Mechanical and Electrical Properties of Polyethylene Terephthalate Glycol/Antimony Tin Oxide Nanocomposites in Material Extrusion 3D Printing.

In this study, poly (ethylene terephthalate) (PETG) was combined with Antimony-doped Tin Oxide (ATO) to create five different composites (2.0-10.0 wt.% ATO). The PETG/ATO filaments were extruded and supplied to a material extrusion (MEX) 3D printer to fabricate the specimens following international standards. Various tests were conducted on thermal, rheological, mechanical, and morphological properties. The mechanical performance of the prepared nanocomposites was evaluated using flexural, tensile, microhardness, and Charpy impact tests. The dielectric and electrical properties of the prepared composites were evaluated over a broad frequency range. The dimensional accuracy and porosity of the 3D printed structure were assessed using micro-computed tomography. Other investigations include scanning electron microscopy and energy-dispersive X-ray spectroscopy, which were performed to investigate the structures and morphologies of the samples. The PETG/6.0 wt.% ATO composite presented the highest mechanical performance (21% increase over the pure polymer in tensile strength). The results show the potential of such nanocomposites when enhanced mechanical performance is required in MEX 3D printing applications, in which PETG is the most commonly used polymer.

Investigation of the Effectiveness of Silicon Nitride as a Reinforcement Agent for Polyethylene Terephthalate Glycol in Material Extrusion 3D Printing.

Polyethylene terephthalate glycol (PETG) and silicon nitride (Si3N4) were combined to create five composite materials with Si3N4 loadings ranging from 2.0 wt.% to 10.0 wt.%. The goal was to improve the mechanical properties of PETG in material extrusion (MEX) additive manufacturing (AM) and assess the effectiveness of Si3N4 as a reinforcing agent for this particular polymer. The process began with the production of filaments, which were subsequently fed into a 3D printer to create various specimens. The specimens were manufactured according to international standards to ensure their suitability for various tests. The thermal, rheological, mechanical, electrical, and morphological properties of the prepared samples were evaluated. The mechanical performance investigations performed included tensile, flexural, Charpy impact, and microhardness tests. Scanning electron microscopy and energy-dispersive X-ray spectroscopy mapping were performed to investigate the structures and morphologies of the samples, respectively. Among all the composites tested, the PETG/6.0 wt.% Si3N4 showed the greatest improvement in mechanical properties (with a 24.5% increase in tensile strength compared to unfilled PETG polymer), indicating its potential for use in MEX 3D printing when enhanced mechanical performance is required from the PETG polymer.

High-Density Polyethylene/Carbon Black Composites in Material Extrusion Additive Manufacturing: Conductivity, Thermal, Rheological, and Mechanical Responses.

High-density polyethylene polymer (HDPE) and carbon black (CB) were utilized to create HDPE/CB composites with different filler concentrations (0.0, 2.0, 4.0, 6.0, 8.0, 10.0, 16.0, 20.0, and 24.0 wt.%). The composites were extruded into filaments, which were then utilized to fabricate 3D-printed specimens with the material extrusion (MEX) method, suitable for a variety of standard mechanical tests. The electrical conductivity was investigated. Furthermore, thermogravimetric analysis and differential scanning calorimetry were carried out for all the HDPE/CB composites and pure HDPE. Scanning electron microscopy in different magnifications was performed on the specimens' fracture and side surfaces to investigate the morphological characteristics. Rheological tests and Raman spectroscopy were also performed. Eleven different tests in total were performed to fully characterize the composites and reveal connections between their various properties. HDPE/CB 20.0 wt.% showed the greatest reinforcement results in relation to pure HDPE. Such composites are novel in the MEX 3D printing method. The addition of the CB filler greatly enhanced the performance of the popular HDPE polymer, expanding its applications.

Medical-Grade PLA Nanocomposites with Optimized Tungsten Carbide Nanofiller Content in MEX Additive Manufacturing: A Rheological, Morphological, and Thermomechanical Evaluation.

