Advantages of a 3-parameter reduced constitutive model for the measurement of polymers elastic modulus using tensile tests

Abstract

International audienceExact 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

Plastic instability studied experimentally on a semi-crystalline polymer through thermomechanical heat source identification: the flow stress concept revisited

“…These have to be accounted for when considering local measurements in the specimen center, as is done for THS in Fig.11. For The model described in Blaise et al, (2016) is used for the inverse determination of the model parameters limited to 5:…”

“…by Röchling Engineering Plastics KG ( ''500 Natural'' grade), a material studied for more than 15 years in our laboratory. It has been characterized at all scales in the Å to m range, with multiple physical investigations of the microstructure and also at the macroscopic scale (Farge et al, 2015;Ye et al, 2015;Blaise et al, 2016).…”

“…For this matrix form of state laws to be operational, the bz  products, which represent the non-elastic or dissipative component of the entropy and stress responses of eqs.2a, 2b, are further elucidated, but this aspect will not be detailed here. The interested reader can refer for example to (Blaise et al, 2016;Andre et al, 2012) to learn more about this part of the theory. g stands for the coupling matrix between internal variables.…”

“…difference between the stress reached when the tensile stage was stopped at a given value of  , and the asymptotic stress , r   reached for indefinite relaxation, also known as the relaxed stress. Both were obtained by an identification process performed on the whole curve due to the model detailed inBlaise et al, (2016) (See Fig. D in Supplementary material…”

Anisotropy development during HDPE necking studied at the microscale with in situ continuous 1D SAXS scans

“…The final motivation was to identify any recursive or fractal behavior of microstructural events (for a homogeneizable bulk microstructure). On the one hand, behavior models that are based on a recursive or fractal spectrum of relaxation times were proved pertinent to describe the kinetics of micromechanisms of deformation through a modal approach [Andre et al, 2003, Blaise et al, 2016. On the other hand, physical evidence of a kind of similarity in the scale-spreading sequence of micromechanisms of deformation have been obtained that are quasi inexistent in polymer science [Farge et al, 2013].…”