A new analytical-numerical method for calculating interacting stresses of a multi-hole problem under both remote and arbitrary surface stresses

Based on the elementary solutions and new integral equations,a new analytical-numerical method is proposed to calculate the interacting stresses of multiple circular holes in an infinite elastic plate under both remote stresses and arbitrarily distributed stresses applied to the circular boundaries.The validity of this new analytical-numerical method is verified by the analytical solution of the bi-harmonic stress function method,the numerical solution of the finite element method,and the analytical-numerical solutions of the series expansion and Laurent series methods.Some numerical examples are presented to investigate the effects of the hole geometry parameters(radii and relative positions)and loading conditions(remote stresses and surface stresses)on the interacting tangential stresses and interacting stress concentration factors(SCFs).The results show that whether the interference effect is shielding(k<1)or amplifying(k>1)depends on the relative orientation of holes(α)and remote stresses(σ^∞x,σ^∞y).When the maximum principal stress is aligned with the connecting line of two-hole centers andσ^∞y<0.5σ^∞x,the plate containing two circular holes has greater stability than that containing one circular hole,and the smaller circular hole has greater stability than the bigger one.This new method not only has a simple formulation and high accuracy,but also has an advantage of wide applications over common analytical methods and analytical-numerical methods in calculating the interacting stresses of a multi-hole problem under both remote and arbitrary surface stresses.

Interacting Stress Intensity Factors of Multiple Elliptical-Holes and Cracks Under Far-Field and Arbitrary Surface Stresses

Calculating interacting stress intensity factors(SIFs)of multiple ellipticalholes and cracks is very important for safety assessment,stop-hole optimization design and resource exploitation production in underground rock engineering,e.g.,buried tunnels,deep mining,geothermal and shale oil/gas exploitation by hydraulic fracturing technology,where both geo-stresses and surface stresses are applied on buried tunnels,horizontal wells and natural cracks.However,current literatures are focused mainly on study of interacting SIFs of multiple elliptical-holes(or circularholes)and cracks only under far-field stresses without consideration of arbitrary surface stresses.Recently,our group has proposed a new integral method to calculate interacting SIFs of multiple circular-holes and cracks subjected to far-filed and surface stresses.This new method will be developed to study the problem of multiple elliptical-hole and cracks subjected to both far-field and surface stresses.In this study,based on Cauchy integral theorem,the exact fundamental stress solutions of single elliptical-hole under arbitrarily concentrated surface normal and shear forces are derived to establish new integral equation formulations for calculating interacting SIFs of multiple elliptical-holes and cracks under both far-field and arbitrary surface stresses.The new method is proved to be valid by comparing our results of interacting SIFs with those obtained by Green’s function method,displacement discontinuity method,singular integral equation method,pseudo-dislocations method and finite element method.Computational examples of one elliptical-hole and one crack in an infinite elastic body are given to analyze influence of loads and geometries on interacting SIFs.Research results show that whenσ_(xx)^(∞)≥σ^(yy′)^(∞),there appears a neutral crack orientation angle b0(without elliptical-hole’s effect).Increasing s¥xx/s¥yy and b/a(close to circularhole)usually decreases b0 of KI and benefits to the layout of stop-holes.The surface compressive stresses applied onto elliptical-hole(n)and crack(p)have significant influence on interacting SIFs but almost no on b0.Increasing n and p usually results in increase of interacting SIFs and facilitates crack propagation and fracture networks.The elliptical-hole orientation angle(a)and holed-cracked distance(t)have great influence on the interacting SIFs while have little effect on b0.The present method is not only simple(without any singular parts),high-accurate(due to exact fundamental stress solutions)and wider applicable(under far-field stresses and arbitrarily distributed surface stress)than the common methods,but also has the potential for the anisotropic problem involving multiple holes and cracks.

