L.C. Brinson

Functionalized graphene sheets for polymer nanocomposites

Polymer-based composites were heralded in the 1960s as a new paradigm for materials. By dispersing strong, highly stiff fibres in a polymer matrix, high-performance lightweight composites could be developed and tailored to individual applications. Today we stand at a similar threshold in the realm of polymer nanocomposites with the promise of strong, durable, multifunctional materials with low nanofiller content. However, the cost of nanoparticles, their availability and the challenges that remain to achieve good dispersion pose significant obstacles to these goals. Here, we report the creation of polymer nanocomposites with functionalized graphene sheets, which overcome these obstacles and provide superb polymer-particle interactions. An unprecedented shift in glass transition temperature of over 40 degrees C is obtained for poly(acrylonitrile) at 1 wt% functionalized graphene sheet, and with only 0.05 wt% functionalized graphene sheet in poly(methyl methacrylate) there is an improvement of nearly 30 degrees C. Modulus, ultimate strength and thermal stability follow a similar trend, with values for functionalized graphene sheet- poly(methyl methacrylate) rivaling those for single-walled carbon nanotube-poly(methyl methacrylate) composites.

Fiber waviness in nanotube-reinforced polymer composites—I: Modulus predictions using effective nanotube properties

Results in the literature demonstrate that substantial improvements in the mechanical behavior of polymers have been attained through the addition of small amounts of carbon nanotubes as a reinforcing phase. This suggests the possibility of new, extremely lightweight carbon nanotube-reinforced polymers with mechanical properties comparable to those of traditional carbon-fiber composites. Motivated by micrographs showing that embedded nanotubes often exhibit significant curvature within the polymer, we have developed a model combining finite element results and micromechanical methods to determine the effective reinforcing modulus of a wavy embedded nanotube. This effective reinforcing modulus (ERM) is then used within a multiphase micromechanics model to predict the effective modulus of a polymer reinforced with a distribution of wavy nanotubes. We found that even slight nanotube curvature significantly reduces the effective reinforcement when compared to straight nanotubes. These results suggest that nanotube waviness may be an additional mechanism limiting the modulus enhancement of nanotube-reinforced polymers. # 2003 Elsevier Ltd. All rights reserved.

Effects of nanotube waviness on the modulus of nanotube-reinforced polymers

Recent experimental results demonstrate that substantial improvements in the mechanical behavior of polymers can be obtained using very small amounts of carbon nanotubes as a reinforcing phase. Here, a method is developed to incorporate the typically observed curvature of the embedded nanotubes into traditional micromechanical methods for determination of the effective modulus of the nanotube-reinforced polymer. Using a combined finite element and micromechanical approach, it was determined that the nanotube curvature significantly reduces the effective reinforcement when compared to straight nanotubes. This model suggests that nanotube waviness may be an additional mechanism limiting the modulus enhancement of nanotube-reinforced polymers.

Fiber waviness in nanotube-reinforced polymer composites—II: modeling via numerical approximation of the dilute strain concentration tensor

Nanotube-reinforced polymers offer significant potential improvements over the pure polymer with regard to mechanical, electrical and thermal properties. This article investigates the degree to which the characteristic waviness of nanotubes embedded in polymers can impact the effective stiffness of these materials. A 3D finite element model of a single infinitely long sinusoidal fiber within an infinite matrix is used to numerically compute the dilute strain concentration tensor. A Mori–Tanaka model utilizes this tensor to predict the effective modulus of the material with aligned or randomly oriented inclusions. This hybrid finite elementmicromechanical modeling technique is a powerful extension of general micromechanics modeling and can be applied to any composite microstructure containing non-ellipsoidal inclusions. The results demonstrate that nanotube waviness results in a reduction of the effective modulus of the composite relative to straight nanotube reinforcement. The degree of reduction is dependent on the ratio of the sinusoidal wavelength to the nanotube diameter. As this wavelength ratio increases, the effective stiffness of a composite with randomly oriented wavy nanotubes converges to the result obtained with straight nanotube inclusions. The approach developed in this paper can also be utilized in the analysis of other problems involving nanotube-reinforced polymers, including alternate nanotube representations, viscoelastic response, assessing the effect of low matrix-NT bond strength and in the determination of thermal and electrical conductivity. # 2003 Elsevier Ltd. All rights reserved.

A Multivariant model for single crystal shape memory alloy behavior

Abstract A general 3-D multivariant model based on thermodynamics and micromechanics for single crystal shape memory alloy (SMA) behavior is presented. This model is based on the habit plane and transformation directions for the variants of martensite in a given material. From this information, the single crystal behavior of the material to temperature and mechanical loads is derived using the concept of a thermodynamic driving force. The Eshelby–Kroner approach is utilized to determine the interaction energy between the variants, where it is assumed that variants can be subdivided into several self-accommodating groups in which variants can grow together compatibly. This model is examined initially for a simple 2-variant case and then extended to the typical 24 variant case. The multivariant model is shown to exhibit appropriate responses for uniaxial results on single crystals : the transformations occur instantaneously when the critical stress\temperature is reached ; both pseudoelasticity and the shape memory effect are captured. The model is also examined for responses to multiaxial loadings and the distinction between perfectly compatible and imperfectly compatible variants (with nonzero volumetric transformation strain) is discussed.

