Critical Depth Research Articles

Numerical Study of MICP Infiltration and Mineralization in Unsaturated Soils: CaCO 3 Distribution and Critical Depth

Numerical Study of MICP Infiltration and Mineralization in Unsaturated Soils: CaCO ₃ Distribution and Critical Depth

Abundant vortex dynamics in spin-1 Bose–Einstein condensates induced by Rashba spin–orbit coupling

The paper studies the dynamics of vortices evolved from the ring dark solitons (RDSs) in spin-1 Bose–Einstein condensates with Rashba spin–orbit coupling (SOC). We find that the SOC induces abundant vortex dynamic phenomena, and the numbers of vortex dipoles and lump-like solitons are all determined by the initial depths’ weighted average of the three components of RDSs. For a shallow RDS, the ring first expands and then contracts into a mini RDS, eventually evolving into late vortex dipoles. For the RDS with a moderate initial depth, during the contraction of the ring, it evolves into early vortex dipoles or lump-like solitons, and they evolve back into the mini RDS, which then evolves into late vortex dipoles during the expansion process. For the deep and black RDSs, the early vortex dipoles continue to transform between vortex dipoles and lump-like solitons without forming mini RDS. The motions of vortices mentioned above have a higher disorder degree than that in the system without SOC, because the SOC breaks the mirror symmetry of the condensate. Finally, we reveal that the SOC strength only influences the number of late vortex dipoles, while it does not affect the number of early vortex dipoles and lump-like solitons. Stronger SOC intensity results in a shallower critical depth, and vortices form only at or beyond this depth.

Research on microscopic fracture mechanism of glass-ceramics grinding surface based on progressive scratch test

Progressive scratch test was carried out on the glass-ceramics to study the continuous micro-fracture mechanism of its surface, which provided an important basis for the research on the grinding mechanism of glass-ceramics. By microimaging of scratch, the continuous material removal process of glass-ceramics from ductility to ductile brittleness to brittleness was observed in micro-view, confirming that there was a ductile brittleness between ductility and brittleness on the surface of glass-ceramics. The critical point for breaking from ductility to ductile brittleness and the critical point for breaking from ductile brittleness to brittleness were measured. The machined critical depth hc1 of the composite domain of ductility and ductile brittleness and the machined critical depth hc2 of the composite domain of ductile brittleness and brittleness for glass-ceramics were further obtained by computational analysis. This study provides valuable insights into the surface machining forming and surface microstructure generating of glass-ceramics material. The research results can also provide reference on determining the critical grinding parameters of glass-ceramics material.

Crack Growth and Fatigue Strength of Deck‐Rib Welded Joints in Orthotropic Steel Decks Integrating Mean Stress Effect

ABSTRACTFatigue tests were conducted to investigate the effects of mean stress, stress range, and deck thickness on crack growth and fatigue failure of the deck‐rib welded joint. According to the experimental results, a fatigue failure criterion and a fatigue evaluation method for deck‐rib welded joints, which consider mean stress effect, was proposed. The results indicated that the stress range remains the dominating factor, but the influence of mean stress cannot be ignored. It was proposed that the crack length reaching approximately 150 mm and the depth reaching around 70% deck thickness can be taken as the fatigue failure criterion, while increase in mean stress would reduce the critical crack length but increase the critical crack depth. Besides, multiple cracks will weaken the fatigue strength. It is recommended to use Walker method and the FAT 71 curve with enhancement factor to evaluate the fatigue strength under symmetrical stress cycle.

