A Friction Physical Model for the Estimation of Hysteretic Dissipations Arising at the Contact Between Rigid Indenters and Visco-Elastic Materials

Friction phenomenon for elastomeric materials has been widely studied: experiments show that friction coefficient is function of several parameters, such as sliding velocity, local pressure, contact surfaces roughness, material characteristics and temperature. Many theories hypothesize resistant forces arising at tyre/road interface as constituted by three components: deforming hysteresis, adhesion and wear. Neglecting wear, the other two components are connected and interact reciprocally, whenever basing themselves on different physical mechanisms and acting on different roughness scales; aim of the present work is to provide a procedure that allows to estimate hysteretic component of friction by means of an indentation model able to calculate stresses and deformations produced by an infinitely rigid sinusoidal indenter in sliding contact with a visco-elastic material. In order to take into account of the phenomena connected with asperities indentation inside tyre tread, it has been necessary to analyze road profiles and to model roughness by means of different magnitude scales; moreover, employing WLF law over these profiles has allowed to analyze rubber master curve both in temperature and frequency domains, providing the dependencies of storage modulus E’ and loss modulus E’’ from sliding velocity and temperature itself. Visco-elastic characteristics of SBR tyre compound, obtained thanks to Dynamic-Mechanical Analysis (DMA) testing machines and to Differential Scanning Calorimetry (DSC) techniques, have been employed as an input for a three dimensional innovative adaptation of the equations provided by YE. A. Kuznetsov since 1980 in various of his works. The stresses and the consequential deformations, representing the causes of the power dissipated inside the considered tread elementary volume, have been calculated and validated together with indentation profiles by means of FEM simulations, finally providing results in good accordance with the expected trends and functionalities