Strength Analysis Research Articles

Turbulence scale and strength analysis in the roughness and inertial sublayers over urban areas: A wind tunnel study

The dissimilarity of dynamics and turbulence structures between the roughness and inertial sublayers (RSL, ISL) over roughness elements show that ISL turbulence is much more homogeneous. Conventional logarithmic law of the wall is merely applicable for the RSL mean-wind-speed profiles. To characterize the turbulence scales and elucidate the mechanism, the flows in the atmospheric surface layer (ASL) over real urban morphology are measured in wind tunnel experiments fabricated by 3D-printing, reduced-scale model of downtown Kowloon Peninsula, Hong Kong. Elevated dispersive stress at urban canopy signifies the influence from individual buildings and inhomogeneous RSL flows. A positive momentum contribution appears in the low-frequency regime. The large-scale turbulence in RSL thus enhances the mixing and transport, resulting in inhomogeneous flows. The contribution from ejection Q2 and sweep Q4 increases and decreases, respectively, with increasing RSL motion strength. The conventional −5/3 law is observed by empirical mode decomposition (EMD) and the largest amplitude fluctuation occurs more often when the turbulence length scale is comparable to the turbulent boundary layer (TBL) thickness. The single-point amplitude modulation (AM) shows that the large- and small-scale turbulence correlates tightly at the bottom of RSL. Besides, the joint probability density function (JPDF) illustrates that accelerating large scales often occur with decelerating small scales, and they are intensified with increasing wall-normal distance. As a result, large-scale turbulence influences substantially the flow structures over urban areas and the small-scale turbulence (even) in RSLs in the vicinity of building obstacles.

Experimental analysis of tensile strength of 6-layer carbon/kevlar/epoxy hybrid composite reinforced with nano-graphene/silica nanoparticles

The main aim of the present research is to improve the static tensile strength of Carbon/Kevlar/Epoxy hybrid composite by adding different nanoparticles. To this end, two well-known nanoparticles namely Nano-Silica and Nano-Graphene were considered. Also, the total percentage of adding nanoparticle reinforcing elements to the hybrid composite was considered equal to 1.5%. In this way, five categories of reinforced hybrid composites, including 0%Nano-Silica+0%Nano-Graphene, 1.5%Nano-Silica+0%Nano-Graphene, 1.2%Nano-Silica+0.3%Nano-Graphene, 1.0%Nano-Silica+0.5%Nano-Graphene, and 0.75%Nano-Silica+0.75%Nano-Graphene, were studied. Composite samples were prepared using manual layout technique and tensile tests were performed according to the ASTM standard. It was found that the tensile strength increases with the addition of nanoparticles to the Carbon/Kevlar/Epoxy hybrid composite, but these two do not always have a direct and linear relationship with each other. Moreover, it was shown that the addition of 1.2% silica nanoparticles and 0.3% nanographene leads to an increase of tensile strength up to 36%, and this is the best optimal percentage of additive nanoparticles in this research.

Utilizing incineration bottom ash-infused steel fiber-reinforced concrete: An analysis of compressive strength and carbonation durability

This study has developed concrete with moderate strength, and excellent carbonation resistance, by blending incineration bottom ash with steel fibers into the concrete mixture. Through single-factor experiments, investigate the effects of bottom ash content and steel fiber volume fraction on the mechanical properties and carbonation resistance of concrete. The results indicate that the addition of steel fibers effectively reduces the adverse effects of incineration bottom ash content on the compressive strength and carbonation level of concrete. When the bottom ash content is 20 % and the steel fiber content is 2 %, the compressive strength of concrete reaches 56.1 MPa, and the carbonation depth drops to 4.19 mm after 28 days. In addition, a carbonation depth prediction model was established based on the compressive performance of concrete, accurately predicting the carbonation depth at different carbonation stages.

