Issue 62

M. Tedjini et alii, Frattura ed Integrità Strutturale, 62 (2022) 336-348; DOI: 10.3221/IGF-ESIS.62.24

(b)

(a)

1.6

Exponential Polynomial Power

1.6

1.4

1.4

Exponential Polynomial Power

1.2

1.2

Creep strain (%)

Creep strain (%)

1.0

1.0

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

1E ‐ 02

1E+00

1E+02

1E+04

1E+06

1E+08

0.0E+00

2.0E+07

4.0E+07

6.0E+07

8.0E+07

Log t (s)

Time (s)

Figure 7: Effect of extrapolation techniques on the prediction of the long term creep, (a) logarithmic time scale, (b) linear time scale.

Polynomial Power Exponential Polynomial fit, R 2 =0.999

4,0

3,5

3,0

1,5 Shift factor, log(   ) 2,0 2,5

1,0

0,5

0,0

0

5

10

15

20

25

30

 -  0 (MPa)

Figure 8: Effect of extrapolation functions on the activation volume

Activation volume The activation volume can be presented as the slope between the log (   ) and the accelerator stress variables, Fig. 8. A parabola trends with a coefficient of determination equal to R 2 =0.999 have been derived from the different fitting functions using experimental data. However, when assessing the quadratic function, the coefficient of the quadratic term is too small compared to the linear term. Instead, a very close linear form can be addressed with (R 2 =0.994). It should be noted that, a parabolic form has been adopted by the co-authors [15], which was shown to be more consistent with the Eyring model given in Eqn. 6, and agree well with the previous results, further details are given in [17]. Therefore, the slightly linear variation in the activation volume of each increased stress creates new configuration of molecular chains. The current chain configuration is a build-up of all the previous creep bearings. The fact that the polymer molecules are continuously pulled during the creep process, the creep behavior of a previously strained material occupies a larger activation volume than an unstrained material [15].

C ONCLUSIONS

I

n the present research, the Stepped Isostress Method is used to predict the long-term creep behavior of moderately thick specimens of polyamide 6. Different empirical model were considered to simulate the strong nonlinearity of the viscoelastic behavior of the considered material under a piecewise constant stress. A third degree polynomial, power and exponential fitting functions are developed and examined trough the construction of the master curve. The assessment of the suggested parameters of the fitted models requires an improved numerical solving method to be considered. The use of Levenberg-Marquardt algorithm allows to overcome the limited use of data points in extrapolation

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