The Strain Hardening of Linear and Long-Chain Branched Polymer Melts

Bastian, Heike; Rubio, P.; Wagner, Manfred H.

doi:10.1002/1522-2640(200111)73:11<1447::aid-cite1447>3.0.co;2-2

Cited by 11 publications

(9 citation statements)

References 4 publications

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“…The molecular stress function (MSF) model in Equation ( 4), which is well described in the literature [35,[39][40][41][42][43][44][45][46] represents a generalized form and further development of the model according to Doi and Edwards (DE) and is used to predict the transient elongational viscosity. The linear viscoelastic memory function m(t − t ′ ) and the time-dependent nonlinear viscoelastic deformation measure S MSF (t, t ′ ) are used to describe the current stress state σ(t) of a volume element at a certain time, taking the deformation history in the time period from time t ′ = −∞ (undeformed state) to the currently deformed state t ′ = t (observation time) into account.…”

Section: Molecular Stress Function Model Extension By Superpositionmentioning

confidence: 99%

“…The time-dependent non-linear deformation measure of the MSF model S MSF (t, t ′ ) is described by Equation ( 6) according to [34,39,41], using the quadratic molecular stress function f 2 and the deformation measure S I A DE (t, t ′ ) according to DE.…”

Section: Molecular Stress Function Model Extension By Superpositionmentioning

confidence: 99%

“…The time-dependent rate of change of the quadratic molecular stress function of the MSF model can be described using Equation (7) for polydisperse (polymers with a molar mass distribution), linear (unbranched) and branched polymers. A detailed description can be found in the literature [34,[39][40][41].…”

Section: Molecular Stress Function Model Extension By Superpositionmentioning

confidence: 99%

“…Experimental investigations have shown that β describes the slope of the transient elongational viscosity function from the beginning of the strain-hardening deformation behavior [34,46]. In the case of polydisperse linear (unbranched) polymers, β = 1, which results in the so-called LMSF model (linear MSF model) [41]. However, the model according to DE results for β = 1 and f 2 max = 1 [34].…”

Section: Molecular Stress Function Model Extension By Superpositionmentioning

confidence: 99%

“…If this is the case, the principle of superposition automatically applies [62], resulting in a transient uniaxial calibration of the MSF model. This allows the transient equibiaxial elongational viscosity function to be predicted [41].…”

Section: Bubble Growth Simulation Using the Single-cell Modelmentioning

confidence: 99%

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Prediction of the Bubble Growth Behavior by Means of the Time-, Temperature-, Pressure- and Blowing Agent Concentration-Dependent Transient Elongational Viscosity Function of Polymers

Schaible,

Bonten

2024

Polymers

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Bubble growth processes are highly complex processes, which are not only dependent on the foaming process parameters (temperature, pressure and blowing agent concentration) but also on the type and structure of the polymer used. Since the elongational viscosity at the bubble wall during bubble growth also depends on these influencing factors, the so-called transient elongational viscosity plays a key role in describing the gas bubble growth behavior in polymer melts. The model-based description of the transient elongational viscosity function is difficult due to its dependence on time, Hencky strain and strain rate. Therefore, representative viscosities or shear viscosity models are usually used in the literature to predict the bubble growth behavior. In this work, the transient equibiaxial elongational viscosity function at the bubble wall during bubble growth is described holistically for the first time. This is achieved by extending the so-called molecular stress function (MSF) model by superposition principles (temperature, pressure and blowing agent concentration) and by using the elongational deformation behavior (Hencky strain and strain rate) at the bubble wall during the initial, and thus viscosity-driven, bubble growth process. Therefore, transient uniaxial elongational viscosity measurements are performed and the non-linear MSF model parameters of the two investigated polymers PS (linear polymer chains) and PLA (long-chain branched polymer chains) are determined. By applying the superposition principles and by changing the strain mode parameter to the equibiaxial case in the MSF model, the transient equibiaxial viscosity master curve is obtained and used to describe the bubble growth process. The results show that the extended MSF model can fully predict the transient equibiaxial elongational viscosity function at the bubble wall during bubble growth processes. The bubble growth behavior over time can then be realistically described using the defined transient equibiaxial elongational viscosity function at the bubble wall. This is not possible, for example, with a representative viscosity and therefore clearly demonstrates the influence and importance of knowing the transient deformation behavior that prevails at the bubble wall during bubble growth processes.

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Section: Molecular Stress Function Model Extension By Superpositionmentioning

confidence: 99%

Section: Molecular Stress Function Model Extension By Superpositionmentioning

confidence: 99%

Section: Molecular Stress Function Model Extension By Superpositionmentioning

confidence: 99%

Section: Molecular Stress Function Model Extension By Superpositionmentioning

confidence: 99%

Section: Bubble Growth Simulation Using the Single-cell Modelmentioning

confidence: 99%

See 3 more Smart Citations

Prediction of the Bubble Growth Behavior by Means of the Time-, Temperature-, Pressure- and Blowing Agent Concentration-Dependent Transient Elongational Viscosity Function of Polymers

Schaible,

Bonten

2024

Polymers

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Review of the hierarchical multi‐mode molecular stress function model for broadly distributed linear and LCB polymer melts

Narimissa

Wagner

2018

Polymer Engineering & Sci

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We developed a novel Hierarchical Multi-mode Molecular Stress Function (HMMSF) model for linear and long-chain branched (LCB) polymer melts implementing the basic ideas of (1) hierarchical relaxation, (2) dynamic dilution, (3) interchain tube pressure, and (4) convective constraint release. With a minimum number of nonlinear free parameters and remarkable quantitative predictions of the rheology of polymer melts, this model is an outstanding option for the simulation of different processing operations in the polymer industry. The excellent predictions of this model were demonstrated in uniaxial, equibiaxial, and planar extensional deformations for linear and LCB melts, as well as in shear flow for a LCB polymer, with a minimum number of adjustable free nonlinear material parameters, that is, one in the case of extensional flows, and two in shear flow. In this contribution, we review the development of the HMMSF model and present a reduced number of welldefined constitutive relations comprising the rheology of both linear and LCB melts. We also extend the comparison of model and data to cover the shear flow of a linear polymer melt. POLYM. ENG. SCI., 59:573-583, 2019. 4. (a) In extensional flow and large strains, any CR effects are compensated by the advection of neighboring topological constraints, leading to a minimum tube diameter a and a maximum molecular stress f max . (b) In shear flow and large strains, the molecule is simply oriented in the flow direction and, due to convective CR above and below the molecular chain, the tube diameter returns to its equilibrium value a 0. Adapted from [15]. FIG.

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Comparison of the elongational behavior of various polyolefins in uniaxial and equibiaxial flows

et al. 2007

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The Strain Hardening of Linear and Long-Chain Branched Polymer Melts

Cited by 11 publications

References 4 publications

Prediction of the Bubble Growth Behavior by Means of the Time-, Temperature-, Pressure- and Blowing Agent Concentration-Dependent Transient Elongational Viscosity Function of Polymers

Prediction of the Bubble Growth Behavior by Means of the Time-, Temperature-, Pressure- and Blowing Agent Concentration-Dependent Transient Elongational Viscosity Function of Polymers

Review of the hierarchical multi‐mode molecular stress function model for broadly distributed linear and LCB polymer melts

Comparison of the elongational behavior of various polyolefins in uniaxial and equibiaxial flows

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