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### RESEARCH PAPERS

J. Eng. Mater. Technol. 2006;128(4):477. doi:10.1115/1.2337527.
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Time dependent behaviors of polymers and polymer matrix composites are important considerations in designing a growing variety of products, for applications under working conditions which may be either harsh or routine. Significant research has been conducted in the past in this field. This special issue of the Journal of Engineering Materials and Technology reflects a selection of innovative current efforts, containing papers delivered at the Symposium on Time-Dependent Behaviors of Polymers and PMCs (Polymer Matrix Composites), held in Orlando, Florida as part of the 2005 ASME International Mechanical Engineering Congress and Exposition.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2006;128(4):478-483. doi:10.1115/1.2345437.

Viscoelastic relaxation curves of thermoset resins may change considerably for relatively small changes in properties of the initial monomer mixture or final conversion level. In order to be able to predict the effect of such changes, a model is proposed which relates the properties of the initial monomer mixture such as the functionality, mixing ratio, and conversion level to changes in the relaxation curves. It basically consists of two parts. Firstly, the crosslink density is calculated based on the exact composition of the monomer mixture and, secondly, the effect of this crosslink density on the position of the glass transition and the rubbery modulus was calculated. The model was tested with a series of Novolac epoxies in which the functionality, mixing ratio, and conversion level were varied systematically. It turned out that changes in the relaxation curves due to variations in conversion level could be predicted quite accurately from the shape and shift factor of the fully cured mastercurve. The agreement between relaxation curve predictions for the series with changing functionality and mixing ratio was only moderate, which was ascribed to errors in the prediction of correct values for the crosslink density.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2006;128(4):484-488. doi:10.1115/1.2345438.

This article concerns the minimization of residual thermal stresses in geometrically constrained adhesive layers and thin polymeric composite lay-ups with emphasis on the role of initial stresses. Such residual stresses evolve during cure and subsequently during post-cure cool-down. The cure stresses play the role of initial stress superimposed on the thermoviscoelastic response that governs to cool-down phase. Optimization is achieved by following a time-temperature path that achieves the best counter play between temperature as a stress inducing and a stress reducing agent. When viscoelastic nonlinearity is considered such contradictory effect is played by stress itself, in which case an initial stress may have a beneficial effect.

Topics: Temperature , Stress
Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2006;128(4):489-494. doi:10.1115/1.2345439.

Rubbery response of polyurea is examined under monotonic loading in the confined compression, composite compression, and Arcan shear configurations. For polyurea prepared by a casting process, it is shown that while the bulk response is significantly nonlinear, and well fitted by the Tait equation, the shear resistance is extremely small. In contrast, polyurea formed by a spray process shows significant compressibility, inelastic volumetric deformation, and significantly enhanced shear resistance.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2006;128(4):495-502. doi:10.1115/1.2345440.

This paper concerns the drying process in the manufacturing of paperboard. Of particular interest are the effects of through-thickness property variation in paperboard during drying. In addition, resulting average properties from different drying histories are discussed. A mathematical model of the drying process is presented. It allows the moisture and temperature histories, the stress and strain histories, and the buildup of mechanical properties to be simulated. The temperature of the heating medium, the humidity and pressure of the ambient air, and either applied loads or prescribed strains are required input data. For symmetric convective drying, the ambient temperature, the humidity, and the thickness of the board were varied. For drying on a heated plate, the temperature of the plate and the thickness of the board were varied. Results regarding the moisture history, the stiffness development, and the buildup of residual stresses are presented and compared to literature experimental data. Also, sheets with a varying fiber base through the thickness, which affects both the moisture history and the influence of moisture on shrinkage, were studied. The model was shown to yield predictions qualitatively inline with empirical knowledge.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2006;128(4):503-508. doi:10.1115/1.2345441.

