This study examined the effects of continuous reactive extrusion on the properties of vitrimerized thermoplastics derived from polybutylene terephthalate (PBT). PBT formulations were prepared using epoxy (crosslinker) and zinc acetylacetonate (transesterification catalyst) to form dynamic covalent networks. Reactive extrusion was performed at different screw rotation speeds (50, 100, 200rpm) with controlled residence times to compare the effects of the shear stress during the formation of crosslinks on the vitrimer properties. The rheological behavior of the extruded vitrimerized PBT suggests that competition between chain scission and branching occurs during the dynamic crosslinking of thermoplastics. Increasing the shear stress and/or time in the extruder was found to favor chain scission over crosslinking which makes gelation unattainable. In the case of injection molded specimens, tensile and X-ray diffraction tests of vitrimerized PBT extruded at different shear stress indicated a significant relationship between the degree of crosslinking, the orientation of crystallites, and the ability of the polymer network to withstand deformation at elevated temperatures.

Plastic deformation mechanisms of Polybutylene terephthalate (PBT) are investigated at 120 degrees C, 150 degrees C and 180 degrees C using tensile experiments, 2D digital image correlation, wide and small angle X-ray scattering measurements.Plots of nominal stress vs true strain (e), true stress vs e and Haward-Thackray representation reveal the same I, II, III regimes in strain ranges virtually independent of temperature. Between e = 0 and the yield strain eY approximate to 0.3 (I) the layer morphology is preserved, the interlamellar distance increases in the drawing direction and the strain is localized in amorphous regions. Between e approximate to 0.3 and e approximate to 1.0 (II), amorphous chains remain describable as gaussian coils while transition from spherulitic to fibrillar morphologies occurs. Beyond e approximate to 1.0 (III) the chains are taut, the fibrillar morphology is established, additional stress causes the transitions between polymorphs, respectively from isotropic amorphous to smectic and from alpha to beta crystalline phases.

Finite Element codes used for solving the mechanical equilibrium equations in transient problems associated to (time-dependent) viscoelastic media generally relies on time-discretized versions of the selected constitutive law. Recent concerns about the use of non-integer differential equations to describe viscoelasticity or well-founded ideas based upon the use of a behavior's law directly derived from Dynamic Mechanical Analysis (DMA) experiments in frequency domain, could make the Laplace domain approach particularly attractive if embedded in a time discretized scheme. Based upon the inversion of Laplace transforms, this paper shows that this aim is not only possible but also gives rise to a simple algorithm having good performances in terms of computation times and precision. Such an approach, which fully relies on the Laplace-defined Behavioral Transfer Function (LTBF) can be promoted if it uses ARX parametric models perfectly substitutable to the real LTBF. They avoid the hitherto prohibitive pitfall of having to store all past data in the computer's memory while maintaining an equal computation precision.

Finite Element codes used for solving the mechanical equilibrium equations in transient problems associated to (time-dependent) viscoelastic media generally relies on time-discretized versions of the selected constitutive law. Recent concerns about the use of non-integer differential equations to describe viscoelasticity or well-founded ideas based upon the use of a behavior's law directly derived from Dynamic Mechanical Analysis (DMA) experiments in frequency domain, could make the Laplace domain approach particularly attractive if embedded in a time discretized scheme. Based upon the inversion of Laplace transforms, this paper shows that this aim is not only possible but also gives rise to a simple algorithm having good performances in terms of computation times and precision. Such an approach, which fully relies on the Laplace-defined Behavioral Transfer Function (LTBF) can be promoted if it uses AutoRegressive with eXogeneous input parametric models perfectly substitutable to the real LTBF. They avoid the hitherto prohibitive pitfall of having to store all past data in the computer's memory while maintaining an equal computation precision.

