MECHANICAL STRENGTH AND DIELECTRIC LOSSES OF A HOT-CURING EPOXY COMPOUND DURING THERMAL AGING

R. M. KESSENIKH, Yu. P. POKHOLKOV, A. V. PETROV, B. L. PETRI

(Presented by the scientific seminar of the Department of Electrical Insulation and Cable Engineering)

It is known that at present epoxy resins cured with various hardeners are widely used. We used a formulation of an epoxy compound based on ED-6 resin with phthalic anhydride. Quartz sand was used as the filler; the curing temperature was 140°C for 24 hours. The indicated compound was used for potting the rotors of small-size electrical machines, and therefore the task arose of studying thermal aging. Mechanical and dielectric properties of epoxy compounds were chosen as the criterion of thermal aging. Thermal aging was studied at three temperatures, 140, 160, and 180°C, for 2000 hours. Dielectric losses (\(\operatorname{tg}\delta\)) were measured by means of a differential bridge at audio frequencies with an accuracy of 10% [1].

The mechanical characteristics (modulus of elasticity, specific impact strength, tensile strength, and flexural strength) were studied by standard methods at the Department of Strength of Materials of TPI.

Experimental Results

1. Specific Impact Strength

The specific impact strength was studied for filled and unfilled compounds aged at temperatures of 140 and 160°C for 600 hours. As can be seen from the curves presented (Fig. 1, a and b), the specific impact strength \((\sigma_{\text{sp.imp}})\) of filled compounds increases during the first 100–150 hours of aging; moreover, at an aging temperature of 160°C a sharper increase in \(\sigma_{\text{sp.imp}}\) is observed than for the epoxy compound aged at a temperature of 140°C. Then an equilibrium value of the specific impact strength is established, and its absolute value lies within the range of \(10 \div 20\ \text{kg}\cdot\text{cm}/\text{cm}^2\). The increase in the impact strength of the epoxy compound is due to additional curing at elevated temperatures; the tendency toward a decrease in \(\sigma_{\text{sp.imp}}\) can be explained by the appearance of brittleness caused by a rigidly cross-linked structure (the result of additional cross-linking). Epoxy compounds belong to structured polymers in the glassy state.

In thermosetting compounds of the epoxy type, a high irregularity of the network with a high frequency of cross-links is observed. Therefore

at the same time hardness and brittleness appear, the modulus of elasticity increases, resistance to compression and tension increases, and relative elongation decreases. However, thermal stability and heat resistance increase [2, 3, 4]. Filling epoxy polymers with finely dispersed quartz sand leads to a significant decrease in specific impact viscosity. During aging of filled compounds for approximately up to 200 h—

Fig. 1. Dependence of $\sigma_{\text{sp.imp.}}$ on the aging time of an epoxy compound: a) at an aging temperature of 140°C: 1—unfilled, 2—filled; b) at an aging temperature of 160°C: 1—unfilled, 2—filled

a monotonic, very slight decrease in specific viscosity is characteristic, and then it increases and stabilizes at one level. The most noticeable changes in specific viscosity occur in the compound aged at a temperature of 140°C, when, up to 500 h of aging, $\sigma_{\text{sp.imp.}}$ decreases at a very low rate. At a temperature of 160°C, a steady behavior is observed—the establishment of $\sigma_{\text{sp.imp.}}$ at one level. Therefore, it may be assumed that curing of the compound would be expediently carried out stepwise at temperatures of 140 and 160°C.

The absolute values of the specific impact viscosity of the filled epoxy compound aged at temperatures of 140 and 160°C lie within the permissible limits characteristic of structured polymers.

2. Modulus of elasticity in tension and normal stress at the moment of failure

The indicated characteristics were determined only for the unfilled epoxy compound aged at three temperatures, 140, 160, and 180°C, for 200 h. The results are summarized in Table 1.

The Young’s modulus of the unfilled and unaged epoxy compound has a value equal to 435 kg/mm²; analogous values of \(E\) are also characteristic of other structured polymers. An increase in the aging temperature leads to a decrease in Young’s modulus by approximately 8–18% over 200 hours of aging.

Table 1

* Averaged values.

The decrease in the modulus of elasticity after aging for 200 hours may serve as some indirect evidence of loosening of the structure of the epoxy compound as a result of weight loss. The tensile strength during aging of the compound decreases insignificantly.

