New mathematical models for predicting the lifetime of EPDM insulators: Effect of elongation at break on the kinetic degradation of EPDM insulators subjected to thermo-oxidation

Received Jul 17, 2018 Revised Sept 9, 2018 Accepted Oct 16, 2018 Ethylene propylene diene monomer (EPDM) is an important polymer extensively exploited in plasturgy. However, relatively few studies have been carried out to predict the lifetime of EPDM in different climatic conditions particularly, thermo-oxidation. Based on this realization, the aim of the present work was to develop mathematical models for predicting the lifetime of EPDM elastomers, used for insulation of electric cables.


Introduction
The ethylene propylene diene monomer (EPDM) rubbers, obtained by polymerization, are synthetic copolymers of the elastomer family [1].They are composed mainly of ethylene, propylene and a small proportion of diene.Due to their outstanding resistance to aging (thermal, atmospheric, radiative), EPDM elastomers are widely used in plasturgy [2].Indeed, they are used mainly for joints and insulation (car, roofing, cables, etc.).Today, EPDM production is growing exponentially.EPDM elastomers are widely exploited in the industry and therefore it is considered expedient to estimate the in-service lifetimes of such rubbers [3][4].The modelling of the kinetic degradation of EPDM under the influence of climatic factors (e.i.heat [5], UV radiation [6][7][8] and ozone [9]) was the subject of several studies to determine their lifetime.However, in contrast, there appears to be relatively little work carried out on the effects of thermal aging (thermo-oxidation) on the kinetic degradation of EPDM [10][11][12].
In view of the deficiencies concerning work carried out in past on degradation of EPDM elastomer, the objective of this work was to demonstrate the influence of thermal aging on the kinetic degradation of EPDM used for insulation of electric cables by predicting half-life times.Kinetic degradation was followed by monitoring changes in elongation-at-break as a function of exposure times.Mathematical kinetic models were employed in an attempt to simulate thermos-oxidative degradation.

Materials
-The ethylene propylene diene (EPDM) elastomers used for preparation the two insulators were: A semi-crystalline EPDM manufactured by Dow chemical Company under the trade name Nordel IP 3722P, composed of 70.5% by weight of ethylene, 29% of propylene and 0.5 % of 5-ethylidene-2-norbornene (ENB).Its density, specified by the manufacturer, is 0.88 g.cm and Mw =100 000 g/mol.An amorphous EPDM manufactured by Dow chemical Company under the trade name Nordel IP 4520, composed of 50% by weight of ethylene, 45% of propylene and 5 % of 5-ethylidene-2-norbornene (ENB).Its density, specified by the manufacturer, is 0.86 g.cm Mw (g/mol) and the mass-average molar mass Mw =115 000 g/mol.

Sample preparation
We prepared a square sheet at the National Company of Plastic and Rubber (ENPC) of Setif, Algeria.The mixing of the raw materials (elastomeric load, plasticizers and implementation agents) at 80 ° C, for half an hour was carried out using a cylinder mixer.After obtaining, the homogeneous mixture in the form of a sleeve and adding the crosslinks agent, the mixture was removed from the cylinder.The removed mixture was allowed to cool before proceeding to the vulcanization stage.Vulcanisation was carried out using compression-moulding techniques.Square sheets (200 × 200 × 2.0 mm) were moulded at 180°C using a cure time of 10 minutes and a compression force of 300 kN.

Mechanical tensile tests
The ℇ r measurements were carried out using a universal traction machine of the "INSTRON MODEL 1185" type, according to the ASTM D882 standard.A strain-rate of 100 mm/minute was used.An average of five trials was performed to confirm the experimental results.Elongation at break was determined using the "equation (1)," [13][14]: Where: L 0 : Initial length of the specimen; L: Length of the specimen at break; ℇ r : Percent elongation at break;

Accelerated aging (thermo-oxidation)
Dumbbell tensile test-pieces (type H 2 ), as shown in "Fig.1," were used throughout the present study.Testpieces were placed in circulating air-ovens; the temperatures used were 70, 90, 110 and 130°C.During the heating regime, test-pieces were removed at selected regular intervals and tested.Tests were carried out in triplicate.