Recycling single use surgical face mask waste for reinforcing cement-treated/untreated dredged marine sediments: Strength, deformation and micro-mechanisms analysis

To prevent the transmission of airborne infectious diseases (SARS, H1N1, COVID-19, and influenza), the use of disposable surgical face masks has increased dramatically in the past few years. To mitigate the environmental consequences associated with mask waste, implementing circular economy strategies with the reuse of mask waste is a sustainable method. This study explores an innovative way to reuse mask fiber (MF) with dredged sediment waste together as road construction materials. First, the MF was introduced into cement-treated/untreated dredged marine sediment mixtures with different content and lengths. Then, a variety of laboratory tests were carried out to explore the basic physical and chemical characterization of raw materials and the development of mechanical properties of mixtures. In addition, the intrinsic mechanism of MF inclusion on cement-treated sediments was analyzed by scanning electron microscope (SEM) test. The results show that the inclusion of MF significantly improves the unconfined compression strength (UCS) and splitting tensile strength (STS) of both treated and untreated specimens. The highest UCS and STS values are at the condition with an MF content of 0.25%, a length of MF of 2 cm, and a curing time of 28 days. The combined strength increase caused by cement-MF together inclusion is much greater than the strength increase caused by either of them separately. It was also found that the elastic modulus (E50) decreased with the inclusion of MF. Furthermore, the addition of MF changes the brittle behavior of the specimens, which also improves the ductility and residual strength of the specimens. The SEM analysis demonstrates the microstructure of MF and MF-reinforced specimens. The creation of a stable and interconnected microstructure is largely attributed to the bridging impact of MF and the binding effect of hydration products, which significantly improves the mechanical behavior of specimens. The MF-reinforced cement-treated sediment could be an innovative, environmentally friendly, and economical material for road construction.

Effects of Titanium Dioxide (TiO2) on Physico-Chemical Properties of Low-Density Polyethylene.

Hazardous chemicals are transported on rail and road networks. In the case of accidental spillage or terror attack, civilian and military first responders must approach the scene equipped with appropriate personal protective equipment. The plausible manufacturing of chemical protective polymer material, from photocatalyst anatase titanium dioxide (TiO2) doped low-density polyethylene (LDPE), for cost-effective durable lightweight protective garments against toxic chemicals such as 2-chloroethyl ethyl sulphide (CEES) was investigated. The photocatalytic effects on the physico-chemical properties, before and after ultraviolet (UV) light exposure were evaluated. TiO2 (0, 5, 10, 15% wt) doped LDPE films were extruded and characterized by SEM-EDX, TEM, tensile tester, DSC-TGA and permeation studies before and after exposure to UV light, respectively. Results revealed that tensile strength and thermal analysis showed an increasing shift, whilst CEES permeation times responded oppositely with a significant decrease from 127 min to 84 min due to the degradation of the polymer matrix for neat LDPE, before and after UV exposure. The TiO2-doped films showed an increasing shift in results obtained for physical properties as the doping concentration increased, before and after UV exposure. Relating to chemical properties, the trend was the inverse of the physical properties. The 15% TiO2-doped film showed improved permeation times only when the photocatalytic TiO2 was activated. However, 5% TiO2-doped film exceptionally maintained better permeation times before and after UV exposure demonstrating better resistance against CEES permeation.

The Strength and Minimum Wall Thickness of Wellhead Equipment for Ultrahigh-Pressure Oil and Gas Wells

Summary As oil and gas wells are drilled to greater depths, wellhead pressure is expected to exceed the 20 ksi (138 MPa) limit specified by API SPEC 6A and other industrial standards, necessitating the development of 25 ksi (172.4 MPa) equipment. This paper focuses on the strength design and analysis of ultrahigh-pressure wellhead equipment, reviewing various wall-thickness calculation formulas and design criteria based on basic mechanical theory. It traces the flange wall thickness calculations in API SPEC 6A, discusses issues with 25-ksi equipment, and analyzes safety factors, methods, and allowable stresses in different standards. The findings of the research indicate that for high-pressure equipment with a pressure of 25 ksi (172.4 MPa), the optimal ratio of outer diameter to inner diameter is 2, and the structure can meet the requisite strength requirements. The wall thickness design method for structures such as flanges in traditional American Petroleum Institute (API) specifications uses the maximum principal stress criterion for calculation, which is not applicable to high-pressure equipment. For high-strength steel with high yield ratio used in high-pressure equipment, yield strength and tensile strength should be combined in design and use, fully utilizing the material’s properties. It is recommended to use finite element analysis for high- and ultrahigh-pressure complex structures, following the latest design concepts such as elastic-plastic ASME standards. The research provides a theoretical basis for designing ultrahigh-pressure wellhead equipment.

