SURFACE STRESS AND SURFACE ENERGY OF SOLIDS AND SIZE-DEPENDENT YOUNGS MODULUS
Following Gibbs approach to interfacial excess quantities,Muller and Saul analyzed the excess of elastic energy at an interface by decomposing stress and strain tensors into perpendicular and parallel contributions 1.Based on traction continuity and non-gliding at the interface,they defined interfacial stress tensor,σsij,and interfacial strain tensor, εsij,as where A is the interfacial area, Vα and Vβ are the volumes of bulk phases a and β extrapolated to the dividing surface,and the integration limits, zα and zβ, include the entire interfacial transition zone.Then,the change in interface energy due to mechanical loading is given by Dingrcville and Qu 2 re-analyzed the problem of interfacial excess energy,excess stress and excess strain of planar interfaces.Their analysis indicates that surface stress and surface strain are not intrinsic properties of materials;rather,the in-plane interfacial stiffness tensor,the out-plane interfacial compliance tensor,and the coupling tensor,which accounts for the Poissons effect of interface,describe fully the elastic behavior of a coherent interface upon deformation. We re-analyzed surface energy,surface stress,and surface elastic constants of a nanowire by treating a nanowire as a composite of a three-dimensional hypothetical nanowire,namely the core,two-dimensional geometric surfaces,and one-dimensional geometric edges 2.When a free-standing nanowire subjected to no external loads is at equilibrium after relaxation,the core usually presents an initial deformation along the nanowire length direction with respect to the stress-free bulk counterpart.When the initial stress field in the core is known,surface stress is determined from the force balance 3.Following the same approach,we investigated the bending behaviors of nanowires 4,5.Taking solid films as typical example,we further studied surface stress of solids.If the bulk counterpart of a nanomaterial is taken as reference,a newly created nanomaterial relaxes inevitably because new surfaces are created 6.We separated the relaxation process into normal relaxation and parallel relaxation and proposed a surface eigenstress model to calculate the energy change during parallel relaxation 6.Parallel relaxation induces in-piane deformation,called initial deformation,which could be large and nonlinear.After parallel relaxation,a tensile (or compressive) surface eigenstress causes a compressive (or tensile) initial strain in the thin film with respect to its bulk lattice.Due to initial deformation,surface energy density and surface stress are both dependent on the film thickness,whereas surface elastic constants are independent of the film thickness.The similar results were obtained before by Dingreville et al.7.Consequently,a general scaling law about the nominal Youngs modulus is derived naturally and directly from the eigenstress model,indicating that the nominal modulus of a thin film is determined generally by nonlinear elastic properties of its core and surfaces with initial strain.If initial deformation is linear,the general scaling law will be reduced to the linear scaling law.A tensile (or compressive) surface eigens.ress makes the nominal modulus of a thin film lager (or smaller),resulting in the thinner-the harder (or softer) elastic behaviour in thin films.The surface eigenstress model was further developed for nanowires under tension/compression and bending,leading to general scaling laws of nominal Youngs modulus of nanowires under tension/compression and bending 8.Recently,we systematically studied the energy change during normal relaxation.The results show that surface elasticity given by Eq.(1) is capable to describe the energy change in a solid surface only after the dimension-conserved normal relaxation,and surface elastic constants,surface eigen-stress and surface eigen-displacement are intrinsic surface properties.
Surface energy surface stress surface elasticity size-dependent Youngs modulus solids
T.Y.Zhang
Department of Mechanical Engineering,Hong Kong University of Science and Technology,Clear Water Bay,Kowloon,Hong Kong,China
国际会议
The Third International Conference on Heterogeneous Material Mechanics(第三届国际非均匀材料力学会议)
上海
英文
483-484
2011-05-22（万方平台首次上网日期，不代表论文的发表时间）