Challenges in Mechanics of Time-Dependent Materials, Volume 2

Shape memory polymers (SMP) utilized in reconfigurable structures have the potential to be used in a variety of settings. This paper is primarily concerned with the use of Veriflex-S shape memory polymer and bi-directional carbon fiber in a unimorph actuator configuration. One of the major deficiencies of SMP unimorphs is the permanent set (unrecovered shape) after a single or multiple temperature cycle(s). The novel concept of incorporating transverse curvature in the composite substrate, similar to that of an extendable tape measurer, was proposed to improve the shape recovery. A set of experiments was designed to investigate the influence of transverse curvature, the relative widths of SMP and composite substrates, and shape memory polymer thickness on actuator recoverability after multiple thermomechanical cycles. Flat carbon fiber and shape memory polymer unimorph actuators were evaluated for performance versus actuators of increasing transverse curvature. Digital image correlation was implemented to quantify the out-of-plane deflection of the unimorph composite actuators (UCAs) during the actuation cycle. Experimental results indicate that an actuator with transverse curvature significantly reduces the residual deformation while increasing the shape memory recoverability which could be further tailored to enhance the performance of shape memory polymers in reconfigurable arrangements.

A polymeric matrix (3501-6) used in composite materials was characterized under multi-axial quasi-static and dynamic loading at varying strain rates. Tests were conducted under uniaxial compression, tension, pure shear and combinations of compression and shear. Quasi-static and intermediate strain rate tests were conducted in a servo-hydraulic testing machine. High strain rate tests were conducted using a split Hopkinson Pressure Bar system built for the purpose. This SHPB system was made of glass/epoxy composite (Garolite) bars having an impedance matching the test polymer closer than metals. The typical stress–strain behavior exhibits a linear elastic region up to a yields point, a nonlinear elastoplastic region up to an initial peak or critical stress, followed by a strain softening region up to a local minimum and finally, a strain hardening region up to ultimate failure. It was observed that under multi-axial loading, yielding is governed by one characteristic property, the yield strain under uniaxial tension. Furthermore, it was found that the yield point varied linearly with the logarithm of strain rate. A general three-dimensional elasto-viscoplastic model was formulated in strain space expressed in terms of an effective strain and its yield point. A unified yield criterion was proposed to describe the onset of yielding under any state of stress and at any strain rate.

The increasing use of soft materials in industrial, commercial and military applications has necessitated a more thorough understanding of their visco-hyperelastic, reactive, and other non-linear properties. Additionally, testing and design methods for components that employ these materials have required innovation. Large-scale computational modeling has become an effective tool to mitigate the increased cost that accompanies the added complexity in testing and design, but modeling error in the forms of inaccuracy and uncertainty must be appropriately accounted for to effectively reduce both design-stage and validation-stage testing costs.

In this work, several models were built to simulate the split Hopkison pressure bar (SHPB) compression of plasticized polyvinyl chloride (PVC), butyl rubber (BR) and vulcanized rubber (VR) samples across a range of medium- to high-strain rates. Using these analyses, hyper-viscoelastic constitutive models were fit to experimental data for a number of samples at each strain rate, and effective material properties were determined for each curve. The model calibration values were also used to generate statistics to compare the utility of different fitting methods for soft materials.

This paper summarizes a 1D adaptation (Hall et al., Math Mech Solids, 2014) of the reactive fluid–solid mixture theory of Hall and Rajagopal (Math Mech Solids 17(2):131–164, 2012), which considers an anisotropic viscous fluid diffusing and chemically reacting with an anisotropic elastic solid. The present implementation introduces a stabilized mixed finite element method for advection–diffusion–reaction phenomena, which is applied to 1D isothermal problems involving Fickian diffusion, oxidation of PMR-15 polyimide resin, and slurry infiltration. The energy and entropy production relations are captured via a Lagrange multiplier that results from imposing the constraint of maximum rate of entropy production, reducing the primary PDEs to the balance equations of mass and linear momentum for the fluid and the solid, together with an equation for the Lagrange multiplier. The Fickian diffusion application considers a hyperbolic first-order system with a boundary discontinuity and stable approach to the usual parabolic model. Results of the oxidation modeling of Tandon et al. (Polym Degrad Stab 91(8):1861–1869, 2006) are recovered by employing the reaction kinetics model and properties assumed there, while providing in addition the individual constituent kinematic and kinetic behaviors, thus adding rich interpretive detail in comparison to the original treatment (Tandon et al., Polym Degrad Stab 91(8):1861–1869, 2006); two adjustable parameters describing coupled chemomechanical and purely chemical dissipation are added. The slurry infiltration application simulates the imposed mass deposition process and consequent effects on the kinematic and kinetic behaviors of the constituents.