Strength and leaching behavior of CaO- and MgO-treated Cd-contaminated soils subjected to partial and full carbonation

Cadmium (Cd)-contaminated soils may pose a significant threat on human health. They are often treated with quick lime (CaO) and reactive magnesia (MgO), but these treatments often result in low strength. Hence, in this study, partial and full carbonation are used to enhance the stabilization/solidification of CaO- and MgO-treated Cd-contaminated soils, aiming to achieve CO2 sequestration, strength improvement, and Cd immobilization. Performance of treated contaminated soils is evaluated through unconfined compressive strength (UCS), leaching, X-ray diffraction (XRD), and thermogravimetric analysis (TGA) tests. The results indicate that carbonation significantly enhances the UCS of both CaO- and MgO-treated Cd-contaminated soils. After carbonation, MgO-treated soils exhibit higher UCS than CaO-treated soils. Partial and full carbonation yield similar UCS in CaO-treated soils, while full carbonation results in higher UCS in MgO-treated soils. For CaO-treated soils, partial carbonation keeps Cd leachability below the 1 mg/kg limit, but full carbonation increases it beyond this limit. In contrast, fully carbonated MgO-treated soils maintain Cd leachability below the limit, though partial carbonation leads to higher leachability. Formation of Ca and Mg carbonates contributes to the strength improvement of soils. Cd(OH)2 and its complex, as well as CdCO3 exist in partially and fully carbonated soils, lowering leached Cd concentration. Overall, partial carbonation is better for CaO-treated soils, while full carbonation is preferable for MgO-treated soils.

Effect of nanoparticles reinforcement of silicon dioxide derived from prosopis juliflora on Silver-Grey magnesium nanocomposite: utilization of silicon dioxide mechanical and tribological properties

Abstract The automotive and aviation industries require lightweight materials to enhance working efficiency. Composites combine materials such as aluminium, magnesium, titanium, steel, and copper with various forms of reinforcements to offer lightweight alternatives for a range of applications. The present investigation aims to fabricate a Silver-Grey Magnesium (Mg-25%Si) alloy-based nanocomposite with silicon dioxide (SiO2) nano reinforcement at weight % of 0, 3.25, 6.5 and 9.75 utilizing the two step stir casting method. Prosopis juliflora is utilized in the production of different weight percentages of SiO2 nano reinforcements. The microhardness, tensile, wear, and impact tests are performed on the Silver-Grey Magnesium nanocomposites (Mg-25%Si/SiO2) utilizing a computerized tensometer testing machine, a Vicker’s hardness tester, a pin-on-disc tribometer, and an Izod impact, respectively. The x-ray diffraction (XRD), Field Emission Scanning Electron Microscope (FESEM), and Energy-dispersive x-ray spectroscopy (EDAX) with elemental mapping microstructure were employed to scrutinize the tensile specimen fracture, EDAX, elemental mapping microstructure, wear, CoF, and worn surface characterization and impact strength analysis. When compared to the Silver-Grey Magnesium (Mg-25%Si) base alloy, the results of the Mg-25%Si/SiO2 nanocomposites demonstrated an increase in SiO2 nano reinforcements that significantly increased microhardness, tensile strength, wear resistance, and impact strength. The corresponding values are 113.36 VHN, yield and ultimate tensile strength of 603.25 MPa and 665.84 MPa, 0.00478 mm3 m−1, CoF of 0.38421 and 400 J m−1.

Investigation of torsional and fatigue resistance properties based on triply periodic minimal surfaces (TPMS)

Abstract Triply periodic minimal surfaces (TPMS) are algebraic surfaces found in nature, defined by implicit functions, and exhibit exceptional properties in various fields such as mechanics, computer graphics, and tissue engineering. This study focuses on four common minimal surface structures: Gyroid, Diamond, I-WP, and Schwarz P structures, and presents two methods for converting these surfaces into TPMS cells. These four surface structures are converted into TPMS cells, which are then organized into TPMS cylindrical units for finite element analysis. Through a comparison of the torsional mechanical properties of different minimal surfaces using the finite element method, the stress-strain curves of TPMS were generated. The findings suggest that the Schwarz P cylindrical structure remains within the elastic deformation stage under the same load, with a stress-load curve exhibiting a smaller slope, indicating superior torsional resistance. Additionally, a fatigue strength analysis of various minimal surface structures revealed that, under equivalent load conditions, the fatigue life of the Schwarz P cylindrical structure tends towards infinity.

