Abstract

AbstractThe paper is concerned with stress transmission in and around the molecular ties which connect lamellae in many semicrystalline polymers. Assuming a continuum model, finite element calculations have been performed to investigate stresses and displacements for a cylindrical tie embedded in a sheath of lamellar crystal. Two specific cases were studied: the single‐ended case where the tie enters the lamella from one side only, and the double‐ended case where it passes right through the lamellar crystal. Elastic constants for crystalline polyethylene were assumed, and a variety of different geometries were investigated, corresponding to single‐chain or multichain ties with sheaths of various diameters. The finite element study confirmed that the distance for stress diffusion from the tie into the lamellar sheath can be quite large, and that there are significant displacements due to tensile deformation of the tie within the crystal and shear deformation of the lamellar sheath. An interesting feature in the case of multichain ties is that tensile stress is concentrated around the outer surface of the tie. An analytical model is proposed, based upon shear lag theory. This model considers only the tensile stresses in the tie and the shear stresses in the sheath, and gives results which are fairly similar to those of the finite element calculations. Finally, the results of this study are applied to the problem of stress transmission in an oriented polymer having a lamellar structure. The main factors influencing stress transmission are: (i) the ratio G/E of the crystalline phase; (ii) the ratio of tie radius to lamellar crystal thickness; and (iii) the proportion of ties in the interface. By examining the range of values which (ii) and (iii) may take, it is concluded that the effective stiffness of intercrystalline ties can only be about 0.25 to 0.7 of the theoretical chain stiffness in most cases.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.