The main objective of this work is to analyze finely the influence of cross-linking on the mechanical properties of polybutylene terephtalate-based vitrimers. Tensile tests were carried out at four temperatures (80, 100, 130, and 160 degrees C) on a series of vitrimer specimens made by injection molding for which the cross-linker concentrations were changed by small increments of 0.25%, from 0% to 2%. The displacement and strain fields were measured on the specimen surfaces through 3D digital image correlation in order to analyze the strain localization/delocalization phenomena that occur during the successive stages of the deformation process. In particular, we measured the yield strain epsilon Y$$ {\varepsilon}_{\mathrm{Y}} $$ (onset of strain localization), and the strain at neck stabilization epsilon NS$$ {\varepsilon}_{\mathrm{NS}} $$ (beginning of the strain delocalization phase). When the degree of cross-linking increases, we observed two complementary effects leading to the decrease of the strain range during which plastic instability develops. Firstly epsilon Y$$ {\varepsilon}_{\mathrm{Y}} $$ increases. Secondly, and this is the main cause of the plastic instability strain range reduction, epsilon NS$$ {\varepsilon}_{\mathrm{NS}} $$ decreases. This latter effect results from the limitation in extensibility of the macromolecular network in the solid state caused by cross-linking. More specifically, cross-linking leads to two distinct modifications of the macromolecular network that both contribute to the reduction of its extensibility. The first is the decrease of the chain length between the network nodes. The second is the pre-orientation of the macromolecular network that occurs during injection molding in the case of vitrimers with high viscosities due to cross-linking. Eventually, when epsilon Y ->epsilon NS$$ {\varepsilon}_{\mathrm{Y}}\to {\varepsilon}_{\mathrm{NS}} $$, the suppression of the yield point on the tensile curve was observed for the most cross-linked vitrimers. Furthermore, in the temperature range of investigation, epsilon NS$$ {\varepsilon}_{\mathrm{NS}} $$ was found to be independent of temperature.

We present an experimental investigation of the mechanical properties of solid vitrimer samples obtained by incorporating a diepoxide into commercial poly(butylene terephthalate) (PBT) in the presence of a Zn(II) catalyst using batch compounder and injection-molding machines. Tensile experiments were carried out at different temperatures (80, 120, and 160 degrees C) below the melting point (220 degrees C) and with various diepoxide concentrations (0, 1, and 2 wt %). We found that vitrimer plastic deformation mechanisms differ drastically from those of the PBT precursor and more generally from the regular behavior of other semi-crystalline polymers. In PBT vitrimers, strain localization (necking) is very weak and can even be suppressed. This type of behavior is due to the increase in strain hardening caused by vitrimer cross-linking. The creep resistance and stiffness of PBT vitrimers are significantly higher than those of pristine PBT. We found that vitrimer modification of PBT at moderate levels improves dimensional stability without inducing brittleness. These promising results highlight the need to find processes which enable significant production levels of these new materials. In the Perspective section, we briefly present a method to produce PBT-based vitrimers using continuous reactive extrusion.

FFT-based solvers are increasingly used by many researcher groups interested in modelling the mechanical behavior associated to a heterogeneous microstructure. A development is reported here that concerns the viscoelastic behavior of composite structures generally studied experimentally through Dynamic Mechanical Analysis (DMA). A parallelized computation code developed with complex-valued quantities provides virtual DMA experiments directly in the frequency domain on a heterogeneous system described by a voxel grid of mechanical properties. The achieved precision and computation times are very good. An effort has been made to illustrate the application of such a virtual DMA tool through two examples from the literature: the modelling of glassy/amorphous systems at a small scale and the modelling of experimental data obtained in temperature sweeping mode by DMA on a particulate composite made of glass beads and a polystyrene matrix, at a larger scale. Both examples show how virtual DMA can contribute to question, analyze, and understand relaxation phenomena on either theoretical or experimental points of view.

A study of methodological nature demonstrates the efficiency of a probation test allowing for the intrinsic character of a rheological constitutive law to be assessed. Such a law is considered here for semicrystalline polymers exhibiting necking and for large deformation. In the framework of a law of behavior of $( \dot{\sigma },\sigma , \dot{\varepsilon },\varepsilon )$ , tensile experiments conducted at an imposed constant strain rate $\dot{\varepsilon }_{0}$ bring true stress responses, from which the constitutive (material) parameters can be identified from model-based metrology concepts. The same experiment repeated at various strain rates gives an access to the dependence of the nonelastic parameters on the strain rate. Then the intrinsic law is tested severely by considering a new set of experiments carried out for constant displacement rates of the grips. In that case the specimens show local strain rates that evolve strongly during the test (by a factor of 5–10). The parameter identification process requires the introduction of the exact realized input strain and strain-rate command into the model. Accounting for strain rate dependency additionally requires the knowledge of the preliminary identified strain rate dependence of the nonelastic constitutive parameters for good predictions of the experimental response directly. This is what is proven here. The conclusion speaks in favor of a possible upgrade of international standards for the mechanical characterization of polymers based on constant strain-rate tensile tests and properly applied model-based metrology.

