Fillet Shape Research Articles

Application of the Phase Field Approach for Crack Propagation in Viscoelastic Solid Materials under Thermal Stress: A Case Study of Solder Fracturing

To date, solder has been a crucial component for interconnecting circuit boards (PCBs) and electronic components in the electronics industry. However, solder faces certain challenges, such as cracking due to thermal changes. This paper investigates solder cracking under thermal expansion. We employ a phase field model to study crack propagation under thermal stress in a square domain and in solder with a fillet shape. The model is based on those proposed by Takaishi-Kimura and Alfat, where the stress and strain tensors are modified to account for variations in the temperature field. In this study, we consider the solder material to be viscoelastic, while the other materials are treated as homogeneous and isotropic. A numerical example is computed using the adaptive mesh finite element method, with the code implemented in FreeFEM software. The results of this study are in good agreement with previous numerical and experimental findings.

Effect of different beam distances in laser soldering process: a numerical and experimental study

PurposeThis paper aims to investigate the effect of different beam distance by understanding laser beam influence on solder joint quality. The utilisation numerical-based simulations and experimental validation will help to minimise the formation of micro void in PTH that can lead to cracks and defects on passive devices.Design/methodology/approachThe research uses a combination approach of numerical-based simulation using Finite Volume Method (FVM) and experimental validation to explore the impact of different laser beam distances on solder joint quality in PTH assemblies. The study visualises solder flow and identifies the optimal beam distance for placing a soldering workpiece and a suitable tolerance distance for inserting the solder wire.FindingsThe simulation results show the formation of micro void that occurs in PTH region with low volume fraction and unbalance heat concentration profile observed. The experimental results indicate that the focus point of the laser beam at a 99.0 mm distance yields the smallest beam size. Simulation visualisation demonstrates that the laser beam’s converging area at +4.6 mm from the focus point which provides optimal tolerance distances for placing the solder wire. The high-power laser diode exhibits maximum tolerance distance at 103.6 mm from the focus point where suitable beam distance for positioning of the soldering workpiece with 50% laser power. The simulation results align with the IPC-A-610 standard, ensuring optimal filling height, fillet shape with a 90° contact angle and defect-free.Practical implicationsThis research provides implications for the industry by demonstrating the capability of the simulation approach to produce high-quality solder joints. The parameters, such as beam distance and power levels, offer practical guidelines for improving laser soldering processes in the manufacturing industry.Originality/valueThis study contributes to the field by combining high-power laser diode technology with numerical-based simulations to optimise the beam distance parameters for minimising micro void formation in the PTH region.

Investigating the impact of different solder alloy materials during laser soldering process

PurposeThis study aims to investigate the influence of different solder alloy materials on passive devices during laser soldering process. Solder alloy material has been found to significantly influence the solder joint’s quality, such as void formation that can lead to cracks, filling time that affects productivity and fillet shape that determines the solder joint’s reliability.Design/methodology/approachFinite volume method (FVM)-based simulation that was validated using real laser soldering experiment is used to evaluate the effect of various solder alloy materials, including SAC305, SAC387, SAC396 and SAC405 in laser soldering. These solders are commonly used to assemble the pin-through hole (PTH) capacitor onto the printed circuit board.FindingsThe simulation results show how the void ratio, filling time and flow characteristics of different solder alloy materials affect the quality of the solder joint. The optimal solder alloy is SAC396 due to its low void ratio of 1.95%, fastest filling time (1.3 s) to fill a 98% PTH barrel and excellent flow characteristics. The results give the ideal setting for the parameters that can increase the effectiveness of the laser soldering process, which include reducing filling time from 2.2 s to less than 1.5 s while maintaining a high-quality solder joint with a void ratio of less than 2%. Industries that emphasize reliable soldering and effective joint formation gain the advantage of minimal occurrence of void formation, quick filling time and exceptional flowability offered by this solution.Practical implicationsThis research is expected not only to improve solder joint reliability but also to drive advancements in laser soldering technology, supporting the development of efficient and reliable microelectronics assembly processes for future electronic devices. The optimized laser soldering material will enable the production of superior passive devices, meeting the growing demands of the electronics market for smaller, high-performance electronic products.Originality/valueThe comparison of different solder alloy materials for PTH capacitor assembly during the laser soldering process has not been reported to date. Additionally, volume of fluid numerical analysis of the quality and reliability of different solder alloy joints has never been conducted on real PTH capacitor assemblies.

The Beneficial Effect of a TPMS-Based Fillet Shape on the Mechanical Strength of Metal Cubic Lattice Structures.

