Composite modeling for the effective elastic properties of semicrystalline polymers

Abstract

It is established that upper and lower bounds predict results far apart from each other for the effective elastic properties of semicrystalline polymers such as polyethylene. This is manly due to the high anisotropy of the elastic properties of the crystals. Composite modeling has been used to predict intermediate results between the bounds. Here, we show the details of composite modeling based on a two phase inclusion (crystalline lamella and amorphous domain) as the local representative element of a semicrystalline polymer. Three approaches, two composite bounds, and a composite self-consistent model, are used to compute the overall elastic properties. Details of the development of these approaches are given in this paper. We find good agreement between results from these approaches and experimental results for polyethylene.

Statistical continuum theory for the effective conductivity of fiber filled polymer composites: Effect of orientation distribution and aspect ratio

“…A class of homogenization methods based on the Eshelby's theory of inclusion [12], predicts the mechanical properties of heterogeneous materials by considering an average shape of the inclusions and interaction between them [13][14][15][16][17]. To take into account more details of the microstructure, statistical continuum approaches have been developed [18][19][20][21][22][23][24][25][26][27][28][29][30].…”

Three‐Dimensional Reconstruction and Microstructure Modeling of Porosity‐Graded Cathode Using Focused Ion Beam and Homogenization Techniques

“…Composite inclusion model (CIM) developed by Ahzi et al [14,15] is another homogenization technique, which is employed here for evaluating the overall properties of the reconstructed microstructure. CIM may be seen as an extended version of the classical Voigt homogenization technique where the property tensors are weighted by certain tensor coefficients.…”

“…The weight functions Q 1 and Q 2 are calculated based on enforcing the continuity of displacement and force equilibrium at the interface of the two phases. The details of calculating these stress concentration tensors, as named by authors in [14], are available. This homogenization approach has been applied to our microstructure as described in the following lines.…”

“…In the later method, a previously developed Monte Carlo methodology based on two-point statistical functions is used for 3D microstructure realization from cross-sectional SEM images of two-dimensional (2D) phase maps (i.e., LSM and pore) [9][10][11][12]. The two-point correlation functions are used for three-point approximation and estimation of the effective elastic Young's modulus of the porosity-graded LSM cathode based on the strong contrast (SC) and the composite inclusion (CI) homogenization techniques [13][14][15]. Results from the two techniques are compared to the FEM results.…”

Microstructural effects on yield surface evolution in cubic metals using the viscoplastic ϕ-model

“…We note that the introduction of e D and e S are necessary to ensure the consistency (average) conditions (Ahzi and M'Guil, 2008). This is a well known normalization procedure in the homogenization theories (see for instance Ahzi et al, 2006;Benveniste, 1987;Walpole, 1969).…”