Geometrical Size Effect Research Articles

Selective laser melting of 316L stainless steel: Porosity dependence on geometric feature size

This technical brief reports an experimental study on the effect of geometric feature size on the porosity in parts made via selective laser melting. Cylindrical features of different diameters were designed on a single part and printed using the same scan strategy. The resultant pores at different cylindrical feature diameters were captured by optical microscopy. The image processing results showed that as the cylindrical feature diameter decreased from 10 mm to 0.8 mm, the porosity increased from 0.11 % to 4.1 %, and the maximum pore size increased from 41.7 µm to 102.2 µm. To identify the reason for this interesting finding, the average areal energy density was calculated at each cylindrical feature diameter. The calculations showed that the different cylindrical feature diameters resulted in local energy density discrepancies. Because the scan strategy had a disparity for the border in comparison to the volume infill, and the areal ratio of the border to the volume infill naturally varied at different cylindrical feature diameters, the average areal energy density was found to vary significantly for cylindrical features of different diameters. The average areal energy density increased from 2.8 J/mm2 to 5.9 J/mm2 as the cylindrical feature diameter decreased from 10 mm to 0.8 mm. That change in the average areal energy density was identified as the cause for the porosity variation in this study.

Fatigue life prediction of notched components based on energy gradient using reconstructed critical distance theory

AbstractIn this paper, a reasonable explanation is given to unify notch effect and geometric size effect into notch geometric feature effect (NGFE), and energy gradient is utilized to depict the influence of the NGFE on the critical distance. The correlation of energy gradient with critical distance and fatigue life is discussed respectively. The weight index of the high energy region is used to quantify the contribution of the high energy region to the fatigue damage. Finally, a model of the reconstructed critical distance theory considering the geometric notch characteristic effect is established. The fatigue test of Q355 (D) alloy steel notched components was carried out, and the evaluation precision of the presented method is compared with Yang’ model and Shen’ model combining with the existing fatigue test data of En8. The results indicate that prediction results of the proposed method are consistent with the test results.

Study on spray characteristics of a compact pressure swirl nozzle integrating tangential inlet flow channel and swirl chamber

Pressure swirl nozzles are widely applied in various heat and mass transfer applications due to advantages of reliable performance, simple structure, and easy processing. However, the complex design of the nozzle structure makes it difficult to miniaturize the pressure swirl nozzle, which restricts its use in limited spaces. In this study, a compact pressure swirl nozzle is proposed by merging a swirl chamber with the tangential inlet flow channel, addressing the issue of liquid atomization in limited spaces. The key geometric parameters are determined based on the internal flow properties by swirl chamber simulation. A spray test bench utilizing a phase Doppler particle analyzer and a high-speed camera was built to study the effect of pressure drop, geometric size, and nozzle inlet shape on spray characteristics. The simulation results show that the nozzle diameter and inlet shape are the main factors affecting flow in the swirl chamber. The experimental results further demonstrate that increasing nozzle diameter increases flow rate and spray cone angle, causing the droplets to move to the spray edge. The spray characteristics are affected by the inlet shape of the nozzle hole: radial velocity and particle size show a wider range of change with a funnel-shaped inlet. Axial velocity and pressure drop are obviously affected by a cylindrical-shaped inlet. This study provided a new design approach for pressure swirl nozzles and achieved flow rate of 5–35 l/h and Sauter mean diameter below 40 μm with an overall weight of 12 g. This compact nozzle construction is a reference for the design of atomizing nozzles in limited spaces.

Probabilistic notch fatigue assessment under size effect using micromechanics-based critical distance theory

Geometrical discontinuities are inevitable in engineering structures due to various functional requirements, which often yield complex stress–strain state and thereby significantly impact their fatigue performances. In this study, crystal plasticity theory is coupled with traditional critical distance theory for notch effect modelling considering microstructural heterogeneity. Specifically, microstructural and geometrical size effects on critical distance and fatigue performance are studied based on Sub-modelling approach. In addition, critical distance theory is coupled with Weibull distribution for probabilistic fatigue life evaluation of notched components. The developed method is verified and compared by using experimental data of GH4169 alloy. The findings demonstrate that the evaluated P-S-N curves exhibit strong agreement with tested data and geometrical size effect poses larger influence than the grain size effect on critical distance and fatigue life.

