Lower Critical Load Research Articles

Experimental and theoretical investigations on out-of-plane buckling of circular aluminum arches with web openings under a central concentrated load

Perforated arches with cellular openings are widely used as roof beams in various buildings due to the functional and appearance requirements of architecture. Perforated arches under a central concentrated load may suffer from out-of-plane buckling when the load reaches to a critical value. This paper presents the analytical solution based on the energy method to predict the critical load of perforated arches under a central concentrated load. Experimental tests and finite element analyses are also carried out for perforated circular aluminum arch specimens to validate the present analytical solution. Good agreement between the analytical, experimental, and numerical results is demonstrated. The present results show that the size of web openings and the slenderness of the arch could affect the out-of-plane buckling behavior of perforated arches significantly. The arch with larger web perforations or larger slenderness ratio has the lower critical load of out-of-plane buckling.

Mode I fracture mechanisms and crack evolution behavior of three-dimensional braided composites

Three-dimensional braided composites possess higher inter-laminar fracture toughness than two-dimensional laminates, while the mode I fracture toughness behavior of three-dimensional braided composites is still unknown. Here we report mode I fracture behavior of three-dimensional braided carbon fiber/epoxy composites tested with the double-cantilever beam method. The samples with a pre-crack were tested using the MTS device, and the fracture process was recorded to calculate the fracture toughness. The effects of different loading rates on fracture behavior were compared. The strain field at the crack tip was obtained by the digital image correlation technique. The damage morphologies were scanned by X-ray microcomputer tomography. It was found that the bridging effect of braiding yarns prevents cracks from initiation and propagation, while the intertwining points of the braiding structure cause crack bifurcation. The braided architecture provides an effective way to hinder crack propagation. The stiffness of composites tends to decrease as the loading rate rises. The higher loading rate results in a lower critical load level for crack propagation and reduces fracture toughness. The results show that the three-dimensional braided structure is an effective method for increasing the fracture toughness. We hope the results can be used for the design of higher fracture toughness composite structures.

Nonlinear axisymmetric buckling analysis of the FGM sandwich shallow spherical shells under thermomechanical loads

Functionally graded material (FGM) sandwich shallow spherical shells are promising composite sandwich structures for modern engineering applications. In this paper, the axisymmetric snap-through buckling of spherical shells under uniform external pressure and non-uniform temperature rise along the shell thickness was studied. Based on the classical shell theory and the Sanders nonlinear kinematics equations, we established a two-point boundary value problem (BVP) posed by the displacement-type nonlinear ordinary differential equations governing the axisymmetric buckling of the FGM sandwich shallow spherical shells and the clamped boundary conditions. Then, the solutions of the above BVP were obtained using the numerical shooting method. The influence of initial term numbers of the infinite series defining the non-uniform temperature field on the accuracy of the solution was examined. Numerical calculations showed that a considerable initial term number of the series were needed to obtain the applicable solutions for engineering. Some valuable conclusions were drawn through detailed parameter studies. As the radius of the bottom circle increases, the lower critical load of shells decreases, the jump amplitude of buckling increases, and the upper critical load remains almost unchanged. The upper and lower critical loads and the jump amplitude increase as the circle radius of the middle surface of shells decreases. When the thickness of shells increases, their upper and lower critical loads increase, whereas the jump amplitude of buckling reduces. The gradient index has a significant effect on the steady-state response of pre-buckling spherical shells but little effect on that of post-buckling spherical shells. When the temperature rises, the upper critical load and the buckling jump amplitude of shells increase, but the lower critical load decreases. When the gradient index is greater (less) than about 0.35, the upper critical load decreases significantly (increases slightly) with the increase in the relative thickness of the FGM core. The present numerical results are well consistent with the finite element results and those in the available literature.

Electrocoagulation pretreatment of pulp and paper wastewater for low pressure reverse osmosis membrane fouling control.

