## 2 Materials and Methods
### Mechanical Analysis  
Stress-strain tests were carried out with an Instron 3366-10 kN universal machine (Instron, High Wycombe, UK), following the specifications of ASTM-D-638 type V. The test speed was 20 mm/min. The test temperature was 23 \(\pm\) 2 \({}^{\circ}\)C, and the relative humidity was of 50 \(\pm\) 5%. The study of mechanical properties, according to the GTR concentration in the matrix and the particle size, included the Young's modulus, tensile stress, elongation at break, and toughness. Five specimens for testing were used (Figure 1). The mean and standard deviation were calculated for each magnitude, leaving out of account those samples with such a result that was proven to be defective. This paper reports laboratory tests conducted on a series of seven polymer matrices blended with an increasing percentage of GTR (0%, 5%, 10%, 20%, 40%, 50%, 70%) in order to evaluate the elastic parameters of the resulting composites. Five specimens (see Figure 4b) were tested until failure for each composite to determine the \(\sigma\)-\(\epsilon\) relationship in uniaxial tension. The pure polymer matrix material can be considered as a homogeneous isotropic material [18], resulting in simple relations between the elastic constants: \(E~{}=~{}2\cdot\)G\(\cdot\)(1 + \(\
u\)), where \(\
u\) is the Poisson's ratio, \(G\) the shear modulus (MPa), and \(E\) the Young's modulus (MPa). The Young's modulus E is a measure of the stiffness of the material, only for the linear strain-stress behavior. The Poisson's ratio \(\
u\) is related to the ratio between lateral and longitudinal strain in uniaxial tensile stress. \begin{table}
\begin{tabular}{c c c c} \hline
**Polymer Type** & **Commercial Name** & **Fluidity Index or Melt Flow Index (g/min)** & **Density (kg/m\({}^{3}\))** \\ \hline PVC & Etinox & 1.35 & 1.225 \\ EVA & Alcula PA 539 type & 0.20 & 937 \\ HDPE & Alcula 4810-B & 1.35 & 960 \\ PA 6 & Ultramid B3S & 1.55 & 1130 \\ ABS & Terluran® HH-106 & 1.45 & 1050 \\ PP & Isplen® 099 K2M type & 0.55 & 902 \\ PS & Polystyrol 486 M & 1.45 & 1050 \\ \hline \end{tabular}
\end{table} 
Table 1: Commercial name, fluidity index, and density for each material. \begin{table}
\begin{tabular}{c c c} \hline
**Polymer** & **Processing Temperature (\({}^{\circ}\)C)** & **Pressing Temperature (\({}^{\circ}\)C)** \\ \hline PVC & 195–200 \({}^{\circ}\)C & 210 \({}^{\circ}\)C \\ EVA & 105–110 \({}^{\circ}\)C & 120 \({}^{\circ}\)C \\ HDPE & 150–155 \({}^{\circ}\)C & 170 \({}^{\circ}\)C \\ PA 6 & 195–200 \({}^{\circ}\)C & 210 \({}^{\circ}\)C \\ ABS & 180–185 \({}^{\circ}\)C & 195 \({}^{\circ}\)C \\ PP & 155–165 \({}^{\circ}\)C & 165 \({}^{\circ}\)C \\ PS & 180–185 \({}^{\circ}\)C & 195 \({}^{\circ}\)C \\ \hline \end{tabular}
\end{table} 
Table 2: Processing temperatures for each material with the _Brabender_ mixing machine and pressing temperatures at constant pressure at 200 bar. Figure 2 shows the curves obtained from the test of the PP and ABS blended with the full range of GTR concentrations. As it can be seen, the mechanical characteristic is greatly influenced by the GTR. At high concentrations of GTR (\(\geq\)30%), the curves are concave (see Figure 2 red curves). In this study case, the complex morphology of the matrix polymer blended with GTR particles does not allow the use of the standard elastoplastic equations or the classical approach. For this reason, and in the same way as [19], a simple uniaxial tensile stress-strain relation is proposed, based on three parameters, \(\sigma_{Y}\), \(\varepsilon_{Y}\), and \(n\). \[\sigma\ =\ \sigma_{Y}\left[1-\left(1+\frac{\varepsilon}{\varepsilon_{Y}} \right)^{-n}\right] \tag{1}\]  
where \(\sigma_{Y}\) is the yield strength and \(\varepsilon_{Y}\) the elongation at yield. The exponent \(n\) is a value greater than 1.