# Determination of Nonlinear Creep Parameters for Hereditary Materials
## 5 Application of Proposed Algorithm and Methods
### Glass-Reinforced Plastic TC 8/3-250
#### 5.2.2 \(\Theta\) = 45\({}^{\circ}\)  
Values of creep strain for glass-reinforced plastic (\(\Theta\) = 45\({}^{\circ}\)) at six stresses are represented in Table 3.  
Figure 5: Creep curves of glass-reinforced plastic (\(\Theta\) = 90\({}^{\circ}\)) at various stresses: 1–104.7 MPa, 2–209.4 MPa, 3–279.2 MPa, 4–349.0 MPa.  
According to test results, it has been determined that the samples of glass-reinforced plastic, cut at the angle of \(\Theta\) = 45\({}^{\circ}\) to textile warp, have been deformed nonlinearly at the tested temperature and applied stresses.  
Creep strains at minimum stress, equal to 20.3 MPa, have been approximated by Rabotnov's fractional exponential kernel. The following values have been obtained for creep parameter: \(\alpha\)= 0.8, \(\epsilon_{0}\) = 0.1093, \(\beta\) = 0.32, and \(\lambda\) = 0.2459.  
Considering the obtained values of parameters \(\alpha\), \(\epsilon_{0}\), \(\beta\), and \(\lambda\), the equation of creep curve for glass-reinforced plastic (\(\Theta\) = 45\({}^{\circ}\)) at minimum stress (\(\sigma\) = 20.3 MPa) has a form of:  
\[\epsilon_{m}(t)\ =\ 0.1093\ \bigg{[}1+0.2459\sum_{n\ =\ 0}^{\infty}\ \frac{(-0.32)^{n}t^{0.2(1+n)}}{\Gamma[0.2(1+n)+1]}\bigg{]}. \tag{30}\]  
Processing of test results allowed determination of the following values of instantaneous strain for stresses 20.3 MPa, 40.6 MPa, 60.9 MPa, 81.2 MPa, 101.5 MPa, and 121.8 MPa: 0.1093%, 0.1982%, 0.5911%, 1.3872%, 2.4874%, and 3.9975%, respectively.  
The model rheological parameter has a form of:  
\[k_{m}(t)\ =\ \frac{\epsilon_{m}(t)}{\epsilon_{0}^{m}}\ =\ \ 1+0.2459\ \sum_{n\ =\ 0}^{\infty}\ \frac{(-0.32)^{n}t^{0.2(1+n)}}{\Gamma[0.2(1+n)+1]}. \tag{31}\]  
Using the abovementioned values of instantaneous strain, one can calculate values of creep strain at all other stresses under formula (21).  
Figure 6 shows experimental and calculated values of creep strain for glass-reinforced plastic (\(\Theta\) = 45\({}^{\circ}\)) at all considered stresses. It is seen that convergence of experimental strains to the calculated ones is good.  
Figure 6: Creep curves of glass-reinforced plastic (\(\Theta\) = 45\({}^{\circ}\)) at various stresses: 1–20.3 MPa, 2–40.6 MPa, 3–60.9 MPa, 4–81.2 MPa, 5–101.5 MPa, 6–121.8 MPa.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline  & \multicolumn{6}{c}{**Strain \(\epsilon_{E}\) (f), \%, at Stress \(\sigma\), MPa**} \\ \cline{2-7}
**Time \(t\), h** & & & & & & \\ \cline{2-7}
**20.3** & **40.6** & **60.9** & **81.2** & **101.5** & **121.8** \\ \hline
0 & 0.1074 & 0.1946 & 0.5805 & 1.3624 & 2.4430 & 3.9262 \\
1 & 0.1302 & 0.2359 & 0.7037 & 1.6515 & 2.9614 & 4.7593 \\
50 & 0.1457 & 0.2639 & 0.7873 & 1.8478 & 3.3134 & 5.3251 \\
200 & 0.1518 & 0.2750 & 0.8204 & 1.9255 & 3.4527 & 5.5489 \\
400 & 0.1548 & 0.2806 & 0.8370 & 1.9643 & 3.5222 & 5.6608 \\
600 & 0.1566 & 0.2838 & 0.8466 & 1.9869 & 3.5629 & 5.7260 \\
800 & 0.1579 & 0.2861 & 0.8533 & 2.0027 & 3.5912 & 5.7715 \\
1000 & 0.1588 & 0.2878 & 0.8586 & 2.0150 & 3.6132 & 5.8068 \\
1320 & 0.1600 & 0.2900 & 0.8649 & 2.0300 & 3.6401 & 5.8500 \\ \hline \end{tabular}
\end{table}
Table 3: Values of creep strain for glass-reinforced plastic (\(\Theta\) = 45\({}^{\circ}\)).