Effect of Laser Power and Diamond Tool Parameters for Micro Laser-Assisted Ductile Mode Material Removal on Fused Silica

Abstract Fused silica is an essential material used in various applications due to its excellent optical and mechanical properties. However, processing it can be challenging due to its high hardness and brittleness, leading to sub-surface damage during grinding and polishing operations. Micro laser-assisted ductile mode material removal is a promising technique for achieving high levels of precision and accuracy in material removal. This technique leads to controlled and precise removal of material without inducing cracks or fractures. Despite its advantages, there are several challenges associated with the process, such as selecting the appropriate laser power and diamond tool geometry. In this study, we employed a Universal Mechanical Tester equipped with modified OPTIMUS, a laser-assisted machining technology to investigate the impact of laser and diamond tool geometry on scratch cut quality. Introducing and increasing the laser power demonstrated an improvement of around 251.7% in cut ductility, leading to a decrease in the severity of sub-surface damage (SSD). Altering the rake angle from -25° to -45° resulted in a 45.3% reduction in the critical depth of cuts (DOCs). However, when laser was employed, the critical DOCs increased around 34.4% in ductile mode material removal on fused silica samples, which underscores the criticality of the laser in this process.

Study on the Influence Law of Micro-Scale Abrasive Wear on a Wind Turbine Brake Pad

The hard particles in the copper-based powder metallurgic material of a brake pad for a wind turbine brake falls off and presses into the surface of the brake disc to form abrasive particles under high-speed and heavy-load working conditions. The presence of abrasive particles will produce abrasive wear with micro-scratch and micro-scribe on the copper-based material of the brake pad. The critical scratch depth effect in the abrasive wear process is proposed based on the critical depth effect of the metal removal process at the micro-scale. The abrasive wear is divided into two types: scratch wear and scratch wear, which is proposed according to the comparison of the actual scratch depth and the critical scratch depth. The range of braking speeds and friction coefficients in abrasive wear is determined by the recommended parameters of the disc brake. The ABAQUS2020 software is used to simulate and analyze the micro-scale abrasive wear of a brake pad. The brake strain/stress curves of the brake pad under different brake speeds and friction coefficients are compared and analyzed for two abrasive wear types based on the range of braking parameters, and the key factors affecting abrasive wear are proposed.

Enhancing Ignition Reliability with Tail-Groove Strut Designs in Cavity-Based Combustors

As the flight envelopes of turbine-based combined cycle (TBCC) engines expand, ensuring reliable ignition and flame stability under varying conditions becomes increasingly critical. Previous work has shown a significantly changed ignition performance and flow pattern in cavity-based combustors when strut structure parameters were altered, indicating a strong correlation between the ignition process, flame structure, and the strut configuration. This suggests that further investigation is required to determine the optimal strut design. Therefore, this study examines the impact of various strut configurations through numerical simulations, validated by high-speed imaging. Findings show that the tail-groove strut designs improve the flame propagation performance compared to the normal struts, with a critical depth beyond which further increases do not enhance performance. Changes in strut length have a lesser impact than depth. Flow analysis indicates that tail-groove struts create additional recirculation zones that enhance fuel atomization and flame stability. These results suggest that optimizing strut configurations is vital for achieving reliable ignition and flame stability, advancing the development of efficient engines across a wide range of operational conditions.

Investigation of the elastic-plastic evolution mechanism of 4H-SiC substrates with external thermal-assisted abrasion

Plastic removal is easier to achieve nanometric surfaces of monocrystalline SiC with brittleness in nano-polishing. This paper mainly focuses on the nano-scale elastic-plastic evolution mechanism of 4H-SiC substrates in thermal-assisted polishing using molecular dynamics simulation. The results show that 4H-SiC substrates undergo elastic deformation, elastic-plastic deformation, and plastic deformation in ramp nano-abrasion. The critical depth from elastic to elastic-plastic deformation rises with higher external temperature, and elastic-plastic deformation stage is compressed. Amorphization dominates the elastic recovery in elastic-plastic deformation stage. Furthermore, the step-terrace structure appears in elastic deformation stage, and is observed at a greater depth rising from 0.679 nm to 1.226 nm with increasing external temperature from 298 K to 700 K. High surface quality and subsurface damage-free of SiC substrates are performed with forming the atomic step-terrace structure.

Continuous Casting Slab Mold: Key Role of Nozzle Immersion Depth.