Optimization of Rolling Parameters for Enhancing Surface Integrity of Aluminum Alloy

In this current work,aluminum alloy grade 2024 is adopted as a plate material that is used in the rolling process with three different parameters including thickness reduction,forming temperature,and density of lubrication type.The experimental procedure of the rolling process is performed using the design of the experiment based on the Taguchi technique(L27),then surface roughness,surface hardness,and surface residual stresses are measured.The results showed that the lubrication density has a significant impact on the surface roughness which depends on the lubrication properties(mineral oil type,natural fat,and kinematic viscosity)while surface hardness and surface residual stresses were strongly affected by thickness reduction.On the other side,the augment in forming temperature can decrease the quality of the final surface finish and the surface hardness but reduce the induced residual stresses.The best surface finish is obtained based on the optimum condition of the rolling factors are(R%_(3),T_(1),andρ_(3))while the optimum condition of rolling parameters that generate higher hardness and compressive residual stresses are(R%_(3)T_(1)ρ_(1)).

Surface stress effect on the vibration and instability of nanoscale pipes conveying fluid based on a size-dependent Timoshenko beam model

Presented in this paper is a precise investigation of the effect of surface stress on the vibration characteristics and instability of fluid-conveying nanoscale pipes.To this end,the nanoscale pipe is modeled as a Timoshenko nanobeam.The equations of motion of the nanoscale pipe are obtained based on Hamilton＇s principle and the Gurtin-Murdoch continuum elasticity incorporating the surface stress effect.Afterwards,the generalized differential quadrature method is employed to discretize the governing equations and associated boundary conditions.To what extent important parameters such as the thickness,material and surface stress modulus,residual surface stress,surface density,and boundary conditions influence the natural frequency of nanoscale pipes and the critical velocity of fluid is discussed.

Influence of cross correlation step length on the surface stress of thin laser cladding Fe314 alloy coatings

To measure the surface stress of thin laser cladding coatings with Rayleigh waves based on the cross correlation function, this pa- per introduced the influence of cross correlation step length on the stress measurement. Flat-shaped specimens made of laser cladding Fe314 alloy coatings were performed by static tensile tests, and Rayleigh wave signals were collected during the test process with an ultrasonic pulser and receiver instrument combined with two Rayleigh wave transducers. The difference in time of flight between two signals was de- termined based on the cross correlation function. The microstructure was observed by scanning electronic microscopy. The influence of the stress on the propagation velocity of Rayleigh waves and the relationship between the difference in time of flight and tensile stress under dif- ferent cross correlation step lengths were analyzed. The inhomogeneous deformation of the coatings affects the relationship between the dif- ference in time of flight and tensile stress; the stress measurement of the coatings is nearly constant with the increase of cross correlation step length when it attains one cycle.

Effect of surface stress and surface-induced stress on behavior of piezoelectric nanobeam

A new continuum model is developed to study the influence of surface stress on the behaviors of piezoelectric nanobeams. Different from existing piezoelectric surface models which only consider the surface properties, the proposed model takes surfaceinduced initial fields into consideration. Due to the fact that the surface-induced initial fields are totally different under various boundary conditions, two kinds of beams, the doubly-clamped beam and the cantilever beam, are analyzed. Furthermore, boundary conditions can affect not only the initial state of the piezoelectric nanobeam but also the forms of the governing equations. Based on the Euler-Bernoulli beam theory, the nonlin- ear Green-Lagrangian strain-displacement relationship is applied. In addition, the surface area change is also considered in the proposed model. The governing equations of the doubly-clamped and cantilever beams are derived by the energy variation principle. Com- pared with existing Young-Laplace models, the proposed model for the doubly-clamped beam is similar to the Young-Laplace models. However~ the governing equation of the cantilever beam derived by the proposed model is very different from that derived by the Young-Laplace models. The behaviors of piezoelectric nanobeams predicted by these two models Mso have significant discrepancies, which is owing to the surface-induced initial fields in the bulk beam.

Size-dependent effect on biaxial and shear nonlinear buckling analysis of nonlocal isotropic and orthotropic micro-plate based on surface stress and modified couple stress theories using differential quadrature method

