Thesis (Ph. D.)--University of Wisconsin--Madison, 1963. / Typescript. Abstracted in Dissertation abstracts, v. 23 (1963) no. 9, p. 3153. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 101-104).

The thesis aims to study the effects of the mixing of immiscible polymers on the frictional properties of rubber compounds. The novelty of this work is to consider the rubber as a heterogeneous material in which the microscopic inhomogeneities are the domains generated from the mixing of immiscible compounds. Systematic experimental tests are performed to investigate the frictional properties of two different groups of tyre compounds, both provided by Pirelli Tyre S.p.A. The first group is represented by the homogeneous compounds realized by using Natural Rubber (NR) or Styrene Butadiene Rubber (SBR) and different amounts of filler and Sulphur. The second group considers heterogeneous compounds, generated by mixing in different percentages the homogeneous compounds, to obtain compounds characterized by microscopic domains of NR and SBR. The experimental outcomes proved that the presence of domains increases the friction coefficients. A Dynamic Mechanical Analysis (DMA) is performed to correlate the dynamic properties of the specimens with the friction coefficient. The results of the DMA of the homogeneous compounds agree with the frictional properties while the heterogeneous compounds show intermediate dynamical properties in contrast with the frictional results. The DMA is not able to recognize the microscopic domains of the heterogeneous compounds interpreting the system as a uniform material, suggesting that more complex dynamics arise during the sliding. The dependence of friction on the composition of the material is also investigated by using a numerical approach. For this purpose, a straightforward model is chosen to investigate numerically the frictional behaviour of a rubber material starting from the microscopic properties. The model is discretized as a chain of blocks connected by springs and dampers. Playing with the microscopic parameters of the model, such as the elastic modulus and the damping coefficient, it is possible to link the macroscopic frictional response of the bulk to the microscopic characteristics that locally describes the interactions between the blocks. Firstly, the frictional properties of compounds characterized by i) uniformly distributed viscoelastic or elastic elements and ii) a combination of purely elastic and viscoelastic elements randomly distributed is compared. The numerical outcomes reveal an increase of the frictional properties for samples realized by mixing elastic and viscoelastic elements pointing out that the presence of different domains due to the mixing of two immiscible materials, affects the macroscopic frictional response. Secondly, a comparison between the experiments and the numerical simulations is performed to verify if the 1D model can correctly predict the observed experimental behaviour. The 1D model, in its simplicity, is unable to predict the increase of frictional properties observed experimentally testing the heterogeneous compounds, confirming that more complex interactions influence the friction as suggested by the DMA.

The thesis presents novel formulations of hereditary cohesive zone models able to capture rate-dependent crack propagation along a defined interface. The formulations rely on the assumption that the measured fracture energy is the sum of an intrinsic fracture energy, related to the rupture of primary bonds at the atomic or molecular level, and an additional dissipation caused by any irreversible mechanisms present in the material and occurring simultaneously to fracture. The first contribution can be accounted for by introducing damage-type internal variables, which are to be driven by a rateindependent evolution law in order to be coherent with the definition as intrinsic energy. It is then proposed that the additional dissipation can be satisfactorily characterised by the same continuum-type material constitutive law obeyed by the interface material considered as a continuum: it is postulated that the dimensional reduction whereby a three-dimensional thin layer is idealized as a surface does not qualitatively alter the functional description of the free energy. The specific application considered is mode-I crack propagation along a rubber interface. After focusing on viscoelasticity as a suitable candidate to reproduce rubber’s behaviour, firstly the most common relaxation function, namely a single exponential term, is considerd after which the attention is turned to the use of fractional calculus and the related fractional integral kernel. A comparison with experimental results is presented. A shortcoming of the proposed approach is then noted, in that certain features of experimentally measured responses (i.e.the non-monotonicity of the critical energy-release rate with respect to crack speed) will be shown to be out of reach for the described modelling paradigm. A novel micromechanical formulation is then sketched in an attempt to qualitatively understand the phenomenon. An additional interface damaging mode is introduced, physically inspired by the desire to reproduce the formation of fibrils in a neighbourhood of the crack tip. Fibril formation is then driven by a variational argument applied to the whole of the interface, yielding its non-local character. Upon the introduction of an anisotropic fracture energy, motivated by experimental considerations, it is noted how the model can predict a non-monotonic energy-release rate vs crack speed behaviour, at least for a simple loading mode.