Based on a physical water model with a scaling factor of 0.5 and a coupled flow-heat transfer-solidification numerical model, this study investigates the influence of the submerged entry nozzle (SEN) depth on the mold surface behavior, slag entrapment, internal flow field, temperature distribution, and initial solidification behavior in slab casting. The results indicate that when the SEN depth is too shallow (80 mm), the slag layer on the narrow face is thin, leading to slag entrapment. Within a certain range of SEN depths (less than 170 mm), increasing the SEN depth reduces the impact on the mold walls, shortening the "plateau period" of stagnated growth on the narrow face shell. This allows the upper recirculation flow to develop more fully, resulting in an increase in the surface flow velocity and an expansion in the high-temperature region near the meniscus, which promotes uniform slag melting but also heightens the risk of slag entrainment due to shear stress at the liquid surface (with 110 mm being the most stable condition). As the SEN depth continues to increase, the surface flow velocity gradually decreases, and the maximum fluctuation in the liquid surface diminishes, while the full development of the upper recirculation zone leads to a higher and more uniform meniscus temperature. This suggests that in practical production, it is advisable to avoid this critical SEN depth. Instead, the immersion depth should be controlled at a slightly shallower position (around 110 mm) or a deeper position (around 190 mm).

Achievement of ductile-regime removal in fabricating Gaussian curved microstructure processed by micro ball-end milling on soft-brittle KDP surface

Laser-induced damage points (known as defects) would seriously reduce the service life of large-aperture KDP optics in high-power laser devices. The ball-end milling procedure is recognized as an efficient method for creating a Gaussian mitigation pit (GMP) to restore the optical transmission performance of functional KDP crystals by removing defects. Nevertheless, achieving smooth and flawless Gaussian curved microstructures is a massive challenge for soft-brittle KDP crystals. Herein, a judging criterion of the ductile-regime machining for the GMP is developed by the models of uncut chip thickness (UCT) and critical milling depth. Simultaneously, the obtained judging criterion can be validated by the microstructure fabrication experiments. Besides, considering the spindle vibration, plowing effect, and machined surface texture, the influence of spindle speed (n), feed rate (f), and tool mark interval (d) on the surface formation mechanism of the GMP is analyzed, respectively. It can be discovered that the n of up to 60,000 r/min can lead to severe velocity fluctuation of the motion system, increasing the UCT and causing brittle fractures on the KDP surface. A low f can result in an undesirable plowing phenomenon, and a large number of crystal materials are accumulated in the up-cut process. Once the f reaches 72 mm/min, the tool path would fluctuate significantly, resulting in poor GMP surface texture. When the d exceeds 15 μm, the surface quality of the GMP can no longer meet the engineering requirements of the Ra ≤ 50 nm. Moreover, the optimized processing parameters of the microstructure fabrication are 47,800 r/min in the n, 30 mm/min in the f, and 5 μm in the d. This study can provide crucial guidance for obtaining the ultra-smooth and defect-free GMP processed in the ductile regime, which would resultantly possess significant theoretical importance and practical value in enhancing the optical properties of flawed KDP crystals.

Analytical study on included angle of double-plate vertically loaded anchors in saturated clay

The double-plate vertically loaded anchor (DPVLA) represents a new type of anchor. To maximize the ultimate pullout capacity of a DPVLA in saturated clay, it is crucial to determine the included angle corresponding to the maximum pullout capacity (IAMPC). An expression for the IAMPC of the DPVLA in saturated clay has been derived based on its mechanical model. Furthermore, the influence of various parameters on the IAMPC is analyzed based on the derived expression. The effect of the IAMPC of the DPVLA on the critical embedment depth has been investigated through finite element analysis. The results indicate that, aside from the area of the auxiliary fluke, the IAMPC of the DPVLA is significantly influenced by other parameters, which also impact the ultimate pullout capacity associated with IAMPC, except for the adhesion factor. Additionally, it is also found that the critical embedment depth of a DPVLA, with the main fluke area equal to that of the auxiliary fluke, increases with the IAMPC until a -maximum critical embedment depth is reached. These findings provide valuable insights for the design and installation of DPVLAs in saturated clay environments.