The goal of this paper is to investigate tungsten carbide (WC) as a reinforcement in the popular material extrusion (MEX) additive manufacturing (AM) procedure. The impressive characteristics of WC demonstrate its potential as a valuable additive for commonly used polymeric matrices in MEX 3D printing, offering reinforcement and stabilization properties. The mechanical properties of hybrid polymer/ceramic nanocomposites made up of various filler loadings (0-10 wt. %) of medical-grade polylactic acid (PLA) and WC were studied. The mechanical characteristics, structure, and thermomechanical properties of the resulting compounds were fully characterized following the respective standards. The fracture mechanisms were revealed with Scanning Electron Microscopy. Overall, a laborious effort was implemented with fifteen different tests to fully characterize the nanocomposites prepared. In comparison to the raw PLA material, the tensile strength of the 4.0 wt. % WC PLA/WC nanocomposite was improved by 42.5% and the flexural strength by 41.9%. In the microhardness test, a 120.4% improvement was achieved, justifying the properties of WC ceramic. According to these findings, PLA nanocomposites reach high-performance polymer specifications, expanding their potential use, especially in wear-related applications.

Box-Behnken modeling to quantify the impact of control parameters on the energy and tensile efficiency of PEEK in MEX 3D-printing.

Currently, energy efficiency and saving in production engineering, including Material Extrusion (MEX) Additive Manufacturing, are of key importance to ensure process sustainability and cost-effectiveness. The functionality of parts made with MEX 3D-printing remains solid, especially for expensive high-performance polymers, for biomedical, automotive, and aerospace industries. Herein, the energy and tensile strength metrics are investigated over three key process control parameters (Nozzle Temperature, Layer Thickness, and Printing Speed), with the aid of laboratory-scale PEEK filaments fabricated with melt extrusion. A double optimization is attempted for the production by consuming minimum energy, of PEEK parts with improved strength. A three-level Box-Behnken design with five replicas for each experimental run was employed. Statistical analysis of the experimental findings proved that LT is the most decisive control setting for mechanical strength. An LT of 0.1 mm maximized the tensile endurance (∼74 MPa), but at the same time, it was responsible for the worst energy (∼0.58 MJ) and printing time (∼900 s) expenditure. The experimental and statistical findings are further discussed and interpreted using fractographic SEM and optical microscopy, revealing the 3D printing quality and the fracture mechanisms in the samples. Thermogravimetric analysis (TGA) was performed. The findings hold measurable engineering and industrial merit, since they may be utilized to achieve an optimum case-dependent compromise between the usually contradictory goals of productivity, energy performance, and mechanical functionality.

The Effect of Nano Zirconium Dioxide (ZrO2)-Optimized Content in Polyamide 12 (PA12) and Polylactic Acid (PLA) Matrices on Their Thermomechanical Response in 3D Printing.

The influence of nanoparticles (NPs) in zirconium oxide (ZrO2) as a strengthening factor of Polylactic Acid (PLA) and Polyamide 12 (PA12) thermoplastics in material extrusion (MEX) additive manufacturing (AM) is reported herein for the first time. Using a melt-mixing compounding method, zirconium dioxide nanoparticles were added at four distinct filler loadings. Additionally, 3D-printed samples were carefully examined for their material performance in various standardized tests. The unfilled polymers were the control samples. The nature of the materials was demonstrated by Raman spectroscopy and thermogravimetric studies. Atomic Force Microscopy and Scanning Electron Microscopy were used to comprehensively analyze their morphological characteristics. Zirconium dioxide NPs showed an affirmative reinforcement tool at all filler concentrations, while the optimized material was calculated with loading in the range of 1.0-3.0 wt.% (3.0 wt.% for PA12, 47.7% increase in strength; 1.0 wt.% for PLA, 20.1% increase in strength). PA12 and PLA polymers with zirconium dioxide in the form of nanocomposite filaments for 3D printing applications could be used in implementations using thermoplastic materials in engineering structures with improved mechanical behavior.

Nanocomposites with Optimized Polytetrafluoroethylene Content as a Reinforcement Agent in PA12 and PLA for Material Extrusion Additive Manufacturing.