The size-dependent effect on the biaxial and shear nonlinear buckling analysis of an isotropic and orthotropic micro-plate based on the surface stress, the modified couple stress theory （MCST）, and the nonlocal elasticity theories using the differential quadrature method （DQM） is presented. Main advantages of the MCST over the classical theory （CT） are the inclusion of the asymmetric couple stress tensor and the consideration of only one material length scale parameter. Based on the nonlinear von Karman assumption, the governing equations of equilibrium for the micro-classical plate consid- ering midplane displacements are derived based on the minimum principle of potential energy. Using the DQM, the biaxial and shear critical buckling loads of the micro-plate for various boundary conditions are obtained. Accuracy of the obtained results is validated by comparing the solutions with those reported in the literature. A parametric study is conducted to show the effects of the aspect ratio, the side-to-thickness ratio, Eringen＇s nonlocal parameter, the material length scale parameter, Young＇s modulus of the surface layer, the surface residual stress, the polymer matrix coefficients, and various boundary conditions on the dimensionless uniaxial, biaxial, and shear critical buckling loads. The results indicate that the critical buckling loads are strongly sensitive to Eringen＇s nonlocal parameter, the material length scale parameter, and the surface residual stress effects, while the effect of Young＇s modulus of the surface layer on the critical buckling load is negligible. Also, considering the size dependent effect causes the increase in the stiffness of the orthotropic micro-plate. The results show that the critical biaxial buckling load increases with an increase in G12/E2 and vice versa for E1/E2. It is shown that the nonlinear biaxial buckling ratio decreases as the aspect ratio increases and vice versa for the buckling amplitude. Because of the most lightweight micro-composite materials with high strength/weight and stiffness/weight ratios, it is anticipated that the results of the present work are useful in experimental characterization of the mechanical properties of micro-composite plates in the aircraft industry and other engineering applications.

SURFACE-ENHANCED CANTILEVER SENSORS WITH NANO-POROUS FILMS

Developing surface-enhanced microcantilevers with improved sensitivities is of longstanding interest. In this paper, the design of surface-enhanced cantilever sensors using nano- （micro-） porous films as surface layers is proposed. The static deformation and resonance frequencies of these surface-enhanced sensors with the simultaneous effects of the eigenstrain, the surface stress and the adsorption mass are analyzed. It is shown that the sensitivities of these novel cantilever sensors for the static deformation and resonance frequencies can be tuned by the porosity, the size of the pores and the structure of the porous films. For the three kinds of cantilever consisting of solid films, films with aligned cylindrical micro-scale pores, and those with nano-scale pores, the nano-porous one has the highest static and dynamic sensitivities, whereas the solid one has the lowest.

Analytical solution approach for nonlinear buckling and postbuckling analysis of cylindrical nanoshells based on surface elasticity theory

The size-dependent nonlinear buckling and postbuckling characteristics of circular cylindrical nanoshells subjected to the axial compressive load are investigated with an analytical approach. The surface energy effects are taken into account according to the surface elasticity theory of Gurtin and Murdoch. The developed geometrically nonlinear shell model is based on the classical Donnell shell theory and the von Karman＇s hypothesis. With the numerical results, the effect of the surface stress on the nonlinear buckling and postbuckling behaviors of nanoshells made of Si and Al is studied. Moreover, the influence of the surface residual tension and the radius-to-thickness ratio is illustrated. The results indicate that the surface stress has an important effect on prebuckling and postbuekling characteristics of nanoshells with small sizes.

Spatio-temporal variability in sea surface wind stress near and off the east coast of Korea

Sea surface wind stress variabilities near and off the east coast of Korea, are examined using 7 kinds of wind datasets from measurements at 2 coastal (land) stations and 2 ocean buoys,satellite scatterometer (QuikSCAT), and global reanalyzed products (ECMWF,NOGAPS,and NCEP/NCAR). Temporal variabilities are analyzed at 3 frequency bands; synoptic (2-20 d), intra-seasonal (20-90 d),and seasonal (>90 d).Synoptic and intra-seasonal variations are predominant near and off the Donghae City due to the passage of the mesoscale weather system. Seasonal variation is caused by southeastward wind stress during Asian winter monsoon. The sea surface wind stress from reanalyzed datasets.QuikSCAT and KMA-B measurements off the coast show good agreement in the magnitude and direction,which are strongly aligned with the alongshore direction.At the land-based sites,wind stresses are much weaker by factors of 3-10 due to the mountainous landmass on the east parts of Korea Peninsula.The first EOF modes(67%-70%) of wind stresses from reanalyzed and QuikSCAT data have similar structures of the strong southeastward wind stress in winter along the coast but show different curl structures at scales less than 200 km due to the orographic effects.The second EOF modes (23%-25%) show southwestward wind stress in every September along the east coast of the North Korea

SHAPE BIFURCATION OF AN ELASTIC WAFER DUE TO SURFACE STRESS

A geometrically nonlinear analysis was proposed for the deformation of a free standing elastically isotropic wafer caused by the surface stress change on one surface. The link between the curvature and the change in surface stress was obtained analytically from energetic consideration. In contrast to the existing linear analysis, a remarkable consequence is that, when the wafer is very thin or the surface stress difference between the two major surfaces is large enough, the shape of the wafer will bifurcate.