Strength analysis due to thermal loading and tensile loading when metals are bonded by heat-curing adhesives

Heat-curing adhesives are widely used after being cured by heating to a temperature higher than room temperature. To evaluate the adhesive strength, therefore, it is necessary to consider both the thermal stress generated during heat curing and external loads such as tensile stress. Butt joint specimens are essential for evaluating tensile adhesive strength but also thermal strength. The interfacial strength can be discussed from the stress intensity factor (SIF) of a fictitious edge interfacial crack assumed at the interface end. This is because the SIF is controlled by the intensity of singular stress field (ISSF) at the crack-free interface end and a constant term associated with the thermal load. In this paper, a useful thermal SIF solution is proposed by superposing the SIF under tensile stress and the SIF under uniform interface stress associated with thermal loading. This general SIF expression provided under arbitrary material combination can be applied for predicting the tensile strength σc and critical temperature change ΔT without performing new FEM calculations. The usefulness of the expression is confirmed through the adhesive strength of Aluminum/Epoxy butt joint experimentally obtained. Once the critical SIF K1C can be obtained from the tensile strength σc and the temperature change ΔT, the adhesive strength can be expressed asK1C = constant of an assumed fictitious interface, and this can be used to predict critical σc for various temperature change ΔT and for various adhesive bondline thickness h.

Sustainable approach to raw clays for ceramic and refractory applications: insights from updated traditional ternary diagrams

Abstract The study analysed 93 samples from four Serbian clay deposits to determine their suitability for ceramics production. The samples were mainly composed of illite and kaolinite. Ternary diagrams were used to classify the samples and evaluate their applicability. Winkler's diagrams, ternary graphs and mineralogical compositions were analysed. The results showed a broader area in these graphs than previously determined for structural ceramics, as well as the potential of these clays for ceramic production. The study used dry-milled, hydraulically semi-dry, pressed and fired samples to assess water absorption and flexural strength and statistical analysis to determine the key parameters influencing final product quality, including that of refractory, wall and floor tiles. This paper evaluates the raw clay materials’ applicability in ceramic production, promoting sustainable use through rapid initial tests, energy savings through dry milling and ecologically sound principles through resource-efficient evaluation.

An investigation of the mechanical strength, environmental impact and economic analysis of nano alkali-activated composite

The current study explores both the mechanical strength and life cycle assessments of fly ash (FA)-based alkali-activated concrete (AAC) with/without colloidal nano-silica (NS) addition at high and low molar concentrations of sodium hydroxide in the activator fluid (12 M and 3 M). The cradle-to-gate approach is used to establish the system boundaries for life cycle assessments (LCA). The environmental impact of AAC (with/without NS) and conventional cement concrete (CC) mixtures was determined using the ReCiPe midpoint and endpoint approaches across various impact categories. The AAC mixes with and without NS addition reduce greenhouse gas (GHG) emissions by 30 % and 25 % with respect to CC mix, respectively. Within the majority of impact categories, sodium silicate and sodium hydroxide production are the primary contributors, accounting for up to 91 %. However, in water depletion, global warming potential, and fuel depletion, the overall contribution is as high as 65 %. Also, the AAC mix with and without NS addition consumes 34 % and 14 % less electricity during its production with respect to the CC mixture. The CC mixes have almost 70 % more ecological damage and approximately 30 % more health risk than AAC with and without NS. However, the NS-modified AAC shows 20 % lower ecological and health risks than AAC without NS. The effect of resource scarcity on NS modified AAC is 50 % less than that of other mixes, including both AAC mix without NS and CC mix. In comparison to AAC without NS, the NS modified AAC demonstrates an 18 % reduced impact on resource scarcity. Finally, cost analysis demonstrates that AAC with NS is 16 % less expensive than CC, while AAC without NS is 26 % cheaper than CC. AAC containing 6 % NS inclusions exhibits environmental and economic benefits in addition to its enhanced mechanical performance, indicating its potential for widespread practical usage.

