| Effective mechanical properties of micro/nanoscale materials and structures（MNMSs）are affected by surface elasticity,and mechanism analysis of failure of such MNMSs plays a significant role in the structures’integrity and reliability.This paper focuses on micro/nanoscale thin plates commonly found in flexible ultra-thin electronic devices,micro/nano-scale electromechanical systems and so on.Based on the classical Kirchhoff elastic thin plate theory with Gurtin-Murdoch surface elasticity theory,a basic theory for the static bending problem of micro/nanoscale plates with consideration of surface elasticity is established.By use of the superposition principle and Fourier integral transform method,the elastic fields induced by cracks or rigid lines in a micro/nanoscale thin plate with surface elasticity under applied loadings are studied.Furthermore,the singular elastic fields of the thin plate and the singularity indexes as well as stress intensity factors（singularity coefficients）near the tips are determined,and the dependence between surface elasticity,the thickness of thin plates,etc.and singularity parameters is analyzed.This paper is to formulate a theoretical model of fracture mechanics of micro/nanoscale elastic thin plates with surface elasticity,develop continuum mechanics research categories,and reveal the failure mechanism of micro/nanoscale elastic thin plates.This paper founds a theoretical basis for the reliability and integrity analysis as well as safety design of micro/nano-scale thin plates.The main research work of this thesis is as follows:（1）The bending fracture model of an infinitely large micro/nanoscale elastic thin plate containing a central thickness-through crack with surface elasticity under uniform constant bending moment,twisting moment and out-of-plane shear force at infinite is proposed.The mixed boundary value problems corresponding to each case are transformed into hypersingular integral equations,respectively,and the exact solution of the elastic field in the whole thin plate can be obtained.The singularity indexes of the elastic field near the crack tip are determined,the bulk stress component,bending moment and twisting moment near the crack tips both have a usual inverse square root singularity,while the effective shear force exhibits an r-3/2singularity,r being the distance from the crack tip.The results show that the stress intensity factors are related to the material properties both of the surface and bulk phases.It is found that positive surface Young’s modulus can reduce the stress intensity factor and improve the fracture toughness of micro/nanoscale elastic thin plates.（2）The bending fracture model of an infinitely large micro/nanoscale elastic thin plate containing two collinear isometric thickness-through cracks with surface elasticity under uniform constant bending moment,twisting moment and out-of-plane shear force at infinite is proposed.For three different loadings,the corresponding singular integral equation is derived,and the singular elastic fields along the crack line and the stress intensity factors at the crack tips are obtained.Based on the study of a single central crack,the influence of the interaction between two cracks on the stress intensity factors at the crack tip is mainly analyzed.The results show that when the distance between two collinear isometric cracks exceeds the length of a single crack,the interaction is negligible.For both cases of bending moment and twisting moment,the inner crack tip is easier to expand than the outer crack tip,and the closer the distance between the two cracks,the stronger the interaction.However,for the case of shear force,if the distance between the two cracks is closer,the interaction between the inner crack tip becomes weaker,while the outer crack tip becomes stronger.（3）The bending fracture model of an infinitely large micro/nanoscale elastic thin plate containing a central rigid line inclusion with surface elasticity when an off-plate rigid rotation is prescribed is proposed.Using the corresponding mixed boundary value condition of this mechanical problem,a weakly singular integral equation with the logarithmic kernel is obtained,and the exact expressions of the elastic field of the whole micro/nanoscale plate and the singularity coefficients at the rigid line inclusion tip are further derived.The results show that the bending moment and bulk and surface normal stress components at the tip of the rigid line inclusion have an r-3/2singularity,while the effective shear force exhibits anr-5/2 singularity,where r denotes the distance from the rigid line inclusion.In addition,positive surface Young’s modulus increases its effective bending strength.（4）The bending model of adhering to a central rigid line on an infinitely large micro/nanoscale elastic thin plate with surface elasticity is proposed.The corresponding mixed boundary value problem is reduced to a standard singular integral equation of the first kind with Cauchy kernel,and the exact solution of the elastic field in the whole plate and the singularity coefficients at the rigid line tip are determined.The results show that the bending moment and bulk and surface normal stress components at the rigid line tips both exhibit a usual inverse square root singularity,while the effective shear force has an r-3/2 singularity,r being the distance from the rigid line tip.The elastic fields of the thin plate,including the bending moment,effective shear force,and bulk and surface stress components,are all dependent on the material properties of the surface and bulk phases.When the thickness of the plate is reduced to the nanometer order,the influence of surface elasticity on the elastic field of the plate is more significant,indicating that there is a strong scale effect at this time.（5）The bending model of adhering a finite-length rigid line to part of the boundary of a half infinity micro/nanoscale plate with surface elasticity is proposed.A mixed boundary value problem related to a parabolic rigid line is solved,and a non-standard singular integral equation with two Cauchy kernels can be obtained.Furthermore,the solution to the singular integral equation is derived,and the accurate oscillating singular elastic fields near the rigid line tips are given in elementary functions.The results show that the bending moments and the normal stress components of the bulk and surface phases in the vicinity of the rigid line tips simultaneously have an oscillator singular behavior like r-3/2-iε,εrelying on the material properties.Besides,the effective shear forces exhibit the r-5/2-iεsingular behavior.Meanwhile,the oscillatory singular behavior is related to the material properties of the surface and bulk phases.This conclusion is helpful to further understand the failure mechanism analysis of micro/nanoscale elastic thin plates. |