Proton Electrolyte Membrane (PEM) fuel cell is a promising energy source because of its high efficiency and zero emission. One of the most important unresolved problems of PEM fuel cells today is the durability issue of its components. For example, the polymeric gasket material of PEM fuel cell must be durable enough to hold the liquid and gas inside the fuel cell channel, as its sealing force decreases gradually with time and also changes with temperature. Liquid Silicone Rubber (LSR) is commonly used as gasket or seal material in many industrial applications including PEM fuel cells. This paper discusses the compression stress relaxation of LSR under temperature cycling, which is to simulate the actual fuel cell operation. It is found that (a) in addition to stress relaxation, thermal expansion or contraction of the material contributes the most in the observed stress variation during temperature change, and (b) the stiffness of LSR appears to change according to temperature history, and (c) the Maxwell stress relaxation model can be used to predict the sealing force only after a correction of the change of material stiffness is implemented into the model.

Cracks in glass-to-metal seals can be a threat to the hermeticity of isolated electronic components. Design and manufacturing of the materials and processes can be tailored to minimize the residual stresses responsible for cracking. However, this requires high fidelity material modeling accounting for the plastic strains in the metals, mismatched thermal shrinkage and property changes experienced as the glass solidifies during cooling of the assembly in manufacturing. Small plastic strains of just a few percent are typical during processing of glass-to-metal seals and yet can generate substantial tensile stresses in the glass during elastic unloading in thermal cycling. Therefore, experimental methods were developed to obtain very accurate measurements of strain near and just beyond the proportional limit. Small strain tensile characterization experiments were conducted with varying levels and rates of strain ratcheting over the temperatures range of −50 to 550 °C, with particular attention near the glass transition temperature of 500 °C. Additional experiments were designed to quantify the effects of stress relaxation and reloading. The experimental techniques developed and resulting data will be presented. Details of constitutive modeling efforts and glass material experiments and modeling can be found in Chambers et al. (Characterization & modeling of materials in glass-to-metal seals: Part I. SAND14-0192. Sandia National Laboratories, January 2014).

Studies of the fracture behavior of adhesive joints can provide scientific understanding of failure processes as well as properties required for engineering design purposes. The focus of the present paper is to discuss the role that locally weakened interfaces in adhesive bonds can have on the fracture behavior of double cantilever beam specimens loaded in both mode I conditions and in mixed (mode I/II) conditions in a dual actuator load frame that permits independent control of the applied loads. Locally weakened areas are created by several methods of contamination of one aluminum adherend, including physical vapor deposition of copper through a mask perforated with the desired size, spacing, and pattern. Results from this experimental study have provided evidence of the size of a weakened zone that is required to be detected by a growing cohesive crack for a commercial adhesive system. The detection size depends on the mode mixity applied, with opening shear conditions rendering detection of smaller weakened zones and closing shear conditions detecting only larger weakened zones. In addition, an interesting rate dependence will be described in which rapidly growing cracks are more likely to detect locally weakened zones than more slowly growing cracks for several systems studied. Possible mechanisms will be suggested.

The object of this paper is to broaden the familiar concepts of viscoelasticity and viscoelastic behavior of polymeric materials to the discussion of the (highly) nonlinear mechanical behavior of composite materials and to introduce relationships between that time-dependent mechanical response and the dielectric character of those materials. The foundation of the paper is a discussion of damage accumulation as the introduction of a ‘second phase’ into heterogeneous material morphologies and the interpretation of the influence of that accumulation process on the time dependent mechanical and electrical properties and behavior of those materials. It is the principal objective of the paper to establish science based relationships between the mechanical behavior of heterogeneous/composite materials under high-strain conditions and the response of those materials to alternating current or voltage inputs. Applications of the concepts will be discussed, including “design-defected composite materials” such as batteries, fuel cells, and separation membranes, and “service-defected composite materials” such as the structural composites used in airplanes, vehicles, and bridges. The purpose of the present work is to provide some coherence to that subject and to provide a foundation for the design of composite material systems.

