Multi-cycle deformation of semicrystalline polymers: Observations and constitutive modeling

Experimental data are reported on isotactic polypropylene in multi-cycle uniaxial tensile tests where a specimen is stretched up to some maximum strain and retracted down to the zero minimum stress, while maximum strains increase with number of cycles. Fading memory of deformation history is observed: when two samples are subjected to loading programs that differ along the first n − 1 cycles only, their stress–strain diagrams coincide starting from the nth cycle. Constitutive equations are developed in cyclic viscoelasticity and viscoplasticity of semicrystalline polymers, and adjustable parameters in the stress–strain relations are found by fitting the experimental data. Results of numerical simulation demonstrate that the model predicts the fading memory effect quantitatively. To confirm that the observed phenomenon is typical of semicrystalline polymers, experimental data are presented in tensile cyclic tests with large strains on low density polyethylene and compressive cyclic tests on poly(oxymethylene).     

Cyclic thermo-viscoplasticity of high density polyethylene

Observations are reported in uniaxial cyclic tensile tests (loading–unloading with various maximum strains) on high density polyethylene at temperatures ranging from room temperature up to 90 °C. It is demonstrated that the maximum stress per cycle and an apparent residual strain (measured at the instant when the tensile force vanishes under retraction) strongly decrease with temperature. The latter seems unexpected as the interval of temperatures covers the α-relaxation temperature, which is conventionally associated with activation of additional mechanisms for inelastic flow. A model is developed that captures the decrease in residual strain with temperature. Adjustable parameters in the stress–strain relations are found by fitting the experimental data. The effects of temperature and maximum strain per cycle on residual strains are studied numerically.     

Influence of temperature and strain rate on the mechanical behavior of three amorphous polymers: Characterization and modeling of the compressive yield stress

Uniaxial compression stress–strain tests were carried out on three commercial amorphous polymers: polycarbonate (PC), polymethylmethacrylate (PMMA), and polyamideimide (PAI). The experiments were conducted under a wide range of temperatures (−40 °C to 180 °C) and strain rates (0.0001 s⁻¹ up to 5000 s⁻¹). A modified split-Hopkinson pressure bar was used for high strain rate tests. Temperature and strain rate greatly influence the mechanical response of the three polymers. In particular, the yield stress is found to increase with decreasing temperature and with increasing strain rate. The experimental data for the compressive yield stress were modeled for a wide range of strain rates and temperatures according to a new formulation of the cooperative model based on a strain rate/temperature superposition principle. The modeling results of the cooperative model provide evidence on the secondary transition by linking the yield behavior to the energy associated to the β mechanical loss peak. The effect of hydrostatic pressure is also addressed from a modeling perspective.     

On the blast resistance of laminated glass

Blast resistant glazing systems typically use laminated glass to reduce the risk of flying glass debris in the event of an explosion. Laminated glass has one or more bonded polymer interlayers to retain glass fragments upon fracture. With good design, the flexibility of the interlayer and the adhesion between layers enable laminated glass to continue to resist blast after the glass layers fracture. This gives protection from significantly higher blast loads when compared to a monolithic pane. Full-scale open-air blast tests were performed on laminated glass containing a polyvinyl butyral (PVB) interlayer. Test windows of size 1.5 m × 1.2 m were secured to robust frames using structural silicone sealant. Blast loads were produced using charge masses of 15 kg and 30 kg (TNT equivalent) at distances of 10–16 m. Deflection and shape measurements of deforming laminated glass were obtained using high-speed digital image correlation. Measurements of loading at the joint, between the laminated glass and the frame, were obtained using strain gauges. The main failure mechanisms observed were the cohesive failure of the bonded silicone joint and delamination between the glass and interlayer at the pane edge. A new finite element model of laminated glass is developed and calibrated using laboratory based tests. Predictions from this model are compared against the experimental results.     

The characteristics of plastic flow and a physically-based model for 3003 Al–Mn alloy upon a wide range of strain rates and temperatures

The uniaxial compressive responses of 3003 Al–Mn alloy upon strain rates ranging from 0.001/s to about 10⁴/s with initial temperatures from 77 K to 800 K were investigated. Instron servohydraulic testing machine and enhanced split Hopkinson bar facilities have been employed in such uniaxial compressive loading tests. The maximum true strain up to 80% has been achieved. The following observations have been obtained from the experimental results: 1) 3003 Al–Mn alloy presents remarkable ductility and plasticity at low temperatures and high strain rates; 2) its plastic flow stress strongly depends on the applied temperatures and strain rates; 3) the temperature history during deformation strongly affects the microstructure evolution within the material. Finally, paralleled with the systematic experimental investigations, a physically-based model was developed based on the mechanism of dislocation kinetics. The model predictions are compared with the experimental results, and a good agreement has been observed.     

