Comparison of micromechanical models for the prediction of the effective elastic properties of semicrystalline polymers: Application to polyethylene

Abstract

In this paper, we discuss the application of different micromechanical composite models to compute the effective elastic properties of semicrystalline polymers. The morphology of these two-phase materials consists of crystalline lamellae and amorphous domains which may form a spherulitic microstructure. The selected models are the Mori-Tanaka type models, the Double-Inclusion models, and the Self-Consistent models. We applied these composite estimates to both fully isotropic and transverse isotropic transcrystalline polyethylene. The results from these different models are compared to the experimental results for different crystallinities. The Generalized Mori-Tanaka (GMT) model and the Self-Consistent Composite-Inclusion (SCCI) model give the best predictions of the effective elastic constants compared to the other models.

Micromechanical modeling and characterization of the effective properties in starch-based nano-biocomposites

“…In the following subsections, we briefly address the micromechanical modeling. The details have been published elsewhere, such as in our previous work [17,25].…”

“…The effective elasticity tensor for N inclusions and their surrounding the matrix is given by [17]: Here A I is the strain concentration tensor (e I = A I E) and f I is the volume fraction of heterogeneities. Similarly, the stress concentration tensor, B I , and the composite effective compliance, S eff , can be derived by imposing a macroscopic stress R(r I = B I R).…”

“…This model takes into account an interaction between the inclusion and the surroundings (inclusions and matrix) through a perturbation term [14,17,26]. In their original model, the inclusions were considered to have the same shape and orientation.…”

“…Thus, to model the mechanical properties of such nanocomposites, it is necessary to replace the Young's modulus of the montmorillonite (E MMT ) by an effective stiffness modulus ðE eff MMT Þ which takes into account the affinity between the nanofiller and the matrix. We use a generalized Mori-Tanaka (GMT) model [17] to predict the effective elastic properties of the nano-biocomposites and to demonstrate the efficiency and the versatility of this model. The Young's modulus variations of starch nano-biocomposites against storage time have also been simulated.…”

A new three-phase model to estimate the effective elastic properties of semi-crystalline polymers: Application to PET

“…For instance, the statistical continuum approach based on the use of probability functions to characterize the media (Adams et al, 1987;Beran et al, 1996;Lin and Garmestani, 2000) and also the continuum mechanics approaches which are based on the Eshelby's theory of an inclusion embedded in an equivalent continuum medium or in a matrix (see for instance : Eshelby, 1957;Benveniste, 1987;Mori and Tanaka, 1973;Hori and Nemat-Nasser, 1993;Ahzi et al, 1995Ahzi et al, , 2007Nemat-Nasser and Hori, 1999;Aboutajeddine and Neale, 2005;Lipinski et al, 2006;Gueguen et al, 2008;El Mouden and Molinari, 1996;Molinari and El Mouden 1996;Hu and Weng, 2000;Ponte Castaneda and Willis, 1995). Application of these approaches to compute the effective mechanical properties of semi-crystalline polymers is currently limited.…”