Sensitivity analysis of geological mining influencing factors on the pressure relief effect of upper protective layer mining

AbstractTo study the influence of different geological and mining factors on the decompression effect of protective layer mining, a numerical simulation was carried out using FLAC3D numerical software. Taking the Hulusu coal mine as the engineering background, numerical simulation studies were carried out under different mining heights, working face lengths, interlayer lithologies and layer spacing by using FLAC3D numerical software, and the effects of different geological and mining factors on the degree of decompression and the scope of decompression were quantitatively investigated through the control of single‐factor variables. The results show that: the stress at the critical depth of impact ground pressure is 16.44 MPa, and the coefficient of unloading degree C = 0.5 is the indicator of sufficient unloading; the unloading effect of the protected layer decreases with the increase of layer spacing, lithological strength, and length of the working face, and increases with the increase of mining height; the geological and mining parameters of the protected layer show a functional relationship with the critical depth of the unloading, and the order of the influence of pressure relief effect is layer spacing > mining height > interlayer lithology > working face length. The results of the study are very important for the determination of the mining parameters of the protective layer, the estimation of the protective effect, and the design of the management programme of impact pressure.

Effect of crack depth on the initiation and propagation of crack-induced sliding in a paleosol area on a loess slope: Three-dimensional investigation based on model testing and laser scanning

On the Chinese Loess Plateau (CLP), crack-induced sliding in paleosols triggers retrogressive slope collapse, compromising the long-term stability of loess slopes. Establishing a quantitative relationship between crack depth and slide size is key to elucidating the progressive evolution of crack-induced sliding in paleosols; however, research on this topic is scarce. In this study, a model test was conducted on a paleosol slope subjected to five drying–rainfall cycles. Three-dimensional (3D) laser scanning technology was employed to accurately quantify the variations in crack depth and slide size, and water content sensors were embedded to monitor the preferential flow changes induced by these cracks. Results reveal that crack depth plays a pivotal role in initiating and controlling the propagation of crack-induced sliding in paleosols by influencing the preferential flow capacity through cracks. In the slide initiation stage, a critical crack depth capable of triggering sliding by inducing a sufficiently significant preferential flow and large saturation zones was identified. The depth at which sliding occurs can be expressed as a variable dependent on crack depth based on the single triggering effect of cracking on sliding. Once a crack-induced slide is initiated, the combined action of prior sliding events and current crack propagation accelerates the subsequent sliding in terms of increased size and varying spatial locations by influencing the preferential flow capacity and sliding force values. A comprehensive empirical formula was established to characterize the depth of crack-induced slides, considering the dominant influence of crack depth and slope gradient on sliding development at this stage of slide evolution. Our findings emphasize the pivotal role of crack depth in triggering progressive crack-induced sliding in paleosols, thereby providing valuable insights for soil conservation in paleosol areas on loess slopes on the CLP.

A novel fatigue life model for MCrAlY coated superalloys considering interfacial microstructure evolution

MCrAlY coatings, extensively utilized for safeguarding turbine blades against oxidation and erosion, encounter impediments due to inter-diffusion between the coating and substrate, thereby exacerbating fatigue life degradation at elevated temperatures. In this study, we introduce a novel approach involving the modification of critical depth in interfacial strain energy density to elucidate the impact of interfacial microstructure evolution on mechanical properties. Building upon this concept, we propose a fatigue life prediction model, which incorporates the dynamic evolution of interfacial structure and mechanical characteristics. Validation against empirical data underscores the commendable precision of the model. Our inquiry not only advances the comprehension of mechanical-chemical coupled behaviors but also yields significant insights for the optimization and maintenance of turbine blades.

