Multiscale Modelling And Numerical Simulation Of The Wear And Elastoplasticity Of Inhomogeneous Materials

With the rapid development of bionics and 3D print technology, the excellent mechanical and tribological behaviors of particle and fiber reinforced composites have been unveiled at different scales and attracted further attention from researchers in the fields of mechanics, materials science and tribology. The existing studies on the wear of inhomogeneous materials (or composites) are limited to some phenomenological descriptions while mostly often considering only the macroscopic scale. Thus, it is impossible to reveal the correlation of the macroscopic wear property with the microstructure and material properties of the constituents. In the purpose of optimizing the tribological design of bionic composite materials with hierarchical structures, the first main objective of the thesis is to propose a micromechanical approach and a numerical method so as to get a better qualitative understanding and a better quantitative estimation of the wear of inhomogeneous composites. The elastic, viscoelastic and elastoplastic constitutive laws of the constituents are taken into account. Besides, in view of the fact that the plastic behavior of the matrix phase is pressure-sensitive for a wide class of polymers and geomaterials, the second part of the thesis is dedicated to the homogenization of the elastoplastic behavior of particle/fiber-reinforced composites with the matrix obeying to some pressure-dependent criteria. The main novel points are summarized as follows:(1) Theoretical estimates of the wear of fiber-reinforced composites by a micromechanical approach:under uniform boundary conditions, the effective wear rate of such a composite are quantitatively determined in terms of the elastic and wear properties of its components. The effect of the viscoelastic and elastoplastic parameters of the matrix on the macroscopic wear is accounted for.(2) A Finite Element-based model simulating the wear process of composites:based on the finite element model of fiber-reinforced composites, the stress distribution over the contact region and the wear rate are calculated during the wear process. The evolution of the worn surface can be illustrated by a post-processing.(3) Due to the fact that the yielding behavior of the matrix may be pressure-sensitive, the homogenization of the elastoplastic behavior of particle or fiber reinforced composites is extended to the cases where the Mohr-Coulomb or Drucker-Prager yielding condition and the non-associated flow rule prevail.The main contents are listed in the following:(1) The key to determining the effective wear property of a fiber-reinforced composite relies on the ratio of the load sustained by the fibers to the one by the matrix. The effective wear compliance of the composite is analytically expressed in terms of the elastic moduli, Poisson's ratios, wear compliances and volume fractions of the constituents. The theoretical estimate obtained under a uniform strain condition turns out to be in good agreement with available experimental results.(2) The effective wear compliance of a composite is shown to depend on the wear and material properties of its constituents. Taking into account the viscoelastic effect of the matrix phase, the macroscopic wear is lowered. In the case of an elastoplastic matrix, the introducing of bulk material nonlinearity makes the effective wear compliance nonlinear, whose value increases with the extension of the plastic region in the composite.(3) The effective wear obtained by numerical simulations is in good agreement with the theoretical estimates under the uniform strain hypothesis. With the accumulation of wear cycles, the load proportion sustained by the better wear-resistant phase increases, resulting in the reduced effective wear rate compared with the initial stage of wear process. Considering the composite reinforced with oblique fibers, the load proportion sustained by two phases varies with the friction coefficient and sliding direction.(4) The pressure-sensitive parameter of Mohr-Coulomb yielding condition has a prominent effect on the effective elastoplastic behavior of particulate composites. The porous media is greatly influenced by the parameters of the non-associated flow rule. For a fiber-reinforced composite with its matrix complying with Drucker-Prager criterion and the non-associated flow rule, the analytical expression of the effective elastoplastic behavior can be obtained if the matrix is assumed to be incompressible.The results obtained in the first part of the thesis can serve for optimizing the tribological design of composites, provide theoretical basis for interpreting experimental results regarding to the evolution of viscoelastic or elastoplastic materials during wear processes. The results of the second part are useful, in particular, as benchmarks for the numerical homogenization of elastoplastic inhomogeneous materials.