MODERN TRENDS AND INNOVATIONS IN THE MODERNIZATION OF RAILWAY LINES BASED ON EXPERIENCE IN THE REPUBLIC OF BULGARIA

The modernization of the Bulgarian railways has been underway for over 20 years. Hundreds of kilometres have been rehabilitated with funds from the European Union. The aim is to join the main Trans-European network, according to Regulation No. 1315/2013 [1] of the EU. Given the complex mountainous relief, the specific engineering objects are now the design and construction of a large number of tunnels (in the Sofia-Plovdiv section alone, over 16 tunnels are planned, the longest of which is 6 km long); the design and construction of railway bridges, some of which have unique dimensions; the rehabilitation of bridges; and the construction of drainage facilities, including drains, ditches, and culverts (some of the culverts have a unique length of about 80 m). The report analyses the main railway projects with a critical analysis of strengths and weaknesses, according to the EU cost-benefit analysis methodology. The analysis presented in this report is unique for Bulgarian railways, as it includes a large volume of projects in the field of designing and building railway infrastructure according to European and world rules, which have not been used in Bulgaria until now. This is only the first stage of scientific research, which involves collecting data, examining the data, and building a working hypothesis. After the completion of the construction (supposedly by around 2029), there will be measurements of the railway and a diagnosis of its condition. At this time, data will be collected again, and the credibility of the presented hypotheses will be verified. The conclusions will serve for the more adequate preparation of the technical assignments for future infrastructure projects in the field of railways.

ANALYSIS OF THE CONSTRUCTION OF THE CAR TRAILER FRAME IN TERMS OF CHANGING THE ASSEMBLY TECHNOLOGY

Car trailers are quite a popular means of transport and are offered in many versions, from single axle light trailers with a maximum permissible weight of 750 kg, through two- or more-axle specialized trailers. The issues of research car trailers focus on two directions: testing the driving properties and analysing the strength of the supporting frame system. Issues related to the construction of light trailers are often common to trailers used in agriculture or general transport. In this article, based on a mass-produced car trailer, an analysis was carried out regarding the choice in the technology of making the supporting structure consisting of a lower frame and an upper frame. The term upper frame should be understood as the structure on which the lifted load box rests. The costs of materials, assembly and technological possibilities of small-scale production were taken into account. In addition, strength analyses of the numerical models were carried out for critical areas of the frame during operation. After considering the unit costs for each of the analysed assembly technologies, it was shown that riveting would be the cheapest. However, the most suitable method of assembly is welding, as it allows the use of standard profiles.

Additive Manufacturing, Numerical and Experimental Analyses for Pentamode Metamaterials

Pentamodes are lattice structures composed of beams. Their main property is the low ratio of the shear to bulk modulus, making them suitable for aerospace, antiseismic, and bioengineering applications. At first, in our study, pentamode structures were fabricated using three-dimensional printing and were tested in a laboratory. Then, computational analyses of bulk strength have been performed. In addition, several preliminary computational analyses have been considered, comparing different pentamodes’ dimensions and topologies in order to understand their behaviour under different loading conditions. Experimental results have been compared with the numerical results in order to validate the forces applied to the lattice structures. Our new contribution is that for the first time, the experimental and numerical results are investigated up to the failure of the specimens, the effective Young’s modulus has been calculated for different pentamode lattice structures, and our results are also compared with analytical equations.

Effect of different ceramsite types on the compressive performance of lightweight engineered geopolymer composites (LW-EGC) exposed to high temperatures

This study investigates the high-temperature performance of lightweight engineered geopolymer composites (LW-EGC) by analyzing the effects of different ceramsite types on thermal stability, compressive strength, and microstructural changes. LW-EGC-M and LW-EGC-C, which incorporate FACM and CC respectively, exhibited higher mass loss, indicating the release of moisture and volatiles. LW-EGC-S, which contains SC, exhibited the lowest mass loss across the entire temperature range. The compressive strength analysis reveals that, although the initial elastic behavior was similar across all aggregates, differences became apparent during the strengthening and yielding phases. At 800 °C, the peak stress of LW-EGC-S decreased significantly, dropping from 20.840 MPa at 20 °C to 6.850 MPa. Microstructural analysis of matrix at elevated temperatures using SEM, XRD, and FT-IR reveals dehydration, shrinkage, and cracking in the matrix, which degrade mechanical performance. However, the melting of PVA fibers in the 200–400 °C range facilitates the release of internal moisture, reducing steam pressure and preventing explosive spalling. While the dehydration of the matrix, the formation of nepheline, and the decomposition of calcite lead to an increase in porosity and a reduction in structural integrity, the fundamental geopolymer network remains stable. This study not only provides new insights into the thermal behavior of lightweight engineered geopolymer composites but also offers a promising approach for enhancing fire resistance in structural applications through the strategic selection of ceramsite types.

