Geometrical Size Effect Research Articles

Probabilistic fatigue assessment of notched components under size effect using generalized weakest-link model

Fatigue assessment in the presence of intricate geometries is critical for ensuring reliability and structural integrity of engineering components. This study proposes a generalized weakest-link model for probabilistic life prediction of notched components considering statistical and geometrical size effects, in which the failure probability of materials at different positions is quantified by a weight function of stress field intensity (SFI) approach. In particular, with a new definition of fatigue failure region (FFR), the size effect on notch fatigue behavior is reasonably characterized. Model validation and comparison are performed with experimental data of GH4169 and TC4 notched specimens. Note that the scattering fatigue data points agree well with the model predicted P–S–N curves. Finally, the proposed generalized weakest-link model is applied to fatigue strength assessment of a turbine bladed disk.

Study on size-related product quality of multiscale central-punched cups fabricated by compound forming directly using brass sheet

Meso/microforming has gained much more attention in the last decades and is widely used as a reliable method to fabricate meso/micro-scaled metallic components. In this research, a compound meso/microforming system which combines deep drawing, punching, and blanking operations was developed to fabricate multiscale central-punched cups by using brass sheets. The parts with three scales were produced by using the brass sheets with various thicknesses and grain sizes to investigate geometrical and grain size effects on the deformation behaviors, dimensional accuracy, and material flow behaviors in the forming process. Through physical experiments and finite element simulations, it is revealed that the ultimate deformation load in the drawing-punching stage is smaller than that in the single deep drawing stage under microscale, but the results in the meso-scaled scenarios are opposite. In addition, the thickness variation is increased with grain size, but the variation of the normalized thickness variation does not show an obvious tendency with different size scales. In the bending area, the material flow is tangential to the thickness direction, leading to the formation of thinning area. In addition, the material flow is almost opposite to the punching direction in the punching area, avoiding the expanding deformation of the hole. Thus, the punching operation barely affects the dimensional accuracy including the thickness and hole diameter of the formed parts. Furthermore, the micro-scaled cups with finer grains have a better surface quality. These findings enhance the understanding of size effect in compound meso/microforming with the combined deep drawing and punching operations.

Ab-Initio Investigation of Finite Size Effects in Rutile Titania Nanoparticles with Semilocal and Nonlocal Density Functionals

In this work, we employ hybrid and generalized gradient approximation (GGA) level density functional theory (DFT) calculations to investigate the convergence of surface properties and the electronic gap of rutile titania (TiO2) nanoparticles with particle size. The surface energies and electronic gaps are calculated for cuboidal particles with minimum dimension ranging from 3.7 Å (24 atoms) to 10.3 Å (384 atoms) using a highly parallel real-space DFT code to enable hybrid-level DFT calculations of larger nanoparticles than are typically practical. We deconvolute the geometric and electronic finite size effects in surface energy and evaluate the influence of defects on the electronic gap and density of states (DOS). The electronic finite size effects in surface energy vanish when the minimum length scale of the nanoparticles becomes greater than 10 Å. We show that this length scale is consistent with a computationally efficient numerical analysis of the characteristic length scale of electronic interactions. The surface energy of nanoparticles having a minimum dimension beyond this characteristic length can be approximated using slab calculations that account for the geometric defects. In contrast, the finite size effects on the electronic gap and DOS are highly dependent on the shape and size of these particles. The DOS for cuboidal particles and more realistic particles constructed using the Wulff algorithm reveal that defect states within the electronic gap play a key role in determining the eigenvalue distribution of nanoparticles and the electronic gap does not converge to the bulk limit for the particle sizes investigated.

Irradiation effects in tungsten—From surface effects to bulk mechanical properties

Advanced materials such as tungsten fibre-reinforced composites allow to overcome severe weaknesses of the baseline materials for plasma-facing components — copper and tungsten. The effect of the fusion environment on the mechanical properties of these materials, e.g. the embrittlement by neutron irradiation, plays a key role for the development of future fusion reactors. To simulate this effect, high-energy ions are used as a substitute for the displacement damage by neutrons. We propose the use of very fine tungsten wire as a possibility of studying the influence of irradiation damage on the mechanical properties. This is possible as they allow full-depth irradiation of almost the entire volume despite the limited penetration depth of ions. Geometrical size effects are mitigated due to the nanoscale microstructure of the wire. In addition, similar wire is used in tungsten fibre-reinforced composites. Thus, the investigation of irradiated wire can directly be used for the prediction of the bulk composite properties. For the proof of this concept tungsten wire with a diameter of 16 μm was electrochemically thinned to 5 μm and irradiated with 20.5 MeV W6+ ions. The mechanical properties were subsequently determined by macroscopic tensile testing. Irradiation to 0.3, 1 and 9 dpa did not lead to a change of the mechanical behaviour. Both strength and ductility, the latter indicated by the reduction of area, were similar to the as-fabricated state.

