Edge Bending Research Articles

Cell geometry effect on in-plane energy absorption of periodic honeycomb structures

With advances in 3D printing technology, now honeycomb structures can be made with virtually unlimited unit cell geometries and cell arrangements giving a wide range of possible mechanical properties. However, studies on such structures have been mainly limited to the hexagonal honeycombs with little work done on other cell geometries. This paper investigates the effect of unit cell geometry on the in-plane compressive response and energy absorption behaviour of honeycombs using full-scale non-linear numerical simulations. Nine types of honeycombs are designed from different unit cell shapes, but having the same relative density. Finite element analysis is used to simulate the honeycombs’ behaviour under uniaxial compression loading. The results showed that unit cell geometry and cell arrangement affect the honeycombs’ compressive response significantly and provide different energy absorption characteristics. This comparison study shows that the honeycombs in which the deformation mode is dominated by bending of cell edges present a lower stiffness (effective modulus) and compressive strength, but a smoother plateau stress. The honeycombs having their deformation mode dominated by plastic buckling present a higher stiffness with less stable and undulated plateau stress. The results of this study provide more understanding in predicting the global behaviour of honeycomb structures and their energy absorption characteristic through their micro-topology. The effect of cell shape and its arrangement on the selection of honeycombs for energy absorption application is discussed and a methodology is proposed to balance the energy absorption with maximum transmitted stress, which is crucial for energy-absorbing design of structures.

Direct and indirect methods for determination of mode I fracture toughness using PFC2D

In this paper, mode I fracture toughness of rock was determined by direct and indirect methods using Particle Flow Code simulation. Direct methods are compaction tension (CT) test and hollow centre cracked quadratic sample (HCCQS). Indirect methods are notched Brazilian disk (NBD) specimen, the semi-circular bend (SCB) specimen, hollow centre cracked disc (HCCD), the single edge-notched round bar in bending (SENRBB) specimen and edge notched disk (END). It was determined that which one of indirect fracture toughness values is close to direct one. For this purpose, initially calibration of PFC was undertaken with respect to data obtained from Brazilian laboratory tests to ensure the conformity of the simulated numerical models response. Furthermore, the simulated models in five introduced indirect tests were cross checked with the results from direct tests. By using numerical testing, the failure process was visually observed. Discrete element simulations demonstrated that the macro fractures in models are caused by microscopic tensile breakages on large numbers of bonded discs. Mode I fracture toughness of rock in direct test was less than other tests results. Fracture toughness resulted from semi-circular bend specimen test was close to direct test results. Therefore semi-circular bend specimen can be a proper test for determination of Mode I fracture toughness of rock in absence of direct test.

Strength modelling of Laminated Veneer Lumber (LVL) beams

This paper develops a mechanical model to accurately predict the strength of Laminated Veneer Lumber (LVL) beams, and illustrates its applications to numerically predict the strength distribution of LVL beams manufactured from veneers rotary peeled from early to mid-rotation subtropical hardwood plantation logs. This resource is not traditionally used in the manufacturing of commercialised LVL beams. In the first part of the paper, the model is described, calibrated against experimental results performed on 8-ply LVL beams and then verified against experimental results performed on 13-ply LVL beams. Results show that the model is able to accurately reproduce the experimental results, both on flat and edge bending, with an average prediction-to-experiment ratio of 1.0 and a relatively low coefficient of variation of 0.10. A sound prediction of the non-linear behaviour of the beams before failure was also observed. In the second part of the paper illustrating the applications of the model, the mechanical properties of veneers analysed by the authors in a previous work are used as input values in the numerical model to predict the strength of six commercially available LVL beam sizes, manufactured from early to mid-rotation subtropical Gympie messmate (Eucalyptus cloeziana), spotted gum (Corymbia citriodora) and southern blue gum (Eucalyptus globulus) plantation veneers. The design strength (5th percentile) of the beams, obtained by Monte Carlo simulations, is reported and found to range from 32.3MPa to 97.2MPa, depending on the quality of the veneers used and the beam size. The LVL beams have design strengths comparable to, and in some cases up to 2.5 times higher than commercially available softwood LVL beams, making them attractive structural products. The strength variability is also reported in the paper for developing probability-based limit state design criteria in future studies.

P‐193: Viewing Angle Performance of Curved Color‐by‐White AMOLEDs

Viewing angle performance of flexible organic light‐emitting displays (FOLEDs) with red‐green‐blue (RGB) side‐by‐side (SBS) architecture plays a major role in the visual appearance in the curved state. In particular, viewing the display from a central‐normal vantage point, the color shift becomes visible when viewing the bent edges of the display. The viewing angle performance of a color‐by‐white FOLED was measured goniometrically and compared with a SBS FOLED.

