Mathematical Modelling of Tensile Mechanical Behavior of a Bio-Composite Based on Polybutylene-Succinate and Brewer Spent Grains

Abstract

A model based on the fitting of stress-strain data by tensile tests of bio-composites made of a bioplastic (polybutylene succinate (PBS)) and brewer spent grain filler (BSGF) is developed. Experimental tests were performed for various concentrations of BSGF in the range from 2% to 30%. The model is suitable for describing the elastic-plastic behavior of these materials in terms of two mechanical parameters, tensile stress and tensile stiffness (or Young's modulus), depending on the filler concentration. The mechanical characteristics, derived from the fit parameters, show good agreement with the experimental data. The mathematical model used here could be an important aid for the experimentation and manufacturing process as it allows the prediction of the mechanical tensile parameters of a mixture with different filler concentrations, avoiding the long and complex preparation cycle of bio-composites, as well as the specific mechanical tests. The physical properties required by the objects created with the PBS-BSGF bio-composite by the partners/stakeholders of the research project co-financing this research can be quite different; therefore, a mathematical model that predicts some of the mechanical properties in terms of the mixture composition may be useful to speed up the selection of the required amount of BSGF in the mixture.

Keywords: agri-food waste; bioplastics; mathematical modelling; poli-butylene-succinate; tensile test.

Figure 1

SEM analysis at 3000× (a), at 8000× (b), and size distribution of BSGF (c).

Figure 2

Scheme of production of PBS–BSGF, from raw materials to bio-compound: the processing of BSG to obtain a fine power (size: 53 micrometer) (a–d), the drying and checking of the humidity level (e,f), the melt-mixing of BSGF with PBS (g,h), the production of sheet (i,j) and of dog-bone (k,l).

Figure 3

Sheets of PBS (a), PBS–BSGF2 (b), PBS–BSGF4 (c), PBS–BSGF6 (d), PBS–BSGF8 (e), PBS–BSGF10 (f), PBS–BSGF12 (g), PBS–BSGF14 (h), PBS–BSGF16 (i), PBS–BSGF18 (j), PBS–BSGF20 (k), PBS–BSGF22 (l), PBS–BSGF24 (m), PBS–BSGF26 (n), PBS–BSGF28 (o), PBS–BSGF30 (p).

Figure 4

Dog-bones blends of PBS–BSGF4 (a,b), PBS–BSGF20 (c,d), PBS–BSGF30 (e,f) before and after the tensile test.

Figure 5

Engineering stress–strain curves of PBS (a) and PBS–BSGF4 dog-bone specimens (b).

Figure 6

Stress–strain curves (blue) and non-linear were curve (red) of bio-compounds at different concentration of BSGF filler, from left to right: PBS–BSGF2 (a), PBS–BSGF4 (b), PBS–BSGF6 (c), PBS–BSGF8 (d), PBS–BSGF10 (e), PBS–BSGF12 (f), PBS–BSGF14 (g), PBS–BSGF16 (h), PBS–BSGF-18 (i), PBS–BSGF20 (j), PBS–BSGF22 (k), PBS–BSGF24 (l), PBS–BSGF26 (m), PBS–BSGF 28 (n), PBS–BSGF30 (o).

Figure 7

α, stress at rupture vs. BSG concentration: experimental points (green line–spot), α parameter (blue line–square dot), linear regression function (red continuous line) (a). β parameters (blue spots) and the linear fitting (red continuous line) (b).

Figure 8

α = 30, β = 10 (dashed red line), α = 30, β = 15 (continuous blue line).

Figure 9

Model (square blue dot) and the polynomial in Equation (5) (dashed red line) vs. BSG content (a); experimental (green line–spot) and its nonlinear fitting according to (6) (continuous red line) vs. BSG content (b); superposition of the plots shown in Figure 9a,b (c); experimental (green line–spot) and its linear regression according to (7) (continuous red line) vs. BSG content (d).

Figure 10

SEM micrographs at 300× of: PBS (a), PBS–BSGF10 (b), PBS–BSGF20 (c), PBS–BSGF25 (d), PBS–BSGF30 (e).

Figure 11

How the mathematical model can help the object production with some examples of prototypes made by some partners/stakeholder of the Life Restart Project with the PBS–BSGF material of this study [47].