To improve the lifetime of proton-exchange membrane (PEM) fuel cells, it is necessary to provide a better understanding of the degradation mechanisms of the perfluorosulfonic acid (PFSA) membranes during fuel cell operation. Despite quantities of work focusing independently on chemical or mechanical degradation, only a few concerned the effect of both combined. The purpose of this study is to analyze the effects of conjoint chemical and mechanical stress on PFSA membranes via an ex-situ approach. First, an investigation of the effects of chemical degradation by radical attacks (i.e. exposure to Fenton reagents) on PFSA membranes was carried out. The results confirm that the chemical decomposition of PFSA membranes is significantly influenced by the concentration of Fenton's reagents, both chemically and morphologically. Second, a custom-made device was developed to examine the impact of coupled chemical and mechanical degradations. The initial results show that fully hydrated membranes seem to withstand severe sinusoidal constraints as no crack formed. However, the application of cyclic compression resulted in accelerated chemical decomposition of PFSA membranes. The results also demonstrate that some microstructural changes can appear and lead to a slight increase in the hydrogen crossover that can be detected before it impacts the cell performances.

ABSTRACT This work aims at identifying defects called deformation heterogeneities developing in polylactide (PLA)‐based materials upon drawing at room temperature. The influence of the initial crystallinity and of the plasticization methodology (physical blending vs. reactive blending) on the type of defect is also investigated. Defects are characterized in situ by (a) calculating the volume strain from digital image correlation (DIC), (b) measuring their surface density from optical microscopy, and (c) assessing their scattering invariant from small‐angle X‐ray scattering. Complementary structural analyses are done by microcomputed X‐ray tomography and atomic force microscopy. Drawing is accompanied by crazing in the case of low‐crystalline PLA, cracking in the case of annealed PLA, no defect in the case of plasticized PLA by physical blending, and shear bands and cracking in the case of plasticized PLA by reactive blending. These observations are discussed based on the initial structural features of the materials. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56 , 1452–1468

The plastic deformation processes that occur in a tensily deformed High Density Polyethylene specimen were studied from full-field strain and strain rate measurements obtained by 3D DIC (Digital Image Correlation). The tensile tests were performed every 10°C from room temperature to 120°C. For temperatures below 60°C, it is shown that the strain localization effect becomes less pronounced when the temperature increases. For temperatures higher than 60°C, the material is found to exhibit double yielding behavior. By analyzing the DIC data in Lagrangian representation, it was possible to quantitatively highlight the strain localization effect that is specifically associated with the second yield. The second yield strain (εY2) was measured and appeared to be nearly independent of temperature. For temperatures smaller than 60°C, it was found that the threshold strain corresponding to εY2 also marks the onset of the deformation process phase during which the volume strain strongly increases. On the basis of previous WAXS (Wide Angle X-ray Scattering) studies of our research team and on literature we concluded that the critical strain εY2 corresponds to the onset of the lamellar morphology destruction. At high strain levels, the neck stabilization phase was shown to proceed according to a strain driven scheme characterized by threshold strains that are temperature-independent. The experimental values of the threshold strain marking the onset of the stabilization phase are found to be in good agreement with those found using the Haward-Thackray model.

Micromechanical deformation phenomena such as those leading to macroscopic viscoelastic and plastic behavior must be studied from a thermodynamic viewpoint, as they induce complex and partly irreversible heat effects. Calorimetric measurements of the intrinsic volumetric thermomechanical heat sources (THS) activated in the material bulk during mechanical loads can produce valuable information with respect to that aim. They can be based on infrared imaging if submitted to inverse algorithms that allow a correct reconstruction of THS to be produced. Here, an inverse method relying on a diffusion-advection heat transfer model is applied to experimental temperature maps recorded during tensile tests. These are made on a semi-crystalline polymer that shows a strong development of plastic instabilities. Along with simultaneous kinematic observables produced with a digital image correlation system, the competition between advection and diffusion phenomena may be clearly established. 1-D profiles of the reconstructed THS and measured strain rates illustrate clearly that thermomechanical effects associated with necking onset and propagation follow the kinematic variable in a rather direct manner. Finally, we show for tensile experiments that THS estimations lead to analyze plasticity as a rheological behavior controlled by the flow stress, responsible of necking development and propagation.

