1. Introduction

2. Materials and Methods

2.1. Materials

In this research we studied the epoxy binder. The same materials as in our previous researches were used [7,12,18,19,20,21,22] (presented in Table 1).

The specimens were cured for 2 hours under 80°C and then kept for 24 hours under 150°C. This post-curing was conducted in order to change the specimen from extremely plastic under-cured state closer to the real construction material.

Table 1. Types of binders investigated.

Table 1. Types of binders investigated.

№	Composition	Name
1	Epoxy (Ker 828 52.5% + MTHPA 44.5% + alkofen 3%) (without thermal aging)	EP
2	Epoxy (Ker 828 52.5% + MTHPA 44.5% + alkofen 3%) (thermally-aged, see 2.2.1)	EP-TR

2.2. Methods

2.2.1. Long Heat Treatment (Thermal Aging)

The same aging conditions were used as in previous studies [28].

2.2.2. Tensile testing chamber

The tests were carried out in a specially manufactured chamber that allowed the ends of the sample to be pinched from longitudinal displacements and to test it for tension by moving one of the chamber parts. Heating elements and a fan were installed in the chamber to create hot air movement and uniformity of heating inside the chamber.

The chamber was installed on a Tinius Olsen h100ku machine (characteristics were presented in previous studies [17,28,31]). The upper part of the camera (see Figure 1) was clamped in the grip of the machine and is able to slip freely relative to the lower part. Clamps had flexibility for turns, so bending moments from eccentricities did not occur in the sample, and it worked only for longitudinal force.

The strain of the sample was controlled by clock-type sensors to eliminate the effect of slippage in the grips of the machine and the test chamber. 4 sensors with an accuracy of 0.01 mm were used, mounted in pairs crosswise (to account for possible slopes relative to both axes of symmetry of the sample section).

To increase the accuracy of determining the calculated length, the contact of the corner shelf with the sample along its length was minimized by inserting the spacer and making sure that the contact of corner and the specimen is concentrated in one spot. The test scheme and the photo of real installation are presented at Figure 2.

2.2.3. Testing for creep

The Tinius testing machine allowed us to make a program for constant loading. The machine automatically increases the strain if the tensile force falls. Consequently, it was used for creep test as it represents the conditions for creep: constant stress and unconstrained displacement.

The sensor readings were recorded at zero force, immediately after applying load and then with the steps of 1, 5, 10, 15, 30, 60 minutes. They were transformed into span change using formulas (1-7) (see Figure 3). Then, the strain $\epsilon$ was calculated by dividing the displacement by the initial span. As the result, creep curves $\epsilon \left(t\right)$ were obtained ($t$ – time).

$$∆L=∆1-∆2$$

(1)

$$d{1}^{\prime }=d1-∆1+D$$

(2)

$$∆1=d1+D-d{1}^{\prime }$$

(3)

$$d{2}^{\prime }=d2-∆2+D$$

(4)

$$∆2=d2+D-d{2}^{\prime }$$

(5)

$$∆L=d1+D-d{1}^{\prime }-d2-D+d{2}^{\prime }$$

(6)

$$∆L=d1-d{1}^{\prime }+d{2}^{\prime }-d2$$

(7)

Where readings $d1$ and $d2$ are average for 2 crosswise sensors for near and far sections, respectively.

Figure 3. The scheme for formulas (1-7).

Figure 3. The scheme for formulas (1-7).

2.2.4. Acquiring rheological parameters

In this research we used the three-element model which is based on Kelvin-Voigt model. This model is described in classical creep theory [23]. The appearance of model is shown at Figure 4.

$E1$ and $E2$ are Young’s modulus for elastic elements. $K$ is a parameter of viscosity of viscous element. ${\sigma }_1,{\sigma }_2,{\sigma }_K,\sigma$ are normal stresses in elastic elements, viscous element and the material overall, respectively. These parameters are connected by following relations [23] (formulas 8-9):

$$H=\frac{E1·E2}{E1+E2}$$

(8)

$$n=\frac{K}{E1+E2}$$

(9)

$H$ is a long-term elastic modulus, $n$ is a relaxation time.

The creep law is described by (10):

$$\epsilon \left(t\right)=\frac{\sigma }{H}+\sigma \left(\frac{1}{E}-\frac{1}{H}\right)e^{-H·\frac{t}{En}}$$

(10)

Experimental creep curves were imported into Mathcad program, which created a system of equations $\epsilon \left(t\right)$ (see (10)), where strain, time and elastic modulus are known parameters and $H,n$ are unknown. The elastic modulus was obtained in previous research [17,31] and checked again in this one at initial loading. By equalizing the theoretical and experimental strain values at given times, the program numerically approximated them and came up with $H,n$ which provided convergence of theoretical and experimental curves.

As $E1=E$ [23], there are 2 unknown parameters left: $E2$ and $K$. By solving the system of equations (8, 9), they were defined.

As a result, all parameters of the model were determined.

2.2.5. Cyclic heating test

The specimen was clamped on both sides and pre-stressed for a load of 1000 N. It was done in order to get rid of possible shifts in installation. After the initial load, the specimen was left to rest for 5 minutes to let the initial fast relaxation slow down and to not disturb the results.

The temperature was automatically controlled by a thermostat, and also checked according to a reference sample of the same thickness as the test sample, with a thermocouple glued inside.

The testing process was: turning on the heating until the desired temperature was reached, turning heating off until the specimen cools down to room temperature, then repeating the cycle a number of times.

The measurements were recorded each 5 minutes during the whole testing period. The temperature was recorded from the reference sample and the variation from the thermostat was no more than 2°C.

From previous research [17], the dependences of the modulus of elasticity ($E$) and coefficient of thermal expansion (CTE) from temperature are known. Previously, the relationship between $E$ and CTE was established and it was found that up to a temperature of about 80 °C, they change weakly and almost linearly. After 80 °C, there is a sharp change in the behavior of the material and a non-linear growth of $E$ and CTE. At this stage of research, it was assumed that the viscoelastic behavior of the material will change in a similar way, since all these processes are related to the internal structure of the material. Since the determination of rheological parameters was carried out at normal temperature (see further), heating tests were carried out at 70°C in order to exclude the possible influence of non-linearities that have not yet been studied.

3. Results and Discussion

3.1. Creep tests

To assess the correctness of measured strains, the Young’s modulus was calculated, using the Hooke’s law. The modulus was $3000MPa\pm 10\%$, what corresponds to our previous research [17,31] and other scientist’s data [6]. Thus, the experimental data was considered to be correct.

The testing equipment did not allow us to test both EP and EP-TR samples under the same stresses. However, the rheological parameters should not depend on stress, which was confirmed in this research (see 3.2).

As we can see at Figure 4 and Figure 5, the behavior of normal and thermally-relaxed binder under constant load is different. EP samples gave us classical creep curves, with strain increasing over time, gradually slowing down. On the other hand, EP-TR show almost no viscosity. There is a rapid increase in strain in the beginning (which was followed by audible crackling) and then the strain change is negligible.

Figure 5. Creep curves for EP.

Figure 5. Creep curves for EP.

Figure 6. Creep curves for EP-TR.

Figure 6. Creep curves for EP-TR.

This difference can be explained by the changes in internal structure of material. As weak volatile bonds are destroyed during thermal aging, the material loses its ability for plastic deformation, becoming brittle[22]. Thus, the hypothesis, mentioned in Introduction (that thermal aging decreases viscosity), seems to be proved by the results of creep tests.

4. Conclusions

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