Equation of state of real networks

Kilian, H. G.

doi:10.1016/0032-3861(81)90200-7

Cited by 134 publications

(80 citation statements)

References 25 publications

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“…These structural features of ICL units in the neck region are strongly supported by the transmission electron microscope (TEM) results of Kanig 24 who found that a network of fibers cross-linked by crystal blocks is formed on deformed PE films. Kilian et al [14][15][16] also identified stacks of several lamellae running parallel to one another and forming clusters, on the basis of TEM observations of a uniaxially deformed PE. Moreover, they showed that the stress-strain curves of a molecular Figure 1 Relationship between tensile stress-extension ratio curve and shape of the specimen.…”

Section: Theorymentioning

confidence: 99%

“…K-h Nitta and M Kuriyagawa network model with bulky junction points can be described by a van der Waals type of equation, 15 and applied this equation to the stressstrain curves of some PE materials. 14 The existence of network structure formed during crystallization of the isotropic PE samples has also been shown experimentally in the textbook by Strobl.…”

Section: Application Of Catastrophe Theorymentioning

confidence: 99%

“…Erickson 13 showed that a remarkable analogy can be made between the necking process of a forced elastic bar and a phase transition in a van der Waals gas. Kilian et al 14,15 showed that the constitutive relation of semicrystalline polymers can be expressed by the extension of the ideal gas model to the van der Waals equation where bulky fragmented lamellar clusters are assumed to behave as junction points. 16 Based on these excellent theoretical considerations, Nitta-Takayanagi 17 explained the initiation of a neck by the mathematical fact that the van der Waals equation shows a first-order catastrophic phase transition.…”

Section: Introductionmentioning

confidence: 99%

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Application of catastrophe theory to neck initiation of metallocene-catalyzed high-density polyethylene

Nitta

Kuriyagawa

2011

Polym J

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This paper examines the initiation of necking in a metallocene-catalyzed high-density polyethylene. When the specimen is uniaxially deformed, the necking is usually initiated between the first and second yield points, and the neck is stabilized at the second yield point. The initiation of necking was explained by a first-order catastrophic phase transition analogous to the model of a van der Waals gas. At the first yield point, the stacked lamellar clusters are fragmented into cubic cluster units of single chain size; the rearrangement of these units under uniaxial tension produces the texture of necking. Catastrophic arrangement of the cluster units results in a sudden emergence of a locally close-packed layer structure. This is the precursor of necking, and several layered plates are stabilized at the second yield point. The layered plate collapses via sliding of the cubic units by means of the interchain links, to form macroscopic neck; the plate thus behaves as a unit for the necking process. The continual collapse from one plate to another corresponds to the neck propagation.

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Section: Theorymentioning

confidence: 99%

Section: Application Of Catastrophe Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Application of catastrophe theory to neck initiation of metallocene-catalyzed high-density polyethylene

Nitta

Kuriyagawa

2011

Polym J

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“…There are a number of models which have been used to describe the non-linear relation of stress-strain in rubbers, of which the most important models are Arruda-Boyce [25], Ogden et al [26], Polynomial (Neo-Hookean, Yeoh, Mooney-Rivlin,..) [27], Van der Waals [28].…”

Section: Hyperelastic Constitutive Model For Rubbermentioning

confidence: 99%

Thermomechanical analysis of an aircraft tire in cornering using coupled ale and lagrangian formulations

Kondé¹,

Rosu

Lebon

et al. 2013

Open Engineering

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Abstract:The thermomechanical behavior of an aircraft tire is predicted, using experimental devices, a model based on finite element software and an appropriate method of expressing the heat generated by skid in terms of the local friction coefficient, depending on the temperature. In the thermomechanical model, a steady state mechanical analysis is combined with a transient thermal problem. This combined approach is based on three main computing steps: the deformation step, the dissipation step and the thermal step. The deformation step calculates the stress and the velocity fields, which are used as inputs in the dissipation step to calculate the heat generated due to friction. The internal dissipation is assumed to be negligible. Finally, the thermal step yields new thermal maps based on the heat flux computed in the dissipation step. The coupling is established by updating the friction coefficient in the first two steps.

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“…32 It should be noted here that the extent of deformation is given by the deviatoric strain in the case of uniaxially stretched Gaussian network. 33 Heise-Kilian et al 23 showed that the constitutive relation of semicrystalline polymers can be expressed by the extension of the ideal gas model to the van der Waals equation. The constitutive relation of the network component can be obtained in the same manner as presented by the construction of the van der Waals equation:…”

Section: Theoretical Partmentioning

confidence: 99%

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

Nitta

Takayanagi

2006

Polym J

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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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Equation of state of real networks

Cited by 134 publications

References 25 publications

Application of catastrophe theory to neck initiation of metallocene-catalyzed high-density polyethylene

Application of catastrophe theory to neck initiation of metallocene-catalyzed high-density polyethylene

Thermomechanical analysis of an aircraft tire in cornering using coupled ale and lagrangian formulations

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

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