Modeling and measuring visco-elastic properties: From collagen molecules to collagen fibrils

Collagen is the main structural protein in vertebrate biology, determining the mechanical behavior of connective tissues such as tendon, bone and skin. Although extensive efforts in the study of the origin of collagen exceptional mechanical properties, a deep knowledge of the relationship between molecular structure and mechanical properties remains elusive, hindered by the complex hierarchical structure of collagen-based tissues. Understanding the viscoelastic behavior of collagenous tissues requires knowledge of the properties at each structural level. Whole tissues have been studied extensively, but less is known about the mechanical behavior at the submicron, fibrillar and molecular level. Hence, we investigate the viscoelastic properties at the molecular level by using an atomistic modeling approach, performing in silico creep tests of a collagen-like peptide. The results are compared with creep and relaxation tests at the level of isolated collagen fibrils performed previously using a micro-electro-mechanical systems platform. Individual collagen molecules present a non-linear viscoelastic behavior, with a Young's modulus increasing from 6 to 16 GPa (for strains up to 20%), a viscosity of 3.84±0.38 Pa s, and a relaxation time in the range of 0.24–0.64 ns. At the fibrils level, stress–strain–time data indicate that isolated fibrils exhibit viscoelastic behavior that could be fitted using the Maxwell–Weichert model. The fibrils showed an elastic modulus of 123±46 MPa. The time-dependent behavior was well fit using the two-time-constant Maxwell–Weichert model with a fast time response of 7±2 s and a slow time response of 102±5 s.     

Mechanics of the rate-dependent elastic–plastic deformation of glassy polymers from low to high strain rates

A combined experimental and analytical investigation has been performed to understand the mechanical behavior of two amorphous polymers—polycarbonate and poly(methyl methacrylate)—at strain rates ranging from 10⁻⁴ to 10⁴ s⁻¹. This range in strain rates was achieved in uniaxial tension and compression tests using a dynamic mechanical analyzer (DMA), a servo-hydraulic testing machine, and an aluminum split-Hopkinson pressure bar. DMA 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 the servo-hydraulic machine (10⁻⁴ to 1 s⁻¹) and the split-Hopkinson pressure bar (10³ to 10⁴ s⁻¹) were used to characterize the rate-dependent yield and post-yield behavior. Both materials were observed to exhibit increased rate sensitivity of yield under the same strain rate/temperature conditions as the β-transition of the viscoelastic behavior. A physically based constitutive model for large strain deformation of thermoplastics was then extended to encompass high-rate conditions. The model accounts for the contributions of different molecular motions which become operational and important in different frequency regimes. The new features enable the model to not only capture the transition in the yield behavior, but also accurately predict the post-yield, large strain behavior over a wide range of temperatures and strain rates.     

The high strain mechanical response of the wet Kelvin model for open-cell foams

Surface Evolver software was used to create the three-dimensional geometry of a Kelvin open-cell foam, to simulate that of polyurethane flexible foams. Finite Element Analysis (FEA) with 3D elements was used to model large compressive deformation in the [0 0 1] and [1 1 1] directions, using cyclic boundary conditions when necessary, treating the polyurethane as an elastic or elastic–plastic material. The predicted foam Young’s moduli in the [0 0 1] direction are double those of foams with uniform Plateau border cross-section edges, for the same foam density and material properties. For compression in the [1 1 1] direction, the normalized Young’s modulus increases from 0.9 to 1.1 with foam relative density, and the predicted stress–strain relationship can have a plateau, even for a linearly-elastic polymer. As the foam density increases, the predicted effects of material plasticity become larger. For foam of relative density 0.028, edge-to-edge contact is predicted to occur at a 66% strain for [1 1 1] direction compression. The foam is predicted to contract laterally when the [1 1 1] direction compressive strain exceeds 25%.     

A 1-D theory for extensional deformation of a viscoelastic filament under exponential stretching

We consider a viscoelastic filament placed between two coaxial discs, with the bottom plate fixed and the top plate pulled at an exponential rate. Using a slender rod approximation, we derive a one-dimensional (1-D) model which describes the deformation of a viscoelastic filament governed by the Oldroyd-B constitutive model. It is assumed that the flow is axisymmetric and that inertia and gravity are negligible. One solution of the model equations corresponds to ideal uniaxial elongation. A linear stability analysis shows that this solution is unstable for a Newtonian fluid and for viscoelastic filaments with small Deborah number (De ≤ 0.5). For Deborah number greater than 0.5, ideal uniaxial elongation is linearly stable. Numerical solution of the nonlinear equations confirms the result of the linear stability analysis. For initial conditions close to ideal uniaxial flow, our results show that if De > 0.5, the central portion of the filament undergoes considerable strain hardening. As a result, the sample remains almost cylindrical and the deformation approaches pure uniaxial extension as the Hencky strain increases. For De ≤ 0.5, the Trouton ratio based on the effective extension rate at the mid-plane radius gives a much better approximation to the true extensional viscosity than that based on the imposed stretch rate.     

