| Interfaces in fiber reinforced composites (FRC) are vital because they ensure stress transfer between matrix and fibers. To characterize the interfacial properties in a fiber reinforced composites, several micromechanical experimental techniques have been developed. These include the single fiber pull out tests, single fiber fragmentation tests, etc. However, experimental work is time consuming and its outcomes are not always repeatable, while analytical solutions are not usually available for solving such complex problems as the characterizations of the interfacial mechanical properties of fiber reinforced composites. As a result, the application of numerical methods in the study of interfacial problems in the field of fiber reinforced composites has attracted more and more attentions.Although numerical methods have frequently been used in the study of FRC, theoretical analyses of such test methods as pull out tests and single fiber fragmentation tests, seemingly simple, remain to be challenging problems. Problems arise when other factors are considered in connection with the various numerical models. These factors include nonlinearities in the properties and/or geometries of the materials, influences of such environmental conditions as temperature (which is also to be studied in the present work).Research work described in this dissertation consists of four parts: application of Finite Element Methods (FEM) in the study of pull out tests of single fiber reinforced composites (SFRC), FEM study of fragmentation tests for single fiber reinforced composites, Monte Carlo simulation of fragmentation tests for single fiber reinforced composites, and a simulation of impact failure behaviors of fiber composites with a mesh free method-the SPH method.In the first part of the research, FEM simulations are carried out in the study of the failure process of a single fiber composite in the pull out tests.To begin with, simulated results of fiber axial stress, interfacial shear stress and variation of axial stress along a SFRC cross section are compared with their analytical solutions by means of a shear-lag method, on the assumption of perfect bonding. The results of numerical simulations and analytical solution show good accordance, except in the region near the fiber ends, where the shear-lag approach causes considerable discrepancy.Next, to overcome the unrealistic assumption of perfect bonding, augmented-Lagrange contact algorithm, element 'birth-death' and FEM are combined in the study of the partial debonding between fiber and matrix under pull out forces. The tendency of the simulated curves of pull out forces vs. displacements agrees well with experimental results, indicating the use and power of the present approach.Finally, an energy approach is combined with the FEM in the simulation of the crack propagation along the fiber/matrix interface in a pull out process. The simulated results are in nice conformity with experimental results.The second part of the research deals with the characterization of the failure process in the fragmentation tests, which is one of the most frequently used test methods in studying thermal mechanical properties of fiber/matrix interfaces. Here, FEM is applied in the analyses of i) fiber axial stress and interphase shear stress in fragmentation tests during initially applied strain, ii) influence of temperature on the stress transfer across the interface, iii) modulus and thickness of the interphase and their influence on interfacial stress transfer, iv) interfacial debonding process, and v) fragment aspect ratio, contact friction along the interface and their influences to the interfacial stress transfer efficiency.Firstly, the effect of initially applied strain is that, when it rises,the fiber axial stress decreases, indicating less efficiency in the stress transfer across the interfaces.The simulation results also show that the modulus of interphase has no significant effect on the fiber axial stress, and increased interphase thickness does...
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