Herein, polytetrafluoroethylene (PTFE) is evaluated as a reinforcement agent in material extrusion (MEX) additive manufacturing (AM), aiming to develop nanocomposites with enhanced mechanical performance. Loadings up to 4.0 wt.% were introduced as fillers of polylactic acid (PLA) and polyamide 12 (PA12) matrices. Filaments for MEX AM were prepared to produce corresponding 3D-printed samples. For the thorough characterization of the nanocomposites, a series of standardized mechanical tests were followed, along with AFM, TGA, Raman spectroscopy, EDS, and SEM analyses. The results showed an improved mechanical response for filler concentrations between 2.0 and 3.0 wt.%. The enhancement for the PLA/PTFE 2.0 wt.% in the tensile strength reached 21.1% and the modulus of elasticity 25.5%; for the PA12/PTFE 3.0 wt.%, 34.1%, and 41.7%, respectively. For PLA/PTFE 2.0 wt.%, the enhancement in the flexural strength reached 57.6% and the modulus of elasticity 25.5%; for the PA12/PTFE 3.0 wt.%, 14.7%, and 17.2%, respectively. This research enables the ability to deploy PTFE as a reinforcement agent in the PA12 and PLA thermoplastic engineering polymers in the MEX AM process, expanding the potential applications.

Optimizing the Rheological and Thermomechanical Response of Acrylonitrile Butadiene Styrene/Silicon Nitride Nanocomposites in Material Extrusion Additive Manufacturing.

The current research aimed to examine the thermomechanical properties of new nanocomposites in additive manufacturing (AM). Material extrusion (MEX) 3D printing was utilized to evolve acrylonitrile butadiene styrene (ABS) nanocomposites with silicon nitride nano-inclusions. Regarding the mechanical and thermal response, the fabricated 3D-printed samples were subjected to a course of standard tests, in view to evaluate the influence of the Si3N4 nanofiller content in the polymer matrix. The morphology and fractography of the fabricated filaments and samples were examined using scanning electron microscopy and atomic force microscopy. Moreover, Raman and energy dispersive spectroscopy tests were accomplished to evaluate the composition of the matrix polymer and nanomaterials. Silicon nitride nanoparticles were proved to induce a significant mechanical reinforcement in comparison with the polymer matrix without any additives or fillers. The optimal mechanical response was depicted to the grade ABS/Si3N4 4 wt. %. An impressive increase in flexural strength (30.3%) and flexural toughness (47.2%) was found. The results validate that these novel ABS nanocomposites with improved mechanical properties can be promising materials.

Mechanical strength predictability of full factorial, Taguchi, and Box Behnken designs: Optimization of thermal settings and Cellulose Nanofibers content in PA12 for MEX AM.

Optimization of reinforced nanocomposites for MEX 3D-printing remain strong industrial claims. Herein, the efficacy of three modeling methods, i.e., full factorial (FFD), Taguchi (TD), and Box-Behnken (BBD), on the performance of MEX 3D printed nanocomposites was investigated, aiming to reduce the experimental effort. Filaments of medical-grade Polyamide 12 (PA12) reinforced with Cellulose NanoFibers (CNF) were evolved. Besides the CNF loading, 3D printing settings such as Nozzle (NT) and Bed (BΤ) Temperatures were optimization goals aiming to maximize the mechanical response. Three parameters and three levels of FFD were compliant with the ASTM-D638 standard (27 runs, five repetitions). An L9 orthogonal TD and a 15 runs BBD were compiled. In FFD, wt.3%CNF, 270 °C NT, and 80 °C BΤ led to 24% higher tensile strength compared to pure PA12. TGA, RAMAN, and SEM analyses interpreted the reinforcement mechanisms. TD and BBD exhibited fair approximations, requiring 7.4% and 11.8% of the FFD experimental effort.

Functionality Versus Sustainability for PLA in MEX 3D Printing: The Impact of Generic Process Control Factors on Flexural Response and Energy Efficiency.

Process sustainability vs. mechanical strength is a strong market-driven claim in Material Extrusion (MEX) Additive Manufacturing (AM). Especially for the most popular polymer, Polylactic Acid (PLA), the concurrent achievement of these opposing goals may become a puzzle, especially since MEX 3D-printing offers a variety of process parameters. Herein, multi-objective optimization of material deployment, 3D printing flexural response, and energy consumption in MEX AM with PLA is introduced. To evaluate the impact of the most important generic and device-independent control parameters on these responses, the Robust Design theory was employed. Raster Deposition Angle (RDA), Layer Thickness (LT), Infill Density (ID), Nozzle Temperature (NT), Bed Temperature (BT), and Printing Speed (PS) were selected to compile a five-level orthogonal array. A total of 25 experimental runs with five specimen replicas each accumulated 135 experiments. Analysis of variances and reduced quadratic regression models (RQRM) were used to decompose the impact of each parameter on the responses. The ID, RDA, and LT were ranked first in impact on printing time, material weight, flexural strength, and energy consumption, respectively. The RQRM predictive models were experimentally validated and hold significant technological merit, for the proper adjustment of process control parameters per the MEX 3D-printing case.