Integral-based constitutive equation for rubber at high strain rates

High-speed experiments were conducted to characterize the deformation and failure of Styrene Butadiene Rubber at impact rates. Dynamic tensile stress–strain curves of uniaxial strip specimens and force–extension curves of thin sheets were obtained from a Charpy tensile impact apparatus. Results from the uniaxial tension tests indicated that although the rubber became stiffer with increasing strain rates, the stress–strain curves remained virtually the same above 280 s⁻¹. Above this critical strain rate, strength, fracture strain and toughness decreased with increasing strain rates. When strain rates were below 180 s⁻¹, the initial modulus, tensile strength and breaking extension increased as the strain rate increased. Between strain rates of 180 and 280 s⁻¹, the initial modulus and tensile strength increased with increasing strain rates but the extension at break decreased with increasing strain rates. A hyper-viscoelastic constitutive relation of integral form was used to describe the rate-dependent material behavior of the rubber. Two characteristic relaxation times, 5 ms and 0.25 ms, were needed to fit the proposed constitutive equation to the data. The proposed constitutive equation was implemented in ABAQUS Explicit via a user-defined subroutine and used to predict the dynamic response of the rubber sheets in the experiments. Numerical predictions for the transient deformation and failure of the rubber sheet were within 10% of experimental results.     

Set up of an experimental apparatus for the study of fragmentation of solid fuels upon severe heating

An experimental apparatus has been developed in order to perform tests of primary fragmentation of solid fuels under severe heating conditions. The device is a modified heated strip reactor, capable to reach 2000 °C in less than 0.2 s. Particles are laid on the strip and pyrolysed under inert or moderately oxidizing conditions. The char particles and their fragments, generated upon pyrolysis, can be recovered and analysed to assess the fragmentation propensity of the fuel.Some preliminary experiments have been carried out on two biomass samples in order to assess the time-temperature history of particles in the experimental apparatus. In particular biomass particles of approximately 2–3 mm have been used. The temperature of the heated strip reactor in such preliminary tests was varied between 1000 and 1600 °C, while the strip nominal heating rate was kept at 10⁴ °C/s and the holding time was set at the value of 10 s. A near infrared fast camera (38,000 frames/s) has been used to measure the temperature of the heated strip and of the particles during the tests. A heat up model was developed and validated against experimental results. The model was then used to estimate the temperature gradients across particles of biomass and of coal as well.Results show that the strip of the reactor reaches the set temperature in less than 0.2 s. When particles are laid on the strip, their bottom surface, which is in physical contact with the strip, immediately reaches the set temperature value. For 1 mm coal particles the upper surface can be considered at the same temperature as well. Under the most severe conditions tested (strip temperature of 1600 °C , biomass particles of 2 mm thickness) the temperature difference between the bottom and the upper face is 200 °C after 3 s and drops to 100 °C after 10 s. On the whole the experimental apparatus simulates uniform heating of the particles with reasonable approximation. In the next future the apparatus will be further upgraded to operate at pressures up to 20 bars.     

Experimental study on the compressive behaviors of CFRP tube-encased concrete columns

Nine square concrete columns including 6 CFRP/ECCs and 3 concrete columns are prepared, which have cross-section of 200 mm × 200 mm and height of 600 mm. The CFRP tubes with fibers oriented at hoop direction were manufactured to have 3 or 5 layers of CFRP with 10 mm, 20 mm, or 40 mm rounding corner radii at vertical edges. A 100 mm overlap in the direction of fibers was provided to ensure proper bond. Uniaxial compression tests were conducted to investigate the compressive behavior. It is evident that the CFRP tube confinement can improve the behavior of concrete core, in terms of axial compressive strength or axial deformability. Test results show that the stress-strain behavior of CFRP/ECCs vary with different confinement parameters, such as the number of confinement layers and the rounding corner radius.     

Ductility of selected metals under electromagnetic ring test loading conditions

Experimental studies on ductility of selected metals differing mechanical properties under strain rates between 4 × 10³ and 2 × 10⁴ s^?1 are presented in this work. The electromagnetic expanding ring experiment was used as the primary tool for examining the ductility behaviour of metals. Through a use of the Phantom v12 digital high-speed camera and specialised TEMA Automotive software, rings expansion velocities were determined with satisfactory accuracy for all ring tests. In this paper, the experimental observations on cold-rolled copper Cu-ETP, aluminium alloy Al 7075, barrel steel and tungsten heavy alloy are reported. Ductility of studied materials was estimated by measuring changes in cross-sectional areas in the uniform strain portions of the recovered ring fragments. In a similar way the metals ductility was defined at the conventional tensile test condition. Moreover, results of analogue investigation for static and dynamic loading at the temperature of about ?40 °C were described. The experimental observations mainly revealed the different ductility behaviour of metals tested at applied dynamic loadings; Cu-ETP and barrel steel demonstrated an increase in ductility, whereas aluminium alloy Al 7075 and tungsten heavy alloy were characterised by lower ductility in comparison to static loading. These results appear to be partially in contrast with the observations reported recently by some other investigators.     

