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### ERRATUM

J. Eng. Mater. Technol. 2006;128(1):1. doi:10.1115/1.2163087.
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Abstract
Commentary by Dr. Valentin Fuster

### PREFACE

J. Eng. Mater. Technol. 2006;128(1):2. doi:10.1115/1.2147846.
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This special issue of the Journal of Engineering Materials and Technology contains 15 papers delivered at the Symposium on Time-Dependent Behaviors of PMCs (Polymer Matrix Composites) and Polymers, held in Anaheim, California as part of the 2004 ASME International Mechanical Engineering Congress and Exposition. A total of 21 talks were delivered in five sessions, which spanned many aspects of the time-dependent behaviors of these materials.

Commentary by Dr. Valentin Fuster

### RESEARCH PAPER: Omitted From October 2005 Issue, Special Section on Nanomaterials and Nanomechanics

J. Eng. Mater. Technol. 2005;128(1):3-10. doi:10.1115/1.1857938.

Carbon nanotubes (CNTs) constitute a prominent example of nanomaterials. In most studies on mechanical properties, the effort was concentrated on CNTs with relatively small aspect ratio of length to diameters. In contrast, CNTs with aspect ratios of several hundred can be produced with today’s experimental techniques. We report atomistic-continuum studies of single-wall carbon nanotubes with very large aspect ratios subject to compressive loading. It was recently shown that these long tubes display significantly different mechanical behavior than tubes with smaller aspect ratios (Buehler, M. J., Kong, Y., and Guo, H., 2004, ASME J. Eng. Mater. Technol. 126 , pp. 245–249). We distinguish three different classes of mechanical response to compressive loading. While the deformation mechanism is characterized by buckling of thin shells in nanotubes with small aspect ratios, it is replaced by a rodlike buckling mode above a critical aspect ratio, analogous to the Euler theory in continuum mechanics. For very large aspect ratios, a nanotube is found to behave like a wire that can be deformed in a very flexible manner to various shapes. In this paper, we focus on the properties of such wirelike CNTs. Using atomistic simulations carried out over a several-nanoseconds time span, we observe that wirelike CNTs behave similarly to flexible macromolecules. Our modeling reveals that they can form thermodynamically stable self-folded structures, where different parts of the CNTs attract each other through weak van der Waals (vdW) forces. This self-folded CNT represents a novel structure not described in the literature. There exists a critical length for self-folding of CNTs that depends on the elastic properties of the tube. We observe that CNTs fold below a critical temperature and unfold above another critical temperature. Surprisingly, we observe that self-folded CNTs with very large aspect ratios never unfold until they evaporate. The folding-unfolding transition can be explained by entropic driving forces that dominate over the elastic energy at elevated temperature. These mechanisms are reminiscent of the dynamics of biomolecules, such as proteins. The different stable states of CNTs are finally summarized in a schematic phase diagram of CNTs.

Commentary by Dr. Valentin Fuster

### RESEARCH PAPERS: Special Issue on Time-Dependent Behaviors of Polymer Matrix Composites and Polymers

J. Eng. Mater. Technol. 2005;128(1):11-17. doi:10.1115/1.2127959.

The objective of this paper is to model the synergistic bond-degradation mechanisms that may occur at the interface between a fiber-reinforced polymer (FRP) that is adhesively bonded to a substrate and subjected to elevated temperature and humidity. For this purpose, a two-dimensional cohesive-layer constitutive model with a prescribed traction-separation law is constructed from fundamental principles of continuum mechanics and thermodynamics, taking into account strain-dependent, non-Fickian hygrothermal effects as well as diffusion-induced degradation in the cohesive layer. In the interest of solution tractability, a simplified approach is employed where the rate-dependent behavior in the cohesive layer is implemented through the characterization of rate dependence of the maximum stresses and maximum strains in the cohesive layer, rather than through the use of convolution integrals in the free-energy definition. The remainder of the polymeric adhesive outside the cohesive layer is modeled as a nonlinear viscoelastic continuum with time-dependent constitutive behavior. The influence of temperature and moisture concentration on the work-of-separation and on crack growth is derived from first principles. The model is implemented in a test-bed finite element code. Results predicted by the computational model are benchmarked through comparison to experimental data from mixed-mode fracture experiments performed using a moving wedge test.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2005;128(1):18-27. doi:10.1115/1.2127960.