Edge geometry of pipe blanks produced by JCOE flexure

For the shaping of welded straight-seam large-diameter pipe in the TESA 1420 production line, methods are proposed for calculating the geometric parameters of the edge of the blank and the profile of the deforming tool. The edge geometry obtained on an edge-bending press is compared when using surface tools of involute and single-radius type. For tools of single-radius type, edge geometry consistent with the required shaping quality may be produced. For the edge-bending presses, a method of calculating the edge geometry in loading and unloading is outlined. The height of the bent edge, the residual radii of curvature, and the coordinates of the loading and unloading points at the external and internal edge contour of the pipe blank are determined. The coordinates of the edge formed by a tool with an involute profile are also calculated. The involute tool profile is universal on passing from one type of tool to another within a standardized group. The calculation permit conversion from an involute edge profile to a multiradial profile, followed by determination of the fixed coordinates of the points of the blank after springback. On the basis of those coordinates, the output edge geometry is estimated. Within the 1220–1420 mm standardized group, the longitudinal edge deformation for the 1220 × 10 mm type is calculated. Standardization is found to be much simpler with a single- radius tool profile. For edge-bending presses, a method of calculating the edge parameters of the pipe blank when using a tool with an involute contact profile is developed and tested in industrial conditions. Single- radius calibration of the profile of the edge-bending tool is proposed, such that fixed time coordinates are ensured. These are analogous to the coordinates with an involute punch profile. The blank’s weighted mean radius of curvature maximizes the agreement of the coordinates of the blank profile at fixed points in both approaches. (The maximum discrepancy is no more than 6–7%.)

Investigation of viscoelastic fracture fields in asphalt mixtures using digital image correlation

In this work we have studied the fracture behavior of asphalt mixtures, a heterogeneous mix of hard aggregates (usually in the form of crushed quarried rock) with a petroleum based asphalt binder, used in paving applications. Specifically, we studied the dependence of asphalt mixes’ fracture response on loading rate, temperature, and recycled content—the latter used primarily to replace virgin materials like aggregates and binder. Fracture tests were conducted on semi-circular bend edge cracked specimens obtained from mixes with different compositions, and the fracture event was recorded with a camera to allow for digital image correlation (DIC) measurements. DIC, with a spatial resolution of about 40 $$\upmu $$ m/pixel, measured the far-field strain and displacement fields developing around a preexisting notch tip. Our focus here is on characterizing the material behavior by quantifying its viscoelastic response and fracture properties. The elastic–viscoelastic correspondence principle was used to extract viscous and elastic components from the full-field DIC-measured strain and displacement fields. Various energy dissipation mechanisms other than the fracture itself were evaluated. Stress–strain response and energy dissipated in the far-field regions were quantified. The pseudo-elastic stress intensity factor was then used to study the fracture properties, and quantify the effects on fracture properties of loading rate, temperature, and recycled content in the binder. It was seen that the viscoelastic characteristics of the material were a dominant factor in the material behavior obtained at room temperature. In general, the elastic component of the displacement was only up to about 30% of the total displacement, indicating a strong influence of viscoelasticity in this state. Loading rate, temperature and recycled asphalt shingles (RAS) content all affected the viscous response by introducing more elastic response when loading rate or recycled content increased or when temperature decreased. It became clear from these macroscopic measurements that the increase of RAS content considerably embrittles the material producing less viscous effects and less energy dissipated in the far-field, almost comparable to reductions associated with the loading rate increase (from 6.25 to 50 mm/min) or the temperature change ( $$-12$$ to $$25\,{^{\circ }}$$ C).

Rook-drawings of Plane Graphs

We introduce a new type of graph drawing called "rook-drawing". A rook-drawing of a graph $G$ is obtained by placing the $n$ nodes of $G$ on the intersections of a regular grid, such that each row and column of the grid supports exactly one node. This paper focuses on rook-drawings of planar graphs. We first give a linear algorithm to compute a planar straight-line rook-drawing for outerplanar graphs. We then characterize the maximal planar graphs admitting a planar straight-line rook-drawing, which are unique for a given order. Finally, we give a linear time algorithm to compute a polyline planar rook-drawing for plane graphs with at most $n-3$ bent edges.