3. Time-Dependent Resistance to Bending

Processing of the results of mechanical tests of specimens of epoxy compounds was carried out in accordance with [5]. Analysis of a number of types of distributions of the values [6, 7, 8, 9] made it possible to use, for describing the distribution of the flexural strength of the epoxy compound, the \(\Upsilon\)-distribution

\[ f(x)=\frac{\lambda^N x^{N-1}\exp[-\lambda x]}{\Gamma(N)}. \tag{1} \]

In [6] this distribution is represented as

\[ \varphi(r)=\frac{r^{m-1}}{C^m(m-1)!}\exp\left(-\frac{r}{c}\right), \tag{2} \]

and, making in equation (2) the substitution \(x=2\dfrac{r}{c}\), one can obtain

\[ \varphi(x)=\frac{x^{m-1}}{2^m\Gamma(m)}\exp\left(-\frac{x}{2}\right). \tag{3} \]

Equation (3) is the equation of the chi-square distribution with \(\lambda=0.5\). In other words, the gamma distribution is a special case of the chi-square distribution.

The parameters \(N\) and \(\lambda\) in expression (1) and the parameters \(m\) and \(c\) in expression (3) are found quite easily.

In accordance with [8],

\[ N=\frac{\overline{x}^{\,2}}{D}, \qquad \text{and} \qquad \lambda=\frac{\overline{y}}{D} \]

at the same time, if \(c=\dfrac{1}{\lambda}\), then \(m=N\). Analyzing the expression of function (3), one can say that the number of degrees of freedom is equal to \(2m\). Then the general expression of the distribution function is

\[ F(r)=p_0\left(\frac{2r}{c}\right). \tag{4} \]

The quantiles of this function are determined from Table 1, item 6 of [6]. From equation (4) there follows a simple expression for the quantiles of the gamma distribution

\[ Z_p=\frac{c}{2}x_p, \]

where \(x_p\) is determined from Table 1, item 6 of [6].

The quantiles can also be determined through the parameters \(m\) and \(c\). If we denote \(\frac{2m}{x_q}=r_1\) (6), and \(\frac{2m}{x_p}=r_2\) (7), with \(q=1-p\), where \(x_p\) and \(x_q\) are the quantiles of the chi-square distribution with \(2m\) degrees of freedom, then from equation (4) we obtain

\[ Z_p=\frac{mc}{r_2}, \tag{8} \]

\[ Z_q=\frac{mc}{r_1}. \tag{9} \]

The values of the coefficients \(r_1\) and \(r_2\) are given in Table 1, item 9 of [6] for \(p=0.8-0.999\).

Applying the described method, we calculated the parameters of the gamma distribution for the quantity \(\sigma_{\mathrm{ult}}\). The calculation data are given in Table 2. In addition to the indicated parameters, the table gives the coeffici-

Table 2

*) At large \(N\) the distribution tends toward the normal distribution; therefore \(q_{486}\) in the last two rows was obtained from the normal law.

coefficient of variation \(v\), expressed in percent. Unaged specimens of the epoxy compound have a mean value of \(\sigma_{\text{bend}}\) equal to \(\simeq 1070\ \text{kg}/\text{cm}^2\) (Table 2). At the same time, 5% of all specimens may have \(\sigma_{\text{bend}} < 486\ \text{kg}/\text{cm}^2\). This value was taken as the control value.

During aging of the epoxy-compound specimens at temperatures of 140, 160, and 180°C, \(\sigma_{\text{bend}}\) was determined after 200, 400, 600, 1000, and 1500 hours. The results of each of the indicated measurements were processed in accordance with the method described. Here \(q\)—for specimens that became unusable as a result of aging—was evaluated as the quantile of the gamma distribution at \(q = 486\ \text{kg}/\text{cm}^2\).

The results of the calculations of \(q_{486}\) make it possible to conclude that aging at temperatures of 140° and 160°C for 1000 hours does not worsen the mechanical properties of epoxy compounds, and even improves them somewhat. The value of \(q_{486}\) decreases from 0.05 to 0.01. The same is confirmed by the change in the mean value of \(\sigma_{\text{bend}}\) (Fig. 2).