The stress relaxation and proton conductivity of Nafion 117 membrane (N117-H) and sulfonated poly(arylene ether sulfone) copolymer membrane with 35% sulfonation (BPSH35) in acid forms were investigated under uniaxial loading conditions. The results showed that when the membranes were stretched, their proton conductivities in the direction of the strain initially increased compared to the unstretched films. The absolute increases in proton conductivities were larger at higher temperatures. It was also observed that proton conductivities relaxed exponentially with time at $30°C$. In addition, the stress relaxation of N117-H and BPSH35 films under both atmospheric and an immersed (in deionized water) condition was measured. The stresses were found to relax more rapidly than the proton conductivity at the same strains. An explanation for the above phenomena is developed based on speculated changes in the channel connectivity and length of proton conduction pathway in the hydrophilic channels, accompanied by the rotation, reorientation, and disentanglements of the polymer chains in the hydrophobic domains.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2006;128(4):509-518. doi:10.1115/1.2345442.

The force-extension behavior of single modular biomacromolecules is known to exhibit a characteristic repeating pattern of a nonlinear rise in force with imposed displacement to a peak, followed by a significant force drop upon reaching the peak. This “saw-tooth” pattern is a result of stretch-induced unfolding of modules along the molecular chain and is speculated to play a governing role in the function of biological materials and structures. In this paper, constitutive models for the large strain deformation of networks of modular macromolecules are developed building directly from statistical mechanics based models of the single molecule force-extension behavior. The proposed two-dimensional network model has applicability to biological membrane skeletons and the three-dimensional network model emulates cytoskeletal networks, natural fibers, and soft biological tissues. Simulations of the uniaxial and multiaxial stress-strain behavior of these networks illustrate the macroscopic membrane and solid stretching conditions which activate unfolding in these microstructures. The models simultaneously track the evolution in underlying microstructural features with different macroscopic stretching conditions, including the evolution in molecular orientation and the forces acting on the constituent molecular chains and junctions. The effect of network pretension on the stress-strain behavior and the macroscopic stress and strain conditions which trigger unfolding are presented. The implications of the predicted stress-strain behaviors on a variety of biological materials are discussed.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2006;128(4):519-526. doi:10.1115/1.2345443.

Coupled computational fluid dynamics and finite element analyses were used to determine the material properties of the egg and jelly layer of the sea urchin Arbacia punctulata. Prior experimental shear flow results were used to provide material parameters for these simulations. A Neo-Hookean model was used to model the hyperelastic behaviors of the jelly layer and egg. A simple compressive simulation was then performed, to compare the maximum von Mises stresses within eggs, with and without jelly layers. Results of this study showed that (1) shear moduli range from $∼100to160Pa$, and $∼40to140Pa$ for an egg without a jelly layer, and jelly layer itself, respectively; and (2) the presence of the jelly layer significantly reduces maximum von Mises stress in an egg undergoing compression.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2006;128(4):527-536. doi:10.1115/1.2345444.

In tensile tests the flax/polypropylene composites clearly show nonlinear behavior in loading and hysteresis loops in unloading. In creep tests performed at different load levels the response was nonlinear viscoelastic, and after recovery, viscoplastic strains were detected. No degradation in stiffness could be seen and thus nonlinear viscoelasticity and viscoplasticity were assumed to be the main cause for the observed behavior. The fracture surface of a specimen that experienced creep rupture at 24 MPa was investigated using a scanning electron microscope. The viscoplastic response was studied experimentally and described by a power law with respect to time and stress level in the creep test. The nonlinear viscoelasticity was described using Schapery’s model. The application of Prony series and a power law to approximate the viscoelastic compliance was investigated. Both descriptions have accuracy sufficient for practical applications. However, at high stresses the attempts to describe the viscoelastic compliance by a power law with a stress-independent exponent failed and therefore stress dependence of this exponent was included in the data analysis. The accuracy within the considered stress range is good, but the thermodynamic consistency of this procedure has to be proven.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2006;128(4):537-542. doi:10.1115/1.2345445.

