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Thermomechanic behavior of a polymer upon its formation in a crystallization process: Theoretical principles, hypotheses, and mathematical model

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Abstract

A model of thermomechanic behavior of a polymer upon its formation in a crystallization process is proposed. Based on methods of nonequilibrium thermodynamics governing relationships are obtained which make it possible to establish the dependence of the final degree of crystallicity of the material on the “history” of the crystallization process and to explain the mechanism of formation of the remanent stresses in a polymer article.

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Abbreviations

u:

translation vector

v:

velocity vector

\(\dot v\) :

acceleration vector

θ:

absolute temperature

ϱ:

density

c :

specific heat capacity

\(\hat \varepsilon\) :

deformation tensor

\(\hat \sigma\) :

strain tensor

η:

specific enthropy

U * :

internal energy

z :

specific free enthalpy

χ i :

internal parameters of state

t :

time

q:

heat flux vector

\(\hat \kappa\) :

matrix of heat conduction coefficients

W * :

energy dissipation

F:

vector of mass forces

\(\hat \hat H\) :

the 4th rank tensor of elastic pliabilities

\(\hat \alpha\) :

matrix of heat expansion coefficients

\(\hat X_i\) :

tensor of contribution of structural variations to deformation

\(\hat \hat H^* ,\hat \alpha ^* ,c^* ,G^* ,K^*\) :

function of equilibrium value χ*

p :

mean pressure

\(\hat e\) :

deviator of the tensor of deformations

ɛ:

spherical part of the deformation tensor

\(\hat S\) :

deviator of the tensor of stresses

K :

volume modulus

\(\hat I\) :

unity tensor

Q :

enthalpy of the crystallization process

Q eq :

enthalpy of the equilibrium crystallization process

θg :

glass transition temperature

χ*(θ):

the curve obtained in the equilibrium crystallization process

χf:

final degree of crystallicity

References

  1. K. Trudcell, Primary Course in Rational Mechanics of Continuous Media [Russian translation], Moscow (1975).

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  4. A. A. Il'yushin, Mechanics of Continuous Medium [in Russian], Moscow (1978).

  5. V. N. Aptukov, Fiz. Goren. Vzryva, No. 2, 120–130 (1986).

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  6. D. Kolarov, A. Baltov, and N. Boncheva, Mechanics of Plastic Media [Russian translation], Moscow (1979).

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Authors
  1. V. N. Aptukov
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  2. S. A. Bolgov
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Additional information

Institute of Mechanics of Continuous Media of the Ural Branch of the Russian Academy of Sciences, Perm', Russia. Institute of Technical Chemistry of the Ural Branch of the Russian Academy of Sciences, Perm', Russia. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 3, pp. 479–485, May–June, 1995.

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Aptukov, V.N., Bolgov, S.A. Thermomechanic behavior of a polymer upon its formation in a crystallization process: Theoretical principles, hypotheses, and mathematical model. J Eng Phys Thermophys 68, 413–418 (1995). https://doi.org/10.1007/BF00859058

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  • DOI: https://doi.org/10.1007/BF00859058

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