Modelling
There are many ways for the modelling of physico-chemical phenomena among these methods: the general linear model (GLM) and the design of experiment [13], in our work, the best approach for the modelling of the kinetic degradation of EPDM insulators is the GLM.The most common general linear model used are derived from the general form given in "equation ( 2)," and "equation (3)," [14-15]: ( With: Y: aging parameter; X: exposure time; C j : Model Coefficients to be calculated (j =1… m); m: Number of coefficients; f j (X) : Regular Function, which may be in one of the following forms given in 4, 5, 6 and 7:

Logarithmic
2.5.4.Trigonometric (7) In this study, X is the exposure time and Y is the ℇ r .We developed a model based on linear multiple regression analysis (LMRA) to predict ℇ r .The linear systems resulting from LMRA were resolved using the Cholesky method.The modelling process consisted of changing the parameter m in the range [ Our experimental results can be fitted well to a Gaussian [16].

Hardware and software used
To complete the work of modelling, we used a standard computer with a Intel (R) core (TM) i3-4160 CPU 3.60 GHz (4 CPUs) processor, a hard disk of 500 GB capacity and 4096 MB of RAM at the Laboratory of Applied Chemistry at the Centre for Biotechnology Research, Constantine.All our programs are written in MATLAB R2009b (64bit).

Results and discussions
The effect of thermo-oxidation at 70, 90, 110 and 130 ° C on the mechanical properties of EPDM insulators was evaluated by measuring the change in the percent ℇ r as a function of the exposure time.The choice of ℇ r is justified by its sensitivity to degradation.Conventionally, when the ℇ r is a physical quantity widely used to measure the degradation and loss of 50% of the ℇ r , which determines the half-life time of the material [14][15] .Conventionally, when the reaches 50% of that of the clean sample, the material is deemed out of service.
The change in the percent ℇ r as a function of the exposure time for the semi-crystalline EPDM insulator and the amorphous EBDM insulator are shown in "Fig.2," and "Fig.3," respectively.Before aging, the elongation at break values of the semi-crystalline EPDM insulator and the amorphous EBDM insulator was 262 and 234 % respectively.This result is consistent with the recommendations of IEC 60502 standard, which requires a minimum value of 200% at 20 ° C.After aging, from "Fig.2," and "Fig.3," it was found that the elongation began to increase from the initial value (before aging) to reach a maximum value and then a regression with a sudden drop was observed.This decrease is all the faster as the temperature of aging is greater (110 and 130 ° C) [17].
The increase in ℇ r during the first exposure times has been attributed to the improvement in insulator quality due to crosslinking.The sudden drop in ℇ r was explained by the chain scission reactions [18][19][20].This phenomenon causes a decrease in the average molecular weight and in the degree of crosslinking on the one hand and in a loss of plasticizers on the other hand.Indeed, the chain scission process increases the mobility of the chains [21][22].
From the curve of "Fig.2," and "Fig.3,", the half-life times of the two insulator was estimated at 9544, 3316, 1868 and 608 hours for semi-crystalline EPDM insulator and 5972, 2516, 1468 and 272 hours for the amorphous EPDM insulator exposed to 70, 90, 110 and 130 ° C respectively.

For the amorphous EBDM insulator
In thermo-oxidation at 70 ° C (12)          -The residual variances tends to zero.This confirms that all the information about the model are appropriate.
-The values obtained of the coefficient of determination is closer to one, which confirms a good fit.
-The calculated values of Student's tests indicate that all the model coefficients are retained because they are higher than the tabulated value.

Estimated half-life time of EPDM by simulation
Table 11 presents the results of the half-life times for the EPDM insulators, obtained in thermo-oxidation.
From the results recorded in Table 11, we observe good agreement between the observed values and the values predicted by the models.The degradation kinetics of EPDM insulators are influenced by the increase in the temperature [23,24].
Table 11.Comparison between the observed and predicted values of the HLT for EPDM insulators.

