Διερεύνηση της επίδρασης των μη-τέλειων διεπιφανειών πάνω στη συνολική μηχανική και θερμική συμπεριφορά των νανο-σύνθετων υλικών. - Καραλής, Νικόλαος (Σχολή Αγρονόμων και Τοπογράφων Μηχανικών, 2015)
The subject of the present doctoral thesis is the investigation of the effect of non-perfect interfaces on the overall mechanical behavior of nano-composite materials for mechanical and thermal actions. The study is done in the framework of linear elasticity and thermoelasticity for infinitesimal strains using the simplified model of an elastic inhomogeneity within an elastic matrix. In this model, the bonding of the two materials is simulated with a two-dimensional continuum medium sticking on its opposite sides with inhomogeneity and matrix and exhibits mechanical behavior of spring or membrane type. The mechanical behavior of both spring-type and membrane-type interface is specified by the constitutive equations of the surface continuum which are derived based on the thermodynamics of continuum media. The constitutive equations derived for a spring type interface coincide with those being proposed empirically in the literature. In the present work, the constitutive equations for a membrane type interface re-derived within the linear elasticity of infinitesimal strains assuming absence of residual stress in the continuum media; it is shown that the elastic constants involved in these equations must be positive in order the elastic energy of the surface continuum to be positive. In the present work, the nature of the surface tension is clarified by introducing the concept of surface eigenstrains for two-dimensional media being the counterpart of eigenstrains defined in volume (bulk) astic media. The surface tension is interpreted as the membrane stress developed due to uniform surface eigenstrains distributed over the surface continuum of a membrane type interface; the surface eigenstrains prescribe the miss-fitting strains induced by the existing difference in the atomic distances of the matrix and inhomogeneity. The effect of both spring-type and membrane type interface on the overall energetic behavior of a nano- composite material is investigated using the inhomogeneity-matrix model prescribed previously. In the analysis, a part of the interface is assumed to correspond to the one of the two types of non-perfect interfaces mentioned previously, while the remaining, to a perfect interface. The inhomogeneity-matrix system is stressed either by a set of equilibrated surface forces acting on the external boundary of the matrix, or by a distribution of eigenstrains within inhomogeneity. For both loadings, the elastic energies stored in matrix, inhomogeneity and non-perfect interface, as well as the total potential energy of the system are defined. Based on these definitions, two new energy propositions regarding the potential energy of the system are established. These propositions allow one to determine the change in potential energy occurred in the system as a non-perfect interface forms or extent while the system is stressed. These two propositions constitute the extension of the Irwin-Bilby-Eshelby theorem developed for cracks to non-perfect interfaces. The general results, regarding the energy state of the system discussed previously, are applied to the case of a cylindrical inhomogeneity of circular crosssectional and infinite length, which is embedded to an unbounded matrix. The deformation of the system is assumed to be two-dimensional (inplane or antiplane) coming either from uniform stress applied at infinity or from eigenstrains acting in the inhomogeneity. For both loadings, the fully elastic fields along with the elastic energies stored in system constituents are obtained explicitly when the non-perfect covers the whole interface. It shown that a significant amount of elastic energy is stored in both non-perfect interfaces as the inhomogeneity size is in the nano-scale. An interesting result was derived with respect to the change in total potential energy occurring in an inhomogeneity-matrix system, as its perfect interface is transformed to a non-perfect one while the system is stressed. For both loadings, it was shown that if a perfect interface is transformed to a spring-type one, the change in the total potential energy of the system is negative and the hoop interface stress in the matrix increases. The opposite occurs if a perfect interface is transformed to a membrane-type interface: the change in the total energy of the system is positive and the hoop interface stress in the matrix decreases. Although this result was produced regarding a cylindrical circular inhomgeneity embedded in an unbounded matrix and for two specific loadings, it is conjured that it is valid for any geometry and any loading of the system. Essentially, this result reveals the identity of a spring type-interface and a membrane type interface, whose behaviors deviates oppositely from that of a perfect one. A spring type interface characterizes a deteriorating behavior of the bonds between the constituents of a composite, and a membrane type interface, an upgrading behavior. In a composite material, the transformation of a perfect interface to a non-perfect one is accompanied with changes in the thermal conditions holding across the interface. It is assumed that a spring type interface exhibits thermal behavior of low thermal conductivity, while a membrane type interface, behavior of high conductivity. The low thermal conductivity behavior is prescribed by a linear relation between heat flow and temperature jump across the interface, while those of a high conductivity, by a linear relationship between the interface which is related linearly with the interface temperature. The effect of non-perfect interfaces on the overall thermal and thermo-mechanical behavior of nano-composite materials is investigate by using the simplified model of a cylindrical circular inhomogeneity embedded in an unbounded matrix. For both non-perfect interface types, complete thermal and thermoelastic fields are obtained, when the inhomogeneity disturbs a linear temperature distribution of the matrix. It is shown that, for both types of non-perfect interfaces, the contribution of a remote uniform thermal flow to the thermo-elastic fields arising in the system becomes insignificant in nanoscale. A special case of the thermal and thermo-elastic fields obtained for a membrane type interface with a high conductivity behavior provides an important result related with the surface tension in interfaces of nano-particles. Misfitting thermal deformation produced by a membrane type interface with a high conductivity behavior induces constants stress in the interface of ‘surface tension’ type. Also, it was shown that the results regarding the stress concentration obtained for the mechanical loadings are valid for the thermal loadings considered.