Mechanical Reinforcement of ABS with Optimized Nano Titanium Nitride Content for Material Extrusion 3D Printing.

Acrylonitrile Butadiene Styrene (ABS) nanocomposites were developed using Material Extrusion (MEX) Additive Manufacturing (AM) and Fused Filament Fabrication (FFF) methods. A range of mechanical tests was conducted on the produced 3D-printed structures to investigate the effect of Titanium Nitride (TiN) nanoparticles on the mechanical response of thermoplastic polymers. Detailed morphological characterization of the produced filaments and 3D-printed specimens was carried out using Atomic Force Microscopy (AFM) and Scanning Electron Microscopy (SEM). High-magnification images revealed a direct impact of the TiN concentration on the surface characteristics of the nanocomposites, indicating a strong correlation with their mechanical performance. The chemical compositions of the raw and nanocomposite materials were thoroughly investigated by conducting Raman and Energy Dispersive Spectroscopy (EDS) measurements. Most of the mechanical properties were improved with the inclusion of TiN nanoparticles with a content of 6 wt. % to reach the optimum mechanical response overall. ABS/TiN 6 wt. % exhibits remarkable increases in flexural modulus of elasticity (42.3%) and toughness (54.0%) in comparison with pure ABS. The development of ABS/TiN nanocomposites with reinforced mechanical properties is a successful example that validates the feasibility and powerful abilities of MEX 3D printing in AM.

Energy Consumption vs. Tensile Strength of Poly[methyl methacrylate] in Material Extrusion 3D Printing: The Impact of Six Control Settings.

The energy efficiency of material extrusion additive manufacturing has a significant impact on the economics and environmental footprint of the process. Control parameters that ensure 3D-printed functional products of premium quality and mechanical strength are an established market-driven requirement. To accomplish multiple objectives is challenging, especially for multi-purpose industrial polymers, such as the Poly[methyl methacrylate]. The current paper explores the contribution of six generic control factors (infill density, raster deposition angle, nozzle temperature, print speed, layer thickness, and bed temperature) to the energy performance of Poly[methyl methacrylate] over its mechanical performance. A five-level L25 Taguchi orthogonal array was composed, with five replicas, involving 135 experiments. The 3D printing time and the electrical consumption were documented with the stopwatch approach. The tensile strength, modulus, and toughness were experimentally obtained. The raster deposition angle and the printing speed were the first and second most influential control parameters on tensile strength. Layer thickness and printing speed were the corresponding ones for the energy consumption. Quadratic regression model equations for each response metric over the six control parameters were compiled and validated. Thus, the best compromise between energy efficiency and mechanical strength is achievable, and a tool creates significant value for engineering applications.

Thermomechanical Response of Polycarbonate/Aluminum Nitride Nanocomposites in Material Extrusion Additive Manufacturing.

Polycarbonate-based nanocomposites were developed herein through a material extrusion (MEX) additive manufacturing (AM) process. The fabrication of the final nanocomposite specimens was achieved by implementing the fused filament fabrication (FFF) 3D printing process. The impact of aluminum nitride (AlN) nanoparticles on the thermal and mechanical behavior of the polycarbonate (PC) matrix was investigated thoroughly for the fabricated nanocomposites, carrying out a range of thermomechanical tests. Scanning electron microscopy (SEM) and atomic force microscopy (AFM) provided information about the morphological and surface characteristics of the produced specimens. Using energy dispersive spectroscopy (EDS), the elemental composition of the nanocomposite materials was validated. Raman spectroscopy revealed no chemical interactions between the two material phases. The results showed the reinforcement of most mechanical properties with the addition of the AlN nanoparticles. The nanocomposite with 2 wt.% filler concentration exhibited the best mechanical performance overall, with the highest improvements observed for the tensile strength and toughness of the fabricated specimens, with a percentage of 32.8% and 51.6%, respectively, compared with the pure polymer. The successful AM of PC/AlN nanocomposites with the MEX process is a new paradigm, which expands 3D printing technology and opens a new route for the development of nanocomposite materials with multifunctional properties for industrial applications.