Low pressure reverse osmosis (LPRO) has been increasingly used in advanced treatment of pulp and paper wastewater (PPWW) for the purpose of water reuse. However, membrane fouling is a major problem encountered by full-scale RO systems due to the organic and inorganic contents of the feedwater. Electrocoagulation (EC) as an effective treatment for foulants removal can be applied in pre-filtration. Therefore, the LPRO membrane fouling mechanism and the membrane fouling control performance by EC treatment were investigated in this study. EC pretreatment could reduce the membrane fouling and improve the membrane flux by 31%, by effectively removing and/or decomposing the organic pollutants in PPWW. Fluorescent spectrometry analyses of the feedwater and the permeate revealed that humic acid-like and fulvic acid-like organics in PPWW were the major foulants for the LPRO membranes. Fourier transformation infrared spectrometry results confirmed that the organic foulants contained benzoic rings and carboxylic groups, which were typical for organic substances. EC effectively removed organic pollutants containing functional groups such as carboxylic acid COH out-of-plane bending, olefin (trans), and NH3+ symmetrical angle-changing. Moreover, the extended Derjaguin-Landau-Verwey-Overbeek model suggested that the membrane filtered 30-min EC-treated PPWW had the strong repulsion force to foulants due to the higher cohesion energy (12.1mJ/m2) and the lower critical load, which theoretically explained the reason of EC pretreatment on membrane fouling control.

Delayed buckling of spherical shells due to viscoelastic knockdown of the critical load

We performed dynamic pressure buckling experiments on defect-seeded spherical shells made of a common silicone elastomer. Unlike in quasi-static experiments, shells buckled at ostensibly subcritical pressures, i.e. below the experimentally determined critical load at which buckling occurs elastically, often following a significant delay period from the time of load application. While emphasizing the close connections to elastic shell buckling, we rely on viscoelasticity to explain our observations. In particular, we demonstrate that the lower critical load may be determined from the material properties, which is rationalized by a simple analogy to elastic spherical shell buckling. We then introduce a model centred on empirical quantities to show that viscoelastic creep deformation lowers the critical load in the same predictable, quantifiable way that a growing defect would in an elastic shell. This allows us to capture how both the deflection at instability and the time delay depend on the applied pressure, material properties and defect geometry. These quantities are straightforward to measure in experiments. Thus, our work not only provides intuition for viscoelastic behaviour from an elastic shell buckling perspective but also offers an accessible pathway to introduce tunable, time-controlled actuation to existing mechanical actuators, e.g. pneumatic grippers.

A molecular dynamics study on the tribological behavior of molybdenum disulfide with grain boundary defects during scratching processes

The effect of grain boundary (GB) defects on the tribological properties of MoS2 has been investigated by molecular dynamics (MD) simulations. The GB defects-containing MoS2 during scratching process shows a lower critical breaking load than that of indentation process, owing to the combined effect of pushing and interlocking actions between the tip and MoS2 atoms. The wear resistance of MoS2 with GB defects is relevant to the misorientation angle due to the accumulation of long Mo-S bonds around the GBs. Weakening the adhesion strength between the MoS2 and substrate is an efficient way to improve the wear resistance of MoS2 with low-angle GBs.

Damage mechanisms evolution of TiN/Ti multilayer films with different modulation periods in cyclic impact conditions

The evolution of cyclic impact damage mechanisms ofTiN/Ti multilayer films were investigated in terms of microstructural transformation as the modulation period decreased sharp from micron-scale (1000 nm) to nano-scale (60 nm). It was found that the ductile Ti phases reduced with decreasing modulation period, and the microstructures of films transformed from TiN/TixNy/Ti to TiN/TixNy (x > y). The cyclic impact results showed that both impact resistance and damage mechanisms of TiN/Ti multilayer films were strongly associated with modulation period. In the cyclic nano-impact conditions, the smaller modulation period of TiN/Ti film, the lower critical fracture load and higher fracture probability, thus worse impact resistance. Furthermore, the evolution of cyclic impact damage mechanisms ofTiN/Ti multilayer films were revealed that in T1000 film, only few cracks were observed and the Ti interlayers could prevent cracks from extending deeper into film, resulting in slight fracture with small chippings. While there were many more cracks in T60 film and these cracks could easily across multilayers, leading to severe brittle spalling with multiple layers. It was demonstrated that with the microstructural transformation from TiN/ TixNy/Ti to TiN/ TixNy, a higher cracking probability was found in TiN/Ti films, and the crack propagation mode changed from horizontal along interface to vertical across multilayers.