Viscoelastic interphases in polymer-matrix composites: theoretical models and finite-element analysis

Abstract We investigate the mechanical property predictions for a three-phase viscoelastic (VE) composite by the use of two micromechanical models: the original Mori–Tanaka (MT) method and an extension of the Mori–Tanaka solution developed by Benveniste to treat fibers with interphase regions. These micro-mechanical solutions were compared to a suitable finite-element analysis, which provided the benchmark numerical results for a periodic array of inclusions. Several case studies compare the composite moduli predicted by each of these methods, highlighting the role of the interphase. We show that the MT method, in general, provides the better micromechanical approximation of the viscoelastic behavior of the composite; however, the micromechanical methods only provide an order-of-magnitude approximation for the effective moduli. Finally, these methods were used to study the physical aging of a viscoelastic composite. The results imply that the existence of an interphase region, with viscoelastic moduli different from those of the bulk matrix, is not responsible for the difference in the shift rates, μ22 and μ66, describing the transverse Youngs axial shear moduli, found experimentally.

Phase diagram based description of the hysteresis behavior of shape memory alloys

Abstract In this paper, we develop a consistent mathematical description of martensite fraction evolution during athermal thermoelastic phase transformation in a shape memory alloy (SMA) induced by a general thermomechanical loading. The global kinetic law is based on an experimentally defined stress–temperature phase diagram, transformation functions for a one-dimensional SMA body and a novel vector hysteresis model. The global kinetic law provides the phase fraction history given a loading path on the stress–temperature phase diagram and an initial value of martensite fraction. The phase transformation is considered to occur only within transformation strips on the phase diagram and only on loading path segments oriented in the transformation direction. The developed procedure can be used to model a range of different SMA transformation behaviors depending on the choice of transformation functions and local kinetic law algorithms. The phase fraction evolution is examined for a number of characteristic examples, including cyclic loading resulting in oscillatory transformation paths, and internal loops of partial transformation with associated attractor loops. Differences between the various local kinetic law algorithms used in the overall framework are highlighted. The simulation results using a cosine transformation function are found to be in excellent agreement with experimental data.

Temperature-induced phase transformation in a shape memory alloy: Phase diagram based kinetics approach

In this article we develop a general framework to model the one dimensional thermomechanical behavior of shape memory alloys (SMAs) based on phase diagram kinetics and a phenomenological constitutive law with martensite fraction as an internal variable. As part of this framework, we construct a consistent mathematical description for martensite fraction evolution to be used in conjunction with an experimentally defined phase diagram; the kinetics formalism is illustrated with examples of isostress and isothermal cycling. As an application, we consider the thermo-induced martensite transformation of a 1D prestressed SMA polycrystalline body which proceeds by migration of the austenite-martensite two-phase zone from the cooled boundary, converting the SMA body from an austenite (A) to a detwinned martensite (M) state. The mathematical model for the two-phase zone migration is based on the nonstationary equation of energy balance and the quasistationary approximation for the linear momentum equation and utilizes a quasistatic kinetic law, a macroscale constitutive law and an incompressibility constraint. To close the formulated system of equations, the internal energy of an A/M mixture in the two-phase zone is heuristically derived. The mixed initial-boundary value problem is then solved numerically and compared to analytical results for a simplified model. The results stress the significance of the stress dependency in the kinetic law and the transformation heat to the progress of transformation.

A Sign Control Method for Fitting and Interconverting Material Functions for Linearly Viscoelastic Solids

The multidata method was originally proposed to fit a Prony exponentialseries function to experimental viscoelastic modulus and compliance data;this was accomplished by the application of a linear least squares solver.This paper considers a similar approach, but extended in two key ways.First, it has been applied to the solution of convolution integralequations; specifically those used for material function interconversion.Second, it has been modified to force the signs of the Prony seriescoefficients to be positive; this is an essential criterion for the properphysical interpretation of a Prony series material function, which istypically not satisfied by multidata method solutions. Sign control isimplemented by an iterative Levenberg–Marquardt solution algorithm withan appropriate constraint, and can be used for both fitting experimentaldata and interconversion. To use the method, a Prony series must becapable of adequately representing the applicable functions. The method isdemonstrated by first fitting and converting experimental modulus data.Formulation for a composite lamina is also shown, in which a system ofintegral equations is reduced to a single integral equation; this can thenbe solved using the new method. Finally, application of the new method tofrequency domain transformations is demonstrated, along with comparisonsto other techniques.

Mechanical response of linear viscoelastic composite laminates incorporating non-isothermal physical aging effects

Abstract This paper presents a method of predicting the mechanical response of composite laminates including the effects of linear viscoelasticity and physical aging. Effective-time theory has been used to characterize the physical aging behavior of each linear viscoelastic lamina. In accordance with experimental findings, the aging behavior of each lamina is allowed to differ in the shear and transverse directions. The mechanical loading is restricted to the linear range, which decouples the aging and load behavior. A recursive algorithm has been used to solve the hereditary convolution integral that governs the response of each ply. Classical thin-laminate theory is then used to assemble the individual ply response equations and determine the overall laminate response to general in-plane force and moment loading. The method automatically recovers the ply-level stresses and strains, which are often critical to strength and durability predictions. The model can use either lamina compliance or modulus properties as its basis. Several illustrative examples of long-term laminate response to variable loading are presented and the impact of physical aging is explored. It is shown that for multidirectional laminates, the stiffness of the lamina in the fiber directions can allow simplifications of the model.