Three-Dimensional Printed Polyamide 12 (PA12) and Polylactic Acid (PLA) Alumina (Al2O3) Nanocomposites with Significantly Enhanced Tensile, Flexural, and Impact Properties.

The effect of aluminum oxide (Al2O3) nanoparticles (NPs) as a reinforcing agent of Polyamide 12 (PA12) and Polylactic acid (PLA) in fused filament fabrication (FFF) three-dimensional printing (3DP) is reported herein for the first time. Alumina NPs are incorporated via a melt-mixing compounding process, at four different filler loadings. Neat as well as nanocomposite 3DP filaments are prepared as feedstock for the 3DP manufacturing of specimens which are thoroughly investigated for their mechanical properties. Thermogravimetric analyses (TGA) and Raman spectroscopy (RS) proved the nature of the materials. Their morphological characteristics were thoroughly investigated with scanning electron and atomic force microscopy. Al2O3 NPs exhibited a positive reinforcement mechanism at all filler loadings, while the mechanical percolation threshold with the maximum increase of performance was found between 1.0-2.0 wt.% filler loading (1.0 wt.% for PA12, 41.1%, and 56.4% increase in strength and modulus, respectively; 2.0 wt.% for PLA, 40.2%, and 27.1% increase in strength and modulus, respectively). The combination of 3DP and polymer engineering using nanocomposite PA12 and PLA filaments with low-cost filler additives, e.g., Al2O3 NPs, could open new avenues towards a series of potential applications using thermoplastic engineering polymers in FFF 3DP manufacturing.

The Effect of Tool Geometry on the Strength of FSW Aluminum Thin Sheets.

Welding tools of different designs have been used to join friction stir welding 2-mm-thick Al 7075 sheets, to investigate the effect of the tool geometry on the weld performance. Five cylindrical tools with different pin geometries were manufactured from heat-treatable low alloy steel WNr 1.6582/DIN 34CrNiMo6. Additionally, the effect of the welding speed was considered in the work, with six different speeds ranging from 80 mm/min to 300 mm/min. The weld tool rotational speed was kept constant at 1000 rpm and all other parameters were also kept constant in the experiments. The tensile strength was measured to investigate the mechanical properties of the weld. Results were processed with statistical analysis tools, which showed that the mechanical strength was affected by tool geometry as well as welding speed. The weld tool with the highest pin diameter achieved the highest tensile strength. The welding speed affected the tensile strength differently in the different weld tool geometries studied. The highest weld efficiency reported in the tests is 72.20%, achieved with a cylindrical pin weld tool at 250 mm/min.

Multifunctional Medical Grade Resin with Enhanced Mechanical and Antibacterial Properties: The Effect of Copper Nano-Inclusions in Vat Polymerization (VPP) Additive Manufacturing.

Vat photopolymerization (VPP) is an additive manufacturing process commonly used in medical applications. This work aims, for the first time in the literature, to extend and enhance the performance of a commercial medical-grade resin for the VPP process, with the development of nanocomposites, using Copper (Cu) nanoparticles as the additive at two different concentrations. The addition of the Cu nanoparticles was expected to enhance the mechanical properties of the resin and to enable biocidal properties on the nanocomposites since Cu is known for its antibacterial performance. The effect of the Cu concentration was investigated. The nanocomposites were prepared with high-shear stirring. Specimens were 3D printed following international standards for mechanical testing. Their thermal and spectroscopic response was also investigated. The morphological characteristics were examined. The antibacterial performance was evaluated with an agar well diffusion screening process. The experimental results were analyzed with statistical modeling tools with two control parameters (three levels each) and eleven response parameters. Cu enhanced the mechanical properties in all cases studied. 0.5 wt.% Cu nanocomposite showed the highest improvement (approximately 11% in tensile and 10% in flexural strength). The antibacterial performance was sufficient against S. aureus and marginal against E. coli.

Silicon Carbide Nanoparticles as a Mechanical Boosting Agent in Material Extrusion 3D-Printed Polycarbonate.