Heat transfer performance of cylindrical heat pipes with axially graded wick at anti-gravity orientations

To increase the heat transfer capability at anti-gravity orientations, heat pipes with homogeneous and axially graded wicks were experimentally investigated. The homogeneous wick (0.8 mm thickness) sintered with 125–150 μm (coarse) copper powder operated at 100 W without dryout at horizontal orientation, while that sintered with 75–97 μm (fine) copper powder had lower critical heat load about 80 W. The critical heat load decreased tremendously with increasing anti-gravity angles and it was about 20 W at totally anti-gravity orientation. However, the axially graded wick, sintered with fine and coarse powder at evaporator section and the rest section of the pipe, respectively, exhibited critical heat load of 35 W, nearly 75% increment than homogeneous wick with same thickness. Further study shows that increasing the thickness of axially graded wick significantly improved the critical heat load although the thermal resistance increased simultaneously. At a tilted angle of 90°, the critical heat load increased from 35 W to 45 W when increasing thickness from 0.8 mm to 1.1 mm and it further increased to 96 W when increasing thickness to 1.35 mm. The reconciliation between the capillary force and the permeability of axially graded structure promoted the increase of the critical heat load notably.

Pin-ended column buckling load is 2.73% lower than Euler's

A verification calculation was aimed at further proving that the least critical load gives the Euler buckling load for a pin-ended column to be : Pcr=(PI)2*EI/L2. Selecting a parabolic function for this purpose, that meets the boundary conditions and is almost exactly similar to the symmetrical function sin(x). It was expected to obtain a critical load that is larger than the load given by the sine function. The parabolic function produced LOWER CRITICAL LOAD by about 2.73%.

Wear Mechanism of Multilayer AlCrWN/AlCrWSiN-coatings on Cemented Carbide Tools Prepared by Arc Ion Plating in Dry Cutting of Hardened Sintered Steel

In this study, to clarify the wear mechanism of the multilayer AlCrWN/AlCrWSiN-coated tool in cutting of hardened sintered steel, the rate of wear in the cutting of hardened sintered steel using three types of coated tools was investigated. The Type I tool had a single layer (Al60, Cr25, W15)N coating film, the Type II tool had a single layer (Al53, Cr23, W14, Si10)N coating film and the Type III tool had a multilayer (Al60, Cr25, W15)N/(Al53, Cr23, W14, Si10)N-coating film. Scanning electron microscope (SEM) observation and electron dispersive X-ray spectrometry (EDS) mapping analysis of the abraded surface of the coating film were performed. The following results were obtained: 1) The wear rate of the Type III tool was the slowest. 2) The area of the worn surface on the rake face “S” and the contact length between the rake face and the chip “D” were measured. Comparing the three types of coated tools, both the “S” and the “D” of Type I tool were the smallest, and those of Type II tool were the largest. 3) The main wear mechanism of Type II and Type III tool showed abrasive wear. However, the main wear mechanism of the Type I tool was both abrasive wear and adhesion wear. 4) The critical scratch load of the Type I tool, 81 N, was lower than that of the Type II or the Type III tool, over 130 N. Therefore, comparing the Type I and Type III tools, due to the wear mechanism of the Type 1 tool being both abrasive wear and adhesion wear, the wear rate of the Type I tool, which has the lower critical scratch load, was slower.