The goal of this paper is to improve the mechanical strength-to-weight ratios of metal cubic lattice structures using unit cells with fillet shapes inspired by triply periodic minimal surfaces (TPMS). The lattice structures here presented were fabricated from AA6082 aluminum alloy using lost-PLA processing. Static and dynamic flat and wedge compression tests were conducted on samples with varying fillet shapes and fill factors. Finite element method simulations followed the static tests to compare numerical predictions with experimental outcomes, revealing a good agreement. The TPSM-type fillet shape induces a triaxial stress state that significantly improves the mechanical strength-to-weight ratio compared to fillet radius-free lattices, which was also confirmed by analytical considerations. Dynamic tests exhibited high resistance to flat impacts, while wedge impacts, involving a high concentrated-load, brought out an increased sensitivity to strain rates with a short plastic deformation followed by abrupt fragmentation, indicating a shift towards brittle behavior.

Numerical investigation of solder joint shape for micro-spring package during vacuum vapor phase soldering

The novel micro-coil spring package has become a new choice for reliable applications in extreme temperature change, high-strength impact, long-term vibration and other harsh environments due to the advantages arising from its special packaging design. The study of solder joint shape is an important step in the characterization of the package reliability. By Ansys Fluent software, the finite volume method was applied to investigate the flow behavior of molten solder during vacuum vapor phase soldering and the volume of fluid model was used to track the solder melt front. The simulation results reveal the effect of two critical process parameters (solder volume and pad diameter) on solder joint shape in micro-spring array package. The fillet height of the solder joint increases with decreasing pad diameter and decreases with decreasing solder volume. The optimal solder volume is 0.07 mm3 coupled a pad diameter of 0.80 mm, producing suitable fillet height and nice concave fillet shape, which is in agreement with the real sample of micro-spring soldering joint. The good consistency between experiment and simulation proves that the finite element method can effectively predict the shape of the melted solder. This work paves the way for the optimization of the solder joint shape in the electronic assembly.

Optimization of Vortex Tube Design and Performance for Cooling Milling Process

The manufacturing process is required to improve cleanliness and reduce environmental pollution and the exploration of natural resources is limited. One of the manufacturing processes is machining, especially the milling process. The phenomenon during the milling process friction occurs when the workpiece is cut by the milling tool, the effect friction between tool and workpiece occurs temperature rise. To reduce the temperature rise of the milling tool during the workpiece cutting process, an effective and efficient alternative cooling is needed through the use of vortex tubes. The research method was carried out using the Computational Fluid Dynamic (CFD) approach and experiments with the use of inlet pressure = 1-5 Bar, and the parameters of variations in valve shape, number of nozzles, and pipe lengths. The overall results of the CFD and experiment of parameters in inlet pressure on the number of nozzles, valve shapes, and tube lengths, have an impact on the increasing inlet pressure, the higher the thermodynamic characteristics that occur in the vortex tube, but there is a loss of outlet pressure in each parameter. The geometry of the vortex tube selected is the number of nozzles 6, valve fillet shape, and tube length of 50 mm, vortex tube can be used for cooling the milling tool with the addition of a flexible hose at a distance of 5 cm from the tooltip.

The advanced concepts for septal l-strut re-designing in septorhinoplasty for better strength and stability by considering of center of gravity.

This study contributes to the multidisciplinary understanding of septal L-strut reshaping and introduces innovative surgical design concepts based on engineering principles of static equilibrium. The objective is to enhance structural strength and stability, ultimately leading to improved surgical outcomes. Finite element analysis is employed to model the three-dimensional septal cartilage in septoplasty. A significant contribution of this work is the introduction of an innovative redesigns for the septal L-strut structure. These redesigns represent the first-ever attempt to incorporate the center of gravity theory into the modeling of the septal L-strut. Our findings emphasize the significance of attaining a lower center of gravity in the design of the septal L-strut, as it contributes to optimal core strength and stability. To achieve this, we recommend widening the caudal septum and shaping the interior fillet corner to its maximum size, taking into account its specific shape. Notably, the utilization of a standard 20x20 mm septal L-strut, the C-shaped technique, and the septal support graft technique provide superior strength due to enhanced basement support. To enhance surgical outcomes in septal L-strut procedures, design modifications are proposed to improve strength and stability, resulting in optimized performance. Recommendations include widening the caudal septum and incorporating fillet shapes in the geometry to lower the center of gravity.

