[Paper Review] Identification of the true elastic modulus of high density polyethylene from tensile tests using an appropriate reduced model of the elastoviscoplastic behavior

A. Blaise, Stéphane André+3 more|arXiv (Cornell University)|Jun 19, 2012

Polymer crystallization and properties31 references3 citations

TL;DR

This paper proposes a thermodynamically consistent reduced model to accurately identify the true instantaneous elastic modulus of high-density polyethylene (HDPE) from tensile tests, moving beyond conventional linear fitting methods. By using only three parameters—instantaneous Young's modulus, maximum relaxation time, and strain hardening modulus—the model captures elastoviscoplastic and hardening behavior up to large strains, significantly improving modulus estimation accuracy compared to standard ISO/ASTM protocols.

ABSTRACT

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.

Motivation & Objective

• To address the scientific inadequacy of conventional methods for determining Young’s modulus in polymers, which rely on arbitrary linear fitting of stress-strain curves.
• To develop a physically grounded, reduced-order model that captures elastoviscoplastic and strain-hardening behavior of HDPE under tensile loading.
• To identify the true instantaneous elastic modulus using a robust parameter estimation procedure based on well-established engineering principles.
• To validate the model’s predictions against independent physical measurements across different time and length scales.

Proposed method

• The authors employ a thermodynamically consistent elastoviscoplastic model with a linear relaxation spectrum described by a universal shape function.
• The model uses only three identifiable parameters: the instantaneous elastic modulus, the maximum relaxation time, and a strain hardening modulus for the relaxed state.
• Parameter identification is performed using established engineering science principles for inverse problems, ensuring consistency and reliability.
• The model is fitted to experimental tensile test data across a range of strain rates and large deformations.
• The identification procedure is validated by comparing predicted responses with measured data and with results from other physical experiments.
• The model’s predictive capability is assessed across multiple temporal and spatial scales to ensure physical coherence.

Experimental results

Research questions

• RQ1 How can the true instantaneous elastic modulus of HDPE be reliably extracted from tensile test data, avoiding the limitations of conventional linear fitting?
• RQ2 What minimal set of parameters is sufficient to accurately describe the elastoviscoplastic and strain-hardening response of HDPE under uniaxial tension?
• RQ3 Can a thermodynamically consistent reduced model reproduce experimental tensile behavior up to large strains with high fidelity?
• RQ4 How does the model’s predicted modulus compare with values obtained from independent physical measurements at different scales?

Key findings

• The proposed model successfully captures the elastoviscoplastic and strain-hardening response of HDPE up to large strains using only three parameters.
• The instantaneous elastic modulus identified via the model shows strong consistency with values obtained from independent physical experiments across different time and length scales.
• The method significantly improves upon standard ISO 527-1 and ASTM D638 protocols, which rely on arbitrary linear fitting and yield less accurate modulus estimates.
• The maximum relaxation time and strain hardening modulus are robustly identified and contribute to the model’s predictive power.
• The identification procedure is stable and physically grounded, enabling reliable modulus extraction from standard tensile tests.