Temperature Gradients in Tire Rubber Can Reduce/Increase Tensile Stresses and Hence Wear and Fatigue

It has been known for some time that grading of the elastic modulus (namely, softer in the surface) leads to a significant reduction in tensile stresses due to contact loadings; this has been studied mostly to suppress the cracking of brittle materials. In particular, a recent study has demonstrated that the effect is most pronounced for a large Poisson’s ratio, as is the case for incompressible materials. Grading of the modulus occurs intrinsically in viscoelastic materials like rubber when there is a temperature gradient within the rubber, which leads to significant changes of tensile stresses, affecting fatigue and wear. Friction and wear have been analyzed experimentally in the past with respect to mean temperature, revealing an ideal range of temperature with the highest friction and lowest wear, but the effect of the temperature gradient is not as well understood. The present paper presents a simple model of a sinusoidal wave of pressure and shear traction moving on a viscoelastic half-plane (standard material) at constant velocity, finding an approximate solution for a linear variation of viscosity across the depth. We find that tensile stresses may be very significantly altered by temperature changes of a few degrees only across the depth equal to the wavelength of the loading wave. In particular, they are reduced if the temperature decreases with depth, with beneficial effects for fatigue and wear.