Challenges in Mechanics of Time Dependent Materials, Volume 2

Foam-like materials are ubiquitously employed in impact protection applications due to their relatively low density and high dissipation capacity under increased strain-rate loading. In our previous work, we have investigated the coupling between the volumetric and distortional responses of open-cell elastomeric foams under the application of large deformations and under quasi-static rates and proposed a hyperelastic model for the equilibrium response. Here, we present data collected from a set of experiments under quasi-static and moderate strain rates for a closed-cell elastomeric foam, which allows the model to be extended to higher loading rates. Two different load frames were constructed to test materials under different loading rates. One is applicable for strain rates between 10⁻⁴ and 10⁻¹ 1/s and the other to achieve maximum strain rates up to 10² 1/s. The data is used to develop a finite viscoelasticity model for closed-cell elastomeric foams.

This paper focuses on developing a time-dependent yield criterion for a polymer thin film, namely StratoFilm 420, under long-term creep conditions. StratoFilm 420 is a linear low-density polyethylene film used in constructing super-pressure balloons in the Ultra-Long Duration Balloon (ULDB) program of NASA. Yielding of StratoFilm 420 under long-term loading has been found to cause balloon failure and limit the operational duration. Knowledge of time-dependent yielding behavior of StratoFilm 420 under different stresses and temperatures is essential to design reliable balloon structures. In this paper, a previously developed nonlinear viscoelastic model for the film and its model parameter calibration are first described. The experimental procedure for characterizing the onset of permanent deformation is presented. The yield limit is determined using the strain recovery method using creep tests with different durations and measuring the corresponding residual strains. The variation of yield strains is presented with respect to stress levels and temperature. A free energy-based criterion combined with nonlinear free volume model is proposed for predicting yielding of StratoFilm 420.

Hydrogels exhibit a fluid-like viscous response under high shear strain rates with significant rate- and microstructure-dependent rheological properties. In this study, the transient shear response of poly(ethylene glycol) diacrylate (PEGDA) hydrogels is characterized by application of the power-law fluid model to incompressible Navier–Stokes equation of start-up planar Couette flow. To impart the necessary boundary conditions for model calibration, a split-Hopkinson pressure bar based single-pulse dynamic simple shear experiment is developed, in which unsteady momentum diffusion between two shear plates is measured using two-dimensional digital image correlation (DIC). The measured shear profiles and their characteristic self-similarity under these boundary conditions are utilized to calculate power-law exponent and transient-state viscosity via finite difference simulations.

Carbon fiber reinforced polymer composites have low density and high tensile strengths. However, their compressive strengths are much lower than their corresponding tensile strengths due to fiber micro-buckling and interface failure between fiber and matrix. To address this issue, we report a method for fabricating carbon nanotube (CNT) sheet scrolled carbon fibers or fiber tows to improve the interfacial shear strengths. A CNT sheet is drawn from a drawable carbon nanotube forest grown on a silicon substrate, it is used to wrap around individual carbon fibers. The CNT wrapped carbon fiber is subsequently impregnated into a polymer to form a composite. Scanning electron micrograph shows that the wettability of CNT wrapped carbon fiber composite increases drastically in comparison with the composite without CNT, indicating significantly increased bonding between carbon fiber and polymer due to the addition of aligned CNT at the interphase. Fiber push-out and push-in nanoindentation characterization indicates increased interfacial shear strengths, consistently at over 80% with the use of wrapped aligned CNT sheet. The results from scrolling CNT sheet around individual carbon fibers to enhance compressive strengths indicate the potential performance enhancement of composites when this approach is scaled up.

The investigation of wood mechanical response in outdoor conditions, subjected to environmental changes, long-term loadings, and time effects, show a complex behavior of this material. This behavior is characterized by a dimensional change which, in most cases, causes initiations and crack propagation until the total collapse of timber structures. This work presents, on the basis of the RDM assumptions of the Timoshenko beam theory, the evolution of notched beam deflection in the time. The model built takes into account the effects of moisture content variations of beam, the crack appeared until its collapse, the intensity of the loading applied and the geometry of the beam. The work is divided into three parts: (1) an experimental study, presenting the specific setup used to record the data; (2) the analytical model based on the classic assumptions of the beam theory starting from the expression of the notched beam’s Young modulus of notched beam (goal of this study); (3) the validation of the model at the end shows that the evolution of the experimental data and the analytical data have a good fit.

