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Calculation of flow-induced residual stresses in injection moulded products

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Abstract

Flow-induced residual stresses that arise during the injection moulding of amorphous thermoplastic polymers are calculated in both the filling and post-filling stage. To achieve this a compressible version of the Leonov model is employed. Two techniques are investigated. First a direct approach is used where the pressure problem is formulated using the viscoelastic material model. Secondly, generalized Newtonian material behaviour is assumed, and the resulting flow kinematics is used to calculate normal stresses employing the compressible Leonov model. The latter technique gives comparable results, while reducing the computational cost significantly.

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Abbreviations

a :

scalar

a :

vector

A :

tensor

A c :

conjugate ofA

A d :

deviatoric part ofA

a.a :

dot product of two vectors

a.A :

dot product of vector with second order tensor

ab :

dyadic product

A.B :

dot product of two second order tensors

tr(A):

trace ofA

A:B :

trace ofA.B

det(A):

determinant ofA

(⩪):

column

(⩪)T :

transpose of a column

(∸):

matrix

(′):

material time derivative

(′) e :

elastic part of (′)

(′) p :

plastic part of (′)

\(\dot \gamma \) :

shear rate

ε :

specific internal energy

λ :

heat conduction coefficient

θ :

relaxation time

η :

viscosity

ρ :

density

ν :

specific volume

a T :

time-demperature shift factor

c p :

specific heat at constant pressure

J :

volume change factor

N 1 :

first normal stress difference

p :

pressure

r :

internal heat source

∇:

gradient operator with respect to current configuration

∇0 :

gradient operator with respect to reference configuration

h :

heat flux

ν :

velocity

x :

position vector

σ :

Cauchy stress tensor

τ :

extra stress tensor

D :

rate of strain tensor

F :

deformation tensor

B :

left Cauchy-Green tensor

L :

velocity gradient tensor

References

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Author information

Authors and Affiliations

  1. Philips Research Laboratories, P.O. Box 80000, 5600 JA, Eindhoven, The Netherlands

    Frank P. T. Baaijens & Lucien F. A. Douven

  2. Faculty of Mechanical Engineering, Section of Engineering Fundamentals, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Lucien F. A. Douven

Authors
  1. Frank P. T. Baaijens
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  2. Lucien F. A. Douven
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Baaijens, F.P.T., Douven, L.F.A. Calculation of flow-induced residual stresses in injection moulded products. Appl. Sci. Res. 48, 141–157 (1994). https://doi.org/10.1007/BF02027964

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  • DOI: https://doi.org/10.1007/BF02027964

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