One group of models proposed for characterizing the mechanical response of glassy polymers is based on a structure that resembles finite plasticity. In most cases, a constitutive equation for stress is proposed, which depends on the elastic deformation gradient, supplemented by a flow rule for the plastic deformation, which depends on the “over stress.” The over stress is a properly invariant difference between the stress and the back stress (equilibrium stress). The back stress represents conditions under which relaxation events should stop and the material should be able to carry an applied load indefinitely without a need to change the strain. Questions that arise in using these models are whether such equilibrium stresses exist, how can they be evaluated, and what experiments can be used to characterize the flow rule. One challenge in accurately evaluating the locus of equilibrium conditions is the fact that the relaxation process substantially slow down around these points, and, therefore, a method that does not directly require being at the equilibrium is desirable. Focusing on shear, a thermodynamic theory for characterizing the response of glassy polymers, similar to models currently used for this purpose, is developed, and using this model it is shown that one can set up a method to calculate the plastic strain rate. This method is based on evaluating the slope of stress-strain response under conditions of similar elastic and plastic strain, but different strain rates. Since the equilibrium stress occurs when the plastic strain rate goes to zero, the evaluated plastic strain rates allow evaluation of the needed information for developing the flow rule and obtaining the back stress. This method is used to evaluate the plastic strain rate and back stress at room temperature for polycarbonate. The evaluated results match well with results obtained by direct probing of the equilibrium stress, in which one searches for points at which the stress remains constant at a constant strain over long durations. The method proposed looks promising in evaluating the back stress of glassy polymers. The added advantage of this method is that it also provides a map of plastic strain rate and tangent modulus over a large range of loading conditions.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2006;128(4):543-550. doi:10.1115/1.2345446.

Polymeric materials are known to exhibit strong time-dependent mechanical behavior, as evidenced by rate-dependent elastic moduli, yield strength, and post-yield behavior. The nature of the rate sensitivity is found to change between different temperature regimes as various primary $(α)$ and secondary ($β$, $γ$, etc.) molecular mobility mechanisms are accessed. The ability to tailor these molecular-level mechanics through the incorporation of nanoscale particles offers new opportunities to design polymer-based material systems with different behaviors (elastic, yield, post-yield) in different frequency∕rate regimes. In this study, the macroscopic rate-dependent mechanical behavior of one particular polymer nanocomposite—polycarbonate compounded with TriSilanolPhenyl-POSS® particles—is compared with that of its homopolymer counterpart. The experimental and theoretical techniques follow those established in previous research into the rate-dependent mechanical behavior of amorphous homopolymers over a wide range of strain rates. On the experimental side, dynamic mechanical analysis tension tests were used to characterize the viscoelastic behavior of these materials, with focus on the rate-dependent shift of material transition temperatures. Uniaxial compression tests on a servohydraulic machine $(10−3s−1to0.3s−1)$ and an aluminum split-Hopkinson pressure bar $(1000s−1to3000s−1)$ were used to characterize the rate-dependent yield and post-yield behavior. The behaviors observed in these experiments were then interpreted within the theoretical framework introduced in previous work. It is concluded that, for this particular material system, the POSS has little influence on the polycarbonate $α$ regime. However, the POSS clearly enhances the mobility of the $β$ motions, significantly reducing the resistance to high rate elastic and plastic deformation. Furthermore, it is shown that the continuum-level constitutive model framework developed for amorphous homopolymers may be extended to this polymer nanocomposite material system, simply by accounting for the reduced deformation resistance in the $β$ process.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2006;128(4):551-558. doi:10.1115/1.2349501.

A microstructually motivated, three-dimensional, large deformation, strain rate dependent constitutive model has been developed for a semi-crystalline, blended, thermoplastic olefin (TPO) (Wang, Y., 2002, Ph.D. thesis, The University of Michigan, Ann Arbor, MI). Various experiments have been conducted to characterize the TPO and to verify the modeling approach (Wang, Y., 2002, Ph.D. thesis, The University of Michigan, Ann Arbor, MI). The model includes a quantitative rate-dependent Young’s modulus, a nonlinear viscoelastic response between initial linear elastic response and yield due to inherent microstructural irregularity, rate and temperature dependent yield with two distinctive yield mechanisms for low and high strain rates, temperature-dependent strain hardening, plastic deformation of crystalline regions, and adiabatic heating. It has been shown to accurately capture the observed TPO stress-strain behavior including the rate-dependent initial linear elastic response; temperature, strain rate, and deformation state-dependent yield; temperature and deformation state-dependent strain hardening; and pronounced thermal softening effects at high (impact) strain rates. The model has also been examined for its ability to predict the response in plane strain compression based on material parameters chosen to capture the uniaxial compression response. The model is predictive of the initial strain rate dependent stiffness, yield, and strain hardening responses in plane strain. Such predictive capability demonstrates the versatility with which this model captures the three-dimensional anisotropic nature of TPO stress-strain behavior.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2006;128(4):559-563. doi:10.1115/1.2345447.