Comparison among four kinds of data of sea surface wind stress in the South China Sea

By using remote sensing (ERS) data, FSU data, COADS data and Hellerman & Rosen-stein objective analysis data to analyze the sea surface wind stress in the South China Sea, it is found that the remote sensing data have higher resolution and more reasonable values. Therefore we suggest that remote sensing data be chosen in the study of climatological features of sea surface wind stress and its seasonal variability in the South China Sea, especially in the study of small and middle scale eddies.

Effect of Surface Topography on Stress Concentration Factor

Neuber rule and Arola-Ramulu model are widely used to predict the stress concentration factor of rough specimens. However, the height parameters and effective valley radius used in these two models depend strongly on the resolution of the roughness-measuring instruments and are easily introduce measuring errors. Besides, it is difficult to find a suitable parameter to characterize surface topography to quantitatively describe its effect on stress concentration factor. In order to overcome these disadvantages, profile moments are carried out to characterize surface topography, surface topography is simulated by superposing series of cosine components, the stress concentration factors of different micro cosine-shaped surface topographies are investigated by finite element analysis. In terms of micro cosine-shaped surface topography, an equation using the second profile moment to estimate the stress concentration factor is proposed, predictions for the stress concentration factor using the proposed expression are within 10% error compared with the results of finite element analysis, which are more accurate than other models. Moreover, the proposed equation is applied to the real surface topography machined by turning. Predictions for the stress concentration factor using the proposed expression are within 10% of the maximum stress concentration factors and about 5% of the effective stress concentration factors estimated from the finite element analysis for three levels of turning surface topographies under different simulated scales. The proposed model is feasible in predicting the stress concentration factors of real machined surface topographies.

Surface deformation-dependent mechanical properties of bending nanowires:an ab initio core-shell model

An ab initio core-shell model is proposed to evaluate the surface effect in bending nanowires,in which the elastic modulus depends on the surface relaxation and deformation induced by external loading.By using first-principles calculations based on the density functional theory(DFT),the surface and bulk properties are calculated for Ag,Pb,and Si nanowires.The obtained theoretical predictions of the effective Young’s modulus of nanowires agree well with the experimental data,which shows that the fixed-fixed nanowire is stiffened and the cantilevered nanowire is softened as the characteristic size of the cross section decreases.Furthermore,the contrastive analysis on the two kinds of nanowires demonstrates that increasing the nanowire aspect ratio would enhance the surface effect.The present results could be helpful for understanding the size effect in nanowires and designing nanobeam-based devices in nanoelectromechanical systems(NEMSs).

A Review on Surface Stress-Based Miniaturized Piezoresistive SU-8 Polymeric Cantilever Sensors

In the last decade, microelectromechanical systems(MEMS) SU-8 polymeric cantilevers with piezoresistive readout combined with the advances in molecular recognition techniques have found versatile applications,especially in the field of chemical and biological sensing.Compared to conventional solid-state semiconductor-based piezoresistive cantilever sensors, SU-8 polymeric cantilevers have advantages in terms of better sensitivity along with reduced material and fabrication cost. In recent times,numerous researchers have investigated their potential as a sensing platform due to high performance-to-cost ratio of SU-8 polymer-based cantilever sensors. In this article, we critically review the design, fabrication, and performance aspects of surface stress-based piezoresistive SU-8 polymeric cantilever sensors. The evolution of surface stress-based piezoresistive cantilever sensors from solid-state semiconductor materials to polymers, especially SU-8 polymer, is discussed in detail. Theoretical principles of surface stress generation and their application in cantilever sensing technology are also devised. Variants of SU-8 polymeric cantilevers with different composition of materials in cantilever stacks are explained. Furthermore, the interdependence of the material selection, geometrical design parameters, and fabrication process of piezoresistive SU-8 polymeric cantilever sensors and their cumulative impact on the sensor response are also explained in detail.In addition to the design-, fabrication-, and performancerelated factors, this article also describes various challenges in engineering SU-8 polymeric cantilevers as a universal sensing platform such as temperature and moisture vulnerability. This review article would serve as a guideline for researchers to understand specifics and functionality of surface stress-based piezoresistive SU-8 cantilever sensors.

