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

  • V. N. Aptukov
  • S. A. Bolgov
Article
  • 17 Downloads

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.

Keywords

Polymer Crystallization Mathematical Model Statistical Physic Crystallization Process 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notation

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

χi

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

Qeq

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

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References

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    K. Trudcell, Primary Course in Rational Mechanics of Continuous Media [Russian translation], Moscow (1975).Google Scholar
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    R. Kristensen, Introduction to Composite Mechanics [Russian translation], Moscow (1982).Google Scholar
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    B. D. Coleman, M. E. Gurtin, J. Chem. Phys.,47, No. 2, 597–613 (1967).Google Scholar
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    A. A. Il'yushin, Mechanics of Continuous Medium [in Russian], Moscow (1978).Google Scholar
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    V. N. Aptukov, Fiz. Goren. Vzryva, No. 2, 120–130 (1986).Google Scholar
  6. 6.
    D. Kolarov, A. Baltov, and N. Boncheva, Mechanics of Plastic Media [Russian translation], Moscow (1979).Google Scholar
  7. 7.
    A. Ya. Malkin, V. P. Begishev, I. N. Shardakov, et al., Vysokomolekulyarnye Soedineniya, AXXIX, No. 9, 1992–1999 (1987).Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • V. N. Aptukov
  • S. A. Bolgov

There are no affiliations available

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