Characterization of the temperature dependent spring-back behavior of poly(methyl methacrylate) (PMMA) is essential to model hot embossing. The constitutive model must capture several deformation modes including uniaxial compression and stress relaxation with cooling in order to predict spring-back. In this work, the thermo-mechanical coupling of spring-back is investigated through finite element simulations utilizing a constitutive model that captures stress relaxation. It was found that the material model successfully predicts spring-back trends under a variety of heat transfer conditions. At the cooling times used experimentally, spring-back decreased with held strain and increased with embossing temperature. Initial simulations utilizing the experimentally obtained platen temperature under predicted spring-back. After performing a simple heat transfer simulation, spring-back predictions were improved by altering the temperature profile according to the heat transfer simulation and matched experimentally obtained values. To investigate the effect of a thermal gradient, a fully coupled thermo-mechanical simulation was performed. From this, it was found that the thermal gradient had a minimal effect on spring-back. Rather, the rapid cooling upon release of PMMA was found to cease spring-back and can be modeled without a fully coupled simulation. These results indicate that temperature, along with strain level, and cooling time are important to the process of spring-back.

Haynes^® 230^® is a Ni–Cr–W–Mo alloy commonly used in aerospace and chemical process industries because of its excellent oxidation resistance, fatigue and creep performance at very high temperatures. In this study, the alloy was evaluated as a candidate for its use as tubing material in solar receivers, where coupled thermal-mechanical cycling is imposed in-use by heating imposed during diurnal cycles. The effect of temperature, 425 and 677 °C, and hold times on isothermal fatigue was evaluated and fatigue-life curves were developed for the alloy in its as-received condition and after aging at 677 °C for 3 months. Experimental apparatus and techniques were developed to apply thermomechanical cycles, between 425 and 677 °C, in an expedited manner to determine fatigue life at low strain ranges, again for both material conditions. The influence of stress ratio, R = −1 and R = ∞, was also assessed. The experimental techniques developed and resulting data and findings will be presented.

Polyethylene is an advantageous material for the construction of buried pipelines. It is corrosion resistant, seismic tolerant, and utilizes low cost installation methods. Pipe sections are often joined using thermal fusion processes. The strength of the joint is related to the ability of the polyethylene chains to inter-diffuse and form inter-crystalline tie-chains across the two polyethylene surfaces. Testing the strength of the fusion bond is difficult and a number of different destructive and non-destructive tests have been developed, but it is not possible to understand the impact of the fusion process on the local microstructure from these tests. In this work, instrumented indentation with a flat punch is used to measure the local viscoelastic behavior of five different polyethylene resins used for pipe manufacturing at short times. High strain behavior related to slow crack growth is measured using a strain hardening measurement under tension. The impact of thermal processing is investigated by imposing three different thermal cooling histories (0.4, 9, and 100 °C/min) on the polyethylenes. The goal is to determine if short-term creep under indentation is capable of accurately measuring; (a) bulk creep behavior, (b) impact of resin architecture, and (c) the impact of thermal processing. The results show that indentation using a flat punch is capable of measuring creep within the range of bulk creep behavior, but not sensitive to the slow crack growth resistance of the resin.

Viscoelastic properties for a polymethyl methacrylate (PMMA) bar were examined using both ultrasonic wave propagation experiments in the higher frequency range of 25–200 kHz and longitudinal wave propagation experiments in the lower frequency range of up to 15 kHz. Since the geometrical dispersion due to three-dimensional deformation was caused by higher frequency components involved in the ultrasonic waves, the three-dimensional wave theory was employed to analyze experimental data of wave propagation. It was found that the 5-element model based on the three-dimensional theory could evaluate the viscoelastic properties of a wide range of frequencies. The peak value of the attenuation coefficient moved to the higher frequency as the diameter of the bar became small. Moreover, the viscoelastic properties could be evaluated only by the solution of the first mode based on the three-dimensional wave theory when the diameter of the bar was thin.

The damping properties of materials, joints, and assembled structures can be modeled efficiently using fractional derivatives in the respective constitutive equations. The respective models describe the damping behavior accurately over broad ranges of time or frequency where only few material parameters are needed. They assure causality and pure dissipative behavior. Due to the non-local character of fractional derivatives the whole deformation history of the structure under consideration has to be considered in time-domain computations. This leads to increasing storage requirements and high computational costs. A new concept for an effective numerical evaluation makes use of the equivalence between the Riemann–Liouville definition of fractional derivatives and the solution of a partial differential equation (PDE). The solution of the PDE is found by applying the method of weighted residuals where the domain is split into finite elements using appropriate shape functions. This approach leads to accurate results for the calculation of fractional derivatives where the numerical effort is significantly reduced compared with alternative approaches. Finally, this method is used in conjunction with a spatial discretization method and a simple structure is calculated. The results are compared to those obtained from alternative formulations by means of accuracy, storage requirements, and computational costs.

