Application of Catastrophe Theory to the Neck-initiation of Semicrystalline Polymers Induced by the Intercluster Links

Abstract

ABSTRACT:This paper deals with the neck initiation in semi-crystalline polymers having lamellar clusters connected by the intercluster links composed of extended-chain bundles as demonstrated by electron microscope pictures of polyethylene and polypropylene. When semicrystalline polymers are uniaxially deformed at a constant rate, the necking is usually initiated and the necking zone propagates at a constant speed along the sample specimen. The necking initiation is explained in this paper by a first order catastrophic phase transition in analogy of the model of van der Waals gas. Catastrophic arrangement of the intercluster links results in sudden emergence of the locally oriented region which will be a seed of the neck formation in further deformation. The analysis succeeded in phenomenological indications of the critical condition determining whether the deformation is accompanied by neck or not. 1 The necking phenomena, i.e., formation of localized ordering within a uniaxially stretched specimen have been widely observed and studied in many polymeric systems. In semicrystalline polymers such as polyethylene (PE) and polypropylene (PP), necking is associated with large-scale morphological transformation from isotropic spherulitic to anisotropic fibril structures accompanied by the destruction and/or rearrangement of the parts of the crystals. The yield point appeared as the maximum point of the nominal stress -elongation curves, accompanied by a lot of microshear bands. Beyond the yield point, the shear bands coalesce into a well-defined neck, the boundary of which propagates under essentially constant flow stress.2 Finally when the necking boundaries have propagated throughout the entire length of the specimen, the deformation will exhibit the character of strain hardening, and the specimen will break.When the specimen is extended at conventional elongation speed, a rise of temperature occurs in the region of the neck. It has long been considered that heterogeneous deformations in necking are caused by the local adiabatic heating. However, Brauwer-Müller 3 and Lazurkin 4 found that necking still take place under quasi-static conditions at very slow extension rates. Vincent 5 and Allison-Ward 6 demonstrated that the increase in temperature is quite small and the adiabatic temperature is not sufficient to give an explanation for necking. Further studies showed that when a necked specimen is heated up to melting temperature, shrinkage is observed which finally results in a recovery of the shape before necking. This forced elasticity effects strongly suggests the existence of molecular networks which have been formed during crystallization of the isotropic sample and the structure of which seems not to be modified significantly during deformation. Detail discussion of these phenomena is found in the text by Strobl.It is well known that the deformation of the sample is homogeneous up to the yield point 8 whereas once a neck forms, the deformation is inhomogeneous and large strains are involved in the neck. Accord...

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