COMPARISON OF STANDARD AND NONSTANDARD GEAR ROOT FILLET CONSIDERING ROOT STRESS AND MANUFACTURING POSSIBILITIES

In this paper, root stress, manufacturing possibilities and limitations of standard and nonstandard tooth root fillet of spur gears are examined. Nowadays, standard trochoidal root fillet is used the most as an economical trade-off between tooth strength and manufacturing complexity. A disadvantage of the trochoidal root fillet, especially in spur gears with less than 17 teeth, is undercutting which minimises strength of tooth root, introduces stress concentration, and deteriorates meshing conditions. This study focuses on different root designs, namely elliptical and novel cycloidal root fillets. Root stress in gears with different root designs is analysed by FEM and compared with analytical equations according to ISO. The possibility of producing nonstandard root fillet gears by hobbing and limitations of surface finishing are considered as well. Analysis reveals stress differences between each of the root fillet shapes and their relative advantages and disadvantages.

Experimental stress analysis of enhanced sliding contact spur gears using transmission photoelasticity and a numerical approach

Free-Form-Gear (FFG) is a recently published title for a gear that has a curved path of contact and offers contact between a convex addendum and a concave dedendum during the meshing cycle. Based on this method of designing a gear pair, the path of contact can be altered to improve the way the gears mesh and slide against each other by only adjusting the maximum pressure angle and the involute curve parameter. The analytical investigations into this gear pair indicated that, when compared to the standard involute gear pair, the sliding velocity, meshing efficiency, contact, and fillet strengths are improved while the contact ratio is decreased. In this study, experimental stress analysis is conducted on various configurations of the tooth profile and tooth fillet shape for the proposed FFG and the standard involute gear to validate the analytical results. Since it is difficult to measure the contact stress for the gear specimens, the contact stresses at critical points are estimated using an effective computational technique based on photoelastic data and a numerical approach utilizing the nonlinear least squares method. At the fillet zone, isochromatic fringe patterns are used to directly measure the maximum fillet stress. Using addendum modification coefficients, the reduction in contact ratio for the proposed FFG is eliminated, and the results are then verified experimentally. Based on the experimental estimations, the finite element analyses are conducted using ABAQUS to simulate the examined gear specimens. Under the same loading conditions, the experimental, analytical, and numerical results have all been in good agreement.

Analysis of failure mechanisms of adhesive joints modified by a novel additive manufacturing-assisted method

The research presented in this paper used an innovative method to modify the configuration of adhesively bonded joints for improved mechanical performance. Additive manufacturing was employed to produce sacrificial support structures with a water-soluble filament (Polyvinyl Alcohol). The design freedom offered by additive manufacturing makes it easy to tailor fixtures to any geometry, which can be used to accurately make the desired fillet shape at the end of the adhesive bond line. In addition to the experimental tests, the finite element method (FEM) was used to study the stress distribution along the bond line for four different modified bonded joints, whilst the discrete element method (DEM) was used to estimate the joint failure load and crack path in the adhesive bond line due to its strength in describing the initiation and progression of micro-cracks. The results show that the novel manufacturing method can produce an accurate fillet at the end of the bond line, regardless of the adhesive type. The mechanical performance of the joints with the modified features increased significantly. Furthermore, the failure load and crack path obtained from the DEM model is in close agreement with experimental and finite element (FE) results. Hence, the failure mechanism of the hybrid joints is then summarised.

Effect of fillets on a blade/vane of wave energy harvesting impulse turbine

Fillets on leading edges (LE) of turbine blades alter flow patterns and change the loss profile. A bidirectional flow impulse turbine utilized for harnessing wave energy is introduced and computational fluid dynamics (CFD) was used to perform various analysis. In the present work, fillets of different radii on the leading and trailing edges of both the rotor blade (RB) and guide vane (GV) are modified to study the change in overall performance. After an appropriate gird convergence study, ANSYS-CFX 16.0 solver is used for solving the Reynolds averaged Navier-Stokes (RANS) equations incorporating the k-ω-SST turbulence closure model. The numerical investigations were performed using the high-resolution scheme with the convergence criteria of 10−6 to produce unwavering results. The results show that the boundary layer near the endwall creates flow blockage and losses. Also, the increase in pressure drop due to the thickening of the boundary layers (BLs) across the blade/vane leads to a depletion in the overall performance of the turbine. The rotor and guide vane filleted turbine experience higher losses than the base model due to the radial pressure gradient that is explained with post-processed figures. The concept of fillet shapes has been applied to gas turbines and which improves the performance of the turbine due to a reduction in the secondary flow losses occurring inside the turbine and the same concept has been applied to wave energy air turbine to check its performance based on the losses present across the turbine passage.

