Modelling long term behaviour of glassy polymers

Modelling long term behaviour of glassy polymers

Klompen, E. T. J., Govaert, L. E., & Meijer, H. E. H. (2002). Modelling long term behaviour of glassy polymers. Poster session presented at Mate Poster Award 2002 : 7th Annual Poster Contest.

Document status and date: Published: 01/01/2002 Document Version:

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department of mechanical engineering

Modelling long term behaviour of glassy polymers

E.T.J. Klompen, L.E. Govaert, H.E.H. Meijer

Eindhoven University of Technology, Department of Mechanical Engineering

Introduction

Long term failure of glassy polymers appears to be governed by plastic localisation phenomena. Whereas at high stresses ductile behaviour prevails, the amount of localisation in-creases with decreasing stress until finally brittle failure oc-curs (Figure 1). 100 101 102 103 104 105 106 107 108 0 10 20 30 40 50 60 70 Time to failure [s]

Applied stress [MPa]

A B C CD2000 tough brittle

Figure 1 Left: Load vs. time to failure for PC CD2000. Right: Different

kinds of failure as indicated in the left figure.

A similar transition in failure mode is also observed in short term loading. Moreover, it proved possible to give good quantitative descriptions of the short term behaviour using the compressible Leonov model [1]. Therefore the objective is to investigate the applicability of the compressible Leonov model to long term loading conditions.

Material parameters

The material parameters required for the calculations can be determined from compression data as shown in figure 2 (left).

0 0.2 0.4 0.6 0 20 40 60 80

Comp. true strain [−]

Comp. true stress [MPa]

10−4 10−3 10−2 50 55 60 65 Strain rate [s−1]

Yield stress [MPa]

experimental calculated

Figure 2 Left: True stress vs. strain for PC at rates from10 4

to10 2

s 1

, experiment and model prediction. Right: Tensile yield stress injection moulded samples.

To compensate for the different thermal history of the injec-tion moulded creep rupture samples the relevant parameters are adjusted using the tensile data in figure 2 (right).

E 790 [MPa]  0.37 [-] 0 0.56 [MPa] A0 1:4
10 27 [sec]  0.075 [-] h 190 [-] D1 38 [-] Gr 30 [MPa] Table 1 Final material

pa-rameters for simulations.

100 101 102 103 104 105 106 107 108 0 10 20 30 40 50 60 70 Time to failure [s]

Applied stress [MPa]

CD2000

experimental calculated

Figure 3 Load vs. time to failure,

experiment vs. prediction.

Observations

From the results of the numerical simulations shown in fig-ure 3 the following can be observed:

1. Time to failure

The slope of the failure curve is captured well, but failure oc-curs too early. Reason for this is the first order evolution of the strain softening, resulting in a too pronounced ing at the yield point (figure 4, left). Reducing the soften-ing strength results in an increassoften-ing time to failure (figure 4, right). A more realistic description of the strain softening would therefore improve the time-to-failure prediction con-siderably. 0 0.1 0.2 0.3 40 50 60 70

Comp. true strain [−]

Comp. true stress [MPa]

h 0 100 200 300 400 0 20 40 60 80 100 h [−] Time to failure [s]

Figure 4 Left: Close-up of the experimental data and the model

de-scription at10 3

s 1

. Right: Influence of the parameterhon the

predicted time to failure. 2. Embrittlement

Due to the absence of a brittle fracture criterion in the model, ductile failure is predicted throughout. A possible ductile fracture mechanism was proposed by van Melick [1] who ob-served an increase in yield stress upon thermal treatment. This leads to an increased load in the neck, that will fail brit-tle if this load exceeds the strength of the material (figure 5, left). Static loading appears to have a similar effect as a ther-mal treatment, see figure 5 (right).

True strain [−]

True stress [MPa]

annealed quenched 103 105 107 0 5 10 Load time [s] ∆σy [MPa] 40 MPa 45 MPa

Figure 5 Left: Effect of annealing on the deformation behaviour of

PC. Right: Increase of yield stress vs. time under static load.

Future work

2 Improve softening description and implement the

im-proved kinetics

2 Modelling of temperature and stress dependence of

ageing kinetics

2 Implementation of ageing kinetics

References: