Study of the Influence of the Type of Aging on the Behavior of Delamination of Adhesive Joints in Carbon-Fiber-Reinforced Epoxy Composites

This study analyzes the behavior under the static delamination and mode-I fracture stress of adhesive joints made on the same composite material with an epoxy matrix and unidirectional carbon fiber reinforcement and two types of adhesives, one epoxy and the other acrylic. Standard DCB tests (for mode-I fracture) were used to quantify the influence on the interlaminar fracture toughness of the type of adhesive used. Both materials were subjected to two different degradation processes, one hygrothermal and the other in a salt-fog chamber. After aging, the mode-I fracture has been evaluated for both materials. From the experimental results obtained, it can be deduced for the epoxy adhesive that exposure to the hygrothermal environment used moderately modifies its behavior against delamination, while its exposure to the saline environment produces a significant loss of its resistance to delamination. For the acrylic adhesive, the hygrothermal exposure causes an improvement in its delamination behavior for all the exposure periods considered, while the saline environment slightly modifies its behavior. There is, therefore, a clear influence of the type of aging on the fracture behavior of both adhesives.     

On the Ablation Behavior of Carbon Fiber-Reinforced Plastics during Laser Surface Treatment Using Pulsed Lasers

This contribution discusses the ablation phenomena observed during laser treatment of carbon fiber-reinforced plastics (CFRPs) with pulsed lasers observed employing laser sources with wavelengths of 355 nm, 1064 nm and 10.6 µm and pulse durations from picoseconds (11 ps) to microseconds (14 µs) are analyzed and discussed. In particular, the threshold fluence of the matrix material epoxy (EP) and the damage threshold of CFRP were calculated. Moreover, two general surface pretreatment strategies are investigated, including selective matrix removal and structure generation through indentation (ablation of both, matrix material and fibers) with a cross-like morphology. The surfaces obtained after the laser treatment are characterized by means of optical and scanning electron microscopy (SEM) and Fourier transform infrared spectroscopy is employed for the analysis of composite and constituent materials epoxy and carbon fibers. As a result, different ablation mechanisms, including evaporation and delamination are observed, depending on the employed laser wavelength and pulse duration. For both 355 nm and 1064 nm wavelength, the laser radiation produces only partial ablation of the carbon fibers due to their higher absorption coefficient compared to the epoxy matrix. Although a selective matrix removal without residues is achieved using the pulsed CO₂ laser. Differently, both constituent materials are ablated with the nanosecond pulsed UV laser, producing indentations. The sum of the investigations has shown that existing theories of laser technology, such as the ablation threshold according to Liu et al., can be applied to composite materials only to a limited extent. Furthermore, it has been found that the pronounced heterogeneity of CFRP mostly leads to an inhomogeneous ablation result, both when creating grooves and during selective matrix removal, where the carbon fibers influence the ablation result by their thermal conductivity, depending on fiber direction. Finally, despite the material inhomogeneity, a scanning strategy has been developed to compensate the heterogeneous ablation results regarding structure depth, width and heat affected zone.     

Assessment of Surface Treatment Degree of Steel Sheets in the Bonding Process

The aim of the paper is to determine the influence of the surface treatment on the adhesive properties of steel sheet surfaces and the strength of the adhesive joints of steel sheets. The paper also aims to assess the degree of steel sheets’ surface treatment in the bonding process. Due to the many methods of surface treatment and types of materials, the assessment of the surface treatment method is extremely important in adhesive processes. Two variants of the surface treatment were used: without a paint coating and with a paint coating, divided into two groups (without degreasing and with degreasing). Additionally, in the case of the analysis of the steel samples without the paint coating, mechanical treatment was applied. Two-component epoxy adhesive, prepared on the basis of bisphenol A and a polyamide curing agent, was used to prepare the single-lap adhesive joints of the steel sheets. The tests determined: (i) the adhesive properties of the steel sheets’ surface based on the measurement of the contact angle of polar and apolar liquids (including wettability, work of adhesion, and surface free energy), (ii) surface roughness parameters (PN EN ISO 4287), and (iii) mechanical properties (load capacity and shear strength) of the steel sheets’ adhesive joints (EN DIN 1465). Contact angle measurements of the steel sheet surfaces showed that the polar liquid better reflects the obtained strength results of the analyzed adhesive joints than the apolar liquid. Furthermore, better wettability of the surface of steel sheets with both polar and apolar liquids was obtained for samples whose surface was subjected to degreasing. It can also be concluded that the wettability of the surface can be used as one of the indicators of the degree of the surface treatment for the bonding process.     