The mechanical behavior of amorphous thermoplastics, such as poly(methyl methacrylate) (PMMA), strongly depends on temperature and strain rate. Understanding these dependencies is critical for many polymer processing applications and, in particular, for those occurring near the glass transition temperature, such as hot embossing. In this study, the large strain mechanical behavior of PMMA is investigated using uniaxial compression tests at varying temperatures and strain rates. In this study we capture the temperature and rate of deformation dependence of PMMA, and results correlate well to previous experimental work found in the literature for similar temperatures and strain rates. A three-dimensional constitutive model previously used to describe the mechanical behavior of another amorphous polymer, poly(ethylene terephthalate)-glycol (PETG), is applied to model the observed behavior of PMMA. A comparison with the experimental results reveals that the model is able to successfully capture the observed stress-strain behavior of PMMA, including the initial elastic modulus, flow stress, initial strain hardening, and final dramatic strain hardening behavior in uniaxial compression near the glass transition temperature.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2006;128(4):564-571. doi:10.1115/1.2345448.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2006;128(4):572-578. doi:10.1115/1.2345449.

The viscoelastic and viscoplastic behaviors of high density polyethylene (HDPE) under uniaxial monotonic and cyclic loading are modeled using the modified viscoplasticity theory based on overstress (VBO). The viscoelastic modeling capabilities of the modified VBO are investigated by simulating the behavior of semicrystalline HDPE under uniaxial compression tests at different strain rates. In addition, the effects of the modification (introducing the variable “$C$” into an elastic strain rate equation) on VBO that has been made to construct the change in the elastic stiffness while loading and unloading are investigated. During first loading and unloading, the modification in the elastic strain rate equation improves the unloading behavior. To investigate how the variable “$C$” that is introduced in the elastic strain rate equation evolves during reloading, the cyclic behavior of HDPE is modeled. For a complete viscoelastic and viscoplastic behavior, the relaxation and creep behaviors of HDPE are simulated as well in addition to stress and strain rate dependency. The influences of the strain (stress) levels where the relaxation (creep) experiments are performed are investigated. The simulation results are compared with the experimental data obtained by Zhang and Moore (1997, Polym. Eng. Sci., 37, pp. 404–413). A good match between experimental and simulation results are observed.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2006;128(4):579-585. doi:10.1115/1.2345450.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2006;128(4):586-594. doi:10.1115/1.2345451.

The increased use of fiber reinforced plastics (FRPs) in ship topside structures necessitates the need to understand how such structures respond to fire exposure. For this reason we have characterized the nonlinear, thermo-viscoelastic behavior of Vetrotex 324∕Derakane 510A-40 using tensile loading of $[±45]2S$ laminates. Nonlinearity is observed at elevated stress and temperatures above $Tg$. The data reduction sufficiently modeled the experimental master-curves over the whole temperature range, but suffered from inconsistencies in the creep data and recovery data, perhaps due to accumulated damage during the creep cycle. Our results indicate that the nonlinear viscoelastic behavior significantly contributes to structural behavior under fire loading conditions.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2006;128(4):595-602. doi:10.1115/1.2345452.