A Novel Fillet Form for Non-Generation Cutting Gear Teeth

Tooth fillets are commonly made of circular profiles because they are easy to define analytically and have been shown to be superior from a bending perspective to the trochoid fillet. For gears that are cast, forged, or 3D printed, the tooth fillet can be any curve as long as it is capable of providing a smooth mesh without interference. For such design flexibility, the circular fillet may not necessarily be the best fillet profile from a bending stress point of view. Therefore, the first aim of this study is to develop a general mathematical model for defining the tooth fillet profile analytically for gears manufactured by non-generation cutting processes. The mathematical model employed a general fillet transition curve (GFTC) to ensure smooth transition surfaces in the fillet zone and an improved radius of curvature as well as tooth form factor compared to the circular fillet profile. The second aim of this work is to examine if increasing the order of the proposed GFTC can enhance the fillet strength of the gear tooth further. The design method is conducted for involute gear and, for the first time, non-involute gears. Various fillet design parameters and tooth numbers are examined. The results showed that by using the proposed fillet shape, the tooth fillet strength can be enhanced by 18–23% for involute gears and by 30–32% for non-involute gears. Also, the results showed that increasing the order of the fillet curves might not always improve the fillet strength of the gear teeth.

Experimental validation of co-cure process of honeycomb sandwich structures simulation: adhesive fillet shape and bond-line porosity

Predictive models describing the co-cure process of honeycomb sandwich structures can increase manufacturing efficiency of aerospace structures by offering rapid, low-cost screening of viable combinations of material and process parameters. Honeycomb sandwich structures are co-cured to bond partially-cured thermoset prepreg facesheets with an adhesive layer to the core structure, during which multiple physical phenomena occur simultaneously. A physics-based predictive tool is developed to simulate this process by integration of sub-models for the adhesive bond-line fillet shape, facesheet consolidation process, and the porosity development within the bond-line, which, due to the coupling effects, is highly dependent on the former two phenomena. In this work, the experimental validation of both the individual sub-models and an integrated model for bond-line porosity is conducted. Despite the stochastic behavior of the co-cure process, the models successfully capture trends in adhesive fillet shape and the bond-line porosity, demonstrating their utility as tools for process screening to maximize the quality of co-cured parts.

Effect of Different Solder Volumes on the Laser Soldering Process: Numerical and Experimental Investigation

Abstract Laser soldering is becoming more popular for soldering pin through-hole (PTH) components onto printed circuit boards (PCBs). Solder volume influences soldering joint reliability. However, it is difficult to accurately measure the effect of solder volume during the laser soldering process. The finite volume method (FVM) is used to simulate the molten solder flow in laser soldering to connect the through-hole capacitor onto the PCB in ansysfluent software. The simulation results reveal the effects of different SAC305 solder volumes on joining quality in terms of fillet shape formation, pressure, and velocity. The preferred solder volume is 1.517 mm3 with a filling time of 1.7 s, a temperature of 642 K, a hole diameter of 1.0 mm, a lead diameter of 0.5 mm and a PCB thickness of 1.20 mm, produces a fillet shape similar to a real sample of PTH laser soldering joint from the industry. This ideal volume was chosen with a suitable pressure and velocity to create a nice concave fillet shape and minimize voids during soldering. The pressure and velocity increase when the solder volume increases causing solidified solder to melt. The discrepancy between numerical and experimental values of fillet height is comparable, which inferred that the numerical model was well-validated. The good consistency between both results proves that the finite volume model will effectively predict the optimum solder volume. This opens up new opportunities for the optimization of the laser soldering parameters in the application of electronic manufacturing.

流体潤滑状態においての凸型テクスチャの形状が摺動特性に及ぼす影響に関する数値的研究

It is shown that convex texture improves the sliding characteristics by experimental studies. In researches of simulations, increase of load capacity and friction reduction are confirmed when using the convex texture those shapes are round, oval, and triangle. However, the detailed consideration of the geometry, such as texture height and fillet shape is insufficient. Therefore, the purpose of this study is to reveal the performance change in the fluid lubrication state by simulation through the detailed shape change of the convex texture.

Fatigue Crack Growth in Welded S355 Samples Subjected to Bending Loading

The paper presents a result of experimental tests of welded S355 samples subjected to bending loading. In order to analyze how the fillet joints’ shape and the load ratio affect the crack growth, we selected two kinds of the fillet shape: concave and convex, and load ratios, namely R = −1. Samples with stress concentrators in form of the two-sided fillet welded joint were tested. The test results were compared to experiments conducted on welds samples with and without heat treatment.