In this work, the effect of silicon carbide (carborundum, SiC), as a boosting agent of the mechanical response of the polycarbonate (PC) polymer, was investigated. The work aimed to fabricate nanocomposites with an improved mechanical performance and to further expand the utilization of 3D printing in fields requiring an enhanced material response. The nanocomposites were produced by a thermomechanical process in various SiC concentrations in order to evaluate the filler loading in the mechanical enhancement. The samples were 3D printed with the material extrusion (MEX) method. Their mechanical performance was characterized, following international standards, by using dynamic mechanical analysis (DMA) and tensile, flexural, and Charpy's impact tests. The microhardness of the samples was also measured. The morphological characteristics were examined, and Raman spectra revealed their structure. It was found that SiC can improve the mechanical performance of the PC thermoplastic. A 19.5% increase in the tensile strength was found for the 2 wt.% loading nanocomposite, while the 3 wt.% nanocomposite showed a 16% increase in the flexural strength and a 35.9% higher impact strength when compared to the unfilled PC. No processability issues were faced for the filler loadings that have been studied here.

Trilateral Multi-Functional Polyamide 12 Nanocomposites with Binary Inclusions for Medical Grade Material Extrusion 3D Printing: The Effect of Titanium Nitride in Mechanical Reinforcement and Copper/Cuprous Oxide as Antibacterial Agents.

In this work, for the first time, polyamide 12 (PA12) nanocomposites with binary inclusions in material extrusion (MEX) 3D printing were developed. The aim was to achieve an enhanced mechanical response with the addition of titanium nitride (TiN) and antibacterial performance with the addition of copper (Cu) or cuprous oxide (Cu2O), towards the development of multi-functional nanocomposite materials, exploiting the 3D printing process benefits. The prepared nanocomposites were fully characterized for their mechanical properties. The thermal properties were also investigated. Morphological characterization was performed with atomic force microscopy (AFM) and scanning electron microscopy (SEM). The antibacterial performance was investigated with an agar-well diffusion screening process. Overall, the introduction of these nanofillers induced antibacterial performance in the PA12 matrix materials, while at the same time, the mechanical performance was significantly increased. The results of the study show high potential for expanding the areas in which 3D printing can be used.

High-performance medical-grade resin radically reinforced with cellulose nanofibers for 3D printing.

The effect of Cellulose NanoFiber (CNF) addition to a medical-grade resin in Stereolithography (SLA) Additive Manufacturing (AM) technology is reported, aiming to elaborate an easily processable, highly stiff bio-compound. CNFs were shear stir blended at various weight ratios with liquid resin. The fabricated nanocomposite materials were introduced in an SLA 3D printer for specimens manufacturing. The mechanical performance was studied according to international standards. Charpy Toughness and Vickers microhardness were calculated for all tested materials. A microscopic and surface analysis was conducted on fractured tensile specimens by Scanning Electron Microscopy (SEM) and Atomic Force Microscopy (AFM), respectively. The thermal and thermomechanical properties were investigated by Thermogravimetric Analysis (TGA), Differential Calorimetry (DSC), and Dynamic Mechanical Analysis (DMA). Significant reinforcement of the medical-grade nanocomposites is reported, with the highest values calculated to be at 1.0 wt% concentration (more than 100% at the tensile strength), while brittleness and rigidity were increased.

Friction Stir Welding Optimization of 3D-Printed Acrylonitrile Butadiene Styrene in Hybrid Additive Manufacturing.

The feasibility of joining material extrusion (MEX) 3D-printed acrylonitrile butadiene styrene (ABS) plates with the friction stir welding (FSW) process was investigated herein as a promising topic of hybrid additive manufacturing (HAM). The influence of three process parameters on the mechanical strength of the joints was thoroughly examined and analyzed with a full factorial experimental design and statistical modeling. Hereto, the welding tool pin geometry, travel speed, and rotational speed were investigated. The joint's efficiency and quality are evaluated through tensile tests and morphological characterization. More specifically, specimens' areas of particular interest were investigated with stereoscopic, optical, and scanning electron microscopy. Throughout the FSW experimental course, the welding temperature was monitored to evaluate the state of the ABS material during the process. The majority of the welded specimens exhibited increased mechanical strength compared with the respective ones of non-welded 3D printed specimens of the same geometry. Statistical modeling proved that all processing parameters were significant. The feasibility of the FSW process in 3D printed ABS workpieces was confirmed, making the FSW a cost-effective process for joining 3D printing parts, further expanding the industrial merit of the approach.