Influence of Surface Treatment on Steel Adhesive Joints Strength—Varnish Coats

The purpose of the paper is to determine the impact of surface treatment on the strength of adhesive joints, made from various steel sheets. Two variants of the surface treatment steel adherends were used: without the varnish coat and with the varnish coat, using three polymer-based varnishes (a simple, a hybrid, and a gel). Two types of the adhesives were used to prepare the adhesive joints: a single-component cyanoacrylate adhesive and a two-component epoxy adhesive. A strength test of the adhesive joints (EN DIN 1465 standard), a coating adhesion test (ASTM D3359-B standard), and surface topography, as well as surface roughness, parameters (PN-EN ISO 11562, PN-EN ISO 4287, and PN-EN ISO 25178 standards) were used. Based on the strength tests, it was observed that the adhesive joints, with the hybrid varnish onto the adherend’s surface, achieved markedly lower shear strength. The best results, in terms of the adhesive joint strength, made using the cyanoacrylate adhesive were achieved for the joints where the adherends were coated with a simple varnish, while in the joints made using the epoxy adhesive, the highest shear strength was achieved by the joints of sheets whose surfaces were coated with the gel varnish.     

Bond Relationship of Carbon Fiber-Reinforced Polymer (CFRP) Strengthened Steel Plates Exposed to Service Temperature

Emerging as a new technology, carbon fiber-reinforced polymer (CFRP) has been introduced to rehabilitate and strengthen steel structures using an adhesive agent. However, the outdoor service temperature is potentially degrading to the mechanical strength of the adhesive, as well as affecting the bonding of the strengthened steel structure. Therefore, this paper aims to investigate the bond relationship of CFRP-strengthened steel plates exposed to service temperatures. Two types of experiments were conducted to determine the tensile and flexural performance of CFRP-strengthened steel plates. The experiments were designed using a Box–Behnken design (BBD) and response surface methodology (RSM) by considering three parameters: service temperature (25 °C, 45 °C and 70 °C), number of CFRP layers (one, three and five layers) and bond length (40, 80 and 120 mm). The findings show the dominant failure mode transformed from adhesion failure between steel and adhesive interfaces to adhesion failure between CFRP and adhesive interfaces as the service temperature increased. The tensile strength improved by 25.62% when the service temperature increased. Field emission scanning electron microscope (FESEM) analysis proved that the strength enhancement is due to the densification and reduction of the adhesive particle microstructure gaps through the softening effect at service temperature. However, service temperature is found to have less impact on flexural strength. Incorporating the experimental results in RSM, two quadratic equations were developed to estimate the tensile and flexural strength of CFRP-strengthened steel plates. The high coefficient of determination, R2, yields at 0.9936 and 0.9846 indicate the high reliability of the models. Hence, it can be used as an estimation tool in the design stage.     

The Influence of Sandblasting Process Parameters of Aerospace Aluminium Alloy Sheets on Adhesive Joints Strength

In this study, the influence of sandblasting process parameters as a surface preparation method on the strength of single-lap adhesive joints of EN AW 2024 T3 aerospace aluminium alloy sheets was determined. Eleven sets of sandblasting parameters were used, which were determined according to a determined experimental plan. The variable factors in the sandblasting process were pressure, nozzle distance, and workpiece displacement speed. The sand jet incidence angle was constant. Garnet 80 E+ was the abrasive material that was used. The joints were made using an epoxy adhesive composition of Epidian 5 epoxy resin and a PAC curing agent. The influence of the surface preparation method on the surface roughness and contact angle to determine the surface free energy was evaluated. The shear strength of the adhesive joints was also determined, which finally allowed the evaluation of the applied surface treatment variants. The obtained results were subjected to statistical analysis, which indicated that the highest shear strength of the adhesive joints was obtained for samples whose surfaces were treated by sandblasting at parameter configurations in which the pressure was 5–6 × 10⁵ Pa; the distance between the nozzle and the sandblasted surface should not be greater than 97 mm, and the speed at which the workpiece moves in relation to the nozzle should not be greater than 75 mm/min.     

Analysis of the Mechanical Properties and Damage Mechanism of Carbon Fiber/Epoxy Composites under UV Aging

The UV durability of carbon fiber composites has been a concern. In this work, UV irradiation on carbon fiber-reinforced polymer (CFRP) materials was performed using an artificial accelerated UV aging chamber to investigate the effect of UV exposure on carbon fiber composites. UV aging caused some of the macromolecular chains on the surface resin to break, resulting in the loss of small molecules and loss of mass. After 80 days of UV irradiation exposure, a significant decline in the macroscopic mechanical properties occurred in the longitudinal direction, with the largest decrease of 23% in longitudinal compressive strength and a decreasing trend in the transverse mechanical properties at the later stage of aging. The microscopic mechanical properties of the CFRP specimens were characterized using nanoindentation, and it was found that UV aging had an embrittlement effect on the matrix, and its hardness/modulus values were higher than the initial values with UV exposure. The fibers were less affected by UV irradiation.     

Development of an Innovative Non-Destructive and Field-Oriented Method to Quantify the Bond Quality of Composite Strengthening Systems on Concrete Structures

Over the last 30 years, structural reinforcement and retrofitting with externally bonded composite materials have proven to be efficient and cost-effective solutions to increase both the safety and the lifespan of civil engineering structures, including nuclear power plants. The effectiveness of the strengthening system highly depends on the level of adhesion between the fiber-reinforced polymer (FRP) composite material and the concrete surface. Therefore, on-site evaluation of the bond quality is critical to assess the performance and predict the durability of the system in place. The direct tension pull-off test is most commonly used to quantify the adhesion level, but this standardized method has many drawbacks. In the present study, it is proposed to evaluate the bond properties by using a nondestructive test (NDT) derived from the standard pull-off test. This innovative test enables the measurement of an interfacial “stiffness” which may be used as a bond quality criterion. This paper gives an insight into the performance of the proposed NDT method, when applied in laboratory conditions to concrete slabs reinforced with bonded pultruded carbon FRP plates (CFRP). Three different epoxy adhesive systems with a broad range of Young’s moduli were used for the specimens’ preparation, in order to vary the stiffness of the concrete/CFRP interface. The purpose was to simulate different levels of interfacial adhesion that could be observed for a single adhesive system. It was shown that the test method was able to detect differences in the interface stiffness beyond experimental uncertainties, and it should therefore enable the detection of differences in the bond quality for a given adhesive system as well. The sensitivity of the NDT was then discussed, and its detection capabilities were predicted for standard field conditions. In the last part, strain measurements were collected during the NDT, thanks to distributed optical fiber sensors (DOFS) embedded in the adhesive joints of the strengthened specimens. An analysis of the strain profiles was found to provide complementary information on the quality of the adhesive bond.     

Comparison of Tensile Strength and Fracture Toughness of Co-Bonded and Cold-Bonded Carbon Fiber Laminate-Aluminum Adhesive Joints

The purpose of this work is to compare the co-bonding vs. cold-bonding route on the adhesive joint performance of a CFRP (Carbon Fiber Reinforced Polymer) laminate–aluminum connection. In particular, the overlap shear, tensile strength and Mode I and Mode II fracture toughness will be evaluated. The adhesives for co-bonding and cold-bonding are, respectively, a thermosetting modified epoxy, unsupported structural film and a two-component epoxy adhesive, chosen as representative of applications in the high-performance/race car field. The emerging trend is that, in tensile e Mode I fracture tests, the failure path is predominantly in the composite. Mode II fracture tests instead resulted in a cohesive fracture, meaning that, under pure shear loading, the weakest link may not be the composite. The lap-shear tests are placed midway (cohesive failure for co-bonding and composite delamination for cold-bonding, respectively), probably due to the different peel stress values related to the different adhesive Young’s modulus. The exploitation of the full capacity of the adhesive joint, hence the possibility of highlighting better, different performances of co-bonding vs. cold-bonding, would require consistent improvement of the out-of-plane strength of the CFRP laminate and/or to someway redistribute the peel stress on the bondline.     

Advances in Titanium/Polymer Hybrid Joints by Carbon Fiber Plug Insert: Current Status and Review

A literature review of up-to-date methods to strengthen Ti/carbon-fiber-reinforced polymer (CFRP) hybrid joints is given. However, there are little or no studies on Ti/CFRP joints by carbon fiber plug insert, which takes advantage of the extremely high surface adhesion area of ~6 μm CFs. Therefore, we cover the current status and review our previously published results developing hybrid joints by a CF plug insert with spot-welded Ti half-lengths to enhance the safety levels of aircraft fan blades. A thermoset Ti/CF/epoxy joint exhibited an ultimate tensile strength (UTS) of 283 MPa when calculated according to the rule of mixtures (RM) for the CF cross-section portion. With concern for the environment, thermoplastic polymers (TPs) allowed recyclability. However, a drawback is easy CF pull-out from difficult-to-adhere TPs due to insufficient contact sites. Therefore, research on a novel method of homogeneous low voltage electron beam irradiation (HLEBI) to activate a bare CF half-length prior to dipping in a TP resin was reviewed and showed that the UTS by the RM of Ti/EBCF/acrylonitrile butadiene styrene (ABS) and Ti/EBCF/polycarbonate (PC) joints increased 154% (from 55 to 140 MPa) and 829% (from 30 to 195 MPa), respectively, over the untreated sample. The optimum 0.30 MGy HLEBI prevented CF pull-out by apparently growing crystallites into the TP around the CF circumference, raising the UTS amount closer to that of epoxy.     

Physico-Mechanical and Rheological Properties of Epoxy Adhesives Modified by Microsilica and Sonication Process

Industrial waste from the production of metallic silicon and silicon–iron alloys, which includes silica fumes (microsilica), is subject to numerous applications aiming at its reuse in concrete and polymeric composites. Recycling solves the problem of their storage and adverse environmental impact. Six different formulas of epoxy resins were tested, differing in the type of polymer, the mixing process (sonication or not) and the presence of microsilica. The study showed that microsilica added to the epoxy resin changes its viscosity and free surface energy, and these are the parameters that determine the adhesion of the polymer to the concrete surface. Strength tests and SEM analysis have determined how microsilica molecules can penetrate the structure of polymer macromolecules by filling and forming temporary chemical bonds. Mixing the fillers with the adhesive was achieved by using a sonication process. The analysis of the obtained results showed that, depending on the initial composition of the polymer, the addition of microsilica can change the chemical, physical and mechanical properties of the hardened adhesive to varying degrees. In the case of adhesives used in the construction industry to strengthen and glue structural elements, these changes significantly affect the durability of the adhesive joints.     

Possibilities of Increasing Effectiveness of RC Structure Strengthening with FRP Materials

Modern composite materials based on non-metallic continuous fibres are increasingly used in civil engineering to strengthen building structures. In the strengthening of reinforced concrete (RC) structures, the utilisation of externally bonded fibre-reinforced polymer (FRP) composites is only up to 35% because of the pilling-off failure mechanism. This problem can be solved using pre-tensioned composite laminates. Due to more complex behaviour, the strengthening of structures by means of prestressing technology needs a careful design approach and a full understanding of the behaviour of both the materials and elements. The advantages and risks of the presented technology, which may determine the success of the entire project, will be highlighted in the paper. The possibility of using a flexible adhesive layer in carbon fibre reinforced polymer (CFRP) strengthening applications for flexural strengthening of RC elements, as an innovative solution in civil engineering, will also be presented. Parallel introduction of the flexible adhesive layer (made of polyurethane masses) and a traditional epoxy adhesive layer in one strengthening system was investigated in the laboratory tests. This solution was used for the repair and protection of a previously damaged RC beam against brittle failure.     

Cyclic Relaxation,Impact Properties and Fracture Toughness of Carbon and Glass Fiber Reinforced Composite Laminates

In this paper, the mechanical properties of fiber-reinforced epoxy laminates are experimentally tested. The relaxation behavior of carbon and glass fiber composite laminates is investigated at room temperature. In addition, the impact strength under drop-weight loading is measured. The hand lay-up technique is used to fabricate composite laminates with woven 8-ply carbon and glass fiber reinforced epoxy. Tensile tests, cyclic relaxation tests and drop weight impacts are carried out on the carbon and glass fiber-reinforced epoxy laminates. The surface release energy G_IC and the related fracture toughness K_IC are important characteristic properties and are therefore measured experimentally using a standard test on centre-cracked specimens. The results show that carbon fiber-reinforced epoxy laminates with high tensile strength give high cyclic relaxation performance, better than the specimens with glass fiber composite laminates. This is due to the higher strength and stiffness of carbon fiber-reinforced epoxy with 600 MPa compared to glass fiber-reinforced epoxy with 200 MPa. While glass fibers show better impact behavior than carbon fibers at impact energies between 1.9 and 2.7 J, this is due to the large amount of epoxy resin in the case of glass fiber composite laminates, while the impact behavior is different at impact energies between 2.7 and 3.4 J. The fracture toughness K_IC is measured to be 192 and 31 MPa √m and the surface energy G_IC is measured to be 540.6 and 31.1 kJ/m² for carbon and glass fiber-reinforced epoxy laminates, respectively.     

Evaluation of Bonding Gap Control Methods for an Epoxy Adhesive Joint of Carbon Fiber Tubes and Aluminum Alloy Inserts

The aim of this paper is to compare two methods of epoxy adhesive bond gap control: one with a geometrical (mechanical) solution and the other with glass beads, which have the diameter of the desired bond gap and are mixed with an epoxy adhesive. The adhered materials were carbon fiber composite tubes and aluminum alloy inserts, which were used as wishbones in a suspension system of a motorsport vehicle. It was assumed that the gap thickness would be equal to 0.2 mm and the length of a bond would be 30 mm. The internal diameter of the tubes was 14 mm and 18 mm, whereas the inserts’ external diameter was 13.6 mm and 17.6 mm. Their surface has been subjected to mechanical treatment with sand paper starting from 240 grit up to 400. The adhesives used were EA 3425 and EA 9466 cured at 80 °C for 2 h. The results showed that the glass beads method provides more consistent and better results as compared to the geometrical (mechanical) method. Further study in the area of fatigue and interfacial failure modes could be useful.     

Material Extrusion of Structural Polymer–Aluminum Joints—Examining Shear Strength,Wetting, Polymer Melt Rheology and Aging

Generating polymer–metal structures by means of additive manufacturing offers huge potential for customized, sustainable and lightweight solutions. However, challenges exist, primarily with regard to reliability and reproducibility of the additively generated joints. In this study, the polymers ABS, PETG and PLA, which are common in material extrusion, were joined to grit-blasted aluminum substrates. Temperature dependence of polymer melt rheology, wetting and tensile single-lap-shear strength were examined in order to obtain appropriate thermal processing conditions. Joints with high adhesive strength in the fresh state were aged for up to 100 days in two different moderate environments. For the given conditions, PETG was most suitable for generating structural joints. Contrary to PETG, ABS–aluminum joints in the fresh state as well as PLA–aluminum joints in the aged state did not meet the demands of a structural joint. For the considered polymers and processing conditions, this study implies that the suitability of a polymer and a thermal processing condition to form a polymer–aluminum joint by material extrusion can be evaluated based on the polymer’s rheological properties. Moreover, wetting experiments improved estimation of the resulting tensile single-lap-shear strength.     

Experimental and Numerical Study of Low-Velocity Impact and Tensile after Impact for CFRP Laminates Single-Lap Joints Adhesively Bonded Structure

To investigate the mechanical behavior of the single-lap joints (SLJs) adhesively bonded structure of carbon fiber reinforced polymer (CFRP) laminates under the low-velocity impact (LVI) and tensile-after impact (TAI), tests and simulations were carried out. A finite element model (FEM) was established based on the cohesive zone model (CZM) and Hashin criterion to predict the damage evolution process of adhesive film, intra- and inter-laminar of the SLJs of CFRP laminates, and its effectiveness was verified by experiments. Moreover, three different overlap lengths (20 mm, 30 mm, and 40 mm) and four different impact energies (Intact joint, 10 J, 20 J, and 30 J) are considered in the present study. Finally, the effects of different impact energies and overlap lengths on the residual strength of SLJs after impact were discussed. The results divulged that numerical results of impact and TAI processes of SLJs were in good agreement with experiment results. During the impact process, the damage of the laminates was primarily fiber and matrix tensile damage, whereas the adhesive film was damaged cohesively; the areas of damage increased with the increase of impact energy, and the normal stress of the adhesive film expanded from the edge to the middle region with the increase of impact force. The influence of LVI on SLJs adhesively bonded structures was very significant, and it is not effective to obtain a higher impact resistance by increasing the overlap length. For the tensile process, the failure mode of TAI of the SLJs was interface failure, the surplus strength of the SLJs gradually decreased with the increase of the impact energy because of the smaller overlap length, the overlap length more than 30 mm, and the low energy impact has almost no effect on the residual strength of the SLJs.     