Metallic materials can exhibit creep or relaxation effects even at room temperature. For technical applications, this is typically not relevant because the effects are usually assumed to be small and therefore not relevant for the failure of components. However, relaxation effects may become important, particularly with regard to the prediction of the residual stress state or the distortion state arising from shot peening or jigging of components.

To investigate the room temperature relaxation behavior quenched and tempered specimens made of 42CrMo4 (AISI/SAE 4140) were deformed up to different total strains with different strain rates. Then the respective total strain was kept constant and the stress relaxation occurring in a hold time up to 1 h was recorded and analyzed. It turns out that even after a relative small plastic deformation significant relaxation effects occur. Regarding the relaxation rate a distinction must be made between short-term and long-term behavior. Typically, the long-term behavior can be described with an exponential approach. Depending on the strain rate, which was used to settle the starting stress, a more or less pronounced short-time relaxation is observed in which the stresses relax faster compared to the long-term behavior. The experimental procedure, the measurements, and the evaluations carried out are presented. The physical reasons for the different relaxation behavior will be discussed.

This paper presents a new design of a striker bar to be used with a split Hopkinson pressure bar that utilizes the idea of a serpentine transmitted bar with threaded joints. The new striker bar provides longer pulse lengths without having to use a longer striker bar. Explicit finite element simulations are used in conjunction with experimental results to validate the design. The serpentine striker bar is then used to test ZEK100 magnesium in high rate compression tests, and the results are compared to low rate compression data and high rate compression data obtained using a traditional striker bar of equivalent pulse length. The new serpentine striker bar design shows good agreement with traditional solid striker bars and, therefore, could be implemented into existing systems in order to obtain longer pulses.

Soft materials exhibit a unique blend of properties resembling either a solid or liquid. Hydrogels and polydimethylsiloxane (PDMS) are a few examples of soft materials. These materials exhibit viscoelastic properties which makes them difficult to determine the mechanical properties through conventional means. In addition, the material properties are highly dependent on their concentration ratios—wt./wt. for PDMS and wt./solvent volume for agarose hydrogel. A new in-plane shear test method, which incorporates 3D printed parts and Digital Image Correlation (DIC), was developed and updated to fully quantify the mechanical shear properties of agarose hydrogels at multiple concentrations (4.0, 2.5, 1.5, and 0.5% wt./vol.) and PDMS at multiple mixture ratios (10:1, 20:1, and 30:1 wt./wt.). The 3D printed parts were used as loading fixtures to ensure the appropriate grip on these soft materials. Verification of the agarose testing was conducted through the use of a plate-plate shear rheometer.

A multimode viscoelastoplastic damage model is developed for application to anisothermal finite deformations of fibrous composites at extreme temperatures with oxidative degradation. Maximization of the rate of entropy production is applied to develop the material model. The oxidation treatment, Parthasarathy et al. (J Am Ceram Soc 101:973–997, 2018), is applied both for points with direct atmospheric exposure via damage, as well as for diffusing reactants. Applications are envisioned to both ceramic matrix and polymer matrix composite materials.

Comprehensive experimental studies are performed to comprehend further the effects of thermal and mechanical aspects of cavitation on polyurea (PU) variants microstructure and molecular transitions. Different polyurea formulations are distinguished by the difference in their pre-polymer mixing ratios, including the chain length distribution of diamines. Virgin, cavitation-erosion damaged, and undamaged (exposed to water) along with annealed polyurea samples are tested for their crosslink density and molecular weight using swelling experiments and gel permeation chromatography (GPC). Additionally, FTIR spectra can be utilized to evaluate crystallinity (in formation and ordering of hydrogen bonds followed by their destruction). Furthermore, FTIR spectra for mechanically damaged samples under cavitation erosion can be related to water absorption and oxidation. It is understood that formulations with a higher hard segment (HS) to soft segment (SS) ratio tend to be more crosslinked. It is also observed that the swelling capacity is decreasing for polyurea with higher HS/SS ratio. It is concluded that the polyurea nanostructure can substantially affect its resistivity against thermal and mechanical damages.

A methodology is presented for characterizing the Taylor impact response of materials using high-speed digital image correlation. The motivation of this work is to understand material failure during high-rate loading and extract high-fidelity, quantitative data which captures the deformation history. Taylor impact experiments were chosen because they are a well-established means of assessing material behavior at high strains and strain rates. They are also particularly useful for exercising computational models. Digital image correlation was then identified as a promising technique to provide time-resolved, full-field characterization of the multi-axial failure behavior. This study shows the high-rate response of copper using symmetrical Taylor impact at several impact velocities. The utility and challenges associated with performing stereo digital image correlation with ultra-high-speed cameras and conducting Taylor impact studies are also discussed. The approach has implications for determining the susceptibility of materials to different failure modes and can provide a robust validation of computational models. One of the key features of interest will be the direct comparison between the experiments and the computational models.