Flow pattern characterization for R-245fa in minichannels: Optical measurement technique and experimental results

An optical measurement method using image processing for two-phase flow pattern characterization in minichannel is developed. The bubble frequency, the percentage of small bubbles as well as their velocity are measured. A high-speed high-definition video camera is used to measure these parameters and to identify the flow regimes and their transitions. The tests are performed in a 3.0 mm glass channel using saturated R-245fa at 60 °C (4.6 bar). The mass velocity is ranging from 100 to 1500 kg/m² s, the heat flux is varying from 10 to 90 kW/m² and the inlet vapor quality from 0 to 1. Four flow patterns (bubbly flow, bubbly–slug flow, slug flow and annular flow) are recognized. The comparison between the present experimental intermittent/annular transition lines and five transition lines from macroscale and microscale flow pattern maps available in the literature is presented. Finally, the influence of the flow pattern on the heat transfer coefficient is highlighted.     

Temperature dependent bulge test for elastomers

The bulge test is a particularly convenient testing method for characterizing elastomers under biaxial loading. In addition, it is convenient to utilize this test for validating material models in simulation due to the heterogeneous strain field induced during inflation. During the bulge test the strain field for elastomers covers uniaxial tension at the border to pure shear and equibiaxial tension at the pole. Elastomeric materials exhibit a hyperelastic material behavior, with a dependency on temperature and loading rate. The temperature effect on the mechanical behavior during biaxial loading is considered in the present study. A bulge test setup combined with a temperature chamber is developed in order to characterize this effect, and an exemplary temperature dependent characterization of a poly(norbornene) elastomer is performed with this setup. The equibiaxial stress–strain curves measured at 60 °C, 20 °C and −20 °C are presented.     

Flow of dilute to semi-dilute polystyrene solutions through a benchmark 8:1 planar abrupt micro-contraction

We have studied the flow of thermodynamically ideal solutions of a high molecular weight (M_w = 6.9 MDa) atactic polystyrene in the θ solvent dioctyl phthalate (aPS in DOP) through a micro-fabricated 8:1 planar abrupt contraction geometry. The channel is much deeper than most micro-scale geometries, providing an aspect ratio of 16:1 and a good approximation to 2D flow in the narrow channel. The solutions span a range of concentration 0.03 wt.% < c < 0.6 wt.%, encompassing the dilute to semi-dilute regimes and providing a range of fluid viscosities and relaxation times such that we achieve a range of Weissenberg numbers (8.7 < Wi < 1562) and Reynolds numbers (0.07 < Re < 11.2), giving elasticity numbers between 31 < El < 295. We study the flow using a combination of micro-particle image velocimetry (μ-PIV) to characterize the flow field, pressure measurements to evaluate the non-Newtonian viscosity, and birefringence measurements to assess macromolecular strain. Flow field observations reveal three broad flow regimes characterized by Newtonian-like flow, unstable flow and vortex growth in the upstream salient corners. Transitions between the flow regimes scale with Wi, independent of El, indicating the dominance of elastic over inertial effects in all the fluids. Transitions in the flow field are also reflected by transitions in the relative viscosity (determined from the pressure drop) and the macromolecular strain (determined from birefringence measurements). The strain through the 8:1 contraction saturates at a value of ～4–5 at high Wi. The results of these experiments broaden the limited set of literature on flow through micro-fluidic planar contractions and should be of significant value for optimizing lab-on-a-chip design and for comparison with modeling studies with elasticity dominated fluids.     

Orientation evolution in Hadfield steel single crystals under combined slip and twinning

The tensile deformation response and texture evolution of aluminum alloyed Hadfield steel single crystals oriented in the 〈1 6 9〉 direction is investigated. In this material, the strain hardening response is governed by the high-density dislocation walls (HDDWs) that interact with glide dislocations. A microstructure-based visco-plastic self-consistent model was modified to account for mechanical twinning in addition to the prevailing contribution of the HDDWs. Simulations revealed the contribution of twinning to the overall work hardening at the later stages of deformation. Moreover, both the deformation response and the rotation of the loading axis associated with plastic flow are successfully predicted even at the high-strain levels attained (0.53). Predicting the texture evolution serves as a separate check for validating the model, motivating its utilization in single and polycrystals of other alloys that exhibit combined HDDWs and twinning.