Inelastic Behavior of Polyoxymethylene for Wide Strain Rate and Temperature Ranges: Constitutive Modeling and Identification †
Abstract
:1. Introduction
- To analyze the behavior of POM, displacement-controlled tensile tests with loading/unloading regimes under different rates and temperatures are performed, and families of stress–strain curves for different strain rates and temperatures are generated.
- Inelastic responses of thermoplastic polymers usually exhibit pressure sensitivity and inelastic dilatation. To analyze inelastic dilatation, digital image correlation (DIC) measurements of transverse strains are performed.
- Polymers exhibit non-linear loading/unloading behavior and strain rate sensitivity, even at room temperature. Although many available constitutive models, for example rheological models, are able to describe non-linearities under constant and monotonic loading, predictions of non-linear unloading responses are usually not accurate. In our study, we apply and develop a composite model of inelastic deformation to characterize the inelastic behavior of POM for both loading and unloading regimes.
2. Basic Features of Material Behavior
3. Constitutive Model
3.1. Composite Model of Inelastic Deformation
3.2. Constitutive and Evolution Equations
3.3. Model Reduction
4. Model Calibration
4.1. Uni-Axial Stress State
4.2. Identification Procedure
- Smooth experimental data and compute stress rates;
- Identify the Young’s modulus as a function of temperature;
- Compute inelastic strains and strain rates for each temperature and strain rate level;
- Identify flow stresses as functions of strain rate and temperature;
- Identify parameters in the composite model from families of stress–strain curves for different strain rates and temperature levels;
- Identify Poisson’s ratios (elastic and inelastic) and the parameter from transverse strains, measured by DIC.
4.3. Transverse Strain and Inelastic Dilatation
5. Conclusions
- The developed composite model is able to capture the non-linearity of stress–strain curves for loading and unloading paths within the small strain regime (axial strains up to 5%). For higher strains, apart from geometrically non-linear theory, several model assumptions should be refined. In particular, for the volume fraction of the constituents, appropriate evolution laws should be formulated and calibrated.
- The Prandtl–Eyring constitutive function of stress (11) is well applicable to describe the strain rate sensitivity in a wide range, from %/s to 0.1%/s.
- To capture the temperature dependence of tensile behavior from −20 °C to 80 °C, the generalized Arrhenius functions of temperature (31) are required.
- For the small strain regime (axial strains up to 1–2%), the inelastic dilatation is small and can be neglected. For higher axial strain values, the decrease in Poisson’s ratio under tension and increase it under compression are observed.
- The Drucker–Prager-type equivalent stress (9) and the flow rule (10) provide a better description of both the transverse and volumetric strains than that of the classical von Mises–Odqvist flow rules. However, for higher values of the axial strain, the non-linearity of the actual volumetric strain vs. axial strain response is not accurately captured. Furthermore, the tension compression asymmetry is underestimated.
- Non-linearity of stress responses for loading/unloading paths under different strain rates should be analyzed.
- The applicability of the model to the lower strain rate regimes of creep and stress relaxation should be examined.
- Systematic analysis of experimental data on transverse strains based on DIC measurements for a wide range of axial stains under tension and compression should be performed.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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MPa | 1536 | MPa | 1907 | ||
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Filanova, Y.; Hauptmann, J.; Längler, F.; Naumenko, K. Inelastic Behavior of Polyoxymethylene for Wide Strain Rate and Temperature Ranges: Constitutive Modeling and Identification. Materials 2021, 14, 3667. https://doi.org/10.3390/ma14133667
Filanova Y, Hauptmann J, Längler F, Naumenko K. Inelastic Behavior of Polyoxymethylene for Wide Strain Rate and Temperature Ranges: Constitutive Modeling and Identification. Materials. 2021; 14(13):3667. https://doi.org/10.3390/ma14133667
Chicago/Turabian StyleFilanova, Yevgeniya, Johannes Hauptmann, Frank Längler, and Konstantin Naumenko. 2021. "Inelastic Behavior of Polyoxymethylene for Wide Strain Rate and Temperature Ranges: Constitutive Modeling and Identification" Materials 14, no. 13: 3667. https://doi.org/10.3390/ma14133667