“JCOE” CALCULATION OF GEOMETRIC PARAMETERS OF PIPE BILLET’S EDGES BY SINGLE-RADIAL SCHEMES

Methods for calculating the geometrical parameters of edge of the billet and the profile of the deforming tool are proposed for the process of forming welded large-diameter longitudinal pipes on the TESA 1420 line. A comparative analysis of geometry of the edge at the hem on the edge press was performed using the working surfaces of the tool, made by involute and single-radial schemes. Single-radial scheme allows to get the edge geometry that meets the technical requirements. For the section of an edge press the calculation procedure is presented, which allows to calculate the geometrical parameters of the edge during loading and unloading. Height of the bent edge, the residual radii of curvature, coordinates of the points of loading and unloading of outer and inner contours of the pipe billet edge have been defined. The involute profile of the tool is universal when changing one pipe size to another from a unifying pipe group. Further, in the calculations, a transition was made from profile of edge contour obtained by involute to the profile obtained by the multi-radial scheme, after which the fixed coordinates of the billet’s points were determined after unspringing. From the obtained coordinates, the output geometric parameters of the edge were estimated. For the unification group of 1220 – 1420 mm the longitudinal deformations of the edge for the size 1220×10 mm have been calculated and it was shown that the unification principles are much easier to implement with a single-radial profile of the tool. A technique for calculating the parameters of the edge of a pipe billet was developed and tested in the field of edge-bending presses using an instrument with a contact profile of a tool made by an involute. A one-dimensional calibration of the profile of an edge-bending tool is proposed, which provides fixed coordinates of the edge, similar to the coordinates for the involute profile of the punch. The calculated value of the weighted average radius of billet’s curvature ensures maximum approximation of the profile coordinates of the billet at fixed points for both calibrations (maximum divergence of coordinates according to the proposed schemes does not exceed 6 – 7 %). edge;

Study the Effects of Spring Back on Sheet Metal Bending using Mathematical Methods

In this study mathematical analysis of spring back was done for optimization of sheet metal bending process. The influence of sheet metal thickness, sheet metal type, friction, tool radius and tool shape on spring back for Aluminium, copper, mild steel and High strength steels, sheet metal have been used as variable to conducted this study. Since, the effects of each variable on the formation of spring back on sheet metal forming are investigated the following way. This empirical result shows that increasing sheet metal thickness from 0.8 mm to 4.5 mm the spring back is reduced 16% and 20.35%. When increasing of sheet metal strength spring back increases because spring back of the sheet should depend on the yield strength of the material. As the materials yield strength increase the spring back after un-loading condition also increases. The effects of material type as shows that, using Aluminium sheet metal instead of high strength sheet metals spring back is reduced by 56.%. Also, for decreasing of the tool radius leads reducing spring back. Spring back of deferential die 12% lower than edge bending die. In addition to these, if increasing the friction coefficient from 0.01 to 0.50 the spring back also increases by 52% because of increasing of friction force and this force generates higher amount of spring back. Thus the effects of material type, tool geometry, working condition and the thickness of sheet metal types were studied and investigated. Since, ultimately utilizing and compensation of tool is considered for prevention of spring back and optimizing of sheet metal bending process as well.

Crack closure and retardation effects – experiments and modelling

The design of cyclically loaded components is in many cases carried out on the basis of experiments on small-scale laboratory specimens. In this approach, many effects such as load ratio, residual stresses and short crack growth are taken into account and described in a computational crack growth model. However, it can be seen that the prediction of the actual component lifetime with such models often is clearly too conservative. The reason for this behaviour can be found in occurring load sequence effects during operation, which are often not dealt with in the context of small-scale experiments.This paper attempts to examine such variations of applied load stresses as they may occur during operation. On the basis of cyclically loaded single edge bending (SEB) specimens, crack retardation effects are investigated in detail. It will be shown that residual stresses and overloads as well as extended operation times under small loads can lead to a significant extension of the lifetime of a component.

An edge moving load on an orthotropic plate resting on a Winkler foundation

Steady-state motion of a bending moment along the edge of a semi-infinite orthotropic Kirchhoff plate supported by a Winkler foundation is considered. The analysis of the dispersion relation reveals a local minimum of the phase velocity, coinciding with the value of the group velocity, corresponding to the critical speed of the moving load. In contrast to a free plate, the bending edge wave on an elastically supported plate possesses a cut-off frequency, arising due to the stiffening effect of the foundation. It is shown that the steady-state solution of a moving load problem corresponds to a beam-like edge behaviour. This feature is then confirmed from the specialised parabolic-elliptic formulation, which is oriented to extracting the contribution of the bending edge wave to the overall dynamic response.

Self-Assembly of Magnetic Bacillus-Shaped Bilayer Vesicles in Catanionic Surfactant Solutions.