The Effect of Tailwater on the USBR Type III Stilling Basin Model

This study evaluates the impact of tailwater on the USBR Type III stilling pond model, which is often used to construct reservoirs with low hydrostatic pressure and small flow rates. The model includes channel blocks, barrier blocks, and end barriers to dampen energy, converting flow from supercritical to subcritical. Hydraulic characteristics, including potential jump types, pressure regimes, and forces on the barrier, are not considered. Any change in discharge during the test also changes the tailwater depth position. The purpose of this study was to determine the effects of tailwater conditions on water height (y1 and y2), pool length (Lj), Froude number (Fr), critical depth (yc), and energy dissipation effectiveness (ΔE). This study shows that the average energy dissipation ratio of USBR Type III Quiet Pool is 87.45% without the effect of Tailwater, with an efficiency rate of 12.55%. When exposed to Tailwater, the average energy dissipation ratio drops to 69.47%, resulting in an efficiency rate of 30.53%. The optimum stilling pond performance is affected by the presence of tailwater (Tw), which reduces the energy dissipation ratio. The depth of the tailwater aids in the dissipation that occurs. Technical abbreviations will be explained in the first use. The water level rise under tailwater conditions exceeds that without tailwater. This finding shows tail water's importance for height rise and flow conditions. Flow conditions with Froude Number (Fr2) values of 0.22 (<1) and Tw are classified as subcritical flow.

Optimal milling cutter helix selection for period doubling chatter suppression

In high speed milling, interrupted cutting conditions can lead to period doubling chatter vibrations. While many studies have already confirmed that the use of helical tools can effectively shrink or remove these regions of unstable cutting, none of them has provided clear guidance to select the minimum helix that completely cancels the period doubling lobes. This study addresses this gap by introducing a novel analytical formula for a critical tool helix pitch: if the helix pitch is below the critical flip depth of cut of the straight helix cutter multiplied by π, the flip lobes will totally vanish. This rule is not only valuable for chatter-free process planning purposes, but it also establishes exact limit below which the fast and simple zeroth order stability algorithm can provide exact stability boundaries for helical tools. The effectiveness of the formula is numerically corroborated over three different milling scenarios: thin wall milling, slender tool and machine tool structure chatter cases. Finally, the findings are validated through experimental cutting tests.

Hydrological Connectivity Response of Typical Soil and Water Conservation Measures Based on SIMulated Water Erosion Model: A Case Study of Tongshuang Watershed in the Black Soil Region of Northeast China

The black soil region of Northeast China is the largest commercial grain production base in China, accounting for about 25% of the total in China. In this region, the water erosion is prominent, which seriously threatens China’s food security. It is of great significance to effectively identify the erosion-prone points for the prevention and control of soil erosion on the slope of the black soil region in Northeast China. This article takes the Tongshuang small watershed (Heilongjiang Province in China) as an example, which is dominated by hilly landforms with mainly black soil and terraces planted with corn and soybeans. Based on the 2.5 cm resolution Digital Elevation Model (DEM) reconstructed by unmanned aerial vehicles (UAVs), we explore the optimal resolution for hydrological simulation research on sloping farmland in the black soil region of Northeast China and explore the critical water depth at which erosion damage occurs in ridges on this basis. The results show that the following: (1) Compared with the 2 m resolution DEM, the interpretation accuracy of field roads, wasteland, damaged points, ridges and cultivated land at the 0.2 m resolution is increased by 4.55–27.94%, which is the best resolution in the study region. (2) When the water depth is between 0.335 and 0.359 m, there is a potential erosion risk of ridges. When the average water depth per unit length is between 0.0040 and 0.0045, the ridge is in the critical range for its breaking, and when the average water depth per unit length is less than the critical range, ridge erosion damage occurs. (3) When local erosion damage occurs, the connectivity will change abruptly, and the remarkable change in the index of connectivity (IC) can provide a reference for predicting erosion damage.