Reduction of noise and vibration coming from the rail transport activities is an important objective of the environmental policy of the European Union, due to its impact on human and animal health. It has been identified that one of the major sources of noise and vibration in rail transport is from the interaction between the wheel and the rail, the so called rolling noise. One way to mitigate this noise is to attach polymeric damping elements to the rail. By modifying bulk properties of polymeric material we can modify its damping characteristics. In this paper we demonstrated on the example of thermoplastic polyurethane (TPU) the effect of inherent hydrostatic pressure on the time- and frequency-dependent behavior of polymers. For the selected TPU material we found that increasing hydrostatic pressure from 1 to 2,000 bar shifts frequency at which material exhibits its maximal damping properties (G″max) from 37 to 235 Hz. It was also found that change of pressure changes values of storage modulus G′ up to 3.5 times (depending on the frequency), while the values of loss modulus G″ are changed up to 5.5 times. Using this property of polymeric materials we designed new generation damping elements composed of glass fiber textile tubes filled with pressurized granulated polymeric materials. Granular material with properly selected multimodal particle size distribution acts as pressurizing agent. At the same time the generated hydrostatic pressure changes frequency dependence of the granular material bulk properties. By modifying material bulk properties we can modify damping characteristics of the new generation damping elements. Applying these damping elements to the rail can substantially reduce vibration amplitudes as well as sound pressure levels, thus reducing exposure of human and animal to noise and vibration.

In proper ranges of operating conditions, granular materials inside rotating drums display a continuum motion near their free surface. The motion of those discrete systems was studied both experimentally and through Discrete Element Method (DEM) numerical simulations. However, it can be regarded as the flow of a continuum medium, thus allowing a continuum mechanics approach. In our work, we solve the continuum dynamic equations by adopting the visco-plastic JFP constitutive model Jop et al. (Nature 441:727–730, 2006) for the stress tensor, and study the continuous flow of dry grains inside axially rotating cylinders through both 2D and 3D finite volume simulations (FVM). Our preliminary results are in qualitative agreement with some experimental data previously published.

The tensile strength along the longitudinal direction of unidirectional CFRP is one of the important data for the reliable design of CFRP structures. This paper is concerned with the statistical prediction of creep failure time under the tension loading along the longitudinal direction of unidirectional CFRP based on the viscoelasticity of matrix resin. It was cleared in this study that the statistical creep failure time under the tension loading along the longitudinal direction of unidirectional CFRP can be predicted by using the statistical static tensile strengths of carbon mono filament and unidirectional CFRP and the viscoelasticity of matrix resin based on Christensen’s model of viscoelastic crack kinetics.

Polyethylene Terephthalate’s (PET) properties are particularly sensitive to its processing history. Processing impacts the extent of crystallinity. Mechanical stretching and melt flow history influence the extent and structure of crystalline domains in the semi-crystalline polymer. Typical processing parameters include the rate of cooling and the amount of stretch. Both influence crystallization differently. Isolating the contribution from stretch or thermal crystallization is valuable for identifying the relationship to mechanical properties. In this work, the influence of thermal crystallinity on the mechanical behavior of PET was observed. Annealed injection molded samples with thermal crystallinity were tested Young’s modulus. Using the two-phase composite approach, mechanical behavior of injection molded semi-crystalline PET samples was modeled based on crystallinity from density. Crystallinity measured from different techniques did not always agree.

Epoxy nanocomposites containing 5 wt% glycidyl Polyhedral Oligomeric Silsesquioxane (POSS) by weight is prepared. Elastic and viscoelastic properties of the neat epoxy and epoxy/POSS nanocomposite has been studied using nanoindentation technique. Elastic modulus of the polymer systems are determined using modified Oliver–Pharr method taking creep rate into account. Creep compliance properties of the studied systems are determined by fitting a standard linear solid model to the creep plot. Both neat epoxy and epoxy/POSS nanocomposite showed an increase in elastic modulus and a decrease in creep compliance as a function of UV exposure time; although, the effect of UV exposure is more pronounced in case of epoxy/POSS nanocomposite. It is speculated that the excess epoxide groups present in the glycidyl POSS is going through further crosslinking during the UV exposure leading to the observed higher rate of property change compared to neat epoxy.

