants and the coefficients of thermal expansion (CTE’s) of [(+θ/−θ)n]s and unidirectional laminates. The approach is used to predict the elastic propertiesof a carbon fiber reinforced epoxy material and the predicted properties are shown to be in good agreement with quoted values. Further, the developed relationships can be used to determine elastic constants over a range of temperatures and, potentially, to study the effects of manufacturing on elastic properties. Therefore, this technique constitutes an additional method for evaluating the elastic constants that characterize a transversely isotropic, fiber-reinforced lamina.

Dynamic behavior of a piezothermoelastic laminate considering the effect of transverse shear

In this paper, we analyze the dynamic behavior of a piezothermoelastic laminate considering the effect of transverse shear. The analytical model is a rectangular laminate composed of fiber-reinforced laminae and piezoelectric layers. The model is assumed to be a symmetric cross-ply laminate with all edges simply supported and to be subjected to mechanical, thermal and electrical loads varying arbitrarily with time. The behavior of the laminate is analyzed based on first-order shear deformation theory. Closed solutions of the following quantities are obtained: (1) the natural frequencies of the laminate, (2) the weight function for the deflection and (3) the unsteady deflection due to loads varying arbitrarily with time. Moreover, numerical examples of the solutions are shown to examine the effect of transverse shear on the dynamic behavior of the laminate and how the voltage applied to the laminate decreases the deflection due to mechanical or thermal loads.

PIEZOTHERMOELASTIC ANALYSIS OF A CROSS-PLY LAMINATE CONSIDERING THE EFFECTS OF TRANSVERSE SHEAR AND COUPLING

In this study, we treat the behavior of a piezothermoelastic composite plate taking into account the effects of transverse shear and coupling among mechanical, thermal, and electrostatic fields. As an analytical model, we consider a rectangular laminate composed of several fiber-reinforced laminae and a piezoelectric layer. All the laminae are assumed to exhibit 2-mm symmetry and the principal axes of anisotropy to coincide with coordinate axes, that is, a cross-ply laminate is considered. We assume that the laminate is subjected to mechanical, thermal, and electrical loads with all edges simply supported and treat the problem as a coupled piezothermoelastic one. Numerical calculation is carried out to examine the effects of transverse shear and coupling on the behavior of the laminate. Moreover, the control of the deflection by applied voltage is examined.

Matrix-dominated viscoplasticity theory for fibrous metal matrix composites

The matrix-dominated mode (MDM) small strain plasticity model of Dvorak and Bahei-El-Din for continuous fiber-reinforced metal laminae is extended to include rate-sensitive matrices, slip direction-dependent material properties, a simple bounding surface representation of the equilibrium plastic modulus and nonnormal plastic flow, with the thermal decomposition procedure of Dvorak employed to address the effects of anisothermal loading. The model is found to adequately describe complex nonproportional loading results obtained by Dvorak et al. for boron fiber-reinforced aluminum at room temperature.

A model of global thermal conductivity in laminated carbon/carbon composites

Starting with thermal conductivity components for the individual continuous unidirectional fiber-reinforced lamina or ply, a method has been developed to determine global conductivities in a laminated carbon/carbon composite. Assuming that all laminae are identical in thickness and in fiber content, effective thermal conductivity in each global direction is determined for the laminated composite. Results are reported for a few selected standard laminate lay-ups and are compared with those reported in the literature.

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.

Comparison of shear-lag theory and continuum fracture mechanics for modeling fiber and matrix stresses in an elastic cracked composite lamina

This study analyzes fiber tensile and matrix shear stresses near the crack tip in a transversely cracked, unidirectional, fiber-reinforced lamina under a remote tensile stress applied in the fiber direction. The two-dimensional lamina consists of parallel, equally-spaced elastic fibers with elastic matrix in-between, and contains a row of up to a few hundred contiguous fiber breaks aligned transverse to the fiber direction forming a central transverse crack. Using the break-influence superposition (BIS) technique, a recently developed method for analyzing a shear-lag model first introduced by Hedgepeth, we calculate the tensile and shear stress concentrations in the fibers and matrix, respectively. These are compared to tensile and shear stresses calculated using Linear Elastic Fracture Mechanics (LEFM) and the complete elasticity solution both for the continuum limit of a homogeneous, orthotropic elastic material with a transverse central crack loaded in Mode I. For the shear-lag model a critical scaling parameter for examining the stress behavior away from the crack tip along the fiber direction is √E∗/G∗, where E∗ and G∗ are composite in-plane stiffness constants along the fiber direction and in shear, respectively. In addition to these parameters, the LEFM and complete elasticity solutions also involve the effective transverse stiffness and Poisson's ratio. For a sizable crack (consisting of 100 or more fiber breaks), the fiber tensile stresses ahead of the crack tip along the crack plane calculated from the BIS approach achieve excellent agreement with the LEFM solution down to the scale of one fiber diameter and even better agreement with the complete solution both in the near crack tip field and far field, regardless of the composite stiffness constants. The profiles of the fiber tensile and matrix shear stresses along the fiber direction show generally good agreement, with the agreement improving as the composite stiffness transverse to the fiber direction grows.