Numerical analysis of shape coefficients and bearing capacity factors of shallow foundations on heterogeneous soil

We often face heterogeneous foundation soils in geotechnics, which significantly influence shallow foundations' shape coefficients and bearing capacity factors. The evaluation of these factors introduces significant uncertainties in the thickness of the upper layer is comparable to the width of the rigid footing placed on the soil surface. This ambiguity depends on the geometry of the footing, the mechanical properties of the soil, and other geotechnical factors. Conducting thorough geotechnical studies and performing specific analyses are essential to accurately assess the effect of clay layering on the shape coefficients and bearing capacity factors of circular and square footings. A numerical analysis using the FLAC 2D and 3D software is carried out to evaluate the effect of the superposition of two undrained clay layers on the bearing capacity and shape factors of circular and square footings subjected to a static axial load. The aspects of homogeneous and heterogeneous shear strength profiles were addressed at various positions of the height of the first clay layer. It was found that the critical depth of the first clay layer necessary to optimize the bearing capacity of a foundation resting on stratified soil is 2, 1.5, and 1, respectively, for strip, square, and circular footings. The shape coefficient values range between 1.14 and 1.22 for square footings and between 0.98 and 1.64 for circular footings. The results are compared to previously published values in the literature.

Investigation on the machining mechanism of silicon modified by Au ion irradiation in elliptical vibration diamond cutting

Single-crystal silicon (Si) has important applications in semiconductor, infrared optics, and photovoltaic industries. However, Si is difficult to be machined precisely due to its hard and brittle characteristics. Ion irradiation is proposed as an advanced technology to reduce the hardness and brittleness for a covalent crystal, which is beneficial for the ductile machining process. In the present research, the simulation and experimental investigation of Si with Au ion irradiation were carried out firstly. As following, the grooving experiment is carried out by elliptical vibration cutting (EVC). the machining performance is compared with ordinary cutting (OC) and the material removal mechanism is elaborated. The critical depth of cut for brittle-to-ductile transition is nearly 7 times higher by EVC compared to OC. Initial verification of material modification was conducted by Raman spectra and cutting microgrooves. Finally, the ion irradiation damage mechanism and amorphous Si (a-Si)/crystalline Si (c-Si) machining deformation mechanism were analyzed in detail by transmission electron microscopy. The irradiated sample contains an amorphous layer of 1050 nm, a transition layer containing dislocations and nanocrystals, and a fully crystalline layer. During machining a-Si/c-Si interface, the machining defects in the amorphous layer will first absorb the energy and ensure that the crystalline layer does not produce subsurface damage. In summary, ion-irradiated Si can be achieved in the amorphous region at any depth position and the substrate ductile machining without subsurface damage generation by EVC.

Brittle-ductile transition mechanism during grinding 4H-SiC wafer considering laminated structure

4H-SiC wafer with alloy backside layer is gradually applied in power devices. However, the laminated structure presents various challenges in manufacturing. In this study, a model for brittle-ductile transition in grinding of laminated materials is established and verified by grinding experiment to ensure the complete removal of the alloy backside layer while achieving ductile removal of the 4H-SiC layer. In the modeling process, the maximum unreformed chip thickness and brittle-ductile transition critical depth of each-layer in the laminated material is deriving, taking into account the laminated structure. Consider the variability in proportion of dynamic active grits during grinding, set operation is introduced to analyze the relationship between sets maximum unreformed chip thickness and brittle-ductile transition critical depth, and to predict the removal mechanism of the 4H-SiC layer. Comparing the predicted results with experimental grinding data, found that under the conditions of grinding wheel with average size of abrasive 10 μm, grinding wheel speed vs of 74 m/s, grinding depth ap of 10 μm, and feeding speed vw of 2 mm/s, the alloy backside layer can complete removal while achieving ductile removal of the 4H-SiC layer. This study provides a new method for predicting removal mechanism in grinding of laminated material and theoretical guidance for optimizing machining parameters of 4H-SiC wafer with alloy backside layer.