A numerical model to study the fatigue crack retardation in a self-healing material (White, 2001, Nature, 409, pp. 794–797) is presented. The approach relies on a combination of cohesive modeling for fatigue crack propagation and a contact algorithm to enforce crack closure due to an artificial wedge in the wake of the crack. The healing kinetics of the self-healing material is captured by introducing along the fracture plane a state variable representing the evolving degree of cure of the healing agent. The atomic-scale processes during the cure of the healing agent are modeled using a coarse-grain molecular dynamics model specifically developed for this purpose. This approach yields the cure kinetics and the mechanical properties as a function of the degree of cure, information that is transmitted to the continuum-scale models. The incorporation of healing kinetics in the model enables us to study the competition between fatigue crack growth and crack retardation mechanisms in this new class of materials. A systematic study of the effect of different loading and healing parameters shows a good qualitative agreement between experimental observations and simulation results.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2006;128(4):603-610. doi:10.1115/1.2345453.

A fully nonlinear finite element analysis for prediction of localization∕delocalization and compression fracture of moderately thick imperfect transversely isotropic rings, under applied hydrostatic pressure, is presented. The combined effects of modal imperfections, transverse shear∕normal deformation, geometric nonlinearity, and bilinear elastic (a special case of hypoelastic) material property on the emergence of interlaminar shear crippling type instability modes are investigated in detail. An analogy to a soliton (slightly disturbed integrable Hamiltonian system) helps understanding the localization (onset of deformation softening) and delocalization (onset of deformation hardening) phenomena leading to the compression damage∕fracture at the propagation pressure. The primary accomplishment is the (hitherto unavailable) computation of the mode II fracture toughness (stress intensity factor∕energy release rate) and shear damage∕crack bandwidth, under compression, from a nonlinear finite element analysis, using Maxwell’s construction and Griffith’s energy balance approach. Additionally, the shear crippling angle is determined using an analysis, pertaining to the elastic plane strain inextensional deformation of the compressed ring. Finally, the present investigation bridges a gap of three or more orders of magnitude between the macro-mechanics (in the scale of mms and up) and micro-mechanics (in the scale of microns) by taking into account the effects of material and geometric nonlinearities and combining them with the concepts of phase transition via Maxwell construction and Griffith-Irwin fracture mechanics.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2006;128(4):611-617. doi:10.1115/1.2345454.

Evolution of various damage modes with time, in multidirectional laminates of a polymer composite (Hexcel F263-7/T300) subjected to a constant load, was experimentally studied and correlated to experimental creep rupture results to understand the influence of the former on the latter. Influence of various parameters, such as stress, temperature, thickness of inner plies, and outer-ply constraint, on damage evolution was evaluated. Observed damages include transverse (also referred in the literature as matrix cracks) cracking due to in-plane stresses, vertical cracking due to out-of-plane normal stress, delamination due to interlaminar stresses, splitting, and fiber fracture. The sequence of evolution of these damages varied with laminate stacking sequence, stress, and temperature. These damages significantly influenced one another and the creep rupture time.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2006;128(4):618-632. doi:10.1115/1.2345455.

In this paper, a conceptual design, fabrication, and testing of advanced polymer matrix composite (PMC) infill system are addressed for seismic retrofitting of steel frames. Such a system is designed to have a multi-panel PMC infill system with passive energy mechanism. The basic configuration of this system is composed of two separate components—namely, an inner PMC sandwich panel and outer damping panels. The inner PMC sandwich infill consists of two fiber-reinforced polymer (FRP) laminates with Divincell® H core, and outer damping panels are made of FRP laminate plates and passive energy constrained damping layers—combining polymer honeycomb and 3M viscoelastic solid materials—at the interface between the laminates. The interactions of these two components produce considerable stiffness and enhanced damping properties in the structure following different drift level. Conceptually, the FRP outer damping panels are designed to produce the damping through the cyclic shear straining of the combined interface damping layers. Moreover, as the lateral drift increases, the inner PMC sandwich infill is designed to provide considerable lateral stiffness to resist severe earthquake excitation and avoid excessive relative floor displacements that cause both structural and non-structural damage. As part of this research, analytical and experimental studies were performed to investigate the effectiveness of the proposed multi-infill panel concept. The prefabricated multi-panel PMC infill holds a great promise for enhanced damping performance, simplification of the construction process, and the reduction of time and cost when used for seismic retrofitting applications.

Commentary by Dr. Valentin Fuster