Size-Dependent Stability of a Cantilevered Piezoelectrically Actuated Micropipe Conveying Fluid

Size-dependent effects of a cantilevered piezoelectrically actuated micropipe conveying fluid are investigated. Based on the modified strain gradient beam theory, the model of system is obtained using Hamilton's principle. The motion equation is discretized into ordinary differential equations by Generalized Differential Quadrature Method (GDQM). A stability analysis of the system is completed through eigenvalue analysis. Numerical results show the effect of geometrical shape size, and length scale parameters on critical flow velocity, and critical voltage. Results prove that the modified strain gradient theory (MSGT) has a higher critical flow velocity and critical voltage than predicted by modified couple stress theory (MCST) and classical theory (CT).

ISPH Simulation of Solitary Waves Propagating Over a Bottom-Mounted Barrier With k–ε Turbulence Model

Solitary wave propagating over a bottom-mounted barrier is simulated using the Incompressible Smoothed Particle Hydrodynamics (ISPH) method in order to study the generation and transport of turbulence associated with flow separation around submerged structures. For an accurate capture of turbulence characteristics during the wave propagation, rather than employing the standard sub-particle scale (SPS) model, the k-ε turbulence model is coupled with the numerical scheme. The results of the numerical model are compared with experimental data, and good agreement is observed in terms of mean velocity, free surface elevation, vorticity fields and turbulent kinetic energy. The numerical model is then employed to investigate the effects of wave non-linearity and geometrical size of the submerged barrier on the flow separation; and calculate the reflection, dissipation and transmission coefficients to evaluate the importance of energy dissipation due to the generation of vortices. The results of this study show that the developed ISPH method with the k-ε turbulence closure model is capable of reproducing the velocity fields and the turbulence characteristics accurately, and thus can be used to perform predictions of comprehensive hydrodynamics of flow-structure interactions in the urban hydro-environment systems.

Large deformation analysis of functionally graded beam with variable cross-section by using peridynamic differential operator

A non-local numerical model for large deformation analysis of functionally graded beam (FGB) with variable cross-section is presented by using peridynamic differential operator (PDDO) in this paper. The nonlinear equilibrium equation and boundary condition of FGB with variable cross-section are reformulated from the local differential form into the non-local integral form based on PDDO. By employing variational analysis, Lagrange multiplier method, and Newton-Raphson method, the non-local governing equations can be solved with iterations. The proposed method is applied to the large deformation analyses of a cantilever homogeneous beam and two cantilever FGBs with linearly varying and parabolic lower surfaces, respectively, and the effects of geometric size and material gradient on mechanical behaviour of FGB are investigated further. Comparison with finite element results validates the convergence and accuracy of the proposed non-local model.

Wave energy extraction and hydroelastic response reduction of modular floating breakwaters as array wave energy converters integrated into a very large floating structure

Combing floating breakwaters with wave energy converters (WECs) and integrating them into very large floating structure (VLFS) can provide a viable option to explore economically offshore wave energy resources and simultaneously to protect marine structures. In this paper, the time-domain numerical model is developed based on the modal expansion theory with nonlinear consideration to optimize the design and layout of an integrated system of modular WEC-type floating breakwaters and a pontoon-type VLFS, with emphasis on the effects of the WEC geometric size and shape, the WEC-VLFS gap distance and the wave nonlinearity. A hybrid finite element (FE)-boundary element (BE) method is presented to simulate the structures as Mindlin plate elements and the water waves as fully nonlinear potential flow boundaries, respectively. Breakwaters as WECs with deeper draft and larger length are found to more fully interact in phase with long-period waves, and receive more wave energy extraction and larger hydroelastic response reduction. The addition of breakwaters has a favorable effect on the wave energy extraction, but a destructive effect on the hydroelastic reduction. Importantly, wave resonance induced by the multi-modal scattering waves in the WEC-VLFS gap leads to multiple peaks of the power capture efficiency. Compared to the symmetric-shape WECs, the asymmetric-shape WECs strengthen the gap resonant effect, which improves both the wave energy extraction and hydroelastic reduction for a broader frequency bandwidth. The findings of this study indicate the synergistic benefits of wave energy exploitation and transmitted wave attenuation at the fore-end of VLFSs.