At a temperature of 180°C, a sharp deterioration of the mechanical properties occurs already after 200 hours of aging. The level of the mean value of \(\sigma_{\text{bend}}\) for the compound aged at \(t = 180^\circ\text{C}\); for the compounds, one may assume that this is the established value of \(\sigma_{\text{bend}}\), resulting from irreversible processes that occurred in the compound. This is also indicated by the value of \(\sigma_{\text{bend}}\) after 1500 hours of aging at temperatures of 140 and 160°C.

According to table [5], for \(\nu = k - 3 = 12 - 3 = 9\), \(P(\chi^2) \simeq 0.95\).

Table 3 gives the results of checking the agreement of the obtained distribution of \(\sigma_{\text{bend}}\) with the gamma distribution by Pearson’s criterion. The obtained probability \(P(\chi^2) \simeq 0.95\) indicates quite satisfactory agreement of the obtained series with the gamma distribution.

Table 3

Check of agreement with the gamma distribution by Pearson’s criterion \((\chi^2)\)

Figure 2 shows the change in the mean value of \(\sigma_{\text{bend}}\) with time at various aging temperatures.

The greatest effect is exerted by the temperature of 180°C. Already after 600 hours of aging at this temperature, $\sigma_{\text{bend}}$ decreases from 1070 kg/cm² to 740 kg/cm² and remains at this level for the rest of the aging time (Fig. 2, curve 3). Compounds aged at temperatures of 140 and 160°C retain the value of $\sigma_{\text{bend}}$ practically at the same level up to 1000 hours of aging; after 1000 hours of aging, a considerable decrease in mechanical strength is observed, with the compound aged at 140°C behaving worse. In this compound, $\sigma_{\text{bend}}$ decreases by approximately 25% (Fig. 2, curve 1) in comparison with $\sigma_{\text{bend}}$ of the compounds aged at temperatures of 160 and 180°C (after 1500 hours of aging).

Fig. 2. Dependence of $\sigma_{\text{bend}}$ on the aging time of the filled epoxy compound: 1 — at an aging temperature of 140°C, 2 — at an aging temperature of 160°C, 3 — at an aging temperature of 180°C.

On the basis of the foregoing, it may be assumed, as already indicated above, that for the epoxy compound of this formulation the most acceptable curing regime would be a stepped heating regime at temperatures of 140, 150, and 160°C. In Fig. 2 it is also noteworthy that up to 200 hours of aging of the compound, regardless of its aging temperature, $\sigma_{\text{bend}}$ increases to a greater or lesser extent, and then, as already noted earlier, a sharp drop in $\sigma_{\text{bend}}$ is observed for the compound aged at $t = 180^\circ$C; for compounds aged at 160 and 140°C, the mechanical strength decreases somewhat and stabilizes at the attained level up to 1000 hours of aging. Meanwhile, the results of studying the elastic modulus of the compounds after their 200-hour aging at temperatures of 140, 160, and 180°C indicate a decrease in $E$.

Consequently, it may be considered that in this case we observe a simultaneous decrease in the mechanical characteristics of aged epoxy compounds after 200 hours of aging at three temperatures. It is noteworthy that curve 1 (Fig. 2) drops sharply after 1000 hours of aging at 140°C. Such behavior of the compound can be explained by the nonuniform structure caused by the curing regime at 140°C.

The onset of brittleness is indicated by a decrease in the specific impact toughness during thermal aging, with the decrease in $\sigma_{\text{sp.imp}}$ beginning considerably earlier than the decrease in $\sigma_{\text{tens}}$. Apparently, a certain induction period is characteristic, during which mechanical stresses gradually accumulate in the structure of the compound, and then a sharp decrease in mechanical strength occurs. It should be noted that the level of the mechanical characteristics of the compound after aging is not so low as to make its use in electrical-engineering structures impossible.

4. Dielectric loss tangent

In the curves of the dependence of $\operatorname{tg}\delta$ on the time spent in the heat chamber (Figs. 3 and 4), a decrease in the dielectric loss tangent can be observed at all three aging temperatures (140, 160, and 180°C)

Fig. 3. Dependence of $\operatorname{tg}\delta$ of an unfilled epoxy compound on aging time ($f = 200$ kc/s), 3—140°C; 2—160°C; 1—180°C

Fig. 4. Dependence of $\operatorname{tg}\delta$ of a filled epoxy compound on aging time ($f = 200$ kc/s), 3—140°C; 2—160°C; 1—180°C

over the course of 1000 hours. With further aging time, there is a monotonic increase in $\operatorname{tg}\delta$, with the greatest change in dielectric properties observed for the filled compound at aging temperatures of 160 and 180°C. However, this change in $\operatorname{tg}\delta$ occurs within a factor, and the order of magnitude is preserved. Thus, the change in $\operatorname{tg}\delta$ is practically small.