Effect of Geometric Patterns Size on the Negative Poisson's Ratio in Uni-stretch Auxetic Woven Fabrics

Effect of Geometric Patterns Size on the Negative Poisson's Ratio in Uni-stretch Auxetic Woven Fabrics

Orbital Hall magnetoresistance in Ni/Ti bilayers

We report the observation of the orbital counterpart of the spin Hall magnetoresistance (SMR): the orbital Hall magnetoresistance (OMR). We measured angular-dependent longitudinal magnetoresistance for Ni/Ti bilayer and Ni single-layer films by rotating a magnetic field along three orthogonal planes. When the magnetic field is rotated in the plane perpendicular to the applied current direction, the angular dependence of the magnetoresistance in the Ni/Ti bilayers is consistent with the prediction of the SMR and OMR, whereas that in the Ni single-layer film can be attributed to the geometrical size effect of the anisotropic magnetoresistance. In the Ni/Ti bilayers, the magnetoresistance ratio is found to be five orders of magnitude larger than the prediction of the SMR, indicating that the OMR plays a dominant role in this system.

Size effects on the structural behaviour of wrapped composite CHS joints

AbstractRecent pilot studies have shown the superior performance of wrapped composite joints as an alternative to conventional welded joints for circular hollow sections (CHS). Considering the large dimensions of CHS joints for field application and potential size effects from testing the structure on reduced scales, geometrical size effects need to be investigated. This work presents an experimental analysis and FE results of wrapped composite joints with three different scale sizes. The size effects on the uniaxial tensile behaviour of specimens were investigated in monotonic loading. The size effects on the structural behaviour of wrapped composite joints were evaluated regarding the performance in ultimate limit states. The outcome of this research supports the structural analysis and modelling of wrapped composite joints with upscaled sizes.

Scaled fatigue cracks under service loads

Scaled experimentation is a powerful engineering tool yet its application to fatigue is limited by significant changes in behaviour with scale. The recent discovery of new similitude rules however opens new possibilities that are explored in this work through numerical experimentation for industrially representative fatigue-crack growth scenarios. It is shown for the first time, how the geometric size effects present in mixed mode fatigue tests are eliminated by performing two appropriately designed scaled experiments. The first order finite similitude theory is applied to mixed mode (modes I and II) fatigue crack growth in three case studies, viz., compact tension shear (CTS) specimen, wing fuselage attachment lug, and a T-joint with an inclined semi elliptical crack. Both planar and non-planar crack growth feature, along with surface and through thickness cracks. Low and high cycle fatigue (up to circa 60,000 cycles) is examined for three different materials (Al-6061 T6 alloy, structural steel, and AISI 316 stainless steel) under a variety of load ratios. The new rules return near exact crack-path predictions whereas lifecycle predictions have errors ranging between 1 % and 9 %. Paris law constants C and m are predicted with up to 99.9 % accuracy supporting the theory that Paris law is a first order similitude rule. Geometric size effects afflicting industrial type scaled-fatigue studies employing a damage tolerant design approach are confirmed to be eliminated on combination of information from two appropriately designed scaled models.

Effect of Graphene Reinforcement on Free Vibration and Material Properties of the FG-GPLRC Porous Cantilever Torsional Plate

This paper researches the free vibrations and corresponding material parameters of a functional gradient graphene platelets-reinforced composite (FG-GPLRC) cantilever torsional plates with both pore and graphene variations in the transverse direction. Utilizing the feature of closed-cell cellular solids, the mixture rule, and the modified Halpin–Tsai model, the material parameters of the composite are determined for different volume fractions of component materials. Then, using the classical plate theory (CLPT), the Rayleigh–Ritz technique and polynomials, the dynamic equation that can be used to obtain the free vibration mode shapes and frequencies of the rotating cantilever torsional plate is given. Comparison studies with the previous calculation results from available literature and the finite element (FE) models of cantilever plates are conducted, and the correctness of the present theoretical formulation and numerical calculation is verified. Finally, the effects of graphene platelet (GPL) distribution, porosity distribution (PD), GPL content, rotational speed, and average geometric size of GPL on free vibrations of the system are studied in depth.

Scaled empirical fatigue laws

A geometric size effect is evident in fatigue loading with a scaled cracked component of the same material appearing stronger in the sense of increased fatigue resistance. The number of cycles to failure can increase markedly with reduction in the size of a component and consequently, the use of scaled components to gauge fatigue life is invariably conservative. A question of some interest however and the focus of this work is whether it is possible to establish a precise analytical relationship between fatigue life and scale. This is shown possible on application of the new scaling theory finite similitude, which connects information across scales and links more than one scaled experiment. Through the design of two scaled-down experiments it is established that the Paris law empirical power-law relationship is precisely a first-order finite similitude identity. The practical applicability of the approach is demonstrated by means of experimental and numerical case studies, which confirm that the complete fatigue response of a structure described by key-fatigue parameters can be captured using two smaller scaled down experiments. High levels of accuracy are shown possible with the two-experiment approach with results returned up to 99% accurate.