This paper presents a model for predicting the damage-induced mechanical response of particle-reinforced composites. The modeling includes the effects of matrix viscoelasticity and fracture, both within the matrix and along the boundaries between matrix and rigid particles. Because of these inhomogeneities, the analysis is performed using the finite element method. Interface fracture is predicted by using a nonlinear viscoelastic cohesive zone model. Rate-dependent viscoelastic behavior of the matrix material and cohesive zone is incorporated by utilizing a numerical time-incrementalized algorithm. The proposed modeling approach can be successfully employed for numerous types of solid media that exhibit matrix viscoelasticity and complex damage evolution characteristics within the matrix as well as along the matrix-particle boundaries. Computational results are given for various asphalt concrete mixtures. Simulation results demonstrate that each model parameter and design variable significantly influences the mechanical behavior of the mixture.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2005;128(1):28-33. doi:10.1115/1.1924564.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2005;128(1):34-40. doi:10.1115/1.2128425.

Structural composites are increasingly being utilized in many large naval and civil structures where it is vital that their long-term performance be predictable and their variability definable over the life of the structure. However, these properties may be influenced by the degree of cure of the resin, particularly for room-temperature-cured systems. Thus, this investigation defines the postcure effects on E-glass/vinyl-ester fiber-reinforced polymer (FRP) composites manufactured using the vacuum-assisted resin transfer molding (VARTM) method, which are typical of those used by the US Navy for ship structures. The composites are differentiated by varying levels of postcure temperature and duration, and examined for the effects of advancing cure at various points in the time after postcure. Pseudo-quasi-isotropic [0/+45/90/−45/0]s and angle ply laminate [±45]2s samples from each level of postcure are examined at 1, 10, 30, 100, and 300 days after postcure in order to track strength, stiffness, failure strain, creep, and fatigue performance as functions of time. In parallel, the matrix polymer is inspected using FTIR (Fourier transform infrared spectroscopy) to directly assess the degree of conversion. Dynamic mechanical analysis and shrinkage measurements are also undertaken to assess the Tg and the amount of shrinkage undergone during post-curing, as well as the advancing of the level of cure during the prescribed aging time. Results suggest that the degree of conversion is limited to 80% for the vinyl-ester oligomer and 90–95% for styrene following a postcure of 93°C. It is observed that after 300 days of ambient storage the nonpostcured samples approach the degree of conversion exhibited by those postcured at 93°C, as measured by FTIR. Resin dominated quasi-static properties are greatly affected by the degree of cure, whereas fiber dominated properties are not. Where the degree of cure is comparatively low, viscoelastic properties cause greater changes in creep response as well as influencing fatigue performance.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2005;128(1):41-49. doi:10.1115/1.2128424.

This paper focuses on the probability modeling of fiber composite strength, wherein the failure modes are dominated by fiber tensile failures. The probability model is the tri-modal local load-sharing model, which is the Phoenix-Harlow local load-sharing model with the filament failure model extended from one mode to three modes. This model results in increased efficiency in the determination of fiber statistical parameters and in lower cost when applied to (i) quality control in materials (fiber) manufacturing, (ii) materials (fiber) selection and comparison, (iii) accounting for the effect of size scaling in design, and (iv) qualification and certification of critical composite structures that are too large and expensive to test statistically. In addition, possible extensions to proof testing and time-dependent life prediction are discussed and preliminary data are presented.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2005;128(1):50-54. doi:10.1115/1.1925287.

The time history of steam pressure inside an isolated spherical micro-cavity in a polymer matrix composite is studied by assuming that the chemical potential of water is continuous across the cavity–polymer interface. Steam pressure inside the cavity is due to heating of moisture-saturated composites from its initial temperature to a final temperature. Exact closed form solutions are obtained for the steam pressure developed under infinitely fast heating in an infinite plate. The effect of cavity shape on the induced steam pressure is studied by comparing this solution with a previous result on cracklike cavities.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2005;128(1):55-63. doi:10.1115/1.2128426.