As viscoelastic materials, polymers exhibit a time-dependent response to loading and unloading. Whilst this response is relatively easy to characterise at low strain rates, it is much more difficult at rates above c. 10 s⁻¹. One way to address this is to use models developed and calibrated based on time-temperature superposition; however, these models must be validated before they can be used in engineering design. Here, dynamic mechanical analysis (DMA) has been used to calibrate models for a commercially available polymer. This model has then been validated against further experiments: quasi-static and split Hopkinson pressure bar (SHPB) compression. The former was performed at a range of temperatures from room temperature to −40 °C. In addition to measuring the specimen behaviour during applied loading, measurements have been made of fast (over ~100 μs) and slow (~1000 s) relaxations of the material, respectively, and, hence, have been used to validate the relaxation response predicted by the model.

Polyvinyl chloride (PVC) foams are widely used in crashworthiness and energy absorption applications due to their low density combined to the capability of crushing up to large deformations with limited loads; the latter property is due to the particular constitutive behavior of such foams. Indeed, the stress–strain curve is characterized, after an initial yield or peak stress, by a relevant plateau region, followed by a steep increase due to foam densification. Furthermore, the mechanical response of PVC foam is strongly influenced by the rate of load or strain application.

In this work, compression tests have been carried out at different speeds on PVC foam samples having different relative density. Quasi-static and intermediate strain rate tests have been performed by pneumatic machine, while high strain rate tests have been conducted by means of a Split Hopkinson Pressure Bar.

The tests highlighted a strong compressibility of foam, with negligible lateral expansion; the energy absorption efficiency as well as the densification strain has been evaluated. Finally, the uniaxial stress–strain curves have been used to calibrate a combined visco-elastic and visco-plastic constitutive model, based on a 2-layer scheme borrowed from the literature. In the model, the material behavior is divided into two parallel branches, the former showing an elasto-plastic behavior, the latter showing a visco-elastic behavior; a multiplicative term, accounting for the strain rate sensitivity of the base material, is included into the plastic branch.

Dynamic mechanical analysis (DMA) provides insight into polymer viscoelastic behavior and its dependence on temperature. In that DMA is applied to a bulk sample, however, inferences about the connection among bulk and molecular behavior are generally speculative. In this work, a strain history similar to that of DMA is applied to atomistic polymer systems in silico. This method, termed Virtual DMA, can provide the data necessary to relate molecular information to bulk response. For example, strain amplitude can be varied to explore the effect of the corresponding small-scale perturbations on the stability of non-bond interactions. In some polymers, statistically significant differences in the glass transition temperature as measured by differential scanning calorimetry and DMA are found in physical experiments. When Virtual DMA results are compared with those from quasi-equilibrium cooling, the differing effects of imposed randomized and deterministic atomic velocities on molecular structure and local order can be identified.

Cohesive zone traction–separation (T–S) relationships of a polymer modified bitumen commonly used as a sealant material in three-tab shingles are obtained by performing both Mode I and Mode II loading of the sealant material using a rigid double cantilever beam (RDCB) fixture. The RDCB experiments are performed for adhesive samples bonded at two different temperatures. The measured T–S relationships show significant differences between the Mode I and Mode II responses. The Mode II facture toughness is found to be much higher than the Mode I fracture toughness and the adhesive is more ductile in Mode II. The maximum traction in the T–S relationship for Mode II loading is marginally lower than measured for Mode I. The adhesive having a higher bonding temperature showed higher toughness and maximum traction for both Mode I and Mode II loading compared to the adhesive bonded at a lower temperature.

The need to invest $2 trillion to improve our aging U.S. infrastructure and the success of fiber reinforced polymer (FRP) composites in providing durable solutions for secondary structures in aerospace, marine, and automotive has led to the integration of FRP composites into primary structural applications, with the most recent being the Boeing 787 Dreamliner and the push to develop FRP rebar for concrete. Using a material in a new application requires knowledge of its failure behavior and long-term durability in the targeted structure. Due to the hierarchical structure of FRPs, the required design parameters exceed those of metallic materials, with these additional parameters lacking standardized tests or evaluation methods to quantify their values. In this chapter, the measurement challenges restricting the universal adoption of FRPs in primary structural applications are highlighted and the new measurement methods being developed at NIST to address some of these challenges are discussed.