Geometric size effect of Lemaitre damage model parameters of rolled CuAl5 alloy

The geometric size effects (GSEs) of Lemaitre damage model parameters (the critical damage value at rupture, Dc, the strain at the damage threshold, ɛD, and the strain at rupture, ɛR) of a rolled CuAl5 alloy were evaluated using uniaxial tensile experiments and the finite element method. The results indicated the presence of size effect on the damage model parameters of the rolled CuAl5 alloy. With an increase in reduction ratio (Rr) at a constant thickness (t), Dc increased; with an increase in t at a constant Rr, Dc decreased and then increased. Both ɛD and ɛR decreased with increasing Rr and decreasing t. New models of the relationship between the damage model parameters and t were established for the three Rr values. The predicted results of the models agreed with the experimental ones. These results help to accurately predict the fracture behavior of microparts during plastic forming.

Geometrical and microstructural size effects in progressive forming using wires

With the increasing trend toward product miniaturization, progressive forming has been widely used in fabricating meso‑/micro-scaled parts using sheet metals. However, there are difficulties for such processes and sheet metals to be employed to manufacture the parts and components with local rotating features, and their rotating axis is not in the extruding/forming direction. In this work, a progressive forming process directly using metal wires was first developed. The constitutive model using the brass CuZn35 wires of different diameters (0.4–1.2 mm) as a case study material with different grain sizes (30.9–159.2 μm) was developed. By using the multi-scaled fork-shaped parts with flat tines and cylindrical heads as case micro-parts to be micro-formed, the dimensional errors induced by springback increased with the grain size while decreasing as the specimen size increased. The surface quality deteriorates with the increase in grain size, and the micro-cracks form more easily on the side surface of micro-parts with larger grains. The undesired geometry issue of the fabricated parts was overcome by optimizing the tool design. This work further expands the promising application of the progressive forming process in the high-efficiency fabrication of meso‑/micro-scaled parts with irregular features.

Nematically Templated Vortex Lattices in Superconducting FeSe.

New pathways to controlling the morphology of superconducting vortex lattices─and their subsequent dynamics─are required to guide and scale vortex world-lines into a computing platform. We have found that the nematic twin boundaries align superconducting vortices in the adjacent terraces due to the incommensurate potential between vortices surrounding twin boundaries and those trapped within them. With the varying density and morphology of twin boundaries, the vortex lattice assumes several distinct structural phases, including square, regular, and irregular one-dimensional lattices. Through concomitant analysis of vortex lattice models, we have inferred the characteristic energetics of the twin boundary potential and furthermore predicted the existence of geometric size effects as a function of increasing confinement by the twin boundaries. These findings extend the ideas of directed control over vortex lattices to intrinsic topological defects and their self-organized networks, which have direct implications for the future design and control of strain-based topological quantum computing architectures.

Opportunities and Challenges in Modelling of Machining Performance with Various Coatings and Lubricants in Inconel 718 Machining

Decades of research and industrial applications have shown the significant impact of tool coatings and lubricants on machining performance, particularly in difficult-to-cut materials such as nickel-based super alloy Inconel 718. However, the ability to quantify and optimize the beneficial effects of coatings and lubricants continues to be primarily driven by empirical approaches. In this paper, a comparison between experimentally measured tool wear and numerically modelled process metrics, such as temperatures and stresses, is presented. Based on the results and observed deviations, future directions for more industrially relevant cutting tool development are proposed. Major challenges include the need for physics-based tribological models that consider different process interactions as well as microstructural and geometric size effects.

Research on Efficiency of New Self-driven Fault Current Limiter Based on the Improved Genetic Algorithm

To study the current limiting characteristics and system efficiency of the new fault short-circuit current limiter, an equivalent geometric model based on the rectangular guide rail, an algorithm analysis model of electromagnetic drive equation and a self-driven process is established. The effect of the geometric size and skin effect of the current limiter on the current limiting characteristics and system efficiency of the current limiter is analyzed. At the same time, the two goals of the initial time of current limiting and system efficiency are considered, and the important parameters of the new fault limiter are optimized by the improved genetic algorithm. The results show that the cross-sectional area of the rectangular guide and the width of the metal slider have a comprehensive effect on the performance. The algorithm model can optimize and analyze the target in a shorter time and a smaller algebra, which provides the theoretical basis and technical support for improving the current limiting characteristics and system efficiency of the new current limiter.

