Certifying the intrinsic character of a constitutive law for semicrystalline polymers: a probation test
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Certifying the intrinsic character of a constitutive law for semicrystalline polymers: a probation test S. André1
· S. Becker1 · L. Farge1 · A. Delconte2
Received: 28 February 2020 / Accepted: 28 August 2020 © Springer Nature B.V. 2020
Abstract 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 (σ˙ , σ, ε˙ , ε), tensile experiments conducted at an imposed constant strain rate ε˙ 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. Keywords Inverse identification · Parameter estimation · Constitutive behavior’s law · Semicrystalline polymer · Tensile test · HDPE
1 Introduction Model-based metrology (MBM) means essentially a whole of procedures, at the heart of which are the principles of parameter estimation theory (identifiability proofs) to treat data
B S. André
[email protected]
1
Université de Lorraine, CNRS, LEMTA, F-54000 Nancy, France
2
Université de Lorraine, CNRS, CRAN, F-54000 Nancy, France
Mech Time-Depend Mater
with the objective of obtaining measurable quantities of physical interest. Such an approach should be a rule of thumb each time a model is used in conjunction with observed quantities because (i) it allows stating in full transparency the performance of the model and the quality of the estimates, but, most importantly, (ii) it gives a feedback of possible missing foundations of a model or theory. These are revealed by the shape of after-identification residuals (the gap curve between observed and model-reconstructed signals). Such practices are very common in other fields of science (especially in the heat transfer community, which was at the origin of the International Conference on Inverse Problems in Engineering ICIPE (but also of course in the aut
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