Conclusion
The results of our work showed that the polynomial models developed to predict the Half-life time of EPDM elastomers, used for insulation of electric cables under thermo-oxidation are reliable.These models are validated by various statistical criteria.Indeed, the results indicate a low residual variance, a coefficient of determination close to unity, and high values of Student coefficients and Fisher-Snedecor.The half-life time values predicted by the models are very close to those obtained experimentally.Finally, the polynomial models developed in our study can contribute to predict the half-life time of EPDM elastomers, used for insulation of electric cables.However, their applicability is likely valid only in an interval of time which depends on the exposure conditions.This requires knowledge of aging mechanisms and kinetics to develop a realistic lifetime model.In perspective, we suggest using the design of experiment (DOE) to develop mathematical models to predict the life time of EPDM insulators, then compare the results obtained by the both (GLM and DOE) methods.

Figure 2 .
Figure 2. Elongation at break as a function of exposure time for semi-crystalline EPDM insulator, in thermooxidation at 70, 90, 110 and 130°C.

Figure 3 .
Figure 3. Elongation at break as a function of exposure time for amorphous EPDM insulator, in thermooxidation at 70, 90, 110 and 130°C.

Figure 4 .
Figure 4. Comparison between the observed and predicted values of elongation at break for semi-crystalline EPDM insulator, in thermo-oxidation at 70 °C.In thermo-oxidation at 90 ° C

Figure 5 .
Figure 5.Comparison between the observed and predicted values of elongation at break for semi-crystalline EPDM insulator, in thermo-oxidation at 90 °C.In thermo-oxidation at 110 ° C

Figure 6 .
Figure 6.Comparison between the observed and predicted values of elongation at break for semi-crystalline EPDM insulator, in thermo-oxidation at 110 °C.In thermo-oxidation at 130 ° C

Figure 7 .
Figure 7.Comparison between the observed and predicted values of elongation at break for semi-crystalline EPDM insulator, in thermo-oxidation at 130 °C.

Figure 8 .
Figure 8.Comparison between the observed and predicted values of elongation at break for amorphous EPDM insulator, in thermo-oxidation at 70 °C.In thermo-oxidation at 90 ° C

Figure 9 .
Figure 9.Comparison between the observed and predicted values of elongation at break for amorphous EPDM insulator, in thermo-oxidation at 90 °C.In thermo-oxidation at 110 ° C

Figure 10 .
Figure 10.Comparison between the observed and predicted values of elongation at break for amorphous EPDM insulator, in thermo-oxidation at 110 °C.In thermo-oxidation at 130 ° C

Figure 11 .
Figure 11.Comparison between the observed and predicted values of elongation at break for amorphous EPDM insulator, in thermo-oxidation at 130 °C.Table 9. Statistical criteria of validity of the model obtained for semi-crystalline EPDM insulator (thermooxidation at 70, 90, 110 and 130 °C).

Table 1 .
Elongation at break for semi-crystalline EPDM insulator, in thermo-oxidation at 70°C.

Table 2 .
Elongation at break for semi-crystalline EPDM insulator, in thermo-oxidation at 90°C.

Table 3 .
Elongation at break for semi-crystalline EPDM insulator, in thermo-oxidation at 110°C.

Table 4 .
Elongation at break for semi-crystalline EPDM insulator, in thermo-oxidation at 130°C.

Table 5 .
Elongation at break for amorphous EPDM insulator, in thermo-oxidation at 70°C.

Table 6 .
Elongation at break for amorphous EPDM insulator, in thermo-oxidation at 90°C.

Table 7 .
Elongation at break for amorphous EPDM insulator, in thermo-oxidation at 110°C.

Table 8 .
Elongation at break for amorphous EPDM insulator, in thermo-oxidation at 130°C.

Table 10 .
Statistical criteria of validity of the model obtained for amorphous EPDM insulator (thermooxidation at 70, 90, 110 and 130 °C).