Simulations of dynamic loading on polymers often require rate dependent, large-strain material test data to sufficiently calibrate material laws such as nonlinear viscoelastic–viscoplastic. Physical testing at intermediate strain rates creates many challenges because the measurements are susceptible to distortion due to factors including: test specimen variations, fixtures, hydraulic actuator control, instrumentation complexity, data acquisition, electrical noise and post processing. For example, hidden time delays within the total data acquisition system (load cells, displacement sensors, amplifiers/conditioners) create confusion when specimen failure captured by a sensor does not agree in time with images from high speed video. Additionally, noise in measurements can occur due to sample misalignment, fixture and test-stand rigidity, subtleties of a slack adapter (if one is used), and distortions caused by the test environment. After care is taken to minimize structural-born distortions, noticeable levels of noise and oscillations may still exist from these mechanical sources as well as electrical sources such as channel cross-talk of a video camera shutter pulse bleeding onto other sensor channels. Ultimately, prudent use of DSP techniques may be needed to further improve data quality and interpretation. This paper demonstrates success over many such difficulties when performing tensile tests of polymer materials up to 100 s⁻¹.

We propose a novel hybrid approach to examine uncertain sources that cause variations in solder joint lifetimes and to predict statistical distributions of solder joint lifetimes under actual operating conditions. The uncertainty in input variables of a life prediction model is propagated to the output by an approximate integration method. The variations in the output are statistically compared to experimentally-measured lifetimes. A set of input variables that minimize the discrepancy between predicted and experimental results is obtained through the optimization technique. The proposed approach is implemented for chip resistor assemblies, and the fatigue life of solder joints under the actual operating conditions is predicted after calibration.

Biocompatible polymers, like SU-8, have become a vital part of Microelectromechanical System (MEMS) devices, especially as a structural layer in biosensors and micro-fluidics. In the present study, effect of moisture and anisotropy on the mechanical response of 2 micron thick SU-8 polymer films was investigated using optical in-situ microtensile experiments. The tensile specimens were fabricated using soft lithography, which consisted of deposition, patterning and release of the film from the silicon wafer. A novel methodology was followed to capture optical images of the patterned SU-8 surface during the experiment, for strain calculations using Digital Image Correlation (DIC). Tensile properties were derived from the uniaxial stress–strain curves. The tensile strength and fracture strain of the multilayer films increased by more than 10 and 5 %, respectively, as compared to the single layer film. Some experimental results along with Fourier Transform Infrared (FTIR) spectroscopy data is shown to support the observations from our experiments.

In order to investigate the material behaviour in reality (macro-level) during drying shrinkage at early age, the shrinkage coefficient (α_sh) is determined in the laboratory at micro-level on specially prepared and dried (1 mm) thick cement paste specimens. Drying shrinkage experiments are performed in Environmental Scanning Electron Microscope (ESEM). For simplicity, a relationship between drying deformations and relative humidity (ε-RH) is assumed linear. It is found out that a certain value of the ‘local’ drying shrinkage coefficient, determined in the RH range (40–20 %), presents a threshold value. Above the threshold α_sh value, microcracks are noticed in specimens.

Friction extrusion is a novel manufacturing process for producing high-value materials (e.g. metal wires) from low-cost precursors (e.g. powders) or through recycling of machining wastes (e.g. chips). In the friction extrusion process, the material experiences high temperature and severe plastic deformation before it forms the final product in the form of a wire. The present work is focused on understanding the heat transfer and material flow phenomena in the friction extrusion process. A numerical thermo-fluid model has been developed and validated by experimental measurements. In the model, the experimentally measured mechanical power is used as the heat input to predict the temperature field in the experiment. The processing material is treated as a non-Newtonian fluid with a viscosity that is temperature and strain rate dependent. Select marker particles in the material are followed and their motions observed in the simulation to study material flow patterns. It is found that predictions of the temperature field and marker particle trajectories match reasonably well with experimental measurements. Results of this study suggest that the proposed thermo-fluid model can capture the main features of the thermo-fluid phenomena in the friction extrusion process and can be used to provide reasonable predictions of the temperature and material flow fields in the friction extrusion process.