Heat capacities and volumetric changes in the glass transition range: a constitutive approach based on the standard linear solid

Lion, Alexander; Mittermeier, Christoph; Johlitz, Michael

doi:10.1007/s00161-016-0551-9

Cited by 14 publications

(2 citation statements)

References 24 publications

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“…Secondly, below θ g , the time constant τ f in Equation becomes very large. Hence, δ f effectively freezes, even if it is out of equilibrium . The Doolittle approach consequently implies that the viscosity does not change below θ g .…”

Section: Modeling Of Viscoelastic Materials Behavior Of Polymer Matricmentioning

confidence: 64%

“…Another approach is to estimate the free volume by relating pressure, temperature and volume data to constitutive equations of state, see for example, White and Lipson and Dlubek et al In the context of thermomechanical modeling, the core volume v f = v f ( p , θ ) is assumed to behave purely elastically and depends only on the present values of temperature θ and pressure p , while the free volume v f creeps towards an equilibrium state v f ∞ = v f ∞ ( p , θ ) over time . This mechanical behavior can be described with the rheological Poynting‐Thomson model depicted in Figure A, which relates dilation:

δ : = tr false(ε false) = \frac{v - v_{0}}{v_{0}},

to hydrostatic pressure:

p : = - \frac{tr false(σ false)}{3} .

…”

Section: Modeling Of Viscoelastic Materials Behavior Of Polymer Matricmentioning

confidence: 99%

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Dynamic mechanical analysis of pure and fiber‐reinforced thermoset‐ and thermoplastic‐based polymers and free volume‐based viscoelastic modeling

et al. 2018

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Fiber‐reinforced polymer composites have gained significant importance in engineering applications and are widely used as structural components. The optimal choice of combinations of the type of polymer matrix and the fiber content depend on the required applications. In view of this, polypropylene (PP), a thermoplastic, reinforced with 30 wt.% of short glass fibers (PP‐GF30) is considered for this study. Additionally, a rather new composite system based on unsaturated polyester‐polyurethane hybrid resin (UPPH) is introduced. This thermoset‐based material is reinforced with 41 wt.% of long discontinuous glass fibers (UPPH‐GF41). Dynamic mechanical analysis (DMA) is performed on the pure polymer and the composite samples to experimentally characterize the temperature‐ and frequency‐dependent material behavior. It is observed that the stiffness of the materials is highly temperature‐dependent. PP exhibits a nonlinear viscoelastic behavior in the temperature range of possible applications whereas the UPPH material shows a less pronounced behavior. The resulting experimental data not only give general information on the material behavior of the composite subjected to a temperature and frequency load but also provide input as well as validation data for the developed material modeling methods. In an industrial environment, homogenized elastic material properties are desirable for analysis of the structural components at room temperature conditions. A mean field homogenization method is introduced to estimate the effective elastic material properties on a macroscopic scale. This method is formulated explicitly in terms of orientation tensors of second‐ and fourth‐order, describing quantitatively the microstructure of the corresponding composite. Additionally, the thermoviscoelastic material behavior for the considered temperature range is modeled by the free volume concept. In this context, the material parameters for the pure PP and UPPH material are identified. The calculated simulation results are compared with the experimental data entailing good agreements.

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Section: Modeling Of Viscoelastic Materials Behavior Of Polymer Matricmentioning

confidence: 64%

δ : = tr false(ε false) = \frac{v - v_{0}}{v_{0}},

to hydrostatic pressure:

p : = - \frac{tr false(σ false)}{3} .

…”

Section: Modeling Of Viscoelastic Materials Behavior Of Polymer Matricmentioning

confidence: 99%

Dynamic mechanical analysis of pure and fiber‐reinforced thermoset‐ and thermoplastic‐based polymers and free volume‐based viscoelastic modeling

et al. 2018

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The Logistic Function in Glass Transition Models of Amorphous Polymers: A Theoretical Framework for Isobaric Cooling Processes

Corbisieri

2024

Macro Theory & Simulations

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Studying the macroscopic‐phenomenological behavior of amorphous polymers at glass transition is often subject to limitations because the ordinary differential equations that describe the material behavior require numerical solution. To avoid these limitations, ad‐hoc‐formulated models of the glass transition have been proposed. However, their scope of application is expected to be limited due to insufficient theoretical foundation. This work establishes a theoretical framework for models that use the logistic function to approximate the macroscopic‐phenomenological behavior of amorphous polymers at glass transition. For this purpose, an exactly‐solvable Riccati equation is derived within thermodynamics with internal state variables. A closed‐form expression in terms of mathematical functions for the temperature derivative of a single internal state variable is the result. This closed‐form expression contains the logistic function thus featuring a continuous transition region centered around a pressure and cooling‐rate dependent transition temperature. Based on comparison of existing models with the exact solution derived from the Riccati equation, generalized models that approximate the thermal expansion coefficient and heat capacity at glass transition are proposed. This work thus demonstrates the validity of the logistic function in glass transition models of amorphous polymers and provides suggestions as to how existing models can be extended in their applicability.

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An Adam‐Gibbs based model for the temperature behavior of polymers near glass transition

Wicht

Kehrer

Wood

et al. 2018

Proc Appl Math and Mech

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The mechanical behavior of polymers and other glass forming materials is strongly time-and temperature-dependent. Based on the rheological Poynting-Thomson Model and the Adam-Gibbs equation, a shift function is developed which relates the time constants of a material to temperature. The behavior of this function is compared to the established Williams-Landel-Ferry and Arrhenius equations in the glassy and rubbery temperature regimes.

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Heat capacities and volumetric changes in the glass transition range: a constitutive approach based on the standard linear solid

Cited by 14 publications

References 24 publications

Dynamic mechanical analysis of pure and fiber‐reinforced thermoset‐ and thermoplastic‐based polymers and free volume‐based viscoelastic modeling

Dynamic mechanical analysis of pure and fiber‐reinforced thermoset‐ and thermoplastic‐based polymers and free volume‐based viscoelastic modeling

The Logistic Function in Glass Transition Models of Amorphous Polymers: A Theoretical Framework for Isobaric Cooling Processes

An Adam‐Gibbs based model for the temperature behavior of polymers near glass transition

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