Heat Build-Up and Rolling Resistance Analysis of a Solid Tire: Experimental Observation and Numerical Simulation with Thermo-Mechanical Coupling Method.

The hysteresis of rubber materials due to deformation and viscoelasticity is the main reason for the heat build-up (HBU) and rolling resistance (RR) of the rolling tire. It is important to realize the high precision prediction of HBU and RR of tire for the optimal design of high-performance fuel-saving tire. In this work, a thermo-mechanical coupling method based on Endurica and Abaqus co-simulation was used to predict the steady-state temperature distribution and RR of three finite element models (Lagrangian-Eulerian model, Lagrangian model, and Plane Strain model) of the solid tires under different loads and rotating speeds. The simulation results were compared with the experimental results. The Kraus self-heating model was utilized in the thermo-mechanical coupling method, which realized the quantitative relationship between the dynamic loss modulus of rubber and the loading conditions (temperature, strain, and strain rate). Special attention was paid to the determination of the material parameters in the Kraus self-heating model. The comparison between simulation results and experimental results shows that the Lagrangian model had the highest prediction accuracy, and the average prediction errors of the steady-state surface temperature and RR under three loading conditions were 3.4% and 7.9%, respectively. The Lagrangian-Eulerian model came in the second with average errors of 9.7% and 11.1%, respectively. The Plane Strain model had the worst prediction accuracy, with the average errors of 21.4% and 44.6%, respectively. In terms of the simulation time, the Plane Strain model had the lowest cost, and the average calculation time was 1143 s. The Lagrangian-Eulerian model took the second place, with an average calculation time of 2621 s. The Lagrangian model had the highest computation cost, with an average time of 5597 s. The comparison between the simulation results and the experimental results verified the effectiveness of the thermo-mechanical coupling analysis method. The methods of three finite element models of the solid tires in this work can provide some reference for the optimization design of elastomeric components (Lagrangian model), pneumatic tires (Lagrangian-Eulerian model), and non-pneumatic tires (Plane Strain model).

Characterizing Distributions of Tensile Strength and Crack Precursor Size to Evaluate Filler Dispersion Effects and Reliability of Rubber.

Undispersed filler agglomerates or other substantial inclusions/contaminants in rubber can act as large crack precursors that reduce the strength and fatigue lifetime of the material. To demonstrate this, we use tensile strength (stress at break, σb) data from 50 specimens to characterize the failure distribution behavior of carbon black (CB) reinforced styrene-butadiene rubber (SBR) compounds. Poor mixing was simulated by adding a portion of the CB late in the mixing process, and glass beads (microspheres) with 517 µm average diameter were introduced during milling to reproduce the effects of large inclusions. The σb distribution was well described with a simple unimodal Weibull distribution for the control compound, but the tensile strengths of the poor CB dispersion material and the compounds with the glass beads required bimodal Weibull distributions. For the material with the lowest level of glass beads-corresponding to less than one microsphere per test specimen-the bimodal failure distribution spanned a very large range of σb from 13.7 to 22.7 MPa in contrast to the relatively narrow σb distribution for the control from 18.4 to 23.8 MPa. Crack precursor size (c0) distributions were also inferred from the data, and the glass beads introduced c0 values in the 400 µm range compared to about 180 µm for the control. In contrast to σb, critical tearing energy (tear strength) was unaffected by the presence of the CB agglomerates and glass beads, because the strain energy focuses on the pre-cut macroscopic crack in the sample during tear testing rather than on the microscopic crack precursors within the rubber. The glass beads were not detected by conventional filler dispersion measurements using interferometric microscopy, indicating that tensile strength distribution characterization is an important complementary approach for identifying the presence of minor amounts of large inclusions in rubber.