A thermodynamic framework is presented that can be used to describe the solidification of polymer melts, both the solidification of atactic polymers into an amorphous elastic solid and the crystallization of other types of polymer melts to semi-crystalline elastic solids. This framework fits into a general structure that has been developed to describe the response of a large class of dissipative bodies. The framework takes into account the fact that the natural configuration of the viscoelastic melt and the solid evolve during the process and that the symmetries of these natural configurations also evolve. Different choices are made as to how the material stores energy, produces entropy, and for its latent heat, latent energy, etc., that lead to models for different classes of materials. The evolution of the natural configuration is dictated by the manner in which entropy is produced, how the energy is stored etc., and it is assumed that the constitutive choices are such that the rate entropy production is maximized, from an allowable class of constitutive models. Such an assumption also determines the crystallization kinetics, i.e., provides equations such as the Avrami equation. Using the framework, a model is developed within which the problem of fiber spinning is studied and we find that the model is able to predict observed experimental results quite well.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2005;128(1):64-72. doi:10.1115/1.1925289.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2005;128(1):73-80. doi:10.1115/1.2130733.

Increased thermal conductivity, electronic conductivity, and reversible capacity (i.e., reduced irreversible capacity loss, or ICL) have been demonstrably achievable by compression of anodes into higher volume fraction plates, though excessive compression can impair $Li$-ion battery performance. In our previous study, we correlated conductivity and compression of these materials. Here, we further investigated the effects of friction and deformability of particles on the compressibility of model carbons of $Li$-ion anodes. First, we implemented a statistically unbiased technique for generating a range of random particulate systems, from permeable to impermeable arrangements, along with a contact model for randomly arranged triaxial ellipsoidal particles, suitable for implementation in finite element analysis of compression of a random, porous system. We then quantified the relationship between interfacial friction and jamming fraction in spherical to ellipsoidal systems and applied these models to correlate maximum stresses and different frictional coefficients, with morphology (obtained by image analysis) of graphite particles in $Li$-ion anodes. The simulated results were compared with the experiments, showing that the friction coefficient in the system is close to 0.1 and that the applied pressure above $200kg∕cm2$$(200MPa)$ can damage the materials in SL-20 electrodes. We also conclude that use of maximum jamming fractions to assess likely configuration of mixtures is unrealistic, at best, in real manufacturing processes. Particles change both their overall shapes and relative orientations during deformation sufficient to alter the composite properties: indeed, it is alteration of properties that motivates post-processing at all. Thus, consideration of material properties, or their estimation post facto, using inverse techniques, is clearly merited in composites having volume fractions of particles near percolation onset.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2005;128(1):81-89. doi:10.1115/1.2132377.

The proper determination of high-temperature constitutive properties and damage of polymer-matrix composites (PMC) in an aggressive environment is critical in high-speed aircraft and propulsion material development, structural integrity, and long-term life prediction. In this paper, a computational micromechanics study is conducted to obtain high-temperature constitutive properties of the PMC undergoing simultaneous thermal oxidation reaction, microstructural damage, and thermomechanical loading. The computational micromechanics approach follows the recently developed irreversible thermodynamic theory for polymer composites with reaction and microstructural change under combined chemical, thermal, and mechanical loading. Proper microstructural modeling of the PMC is presented to ensure that reaction activities, thermal and mechanical responses of the matrix, fibers, and fiber-matrix interface are fully addressed. A multiscale homogenization theory is used in conjunction with a finite element representation of material and reaction details to determine continuous evolution of composite microstructure change and associated degradation of the mechanical and physical properties. Numerical examples are given on a commonly used G30-500/PMR15 composite for illustration.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2005;128(1):90-95. doi:10.1115/1.2148421.