ABSTRACTTo improve our understanding of the rheology of solid semi‐crystalline polymers, descriptions of the deformation‐induced microstructural reorganization mechanisms with precise and local quantitative data are needed. The novel results presented in this paper for high‐density polyethylene (HDPE) were obtained in situ on a coherent synchrotron beamline specifically developed to allow very fast scanning of a specimen under tensile test. From the recorded small angle X‐ray scattering (SAXS) patterns, a quantitative index characterizing the microstructure local anisotropy was calculated. With the scanning operating mode, many different material points could be studied. These material points were subjected to various deformation paths in the plastic regime due to the necking development and its propagation. Their positions and strain evolutions were obtained through digital image correlation (DIC). With an appropriate analysis coupling the bulk‐averaged SAXS and DIC surface measurements, the microstructural anisotropy index is shown to have a given value at a given true strain. This means that the microstructure morphology is only governed by the current strain level. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018, 56, 170–181

This paper is devoted to a theoretical and numerical study of different ways of calculating the Fourier transform of a noisy signal where the boundary conditions at the lateral boundaries of the measurement interval are not precisely known. This happens in different characterization problems where infrared camera is used for temperature measurements. In order to overcome this difficulty, the interval where the Fourier transform (its support) is supposed to be larger than the measurement domain is defined. Thus, this virtual interval larger than the measurement interval is used. We show that regularization by truncated singular value decomposition is able to yield good estimates to this very ill-posed inverse problem.

In order to better understand micromechanical phenomena such as viscoelasticity and plasticity, the thermomechanical viewpoint is of prime importance but requires calorimetric measurements to be performed during a deformation process. Infrared imaging is commonly used to this aim but does not provide direct access to the intrinsic volumetric Thermomechanical Heat Sources (THS). An inversemethod is needed to convert temperature fields in the former quantity. The one proposed here relies on adiffusion-advection heat transfer model. Advection is generally not considered in such problems but due to plastic instabilities, a heterogeneous and non-negligible velocity field can play a role in the local heat transfer balance. Discretization of the governing equation is made through appropriate spectral approach. Spatial regularization is then achieved through regular modal truncation. The objective of the inversion process lies in a proper identification of the decomposition coefficients (states) which minimize the residuals. When a Conjugate Gradient Method (CGM) is applied to this nonlinear least square optimization, the use of Karhunen-Loeve Decomposition (KLD) or Singular Value Decomposition (SVD) on gradient vectors is shown to produce very good temporal regularization. Two test-cases were explored for noisy data which show that this algorithm performs very well when compared to the Tikhonov penalized conjugate gradient method.

Exact measurements of the rheological parameters of time-dependent materials are crucial to improve our understanding of their intimate relation to the internal bulk microstructure. Concerning solid polymers and the apparently simple determination of Young's modulus in tensile tests, international standards rely on basic protocols that are known to lead to erroneous values. This paper describes an approach allowing a correct measurement of the instantaneous elastic modulus of polymers by a tensile test. It is based on the use of an appropriate reduced model to describe the behavior of the material up to great strains, together with well-established principles of parameter estimation in engineering science. These principles are objective tools that are used to determine which parameters of a model can be correctly identified according to the informational content of a given data set. The assessment of the methodology and of the measurements is accomplished by comparing the results with those obtained from two other physical experiments, probing the material response at small temporal and length scales, namely, ultrasound measurements with excitation at 5 MHz and modulated nanoindentation tests over a few nanometers of amplitude.

In the study presented in this paper, we analyzed the mechanical response of a glass fiber plain weave/polymer composite at the fabric millimetric mesoscale. The detail of the stress and strain fields in a fabric repeating unit cell was numerically calculated using CraFT (Composite response and Fourier Transforms), a code specifically conceived for simulating the mechanical behaviour of materials with complex microstructure. The local strain fields obtained by simulation were found to be in very good agreement with measurements carried out using 3D Digital Image Correlation (3D DIC). From numerical stress fields calculated with the CraFT solver, we also highlighted the subregions inside the periodic mesostructure where there is maximum stress. Furthermore, with X-ray tomography post mortem measurements, we were able to confirm that certain damage modes were well initiated in these microstructure subregions of stress concentration.