Considering the Effect of Non-Propagating Cracks on Fatigue Limit Prediction in the Critical Distance Method Framework

Although the material has developed micro-scale cracks, the micro-cracks stop propagating and transform into non-propagating cracks (NPCs) under fatigue limit loading. The movement of the crack tip position caused by the non-propagating crack will generate a small change in the notch geometry, which easily triggers the geometric size effect. Since the critical distance method focuses on evaluating the limit of fatigue in terms of the material’s cracking conditions, the present study attempted to develop a notched fatigue analysis model to consider the effect of non-propagating cracks on fatigue limit prediction in the critical distance method framework. The effectiveness and capability of the proposed model were demonstrated by the fatigue experimental data of Q345qD low carbon steel.

Size effect on nonlinear unloading behavior and Bauschinger effect of Ni-based superalloy ultrathin sheet

• Cyclic deformation behavior of superalloy foil is represented by cyclic shear test. • Nonlinear unloading behavior at microscale becomes evident. • Bauschinger effect are affected by both geometric and grain size effect. • Size effect on instantaneous and permanent softening is revealed. • Work hardening stagnation is related to dislocation evolution and size effect. Superalloy ultrathin sheet is widely utilized in thin-walled components of aero-engine because of its excellent comprehensive performance. Nevertheless, it is hard to precisely predict the springback phenomenon during the plastic deformation of superalloy ultrathin sheet due to the size effect. To explore size effect on nonlinear unloading behavior and Bauschinger effect of Ni-based superalloy sheets, the uniaxial tensile, cyclic loading and unloading, and cyclic shearing tests were conducted on superalloy ultrathin sheets with diverse grain sizes and thicknesses of 0.2 and 0.25 mm. The experimental results demonstrated that the increasing grain size is accompanied with the decrease of flow stress of superalloy ultrathin sheet and the change of density of forest dislocation and moving dislocation. The dislocation annihilation rate of superalloy ultrathin sheet increases with decreasing t / d ratio, and the nonlinear unloading behavior becomes more obvious. Meanwhile, the degradation of elastic modulus becomes more evident with the increasing grain size. Driven by back stress, Bauschinger effect of superalloy ultrathin sheet becomes more apparent with larger t / d ratio. In addition, the fine-grained superalloy ultrathin sheet shows obvious earlier re-yielding and large instantaneous softening rates and the variation of t / d ratio also affect the permanent softening and work-hardening stagnation of superalloy ultrathin sheet.

Geometrical size effect on tensile properties of ultrathin current collector foils for lithium-ion batteries

Geometrical size effect on tensile properties of ultrathin current collector foils for lithium-ion batteries

Tunability of Band Gaps of Programmable Hard-Magnetic Soft Material Phononic Crystals

In this paper, the elastic wave band gap characteristics of two-dimensional hard-magnetic soft material phononic crystals (HmSM-PnCs) under the applied magnetic field are studied. Firstly, the relevant material parameters of hard-magnetic soft materials (HmSMs) are obtained by the experimental measurement. Then the finite element model of the programmable HmSM-PnCs is established to calculate its band structure under the applied magnetic field. The effects of some factors such as magnetic field, structure thickness, structure porosity, and magnetic anisotropy encoding mode on the band gap are given. The results show that the start and stop frequencies and band gap width can be tunable by changing the magnetic field. The magnetic anisotropy encoding mode has a remarkable effect on the number of band gaps and the critical magnetic field of band gaps. In addition, the effect of geometric size on PnC structure is also discussed. With the increase of the structure thickness, the start and stop frequencies of the band gap increase.

Study of the Influence of Cutting Edge on Micro Cutting of Hardened Steel Using FE and SPH Modeling.

Micromachining allows the production of micro-components with complex geometries in various materials. However, it presents several scientific issues due to scale reduction compared to conventional machining. These issues are called size effects. At this level, micromachining experiments raise technical difficulties and significant costs. In this context, numerical modeling is widely used in order to study these different size effects. This article presents four different numerical models of micro-cutting of hardened steel, a Smooth Particle Hydrodynamics (SPH) model and three finite element (FE) models using three different formulations: Lagrangian, Arbitrary Eulerian–Lagrangian (ALE) and Coupled Eulerian–Lagrangian (CEL). The objective is to study the effect of tool edge radius on the micro-cutting process through the evolution of cutting forces, chip morphology and stress distribution in different areas and to compare the relevance of the different models. First, results obtained from two models using FE (Lagrangian) and SPH method were compared with experimental data obtained in previous work. It shows that the different numerical methods are relevant for studying geometrical size effects because cutting force and stress distribution correlate with experimental data. However, they present limits due to the calculation approaches. For a second time, this paper presents a comparison between the four different numerical models cited previously in order to choose which method of modeling can present the micro-cutting process.