Bacillus-shaped bilayer vesicles of nanoscale size are very rare structures of stable surfactant self-assembly, because they are both thermodynamically and electrostatically unfavorable in solution. It is evidently demonstrated that appropriately aqueous mixtures of single-tailed cationic and anionic (catanionic) surfactants can produce rigidly bacillus-shaped bilayer vesicles with both flat parts and bent edges. The crucial requirement for forming bacillus-shaped bilayer vesicles is the use of cationic surfactants with relatively hydrophobic [FeCl3Br]- as counterions. [FeCl3Br]- can strongly associate with cationic surfactants to partition into the hydrophobic bilayer of bacillus-shaped bilayer vesicles, significantly increasing the edge energy of cationic surfactants to make them distribute in the low curvature part of bilayers. This causes the formation of bacillus-shaped bilayer vesicles, but not completely bent spherical vesicles, in the case of cationic surfactant excess. The specificity of hydrophobic counterions, [FeCl3Br]-, could also make the catanionic mixtures do not precipitate at the stoichiometric point. This new self-assembly on catanionic systems is culminated in the discovery of beautifully structured colloidal objects which are of practical use for molecular templating and controlled drug or DNA release.

Numerical simulation of ductile crack growth in medium wide plate specimens using 3-D computational cells

This work examines the applicability of a local damage method based on the computational cell methodology, incorporating the Gurson-Tvergaard (GT) yielding model, to predict ductile crack extension of circumferential crack-like defects in Medium Wide Plates (MWP) specimens, extracted from girth welds of pipelines, using standard single edge bend SE(B) specimen and recently standardized clamped single edge tension SE(T) specimens to obtain model parameters. Laboratory testing of SE(B) and SE(T) specimens at room temperature provides necessary and sufficient information to calibrate the parameters of the GT yielding law. After the model parameters have been defined using small specimens, predictions of crack growth behavior can be carried out for other geometries and loading modes. Therefore, parameter transferability between different specimens can be investigated and comparative studies of predicted crack driving forces can be performed. In this study, the simulated tearing resistance curves are compared to experimental data of MWP specimens, where the former is obtained by the cell model calibrated using either SE(T) or SE(B) specimens and the latter is obtained by large-scale experiments. Overall, a good agreement between numerical and experimental δ-Δa curves was observed demonstrating that the cell methodology can be considered as a valid engineering tool for studying the integrity of structural components.

Highly Facet‐Dependent Photocatalytic Properties of Cu2O Crystals Established through the Formation of Au‐Decorated Cu2O Heterostructures

This work confirms the presence of a large facet-dependent photocatalytic activity of Cu2 O crystals through sparse deposition of gold particles on Cu2 O cubes, octahedra, and rhombic dodecahedra. Au-decorated Cu2 O rhombic dodecahedra and octahedra showed greatly enhanced photodegradation rates of methyl orange resulting from a better separation of the photogenerated electrons and holes, with the rhombic dodecahedra giving the best efficiency. Au-Cu2 O core-shell rhombic dodecahedra also displayed a better photocatalytic activity than pristine rhombic dodecahedra. However, Au-deposited Cu2 O cubes, pristine cubes, and Au-deposited small nanocubes bound by entirely {100} facets are all photocatalytically inactive. X-ray photoelectron spectra (XPS) showed identical copper peak positions for these Au-decorated crystals. Remarkably, electron paramagnetic resonance (EPR) measurements indicated a higher production of hydroxyl radicals for the photoirradiated Cu2 O rhombic dodecahedra than for the octahedra, but no radicals were produced from photoirradiated Cu2 O cubes. The Cu2 O {100} face may present a high energy barrier through its large band edge bending and/or electrostatic repulsion, preventing charge carriers from reaching to this surface. The conventional photocatalysis model fails in this case. The facet-dependent photocatalytic differences should be observable in other semiconductor systems whenever a photoinduced charge-transfer process occurs across an interface.

Analysis of Kinematics of Flapping Wing UAV Using OptiTrack Systems

An analysis of the kinematics of a flapping membrane wing using experimental kinematic data is presented. This motion capture technique tracks the positon of the retroreflective marker(s) placed on the left wing of a 1.3-m-wingspan ornithopter. The time-varying three-dimensional data of the wing kinematics were recorded for a single frequency. The wing shape data was then plotted on a two-dimensional plane to understand the wing dynamic behaviour of an ornithopter. Specifically, the wing tip path, leading edge bending, wing membrane shape, local twist, stroke angle and wing velocity were analyzed. As the three characteristic angles can be expressed in the Fourier series as a function of time, the kinematics of the wing can be computationally generated for the aerodynamic study of flapping flight through the Fourier coefficients presented. Analysis of the ornithopter wing showed how the ornithopter closely mimics the flight motions of birds despite several physical limitations.