VIBRATION OF CANTILEVERS WITH ROUGH SURFACES

We study the effect of surface roughness on the resonance frequency of micro-cantilever sensors. The analysis demonstrates that surface roughness can enhance, decrease or even annul the effect of surface stress on the resonance frequency, depending on the surface inclination angle and the Poisson ratio of the coating film on the cantilever.

A NEW METHOD OF ANALYZING SURFACE CRACKS

The authors have developed a new line-spring boundary element method in the present paper, which combines the advantage of the line-spring model with that of the boundary element method. This method reduces the three-dimension problem of the surface cracks into a quasi-one-dimension problem and can be used to analyze the surface cracked plate under various loading conditions. In this paper theoretical analyses and numerical verifications are carried out. The calculated results are reported, which indicate that the present method is efficient and can be used to analyze the surface crack problem on a personal computer.

Transformation toughening of Al_2O_3/ZrO_2 laminated ceramics with residual compressive stress

With the help of scanning electronic microscopy and X-ray diffraction, the relationships of microstructure characteristics, phase assemblage, and fracture micrograph of Al2O3/ZrO2 laminated ceramics were studied. Compared with monolithic Al2O3/ZrO2 ceramics, the existence of surface compressive stresses greatly restrained the growth of ZrO2 and Al2O3 grains at high sinter temperature, fined the grain size, and increased the content of metastable t-ZrO2, which made the fracture transformation energy quantity 70% higher than that of the monolithic ceramics. The trans-granular and inter-granular fracture features were observed in the surface and center layers, which further verified that transformation toughening is the main mechanism, whereas, micro-crack toughening is helpful for enhancing fracture toughness.

Turbulent mixing above the Atlantic Water around the Chukchi Borderland in 2014

This study presents an analysis of the CTD data and the turbulent microstructure data collected in 2014, the turbulent mixing environment above the Atlantic Water（AW） around the Chukchi Borderland region is studied.Surface wind becomes more efficient in driving the upper ocean movement along with the rapid decline of sea ice,thus results in a more restless interior of the Arctic Ocean. The turbulent dissipation rate is in the range of4.60×10–10（–3.31×10–9 W/kg with a mean value of 1.33×10–9 W/kg, while the diapycnal diffusivity is in the range of1.45×10–6–1.46×10–5m2/s with a mean value of 4.84×10–6 m2/s in 200–300 m（above the AW）. After investigating on the traditional factors（i.e., wind, topography and tides） that may contribute to the turbulent dissipation rate, the results show that the tidal kinetic energy plays a dominating role in the vertical mixing above the AW. Besides, the swing of the Beaufort Gyre（BG） has an impact on the vertical shear of the geostrophic current and may contribute to the regional difference of turbulent mixing. The parameterized method for the double-diffusive convection flux above the AW is validated by the direct turbulent microstructure results.

Selective generation of ultrasonic Lamb waves by electromagnetic acoustic transducers

In this paper, we describe a modal expansion approach for the analysis of the selective generation of ultrasonic Lamb waves by electromagnetic acoustic transducers （EMATs）. With the modal expansion approach for waveguide excitation, an analytical expression of the Lamb wave＇s mode expansion coefficient is deduced, which is related to the driving frequency and the geometrical parameters of the EMAT＇s meander coil, and lays a theoretical foundation for exactly analyzing the selective generation of Larnb waves with EMATs. The influences of the driving frequency on the mode expansion coefficient of ultrasonic Lamb waves are analyzed when the EMAT＇s geometrical parameters are given. The numerical simulations and experimental examinations show that the ultrasonic Lamb wave modes can be effectively regulated （strengthened or restrained） by choosing an appropriate driving frequency of EMAT, with the geometrical parameters given. This result provides a theoretical and experimental basis for selectively generating a single and pure Lamb wave mode with EMATs.