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The plastic deformation of Polybutylene terephthalate (PBT) is investigated at three temperatures (120$^\circ$C, 150$^\circ$C, 180$^\circ$C) representative of the span between glass transition, $T_g \approx 55^\circ$C and melting $T_m \approx 225^\circ$C temperatures. The mechanisms of tensile deformation are analyzed as a function of the true strain using a combination of temperature-controlled tensile experiments coupled with 2D digital image correlation and synchrotron sourced wide angle (WAXS) and small angle (SAXS) X-ray scattering the amorphous and crystalline regions causing the transition between polymorphs, respectively from the isotropic amorphous phase to a smectic phase and from the $\alpha$ crystalline phase to the $\beta$ phase.

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.

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 under complex-valued quantities provides virtual DMA experiments directly in the frequency domain on a heterogenous system described by a voxel grid of mechanical properties. The achieved precision and computation times are very good. An effort has been made to show the application of such virtual DMA tool starting from two examples found in 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, understand relaxation phenomena either on the theoretical or experimental point 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 Semi-Crystalline Polymers exhibiting necking and for large deformation. In the framework of a $(\dot\sigma, \sigma, \dot\varepsilon, \varepsilon)$ behavior's law, tensile experiments conducted at an imposed constant strain rate $\dot\varepsilon_0$ bring true stress responses from which constitutive (material) parameters can be identified from Model-Based Metrology concepts. The same experiment repeated at various strain rates gives then access to the dependence of the non-elastic 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 which evolve strongly during the test (by a factor of 5-10 here). The parameter identification process requires then the introduction of the exact realized input strain and strain-rate command into the model. Accounting for strain rate dependency requires additionally the knowledge of the preliminary identified strain rate dependence of the non-elastic 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.

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{\textdegree}C from room temperature to 120{\textdegree}C . For temperatures below 60{\textdegree}C , it is shown that the strain localization effect becomes less pronounced when the temperature increases. For temperatures higher than 60{\textdegree}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 (E_{Y_2}) was measured and appeared to be independent of temperature. For temperatures smaller than 60{\textdegree}C , it was found that the threshold strain corresponding to (E_{Y_2}) also marks the onset of the deformation process phase during which the volume strain strongly increases. Based on previous studies of our research team and on literature we concluded that the critical strain (E_{Y_2}) 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.

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.

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.

The rheological parameters of materials are determined in the industry according to international standards established generally on the basis of widespread techniques and robust methods of estimation. Concerning solid polymers and the determination of Young's modulus in tensile tests, ISO 527-1 or ASTM D638 standards rely on protocols with poor scientific content: the determination of the slope of conventionally defined straight lines fitted to stress-strain curves in a given range of elongations. This paper describes the approach allowing for a correct measurement of the instantaneous elastic modulus of polymers in a tensile test. It is based on the use of an appropriate reduced model to describe the behavior of the material. The model comes a thermodynamical framework and allows to reproduce the behavior of an HDPE Polymer until large strains, covering the elastoviscoplastic and hardening regimes. Well-established principles of parameter estimation in engineering science are used to found the identification procedure. It will be shown that three parameters only are necessary to model experimental tensile signals: the instantaneous ('Young's') modulus, the maximum relaxation time of a linear distribution (described with a universal shape) and a strain hardening modulus to describe the 'relaxed' state. The paper ends with an assessment of the methodology. Our results of instantaneous modulus measurements are compared with those obtained with other physical experiments operating at different temporal and length scales., Comment: 43pages