Studies On The Elastic Fields And Strain Energies Of Plane Circular Inhomogeneity And Ellipsoidal Inclusion In Half-space

Key machine components in mechanical transmission systems and precision transmission systems in aerospace present new serious challenge to the good durability,high-strength and well reliability properties of the materials.Inclusions or inhomogeneities affect the characterization of the microstructure and macroscopic properties of the material.Therefore,it is of great theoretical significance and application value to carry out basic theoretical research on the inclusions and inhomogeneities.This work is supported by the Fundamental Research Funds for the Central Universities entitled“The Theoretical and Experimental Study of Micromechanical Mechanisms of the Contact Fatigue for the Inhomogeneous Materials(No.106112017CDJQJ328839)” and the National Science Foundation of China titled "A Micromechanical Study of the Friction and Wear Behavior of Inhomogeneous materials containing Inclusions and Cracks(No.51875059)".Based on the foundamental theories of micromechanics and material sciences,combined with theoretical derivation,numerical calculation and finite element simulation,the elactic field and the elastic strain energy of plane circular inhomogeneity and ellipsoid inclusion in half-space are studied.Explore the mechanism of failure in microscale.The main contents of the thesis are as follows:Firstly,based on the fundamental governing equations of micromechanics,take the relatively simple two-dimensional problem as an example to demonstrate the basic ideas and research routes of micromechanics to solve the problem of inclusions and inhomogeneities.Present a complete set of the Eshelby tensors including stress,strain,displacement and displacement gradient tensors of circular inclusion problem.Based on the classical solution of circular inclusion and the equivalent inclusion method,stress and strain corresponding to the plane circular inhomogeneity problem are derived in closedform.The equivalent inclusion method can also be used to solve the plane circular cavity problem.The closed-form solutions for stress and displacement of a circular cavity problem under normal and tangential boundary tractions are derived,where the results are expressed in polar coordinates.The validity is confirmed both in the circular inhomogeneity and the circular cavity problems.The applicability of the equivalent inclusion method to the circular inhomogeneity and circular cavity problems are exemplified.Secondly,two numerical approaches are proposed to solve the ellipsoidal inclusion in a half-space by the method of images.The numeirical solutions of surface tractions in this two methods may have discrete error caused by meshing numbers and truncation error due to magnification factor of the computation domain contain the surface tractions.Comparisons and parametric studies for the two different methods are carried out,including the accuracy of different meshing numbers and magnification factors.The FFT algorithm is added to the numerical solutions and the comparison of the computational time of the two methods proved that the applications of FFT can greatly improve the calculational efficiency.Lastly,based on the solutions of plane circular inclusion and ellipsoidal inculsion in half-space,the elastic strain energy of single inclusion in this two problems are solved.The validity is confirmed in both problems and parametric studies are carried out in the strain energy change along with the size of the plane circular inclusion and the depth of the ellipsoidal inclusion in half-space.The strain energy of multiple plane circular inclusions and half-space ellipsoidal inclusions with uniform or non-uniform eigenstrain are studied by the finite element method.The strain energy density of double-layer circular and ellipsoidal inhomogeneities are also analyzed.Further,extend the half-space problem to the contact problem with inhomogeneities,compare the strain energy of stiff and compliant inhomogeneities.