Numerical Analysis of Fillet Shape and Molten Filler Flow during Brazing in the Al–Si Alloy of Automotive Radiator

In the brazing process of an automobile radiator, eutectic melting of the Al–Si filler alloy of the clad sheets, fillet formation in the brazed joints, and the flow of the molten filler metal on the solid core metal between joints occur continuously. With regard to designing heat exchangers, the optimum placement of the filler metal, considering the flow of the molten filler metal, is an important subject. In this study, a new numerical analysis was applied to predict the shape of the fillets and the molten filler flow. The molten filler flow was calculated using the difference method applied to a one-dimensional unsteady flow that is assumed to be a uniform flow of incompressible viscous fluid between two parallel plates. Among some numerical results, when the hydraulic mean depth of the flow path was reduced 0.3 times, the calculation results were consistent with the actual values. It was necessary to narrow the flow path because it was calculated assuming that the flow of brazing was between two parallel flat plates, whereas the actual flow path of the molten filler metal was not flat and a large flow resistance was produced.

Shoulder fillet effects in strength distributions of microelectromechanical system components

The failure forces and fracture strengths of polysilicon microelectromechanical system (MEMS) components in the form of stepped tensile bars with shoulder fillets were measured using a sequential failure chain methodology. Approximately 150 specimens for each of four fillet geometries with different stress concentration factors were tested. The resulting failure force and strength distributions of the four geometries were related by a common sidewall flaw population existing within different effective stressed lengths. The failure forces, strengths, and flaw population were well described by a weakest-link based analytical framework. Finite element analysis was used to verify body-force based expressions for the stress concentration factors and to provide insight into the variation of specimen effective length with fillet geometry. Monte Carlo simulations of flaw size and location, based on the strength measurements, were also used to provide insight into fillet shape and size effects. The successful description of the shoulder fillet specimen strengths provides further empirical support for application of the strength and flaw framework in MEMS fabrication and design optimization.

A bond-line porosity model that integrates fillet shape and prepreg facesheet consolidation during equilibrated co-cure of sandwich composite structures

Honeycomb core sandwich structures are co-cured to bond partially cured thermoset prepreg facesheets with an adhesive layer to both sides of the honeycomb core under a pre-defined pressure and temperature cycle in an autoclave. In the Equilibrated (Open-core) co-cure process, the honeycomb core cells are vented to the vacuum bag. Although the co-curing is advantageous over the secondary bonding process of sandwich structures, it is strongly dependent on the materials and process parameters and could result in high porosity within the bond-line. In this paper, we present a comprehensive model for the evolution of the bond-line porosity in which we introduce and couple new models for the bond-line fillet shape and the void escape process from the bond-line with the facesheet consolidation and the porosity models. First, a model is proposed to simulate the adhesive bond-line fillet shape. Next, a previously formulated prepreg facesheet consolidation model is used to calculate the amount of prepreg resin containing voids that bleed into the bond-line. A diffusion model of bubble growth tracks the porosity within the bond-line as a function of the cure cycle. The fillet shape allows one to estimate the number of bubbles that escape from the bond-line. The cure kinetics and the gelation time of the prepreg resin and the adhesive dictate the entrapment of the voids and the porosity evolution within the bond-line. The usefulness of the integrated model is demonstrated with an example in which it is shown that if an adhesive with perforations is used or if the gelation of the adhesive triggers after the gelation of the resin it will result in lower porosity. The results of this example are validated with a reported experimental study with the same material properties and processing conditions.

Effect of T-shape Shoulder Fillet on the Plastic Deformation Properties of SS400 and LYS160 Steel.

Shoulder fillets are widely used in the structural optimization design of metal dampers. However, the plastic deformation property of dampers affected by stress concentration, owing to different fillets, has not been explored in-depth. In this study, two typical metal damper materials with different plastic deformation, i.e., ordinary steel SS400 and low-yield-strength steel LYS160, were investigated. The strengthening effect of fillets under different loading is evaluated by comparing the mechanical properties of different fillet heights. Furthermore, the effect of the stress concentration caused by different fillet shapes, based on the failure mode of materials, is discussed. Subsequently, the fatigue degradation effect under the reciprocating shear loading is studied. Based on a series of studies on the deformation properties of fillets in different ductile materials, the basis for the structural optimization design under plastic deformation is provided.