Determining the efficiency of functioning of systems of temperature stabilization of soils with horizontal evaporator filled with different refrigerants

The construction of buildings and structures in the zones of distribution of frozen soils follows the principle I. The bearing capacity of frozen soils significantly depends on their value of negative temperature. When thawed, such soils shrink, which negatively affects the objects built on them. To prevent this, temperature stabilization systems for frozen soils are used. Simultaneous accounting of the thermal effect on the frozen soil of an engineering object, as well as the temperature stabilization system of soils, is a difficult task, the accuracy of determining the strength characteristics of the soil will depend on the correctness of its solution. This paper presents calculations of the temperature fields of frozen soils with simultaneous exposure to an object with intense heat (RVS with hot oil) and soil temperature stabilization system of the horizontal natural-acting tubular system (GET) type. The calculations follow the previously developed mathematical model of the temperature stabilization system with a horizontal evaporator. The authors consider the efficiency of the operation of the GET system charged with different refrigerants (ammonia and carbon dioxide) for different geocryological subzones of Western Siberia. Particular attention should be paid to the fact that the soil was initially at a close to positive temperature (−0,1 °C), but after calculating for 10 years, the entire soil mass around the evaporation part of the temperature stabilization system froze because of the soil temperature stabilization system. Systems charged with carbon dioxide showed better work efficiency. This is due to two factors: a lower value of the lower critical heat load, which gives more working days per year relative to the system charged with ammonia; and the evaporative part of the system on carbon dioxide, which has the average temperature 1 °C lower than ammonia systems. The results show that carbon dioxide as the heat carrier for the GET system is the most effective.

Communication—Fracture Behavior of Single LiNi0.33Mn0.33Co0.33O2 Particles Studied by Flat Punch Indentation

The fracture of lithium nickel manganese cobalt oxide (NMC) particles can affect the electrochemical performance and manufacturing process of NMC electrodes. Here, we report the fracture behavior of single LiNi0.33Mn0.33Co0.33O2 (NMC111) secondary particles studied by flat punch indentation. The critical load corresponding to the fracture of NMC111 secondary particles increases with increasing particle size, while the fracture strength is unaffected by the size of the secondary particles. Particles at the first delithiation and lithiation states have significantly lower critical load and fracture strength than the pristine ones, suggesting that electrochemical cycling strongly affects the mechanical integrity of NMC111 secondary particles.

Numerical Analysis of the Structural Stability of Ideal (Defect-Free) and Structurally and Morphologically Degenerated Homogeneous, Linearly- and Angle-Adjoined Nanotubes and Cylindrical Fullerenes Under Axial Loading Using Finite Element Method

We report on the structural stability of ideal (defect-free) and structurally and morphologically degenerate carbon nanotubes and nanotube junction systems under axial loading based on the finite element method. We estimated the values for critical buckling load for uncapped and capped single-walled carbon nanotubes (SWCNTs) and linear and angle-adjoined SWCNT heterojunctions in ideal and structurally degenerate systems containing single-, double-, triple-, pinhole- and pentagon–heptagon (i.e., 5–7) structural defects and also containing a substitutional nitrogen (N) atom inclusion under compressive loading. Absolute atomic vacancy (defect) concentration in studied SWCNTs models was assumed to be nil for ideal systems, and was up to 3.0 at.% for structurally and morphologically degenerate systems. It was found that all types of structural defects and the morphological N-defect had reduced the load carrying capacity and mechanical strength in all SWCNT systems studied. The SWCNT models containing physically large vacant sites, such as triple- and pinhole-defects, displayed significantly lower critical load values compared to the systems that contained only a single-, double- or triple-vacancies. In addition, we found that capped SWCNTs performed marginally better in critical load carrying capacity compared to uncapped SWCNT systems. Furthermore, majority of the investigated structures displayed reduced load in SWCNTs with narrower tube widths, proportional to the size and the type of the defect investigated. The effects of chirality, such as zigzag- versus armchair-type, on the structural stability of the investigated SWCNT models were also investigated.