The ability to manufacture thermoset matrix composite materials into large and complex structures can be significantly enhanced by modeling the behavior of the system during the process. As a result there has been much research on all aspects of the cure of these materials. A particularly important aspect is the development of mechanical properties in the thermoset matrix as it evolves from a low molecular weight material into a fully cross-linked solid. The behavior is generally acknowledged to be viscoelastic, and as both temperature and degree of cure vary with time, the characterization and representation of the behavior is both critical and complex. Many approaches have been suggested and tried, ranging from 1D or 2D implementations of simple linear elastic cure hardening responses (which have been shown to be essentially pseudo-viscoelastic formulations) through to more sophisticated representations of viscoelastic behavior as Prony series of Maxwell elements coded in 3D hereditary integral FE implementations. In this paper we present a differential approach for the viscoelastic representation of a curing thermoset matrix composite undergoing an arbitrary temperature cycle by noting that the viscoelastic response can be represented very well by a Prony series. For this case, we show that a differential approach is equivalent to an integral formulation, but appears to have some significant benefits in terms of extension to more general descriptions (e.g., thermo-viscoelastic behavior), ease of coding and implementation, and perhaps most importantly, computer runtimes. Rather than using a differential approach where the order of the governing differential equation grows very fast with the number of springs or dashpots, we use the stresses in the individual Maxwell elements to capture the complete history of the material and allow for a much simpler formulation. A 1D formulation of this differential approach, including thermo-viscoelasticity, is developed, and results and benchmarks are presented.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2005;128(1):96-106. doi:10.1115/1.1925293.

This paper is aimed at analyzing stresses and fiber-matrix interfacial debonding in three-dimensional composite microstructures. It incorporates a 3D cohesive zone interface model based element to simulate interfacial debonding in the commercial code ABAQUS. The validated element is used to examine the potential debonding response in the presence of fiber–fiber interactions. A two-fiber model with unidirectional fibers is constructed and the effect of relative fiber spacing and volume fraction on the stress distribution in the matrix is studied. In addition, the effect of fiber orientation and spacing on the nature of initiation and propagation of interfacial debonding is studied in a two-fiber model. These results are expected to be helpful in formulating future studies treating optimal fiber orientations and payoff in controlling fiber spacing and alignment.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2005;128(1):107-116. doi:10.1115/1.2128427.

This paper describes modeling of degradation behavior of high-temperature polymers under thermo-oxidative aging conditions. Thermo-oxidative aging is simulated with a diffusion-reaction model in which temperature, oxygen concentration, and weight-loss effects are considered. A parametric reaction model based on a mechanistic view of the reaction is used for simulating reaction-rate dependence on the oxygen availability in the polymer. Macroscopic weight-loss measurements are used to determine the reaction and polymer consumption parameters. The diffusion-reaction partial differential equation system is solved using Runge-Kutta methods. Simulations illustrating oxidative layer growth in a high-temperature PMR-15 polyimide resin system under isothermal conditions are presented and correlated with experimental observations of oxidation layer growth. Finally, parametric studies are conducted to examine the sensitivity of material parameters in predicting oxidation development.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2005;128(1):117-122. doi:10.1115/1.2128428.

In this study, we develop a model for buckling of a partially delaminated composite plate with transverse stitching to resist out of plane deformations. The model applies to carbon fiber/polyimide matrix composites rapidly heated to around 370 °C, where it is known that steam-induced delamination (the popcorn effect) becomes an issue as the pressures generated approach the tensile strength of the matrix. Thus, a key element is the incorporation of this hygrothermal pressure within the formulation. This complex composite structure is modeled as two adhesively connected, specially orthotropic, rectangular plates, and the delaminations with internal vapor pressure are considered as holes in the adhesive layer. The intact regions of the adhesive layer and the stitches are modeled by continuous and discrete linear mechanical springs, respectively. The energy contributions of each component in the system are expressed in terms of out-of-plane displacements. The boundary conditions are that the system is simply supported along all edges so as to permit a Fourier sine series to approximate the transverse displacements. Application of the energy minimization approach gives a system of algebraic equations to determine the unknown weighting coefficients of the functions describing the transverse deflections of each plate layer. Deformed shapes of the system under axial compressive loads are obtained for different hygrothermally induced pressure conditions so as to show that the model works well. Parametric studies on critical buckling loads are performed for a few stitch and delamination configurations. It is found that stitching through delaminated areas can increase critical buckling loads and alter the sequence of corresponding mode shapes.

Commentary by Dr. Valentin Fuster