Influence of the Arrangement of Mechanical Fasteners on the Static Strength and Fatigue Life of Hybrid Joints

This paper presents the results of experimental research and numerical calculations regarding the static strength and fatigue life of hybrid joints. In the experiments, specimens built as single-lap adhesive–mechanical joints (hybrid joints) were tested. In a two-stage process of the failure of the hybrid joints, the adhesive joint was damaged first. Therefore, it was assumed that the assembly of fasteners closer to the edge of the overlap (beyond the ranges recommended for mechanical joints) limits the negative impact of the peeling phenomenon on the strength and performance properties of hybrid joints. The specimens used in the experiments were prepared from composite elements (i.e., carbon fiber-reinforced polymer (CFRP)), as well as from the aluminum alloy 2024T4. Because the detection of fatigue damage in composite materials is a complex problem, computed tomography was used to evaluate the degradation of the composite material. Experimental and numerical comparative analyses of the static strength and fatigue life of hybrid joints with adhesive and mechanical joints confirmed the assumptions made.     

The Thickness Effect of PSF Nanofibrous Mat on Fracture Toughness of Carbon/Epoxy Laminates

The geometrical features of nanofibers, such as nanomat thickness and the diameter of nanofibers, have a significant influence on the toughening behavior of composite laminates. In this study, carbon/epoxy laminates were interleaved with polysulfone (PSF) nanofibrous mats and the effect of the PSF nanomat thickness on the fracture toughness was considered for the first time. For this goal, the nanofibers were first produced by the electrospinning method. Then, double cantilever beam (DCB) specimens were manufactured, and mode-I fracture tests were conducted. The results showed that enhancing the mat thickness could increase the fracture toughness considerably (to about 87% with the maximum thickness). The toughening mechanism was also considered by presenting a schematic picture. Micrographs were taken using a scanning electron microscope (SEM).     

The electrical characteristics of some commercial ECG electrodes

The impedance and offset potential of six disposable and two non-disposable electrodes were measured on 80 subjects. A total of 160 measurements were made on skin prepared by wiping with alcohol or acetone. For 640 measurements the skin was prepared by lightly sanding. The sanding of the skin reduced the impedance by a factor of approximately 50 for males and 100 for females. The offset potential for sanded skin was reduced by approximately 2. The performance of the disposable electrodes showed no great practical difference when applied on sanded skin. The median impedance ranged from 1500 to 3250 ohms. The median offset potential ranged from 0.5 to 4 mV. It was shown that a small DC current of 100 nA applied to stainless steel electrodes could cause a polarization voltage of approximately 0.5 volts to appear in 25 min.     

Method of Designing a Friction-Based Wedge Anchorage System for High-Strength CFRP Plates

The cables of high-strength carbon fiber reinforced polymer (CFRP) plates are starting to be applied to large spatial structures. However, their main anchorage systems rely on the adhesive force, which entails risks to their integrity resulting from aging of the binding agent. In this study, a friction-based wedge anchorage system was designed for CFRP plates. The working mechanism of the proposed anchorage system was explored both theoretically and experimentally. The anti-slip mechanism and condition of CFRP plates were formulated so that the equivalent frictional angle of the contact surface between a CFRP plate and wedges must not be smaller than the sum of the dip angle of the wedge external conical surface and the frictional angle between the wedges and barrel. An analysis of the stress distribution in the anchorage zone of the CFRP plate was conducted using the Tsai-Wu failure criterion, which concluded that the compressive stresses should be reduced on the section closer to the load-bearing end of the anchorage system. Furthermore, the anchorage efficiency coefficient was proposed, which depends on stress concentration coefficients, plate thickness, length of anchorage zone, dip angle of wedge external conical surface, and its frictional angle. Then, it was determined that the minimum length of an anchorage zone for the CFRP plates with various specifications should be at least 49 times larger than the CFRP thickness. A finite element analysis and static tensile tests on six specimens were carried out. The experimental results revealed that the anchorage efficiency coefficient of the optimized anchor reached 97.9%.