The improvement in dielectric properties that we observe during the thermal aging process (up to 1000 hours) of the epoxy compound indicates the occurrence of an additional crosslinking process or the removal from the volume of the compound of monomeric products (residues of phthalic anhydride). The simultaneous action of these two factors is possible. The increase in dielectric characteristics after 1000 hours of aging,

probably is due to the appearance of destruction products in the bulk of the compound. However, this increase is so small that the value of \(\lg\delta\) is quite acceptable for practical purposes. To make sure that measurement of dielectric losses at room temperature does not reveal the full picture of the changes that have occurred in the structure of the compound during thermal aging, we studied the effect of moisture absorption on \(\tg\delta\) of aged compound specimens (Table 4).

Table 4

Results of the effect of elevated moisture on the dielectric properties of aged epoxy compound

tangent of the dielectric loss angle \(10^4\) at \(f = 50\) Hz

The increase in the \(\tg\delta\) value of epoxy aged compounds after prolonged exposure to water indicates that its absorption by the specimens is due not only to the mechanism of activated sorption, but is also associated with structural defects arising when phthalic anhydride residues leave the bulk of the compound. The greatest deterioration is observed in compounds aged at a temperature of 180°C.

5. Study of weight loss in the process of thermal aging

During thermal aging at temperatures of 140, 160, and 180°C, filled and unfilled epoxy compounds show a decrease in weight. The higher the aging temperature, the greater the weight loss (Fig. 5). The decrease in weight of epoxy compounds with aging time can apparently be associated with diffusion of unreacted phthalic anhydride from the cured compound. Owing to the significant dependence of the diffusion coefficient on temperature, the highest aging temperature causes more intensive removal of the anhydride from the bulk of the compound. The greatest decrease in compound weight at the three aging temperatures is observed up to 1000 hours of aging, and subsequently practically ceases. It should be noted that the decrease in weight of the filled compound proceeds more slowly than that of the unfilled compound. This can be explained by the fact that the filled compound contains a relatively smaller amount of

resin. Comparison of Figs. 3 and 4 with Fig. 5 makes it possible to consider that the decrease in \(\operatorname{tg}\delta\) and the decrease in weight up to 1000 hours of aging correlate fairly well.

Fig. 5. Weight-loss curves of aged epoxy compounds:

1 — with filler
2 — without filler \(\}\) 140°C,

3 — with filler
4 — without filler \(\}\) 160°C,

5 — with filler
6 — without filler \(\}\) 180°C.

Conclusions

1. The mechanical strength of an unfilled epoxy compound decreases during thermal aging. It may be assumed that the main reason for the decrease in mechanical strength during thermal aging is brittleness, which appears as a result of additional cross-linking of the structure under the action of elevated temperatures.

2. Between the tangent of the dielectric loss angle and the mechanical strength of the epoxy compound during aging, a certain correlation is observed. Thus, for example, \(\operatorname{tg}\delta\) decreases only slightly during 1000 hours of aging, remaining practically, on average, at the initial level. The behavior of \(\sigma_{\text{bend}}\) of the compound at aging temperatures of 140 and 160°C is analogous—when the mechanical strength, up to 1000 hours of aging, remains unchanged.

3. In aged epoxy compounds, losses in weight are observed up to 1000 hours of aging; with further aging the weight remains practically unchanged. The greatest weight loss is observed in compounds aged at an aging temperature of 180°C (8–10%). Apparently, the loss in weight of the compounds is due to diffusion from its volume of residues of phthalic anhydride.

4. As a criterion of thermal aging of a hot-curing epoxy compound, it is technically expedient to choose mechanical strength. The dielectric characteristics in this case provide limited information.

5. The value of the mechanical strength of the epoxy compound at aging temperatures of 140 and 160°C remains at a high level up to 1000 hours. After 1000 hours of aging the value of the mechanical strength

approaches a constant value of 750 kg/cm² (curves 2 and 3, Fig. 2). Such a value of mechanical strength is characteristic of many thermosetting plastics and compounds.

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