Micromechanical modeling of isotropic elastic behavior of semicrystalline polymers

doi:10.1016/j.actamat.2005.11.028

Acta Materialia

Volume 54, Issue 6, April 2006, Pages 1513-1523

https://doi.org/10.1016/j.actamat.2005.11.028 Get rights and content

Abstract

Considering semicrystalline polymers as heterogeneous materials consisting of an amorphous phase and crystallites, several micromechanical models have been tested to predict their elastic behavior. Two representations have been considered: crystallites embedded in a matrix and a layered-composite aggregate. Several homogenization schemes have been used in these representations. Firstly, comparisons between the models and experiments show that the micromechanics approach applies at this scale. Secondly, the results differ according to the rubbery or glassy state of the amorphous phase. Finally, the results suggest that the spherulitic mesostructure does not affect the material behavior while infinitesimal elastic strains are considered.

Introduction

Semicrystalline polymers are increasingly being used as structural materials. Much work has focused on the prediction of the crystallinity and microstructure morphology of these materials [1], [2], [3], [4], and several methods have been developed to characterize this microstructure by optical microscopy or scanning electron microscopy (SEM) after an etching processing [5] or by X-ray scattering [6]. Less work has been done in terms of relating the microstructure to the mechanical behavior. Semicrystalline polymers may be considered as heterogeneous materials, and micromechanical models can be used to estimate or predict their mechanical properties. Recent work [7], [8], [9], [10] has explored this area, focusing on large-strain-scale elastoplastic or elastoviscoplastic behaviors. Very little work has been done at the small-strain level [11]. Even less is known about the elasticity of these materials.

Previous work [12] has made it possible to understand a paradox involving polypropylene (PP) and polyethylene (PE) using micromechanical modeling. It has been shown that using a micromechanics approach may help explain why PP is more rigid than PE despite a lower crystallinity and less rigid amorphous and crystalline phases. Beyond this qualitative result, the applicability of micromechanical modeling for the quantitative prediction of the elastic properties of semicrystalline polymers remains an issue. In order to decide whether micromechanical modeling applies at the scale of the crystallites, three semicrystalline polymers are considered: an isotactic PP, a PE, and a polyethylene terephthalate (PET) crystallized by annealing. Firstly, the mechanical properties of the homogeneous materials were measured and the results considered in terms of crystallinity. Secondly, the microstructure was observed and the crystallite lamellae dimensions were estimated when possible. Finally, considering two schematic representations and several homogenization schemes, the estimates of the models were compared with experimental data.

Section snippets

Mechanical properties

Three commercial homopolymers were chosen for this study: a PP (ELTEX PP HV 252) and a high-density PE (HD6070 EA) supplied by Solvay, and a PET (ARNITE 00D301) supplied by DSM. We are interested in the elastic isotropic behavior of these materials, and thus we focus on measurements and estimates of Young’s modulus. A few Poisson’s ratio values were also estimated.

PP plates with a thickness of 1 and 3 mm were obtained by injection molding. Isotropic samples were taken from the core of the

General theory

Considering semicrystalline polymers are heterogeneous materials, micromechanical modeling is used to estimate the mechanical properties of equivalent homogeneous materials. Two material representations are commonly used for polymers. The first representation is the model arising from the Eshelby inclusion theory [35] for which the reinforcing phase of ellipsoidal shape is embedded in a matrix. In the present case, crystalline lamellae are the reinforcing phase while the amorphous phase is the

Results

For both PP and PE there is a strong contrast between the mechanical behaviors of the two constitutive phases. PP morphology is relatively well estimated in Section 2.1.2, and none of the inputs required by micromechanical modeling is unknown. Considering PE, the crystallite dimensions, which provide inclusion shape ratios, remain unknown. However, Young’s modulus of the homogeneous material has been measured for a large range of crystallinity, which provides a good database to estimate the

Conclusion

In this paper we have compared several micromechanical models in order to study the applicability of micromechanical modeling at the nanoscale of crystallites of semicrystalline polymers in the context of elasticity. For this purpose, three commonly used semicrystalline polymers have been considered: PP, PE, and PET. Comparisons between experiment and the models have shown that the micromechanical approach may be applicable for semicrystalline polymers. More precisely, a very good estimate of

Acknowledgements

The authors are grateful for the helpful discussion on theoretical aspects of homogenization with M. Pierre Gilormini. We very much thank M. Carlos N. Tomé for sharing some of his numerical routines, which have significantly increased the accuracy of our results.

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