Micromechanical modeling of the elastic properties of semicrystalline polymers: A three‐phase approach

Abstract

The mechanical performance of semicrystalline polymers is strongly dependent on their underlying microstructure, consisting of crystallographic lamellae and amorphous layers. In line with that, semicrystalline polymers have previously been modeled as two and three‐phase composites, consisting of a crystalline and an amorphous phase and, in case of the three‐phase composite, a rigid‐amorphous phase between the other two, having a somewhat ordered structure and a constant thickness. In this work, the ability of two‐phase and three‐phase composite models to predict the elastic modulus of semicrystalline polymers is investigated. The three‐phase model incorporates an internal length scale through crystalline lamellar and interphase thicknesses, whereas no length scales are included in the two‐phase model. Using linear elastic behavior for the constituent phases, a closed form solution for the average stiffness of the inclusion is obtained. A hybrid inclusion interaction model has been used to compute the effective elastic properties of polyethylene. The model results are compared with experimental data to assess the capabilities of the two‐ or three‐phase composite inclusion model. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2010

Micromechanical characterization of the interphase layer in semi‐crystalline polyethylene

“…As obtaining fully amorphous PE samples at relevant temperatures is nearly impossible, the reported elastic values are either based on theoretical arguments or based on extrapolation to zero crystallinity of measurements made at nonzero crystallinities. Using the theoretical relationship for the plateau shear modulus and an amorphous bulk modulus of , Bédoui et al and Sedighiamiri et al estimated the amorphous Young's modulus and Poisson's ratio to be E am = 4.5 MPa and υ am = 0.49975, respectively. In eq , ρ is the amorphous phase density, T is the absolute temperature, R is the ideal gas constant, and M e is the molecular mass between entanglements.…”

Designing polymer crystallinity: An industrial perspective

“…Studies with a certain focus on processing parameter have been extended to morphology development and modification variation like β‐phase formation in molding, but also to investigations concerning shrinkage and dimensional stability, with holding pressure found as a dominant factor for the latter. A final target is the prediction of mechanic, for which mechanical concepts regarding the crystal structure and factors like lamellar thickness and the distribution between crystalline phase, rigid and mobile amorphous phase are required . Composite inclusion models have already been demonstrated to work for both HDPE and PP, but deformation involving high strains and strain rates up to the point of failure are still out of reach except for highly idealized cases.…”

“…A logical next step should be to relate crystalline morphology to mechanics with realistic structural models. This implies progressing from continuum approaches to a more realistic image of the structure of semi‐crystalline solids while maintaining practically affordable calculation times . Multi‐phase systems either with particulate inclusions (like elastomer particles) or with more regular structure from co‐processing or phase separation will probably continue to present problems for coming years, even at least numerical work has been done already …”

“…This implies progressing from continuum approaches to a more realistic image of the structure of semi-crystalline solids while maintaining practically affordable calculation times. [22] Multi-phase systems either with particulate inclusions (like elastomer particles) or with more regular structure from coprocessing or phase separation will probably continue to present problems for coming years, even at least numerical work has been done already. [23,24] The present review will present three approaches to control crystal structure and resulting along the product design path: By modifying the polymer, by additivation and blending, and finally through the processing step.…”

Structural mechanics of semicrystalline polymers prior to the yield point: a review

“…However, structural properties are treated implicitly in this approach. Another group of papers [108][109][110][111][112][113][114][115][116][117][118][119][120][121] uses conception of two-phase continuum containing rigid and soft components (crystalline and amorphous phases) with essentially different mechanical properties. The main distinction of semicrystalline polymers from the particulate composites is their peculiar self-organized structure containing stacks of crystal lamellae alternating with thin amorphous layers.…”