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Modulus-maps for amorphous polymers

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Abstract

This paper explores the possibility of constructing modulus-mechanism maps for amorphous polymers. Four regimes are identified: the glassy regime, the visco-elastic regime, the rubbery regime and the regime of viscous flow (melting), truncated by decomposition. Constitutive laws for each regime are assembled and adapted to give a good description of a large body of experimental data for amorphous polymethylmethacrylate and polystyrene. The adjusted laws are then used to construct diagrams which relate the time and temperature-dependent modulus,E(t, T), to the temperature and the loading time (or frequency). The diagrams are divided into fields corresponding to the four regimes. A diagram summarizes the small-strain mechanical behaviour of the polymer over a wide range of conditions.

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Abbreviations

T :

Temperature (K)

σ :

Tensile or compressive stress (MPa)

ε :

Tensile or compressive strain

∴ε :

Tensile or compressive strain rate (sec−1)

t :

Time (sec)

Ν :

Frequency (sec−1)

E :

Time and temperature dependent Young's modulus (GPa)

E 0 :

Modulus of 0 K (GPa)

αm :

Temperature coefficient of modulus

T g :

Glass temperature (K)

T D :

Depolymerization temperature (K)

¯M w,M cr,¯M e :

Molecular weights (kg mol−1)

Q m :

Mean activation energy (kJ mol−1)

δQ/Q m :

Fractional standard deviation of activation energy

δE/E 0 :

Fractional modulus drop at a transition

a T :

Shift factor for time-temperature equivalence

η :

Viscosity (Nsec m−2)

η 0 :

Pre-exponential for viscosity (Nsec m−2)

αg, αv :

Bulk thermal expansion coefficient below and aboveT g (K−1)

C 1,C 2 :

WLF constants (-, K)

ρ :

Density (kg m−3)

f v :

Fractional free volume

V(ε) :

Internal energy per unit volume (J m−3)

R :

Gas constant (8.314 J mol−1 K−1)

Ν 0 :

A pre-exponential frequency factor (sec−1)

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Authors and Affiliations

  1. BP Research Centre, Chertsey Road, TW16 7LN, Sunbury-on-Thames, Middlesex, UK

    D. G. Gilbert

  2. Engineering Department, Cambridge University, Trumpington Street, CB2 1PZ, Cambridge, UK

    M. F. Ashby & P. W. R. Beaumont

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  1. D. G. Gilbert
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  2. M. F. Ashby
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  3. P. W. R. Beaumont
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Gilbert, D.G., Ashby, M.F. & Beaumont, P.W.R. Modulus-maps for amorphous polymers. J Mater Sci 21, 3194–3210 (1986). https://doi.org/10.1007/BF00553357

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