An analytical study of mechanical behavior of polypropylene/calcium carbonate composites under uniaxial tension and three-point bending

Analytic solutions of test curve are beneficial to analyze mechanical properties and to understand the reason behind mechanical behaviors of materials. Herein, two relationships about both average true strain and average true stress on necking were obtained. Further, the homogenizing constitutive equation was obtained according to the linear viscoelastic constitutive equation becoming the foundation of solving analytic solutions of material behavior. The applicability of analytic solutions in the entire test range was discussed and improved by experimental results of both uniaxial tension and three-point bending. Analytic solutions of test curve in this work conform well to the experiments. The moduli and strengths of polypropylene/calcium carbonate composites were predicted according to this model. This mathematical model indicates that mechanical behavior of linear viscoelastic material was the outcome of competition between stress-increasing of extension and stress-decreasing of relaxation. It is hoped that the empirical formulae of two routine test curves can bring convenience for an analytical study of mechanical behavior of linear viscoelastic materials.