Nonlinear vibration behavior of CNTRC plate with different distribution of CNTs under hygrothermal effects

Hygrothermal effects and periodic loading often occur in carbon nanotube-reinforced composite (CNTRC) during their service life. For the effective use of such materials for high-performance applications, their nonlinear vibration behavior under hygrothermal effects should be clearly understood. Firstly, this paper establishes a nonlinear vibration mechanical model of the CNTRC plate with different distributions of carbon nanotubes (CNTs). Then, ordinary differential equations of nonlinear vibration are given by using the Galerkin method and solved by using the harmonic balance method; additionally, a primary resonance and stability of the CNTRC plate under transverse harmonic loads are analyzed by employing the multi-scale method. Finally, for a fixed shear deformation function, effects of geometric size, volume fraction, CNT distribution, and damping coefficient on the nonlinear vibration behaviors of the CNTRC plate are discussed.

Theoretical Analysis of Experimental Data of Sodium Diffusion in Oxidized Molybdenum Thin Films

In this work, the diffusion process of sodium (Na) in molybdenum (Mo) thin films while it was deposited on soda lime glass (SLG) was studied. A small amount of oxygen was present in the chamber while the direct-current (DC) magnetron sputtering was used for the deposition. The substrate temperatures were varied to observe its effect. Such molybdenum films, with or without oxidations, are often used in thin film solar cells, either as back contact or as hole transport layers. Secondary ion mass spectrometry (SIMS) was used to quantify the concentration of the species. A grain diffusion mechanistic model incorporating the effect of grain and grain boundary geometrical shape and size was developed. The model was used to provide an in-depth theoretical analysis of the sodium diffusion in molybdenum thin films that lead to the measured SIMS data. It was observed that not only diffusion coefficients should be considered when analyzing diffusion processes in thin films but also the ratio of grain boundary size to grain size. Both depend on substrate temperature and directly affect the amount of diffused species in the film. The data were analyzed under the light of the film growth speed versus diffusion front speed, the effect of oxygen content, and the effect of substrate temperature on the overall diffusion process. The temperature inversely affects the ratio of grain boundary size and grain size and directly affects the diffusion coefficient, which leads to a preferable temperature at which the highest amount of alkali can be found in the film.

Effects of Size and Surface Treatment on Fatigue Life of Fused Filament Fabrication Manufactured Acrylonitrile Butadiene Styrene Parts

Abstract An experimental study was conducted to study the effects of geometric size and surface treatment on the fatigue life of fused filament fabrication (FFF) manufactured acrylonitrile butadiene styrene (ABS) parts. Moore rotating-beam fatigue tests were conducted with four different levels of loadings to obtain the S–N curves. Two different sizes (control size and large size) and three different surface treatment methods (as-printed, acetone-treated, and sandpaper polished) were studied. The larger specimens had significantly decreased fatigue life because of a larger volume, and hence a greater probability of defects for crack initiation and propagation, as compared with the control specimen. The acetone-treated specimen had a smooth surface. Its fatigue life, however, decreased significantly because the acetone treatment caused internal damage that weakened the specimen and was reported for the first time. The sandpaper polished specimen also had a smooth surface, but its effect on the fatigue life was insignificant because the extruded filament direction on the specimen surface was parallel to the loading direction. The present results lead to a better understanding of the effects of geometric size and surface treatment on the fatigue performance of FFF specimens. The study also provides important insights for the design of part size and surface treatment of three-dimensional (3D) printed plastic components for fatigue loading end-use applications.

Recent advances on size effect in metal fatigue under defects: a review

Structural components with different scales normally show different fatigue behaviors, which are virtually dominated by defects originated from multiple sources, including manufacturing processes. This paper reviews three types of size effects (statistical, geometrical, technological) as well as their recent advances in metal fatigue, aiming to provide a guide for fatigue strength assessment of engineering components containing defects, inclusions and material inhomogeneity. Firstly, the background of inherent defects and defect-based failure mechanism are briefly outlined, and fatigue failure analysis based on fracture mechanics as well as statistics theory are emphasized. Then, two approaches commonly applied in statistical size effect modeling, i.e. critical defect method and weakest link method, are elaborated. In addition, the highly stressed volume method is introduced for considering the geometrical size effects, and the technological (production and surface) size effect is briefly overviewed. Finally, further directions on size effect in metal fatigue under defects are explored.