Analysis of strength and resistance to loss of stability of thin-walled channel columns with non-standard cross-sectional shape

Analysis of strength and resistance to loss of stability of thin-walled channel columns with non-standard cross-sectional shape

Structural design and experimental verification of a thin-walled plastic chairs based on the finite element method

This study focuses on the design and preparation of a thin-walled plastic chair, and its mechanical properties were investigated by high load, cyclic load and drop impact. The finite element method (FEM) was employed to accurately evaluate the chair’s safety under these forces. Additionally, the effects of important structural parameters on the loading process in different states were investigated. Furthermore, a solid plastic chair prototype was created for experimental analysis. The findings revealed that increasing the thickness of the key structural parameters enhanced the safety properties of the chair under various load conditions. Optimal results were obtained when both dimensions were set to 5 mm. The deformation errors in FEM, experimental strength analysis, fatigue analysis, and drop impact analysis were measured at 3.7%, 3.6%, and 11.7%, respectively. Similarly, the stress errors were determined to be 5.9%, 5.2%, and 6.5%. These results suggest that the structural design of the chair demonstrates excellent reliability. Studying the crucial structural parameters of a plastic chair can provide valuable insights for the scientific design and safety evaluation of thin-walled furniture.

Design of a Human Muscle-Powered Flying Machine

This study explores the design and development of a human-powered aircraft (HPA), leveraging modern engineering techniques, materials science, and advanced CAD/CAM tools. The project addresses key aspects of aircraft design, including the geometry of wings and tail, control and power transmission mechanisms, propeller selection, and material identification to achieve ultra-lightweight construction. The 3DExperience platform facilitated comprehensive model creation, simulation, and production process development, while XFLR5 was employed for aerodynamic profile analysis using the vortex lattice and panel methods. JavaProp aided in evaluating propeller thrust and power requirements. Computational fluid dynamics (CFD) simulations using the SST k-ω turbulence model provided critical insights into flow behavior. The design was found to be theoretically capable of flight, although challenges arose in selecting appropriate software for aerodynamic analysis, leading to the use of XFLR5 for early-stage design and the more advanced 3DExperience platform for final evaluations. Although structural strength analyses were not performed due to the complexity of composite materials, future work in this area could enhance the precision of component selection and aircraft mass estimation.

Fracture strength analysis of large-size and thin photovoltaic monocrystalline silicon wafers

Diamond wire slicing technology is the main method to manufacture the substrate of the monocrystalline silicon-based solar cells. With the development of technology, the size and thickness of monocrystalline silicon wafer are respectively getting larger and thinner, which cause an increase in silicon wafer fracture probability during wafer processing and post-processing. And the change of the sawing speed, saw wire diameter and abrasive size also affect the wafer’s surface characteristics, thereby affect its fracture strength. In this paper, monocrystalline silicon wafer with large size of 210 mm × 210 mm was taken as the research object, 4-point bending test was carried out on each series of silicon wafers. The load–displacement curves during bending test were collected, and the fracture stress values were calculated by finite element method. The characteristic fracture strength and Weibull modulus of each series of silicon wafers were obtained through the statistical analysis of the data using Weibull distribution function. The effect of the silicon wafer thickness, the position of the silicon wafer in the silicon brick (usage time of the saw wire varies), and the bending test direction on the fracture characteristics was analyzed. The results showed that the increase of thickness increase the characteristic fracture strength of silicon wafer. The characteristic fracture strength of the front wafers (sawn by the fresh wire) is the smallest, while the characteristic fracture strength of the middle wafers and the rear wafers (sawn by the worn wire) are similar. The characteristic fracture strength of bending in the direction of perpendicular to the saw marks is 2–3 times that of bending in the direction of parallel to the saw marks. The reason of the difference of characteristic fracture strength was analyzed based on the surface morphology, roughness, and the saw marks of silicon wafer. In this paper, the fracture characteristics of large size monocrystalline silicon wafer are studied to provide fracture data support for industry production. The mechanism and main effect factors of silicon wafer fracture are revealed, which provides directions for improving the sawing quality and reducing the fracture probability during wafer production process and post-processing.