Papers by Keyword: Size Dependence

Abstract: The paper presents a study of the behavior of particles of different sizes in a medium, focusing on their settling rate, hardness and elastic modulus. The settling rate was calculated using Stokes’ law, which shows a quadratic dependence on the particle radius. The results demonstrate that particles with a diameter of 100 μm settle significantly faster compared to smaller particles (1 μm and 10 μm), while the latter remain suspended for a long time due to the significant influence of viscosity. Mechanical properties of particles, such as hardness and elastic modulus, exhibit size dependence: hardness decreases with decreasing particle size, making smaller particles more vulnerable to mechanical stress. The elastic modulus shows a weak decrease for small particles, which may affect their resistance to deformation during collisions. The results obtained are important for the practical use of particles in various technological processes, such as liquid purification, development of nanomaterials, transport of solid particles in liquid or gas flows. The study emphasizes the need to consider the relationships between the physical, mechanical and dynamic characteristics of particles for optimizing technological processes and developing new materials.

Abstract: This paper presents the complete elastic field of a half space under axisymmetric surface loads by taking the influence of material microstructures into account. A well-known couple stress theory is adopted to handle such small scale effect and the resulting governing equations are solved by the method of Hankel integral transform. A selected numerical quadrature is then applied to efficiently evaluate all involved integrals. A set of results is also reported to not only confirm the validity of established solutions but also demonstrate the capability of the selected mathematical model to simulate the size-dependent characteristic of the predicted response when the external and internal length scales are comparable.

Abstract: The eutectic composite ceramic is composed of parallel lamellar inclusions distributed in the matrix. First, the recessive expression for the effective stress and the flexibility increment tensor of eutectic composite ceramic are obtained according to the four-phase model. Second, the analytical formula which contains elastic constant is given by applying Taylor’s formula. The eutectic composite ceramic is transverse isotropy, so there are five elastic constants. Third, the effective elastic constants of composite ceramics are predicted.

Abstract: The object of this work is to investigate the interface and size effects on the structural phase transition of Nb nanoparticles (NPs) embedded in Cu matrix. By means of X-ray diffraction analysis and high-resolution transmission electron microscopy observation, it is found that higher coherency of the Cu/Nb interface benefits the occurrence of phase transition in Nb NPs with larger sizes. The sufficient conditions for the transition are: (1) the size of Nb NPs should be smaller than 8 nm; (2) the Cu/Nb interfaces should be semi-coherent or coherent. The experimental results are consistent with the predictions of Bond Energy model.

Abstract: According to the interaction between lamellar inclusion and interphase, forth-phase model is suggested to determine the micro-stress-field distribution of three-phase cell in eutectic composite ceramic. On the basis of the volumetric average strain, the effective compliance tensor increment of eutectic composite ceramic is obtained. The remote stress boundary condition of the eutectic composite ceramic is accounted for getting the micro-stress-field of lamellar inclusion in eutectic composite ceramic. Analysis shows that the micro-stress-field of the lamellar inclusion in eutectic composite ceramic is associated with the stiffness and the volume fractions of each component in eutectic composite ceramic, the shape of interphase and lamellar inclusion. The-micro-stress field has apparent size effect: three direction stresses increase with the thickness of lamellar inclusion.

Abstract: On basis of the residual-stress-field of the composite ceramic, the frictional force on the boundary of the lamellae can be computed. Then the frictional work is determined. The pull-out toughening mechanism is gotten. The result shows that the toughening value is dependent on the size of lamellae: the pull-out toughening value will increase as the thickness of the lamellae increase.

Abstract: Within a micromechanical framework, the effect of surface energy is taken into account to explore the size-dependent yield criterion of nanoporous materials under complex stress states. A theoretical picture of the yield behavior on an octahedral plane is illustrated as functions of the surface properties and void size. The prominent size dependence of the yield criterion of nanoporous materials highlights the importance of the surface effect in analyzing the strength of nanostructured materials. The results demonstrate a fundamental framework to extend continuum strength theories to the nanoscale with substantial surface effect, which may be useful for evaluating the mechanical integrity of nanostructured materials.

Abstract: According to the microstructures in eutectic composite ceramic containing lamellae, the four phase model, which is composed of lamellae, eutectic interphase, matrix-atmosphere and effective medium, is put forward. Three phase cell that is composed of lamellae, eutectic interphase and matrix-atmosphere can be regarded as a composite inclusion. In view of Eshelby theory, the effective thermal expansion coefficients of eutectic composite ceramic containing the same orientation lamellae are determined. The eutectic composite ceramic is transverse isotropy and has two independent thermal expansion coefficients. The quantitative analysis shows that the effective thermal expansion coefficients have obvious size dependence.

Abstract: Based on the interaction between nano-fiber and eutectic interphase, forth-phase mode is used to get the mechanical stress field of matrix in eutectic composite ceramics. The effective flexibility increment tensor of eutectic ceramic composite is obtained by the volumetric average strain. The remote stress boundary condition of the eutectic composite ceramis is accounted for getting the mechanical stress field in matrix. The results show the mechanical stress field of the matrix is associated with the stiffness and the volume fractions of each component in eutectic composite ceramic , the shape of interphase and nano-fiber. The stresses in matrix will decrease due to the strong constraining effects of the eutectic interphase. The eutectic interphase make the eutectic composite ceramics strengthen.

Abstract: Considering the interaction between fiber-inclusion and strong constraining interphase, forth-phase model is suggested to determine the local stress field distribution of three-phase element in eutectic ceramic rod. On the basis of the volumetric average strain, the effective compliance tensor increment of eutectic ceramic rod is obtained. The remote stress boundary condition of the eutectic ceramic rod is accounted for getting the micro stress field of fibers in eutectic ceramic rod. The results show the micro stress field of the fiber-inclusion in eutectic ceramic rod is associated with the stiffness and the volume fractions of each component in eutectic ceramic rod, the shape of interphase and fiber. The micro stress field has apparent size effect: three direction stresses increase with the diameter of fiber- inclusion.