Detection of symmetry breaking bifurcations using finite element analysis packages

Trusses with geometric and loading symmetries have been used in many structures to reduce the complexity of the design. Slight asymmetries in geometry and in loading could lead to bifurcation in the structural response. Failure of such structures still occur occasionally causing major damage to the property and to the human lives. A fully nonlinear structural analysis is expected to detect such symmetry breaking bifurcations. In this paper, we conducted the bifurcation analysis of a two-bar truss and a shallow arch structure with seven bars. Two program packages Gesa and Ansys based on finite elements method have been used to detect the symmetry breaking bifurcation points. However, unlike typical bifurcation analysis packages they cannot detect the bifurcation point without inserting a small perturbation in the initial geometry or the loading of the structure. Such a bifurcation can be easily missed in finite element-based analysis. The theoretical analysis reveals that the bifurcation leads to a much lower critical load in the presence of small asymmetry compared to the symmetric case. The results are verified by using Gesa program in Matlab for fully nonlinear analysis and with results by using Ansys commercial program. The two structural examples serve to illustrate the limitations of widely used finite element analysis packages for nonlinear bifurcation analysis.

Symmetrical or Non-Symmetrical Debonds at Fiber–Matrix Interfaces: A Study by BEM and Finite Fracture Mechanics on Elastic Interfaces

A recently proposed criterion is used to study the behavior of debonds produced at a fiber–matrix interface. The criterion is based on the Linear Elastic–(Perfectly) Brittle Interface Model (LEBIM) combined with a Finite Fracture Mechanics (FFM) approach, where the stress and energy criteria are suitably coupled. Special attention is given to the discussion about the symmetry of the debond onset and growth in an isolated single fiber specimen under uniaxial transverse tension. A common composite material system, glass fiber–epoxy matrix, is considered. The present methodology uses a two-dimensional (2D) Boundary Element Method (BEM) code to carry out the analysis of interface failure. The present results show that a non-symmetrical interface crack configuration (debonds at one side only) is produced by a lower critical remote load than the symmetrical case (debonds at both sides). Thus, the non-symmetrical solution is the preferred one, which agrees with the experimental evidences found in the literature.

Natural organic matter fouling behaviors on superwetting nanofiltration membranes

Nanofiltration has been widely recognized as a promising technology for the removal of micro-molecular organic components from natural water. Natural organic matter (NOM), a very important precursor of disinfection by-products, is currently considered as the major cause of membrane fouling. It is necessary to develop a membrane with both high NOM rejection and anti-NOM fouling properties. In this study, both superhydrophilic and superhydrophobic nanofiltration membranes for NOM removal have been fabricated. The fouling behavior of NOM on superwetting nanofiltration membranes has been extensively investigated by using humic acid (HA) as the model foulant. The extended Derjaguin−Landau−Verwey−Overbeek approach and nanoindentor scratch tests suggested that the superhydrophilic membrane had the strongest repulsion force to HA due to the highest positive total interaction energy (ΔGTOT) value and the lowest critical load. Excitation emission matrix analyses of natural water also indicated that the superhydrophilic membrane showed resistance to fouling by hydrophobic substances and therefore high removal thereof. Conversely, the superhydrophobic membrane showed resistance to fouling by hydrophilic substances and therefore high removal capacity. Long-term operation suggested that the superhydrophilic membrane had high stability due to its anti-NOM fouling capacity. Based on the different anti-fouling properties of the studied superwetting membranes, a combination of superhydrophilic and superhydrophobic membranes was examined to further improve the removal of both hydrophobic and hydrophilic pollutants. With a combination of superhydrophilic and superhydrophobic membranes, the NOM rejection (RUV254) and DOC removal rates (RDOC) could be increased to 83.6% and 73.3%, respectively.