Investigation of the statistical and geometrical size effect on the fatigue strength of EN-GJL-300 under consideration of the graphite morphology

Grey cast iron (GJL) is one of the most important materials for numerous components in car, utility vehicle and ship engines, power generation units and machine beds in various branches of mechanical engineering. In order to optimize the design of grey cast iron components for applications subjected to cyclic loading, a precise knowledge of the fatigue mechanisms is necessary. In the framework of a research project, the statistical and geometrical size effect on the fatigue strength of EN-GJL-300 is investigated. The statistical size effect describes the relationship between the fatigue strength and a changing stressed volume or surface and can be expressed with the highly stressed volume (HSV) of the component. The geometrical size effect instead takes into account the influence of a stress gradient e.g. due to notches on fatigue strength. Knowledge of the statistical and geometrical size effect allows the transfer of the fatigue strength from small specimens with different notch factors to complex large-scale components. For the investigation, unnotched and notched specimens with different highly stressed volumes are removed from cast samples as well as from a gearbox housing to determine the cyclic material behavior by stress controlled axial fatigue tests. The investigations are complemented by metallographic analyses to describe the influence of the graphite morphology on fatigue strength. The data obtained in this study serve as a contribution to the development of a design and lifetime assessment concept enabling an estimation of the local lifetime of the component as a function of the highly stressed volume and the local microstructural properties.

Effects of Geometric Array and Size of Internal Voids on Tensile Ductility of AZ31 Magnesium Alloy Sheets

This study aims to investigate the contributions of the geometric array and size distribution of perforated cylindrical voids to the tensile elongation of a metallic sheet through the numerical correction of the plastic constraint factor with regard to the geometric array of internal voids. In AZ31 alloy sheets fabricated via strip casting, internal voids were formed via mechanical drilling in the form of perforated cylindrical holes. The tensile strain decreased significantly (from 0.18 to 0.01) as the void area fraction increased to 40%, and its nominal value decreased with an increase in the void size, even when the geometric array (ratio of void size to ligament distance between voids, a/l) was maintained. A plastic constraint factor describing the geometric array and size distribution of perforated cylindrical voids was proposed through the modification of an original form for isolated spherical voids, and the theoretical prediction using a modified constitutive model agreed well with the experimental results. The tensile ductility of a metallic sheet with perforated cylindrical voids depends more sensitively than isolated spherical voids on the variation in the void area fraction, because the effective void area fraction is overestimated by the exclusion of the strain-hardening exponent term in the modified plastic constraint factor. Additionally, increases in the void size and void area fraction at a fixed a/l ratio lead to a reduction in the tensile strain, by the increase of the plastic zone and the intensification of stress concentration around a void.

Effects of geometrical size and structural feature on the shape-distortion behavior of hollow Ti-alloy blade fabricated by additive manufacturing process

In the additive manufacturing (AM) process, metal powder can be directly used to produce metal components. Unfortunately, a large thermal gradient is developed during the AM process, which leads to the generation of residual stress and complex shape-distortions. In this study, the influence of the geometrical size and structural features of a hollow Ti-alloy blade prepared by the AM process on the shape-distortion behavior was systematically investigated using the three-dimensional (3D) blue-light scanning technology. The results indicated that the concentrated residual stress was developed on the surface of the blade. The compressive residual stress induced a bulging distortion, while the tensile residual stress resulted in denting distortion on the blade surfaces. When the blade height and torsion angle increased, the shape-distortion was aggravated owing to the accumulation of microscopic strain and the elevated temperature gradient. However, the shape-distortion mitigated when the wall thickness significantly increased or the stiffened plates were set within the blade cavities, owing to a strengthening structural constraint which inhibited the distortion behavior. In addition, a control method for the shape-distortion during AM process was able to implement based on the proper optimization of the geometrical sizes and structural features of complex 3D-printed components.

A calibrated weakest-link model for probabilistic assessment of LCF life considering notch size effects

This study proposes a calibrated weakest-link model for probabilistic life in low cycle fatigue (LCF) regime considering the geometric size effect and the statistical size effect. Weakest-link model is first extended to LCF regime by using damage parameter, and then calibrated based on crack propagation process. Meanwhile, experiments on standard smooth specimens and central hole plate (CHP) specimens are conducted. To improve model accuracy, parameters in the proposed model are calibrated by using Bayesian inference method. Finally, probabilistic LCF life is predicted for CHP specimens with different scales, which shows good agreement with test data.