Thermo-mechanical studies on bending mechanism, bend angle and edge effect during multi-scan laser bending of magnesium M1A alloy sheets

This paper presents numerical as well as experimental studies carried out to obtain large bend angle (of the order of 10°) in difficult-to-form material, magnesium M1A alloy. Experimental studies were conducted to check the feasibility for bending of material using laser bending process. A finite element based three-dimensional non-linear thermo-mechanical numerical model was developed to simulate the multi-scan laser bending process. The computations provided by the numerical model were validated with experiments; and the validated model was used to investigate the bending mechanism and deformation behavior of the worksheet during multi-scan laser bending process. It was observed that the number of scans has a profound influence on the bending mechanism and deformation behavior. The results showed that the induced thermal stresses decrease and plastic strains increase with number of scans. Edge effect decreases with the increase in number of scans and laser power; whilst it increases with the increase in beam diameter and scan speed. The presented results provide a useful insight into the processing mechanism and will be useful in the selection of suitable process conditions for obtaining large bend angles with minimal edge effect.

Shaping of sheet to produce large-diameter welded pipe

The quality of welded pipe (diameter 508–1420 mm; wall thickness 8–48 mm) of strength class up to K80 (X100) is investigated. Plastic shaping is simulated, with quantitative estimation of the stress–strain state of thick-walled pipe blanks in TESA 1420 presses during edge bending and stepwise shaping. The corresponding computer program permits calculation of the setup of the equipment and determination of the geometric parameters of the pipe blank specified in the standards. Theoretical results are presented for a range of large-diameter pipe produced on the TESA 1420 system.

Edge bending wave on a thin elastic plate resting on a Winkler foundation

This paper is concerned with elucidation of the general properties of the bending edge wave in a thin linearly elastic plate that is supported by a Winkler foundation. A homogeneous wave of arbitrary profile is considered, and represented in terms of a single harmonic function. This serves as the basis for derivation of an explicit asymptotic model, containing an elliptic equation governing the decay away from the edge, together with a parabolic equation at the edge, corresponding to beam-like behaviour. The model extracts the contribution of the edge wave from the overall dynamic response of the plate, providing significant simplification for analysis of the localized near-edge wave field.

Parameter optimization for high speed remote laser cutting of electrodes for lithium-ion batteries

To reduce carbon emission, transportation sector has adapted lithium-ion battery-based hybridization of gasoline and diesel engines due to its efficiency, the availability of technologies, and nation-wide infrastructures. To cut prismatic and cylindrical electrodes for lithium-ion batteries, die cutting and rotary knife slitting have been used. Both techniques have disadvantages such as tool wear, process instability, inconsistency of cut quality, and redesign of mechanical cutting processes due to various battery sizes. High speed remote laser cutting overcomes these disadvantages with characteristics such as contact-free process, high energy concentration, low noise level, fast processing speed, very narrow heat affected zone, applicability to nearly all materials, and flexibility of laser power. Optimization of key parameters, or power and scanning speed, has been presented for laser cutting of electrodes for lithium-ion batteries. An acceptable clearance width is observed. The line energy is defined as dividing laser power by scanning speed and spot size. A good quality of cut surface, with no defects, such as delamination, burrs, edge bending, or microsized material attachments, is achieved with line energies between 0.8 × 1012 and 2.5 × 1012 J m−3 for anode and 0.31 × 1012 J m−3 and less than 3.5 × 1012 J m−3 for cathode.

Energy Landscapes for the Self-Assembly of Supramolecular Polyhedra

We develop a mathematical model for the energy landscape of polyhedral supramolecular cages recently synthesized by self-assembly [Sun et al., Science 2010]. Our model includes two essential features of the experiment: (i) geometry of the organic ligands and metallic ions; and (ii) combinatorics. The molecular geometry is used to introduce an energy that favors square-planar vertices (modeling $\mathrm{Pd}^{2+}$ ions) and bent edges with one of two preferred opening angles (modeling boomerang-shaped ligands of two types). The combinatorics of the model involve $2$-colorings of edges of polyhedra with $4$-valent vertices. The set of such $2$-colorings, quotiented by the octahedral symmetry group, has a natural graph structure, and is called the combinatorial configuration space. The energy landscape of our model is the energy of each state in the combinatorial configuration space. The challenge in the computation of the energy landscape is a combinatorial explosion in the number of $2$-colorings of edges. We describe sampling methods based on the symmetries of the configurations and connectivity of the configuration graph. When the two preferred opening angles encompass the geometrically ideal angle, the energy landscape exhibits a very low-energy minimum for the most symmetric configuration at equal mixing of the two angles, even when the average opening angle does not match the ideal angle.