Influence of combined loading on the structural stability of carbon nanotubes

Numerous armchair and zigzag carbon nanotubes (CNTs) in their perfect and geometrically modified form were simulated and their buckling behavior was investigated through performing computational tests with different boundary conditions. Both computational and analytical results were compared in the case of perfect tubes. Then, three kinds of geometrical modifications, i.e. twisting angle, z-distortion along the longitudinal axis, and xy-distortion along the radial axis, were introduced to the configuration of perfect CNTs and the buckling behavior of geometrically modified CNTs was numerically evaluated and compared with the behavior of the perfect ones. It was shown that the first critical buckling load of both perfect armchair and zigzag CNTs increases by increasing the chiral number. In addition, it was also concluded that the existence of any type of geometrical modifications in the configuration of CNTs leads to a lower critical load and as a result, lower buckling properties. Finally, it was revealed that by increasing the length of the tubes, the critical buckling load of the CNTs reduces significantly while addition of further walls increases significantly the critical buckling load.

ON THE INFLUENCE OF ATOMIC MODIFICATIONS ON THE STRUCTURAL STABILITY OF CARBON NANOTUBE HYBRIDS: NUMERICAL INVESTIGATION

Connected carbon nanotubes (CNTs) with parallel longitudinal axes and with bending angles were simulated by a commercial finite element package and their buckling behavior was investigated by performing several computational examinations. In addition, the effect of defects on the structural stability of these heterojunctions was analyzed. For this purpose, two different nanotube hybrids (straight and kink heterojunction) were constructed in their perfect forms. In the second phase, three most likely atomic defects, i.e., impurities (doping with Si atoms), vacant sites (carbon vacancy) and introduced perturbations of the ideal geometry in different amounts to the perfect models, were simulated. To conclude our study, the buckling behavior of imperfect heterojunctions was numerically evaluated and compared with the behavior of the perfect ones. It was concluded that the existence of any type of defects in the configuration of nanotube hybrids leads to a lower critical load and as a result, lower buckling properties. This study provides a better insight into the prediction of straight and kink heterojunction CNTs behavior.

On the nucleation and growth of kink and shear bands

Similarities and differences between the phenomena of kink banding in compressed layered structures and shear banding in compressed granular media are explored. Simple models are introduced for both, and the focus is directed onto how they can nucleate from the perfectly flat state. A convincing scenario is found for each in which a mode develops from an initial bifurcation into a periodic state, followed by rapid localization under falling load, while retaining decaying but wavy tails. At a certain lower critical load, the tails lose their waviness, and the expected form of the kink or shear band appears. In each case, good numerical evidence is provided for the existence of this form of behaviour. A second potential instability for the layered case is also explored, linked to the appearance of a critical force dipole that overcomes bending stiffness locally at some point along the length. This mode, which should appear with non-wavy decaying tails at the lower of the two critical loads mentioned earlier, proves somewhat elusive. Evidence is found for its existence in the linearized approximation to the layered model, but the search for numerical solutions to the underlying nonlinear equation is hindered by a shortage of suitable boundary conditions.

Numerical investigation on the influence of defects on the buckling behavior of single-and multi-walled carbon nanotubes

The effect of defects on the buckling behavior of single- and multi-walled carbon nanotubes based on the finite element method was analyzed. For this purpose, two fundamental carbon nanotubes (armchair and zigzag) were constructed in their perfect forms. Then, the buckling behavior of carbon nanotubes was evaluated by comparing their critical loads obtained from the simulation and analytical calculations. In the second phase, three most likely atomic defects, i.e., impurities (doping with Si atoms), vacant sites (carbon vacancy) and introduced perturbations of the ideal geometry in different amounts to the perfect models were simulated. Finally, the buckling behavior of imperfect carbon nanotubes was numerically evaluated and compared with the behavior of the perfect ones. In addition, simple relations were developed from the obtained results for prediction of the buckling behavior of imperfect carbon nanotubes as a function of the amount of defects. The results reveal the fact that the existence of any type of defects in the structure of carbon nanotubes leads to a lower critical load and as a result, lower buckling properties. As an outlook, curved and composite single walled carbon nanotubes were exemplarily considered as a deviation from the perfect straight form. Investigating this effect yielded that the existence of any curvature or kink in the structure of nanotubes decreases their buckling strength. This study provides a realistic prediction of buckling properties of carbon nanotubes which is of high importance in nano-industry and the production of nano-composites and reinforced materials.