Anomalous Hall magnetoresistance in single-crystal Fe(001) films

The angular-dependent magnetoresistance (MR) in epitaxial Fe(001) films grown on MgO(001) is systematically investigated at room temperature. The resistivities with in-plane magnetic fields parallel (ρx) and transverse (ρy) to a current and a perpendicular field (ρz) show a correlation of ρz ≈ ρx > ρy for Fe film thickness (dFe) between 3 and 50 nm, which is distinctly different from the conventional anisotropic MR relation of ρx > ρy ≈ ρz. The dependence of such unusual MR on dFe is quantitatively explained by the competition between the anomalous Hall MR, intrinsic anisotropic MR, and the MR induced by the geometrical size effect in Fe films. Our results also reveal the strong four-fold symmetric terms in the measured angular-dependent MR with a linear dependence of 1/dFe.

Enhanced photoelectrocatalytic performance from size effects in pure and La-doped BiFeO3 nanoparticles

Due to the energy crisis, the development of high-performance photoelectrocatalysts is becoming a hot research area in recent years. Among the materials studied, BiFeO3 (BFO) exhibits excellent photoelectrocatalytic performance due to its moderate bandgap and unique band structure. In this paper, both pure BFO and La-doped BFO were synthesized by solgel method. The average size of the BFO nanoparticles was tuned from 65 to 440 nm. For the La-doped BFO, the average size of the nanoparticles was reduced from 95 to 40 nm with the increase in doping level from 0 to 30%. Next, the photoelectrocatalytic performance of the pure BFO nanoparticles were enhanced with the reduction in nanoparticle size, which was possibly caused by increased surface-to-volume ratio. For the increase in doping of La, the corresponding photoelectrocatalytic performance was first enhanced and then degraded. To understand the obtained results, a mechanism was proposed, which can be attributed to the competition between geometric size effects and surface effects. Our findings provided a controlled way to tune the photoelectrocatalytic performance of BFO system, which is crucial for practical applications.

An investigation on shielding effectiveness of conductive adhesive

The use of metal shell is an effective method to solve electromagnetic interference caused by printed circuit board (PCB) of electronic equipment. Electromagnetic leakage mainly occurs at the junction of the upper metal shell and the lower metal shell. In order to reduce the electromagnetic interference caused by the electromagnetic leakage, the conductive adhesive is coated on the connection between the upper shell and the lower shell. In this paper, a simulation model of shielding effectiveness is established in CST STUDIO SUITE. It is mainly used to calculate the effects of conductivity and geometric size of conductive adhesives on shielding effectiveness. In the actual design process of electronic equipment, we can find a more economical combination of size and conductivity of conductive adhesives through the simulation of shielding effectiveness. The results can be used to guide the design of conductive adhesives to solve the electromagnetic compatibility problems of electronic equipment.

The effects of surface orientation, heater size, wettability, and subcooling on the critical heat flux enhancement in pool boiling

Enhancing Critical Heat Flux (CHF) in pool boiling significantly extends the safety limit in the nuclear system, especially under the In-Vessel Retention-Reactor Vessel Cooling (IVR-ERVC) severe accident management strategy to avoid the failure of the lower head reactor pressure vessel. In this work, the lattice Boltzmann method (LBM) is employed to simulate the effect of surface orientation, wettability, geometric size, and subcooling of the downward-facing lower head on the CHF enhancement. It was found that for the downward-facing surface, the CHF increases with increasing surface orientation, while a vertical surface gives a slightly lower CHF compared to a near-vertical surface. Besides, the CHF for a downward facing surface increases with increasing wettability. The CHF performance of the near-vertical and vertical surfaces exhibits the largest improvement with decreasing surface contact angle. Moreover, it reveals that with an increased radius of the lower head, the CHF decreases for all curved surfaces, especially obvious for the inclination angle smaller than 90∘. For a vertical surface, increasing the length of the heated surface has no obvious improvement on the CHF. This study also provides a discussion regarding the effect of subcooling on the CHF enhancement. It was found that the CHF increases with the increase of subcooling and the simulation results agree with the Elkassabgi-Lienhard and Zuber correlations.