Results Of Bending Tests Research Articles

An investigation into the three-point bending properties and the vickers microhardness of dental composites reinforced with nylon 66 nanofibers

The aim of this research work is to study the reinforcement effect of nylon 66 nanofibrous mats on the mechanical properties of the three different dental composites, termed as Nanohybrid, Microhybrid and, Microfill. Nylon 66 nanofibrous mats were prepared by using the electrospinning technique at different spinning dope concentrations (17%, 20% and 23% wt.) and characterized by a scanning electron microscopy and a mechanical tester. The obtained mats were added to the dental composites in a laminate form with the weight fraction of 0, 0.5, 1.5, 3 and 6%. The flexural strength (FS), elastic modulus (EY), and work of fracture (WOF) of the dental composites were evaluated using three-point bending test and the Vickers hardness of the composites was studied using microhardness test. Obtained results showed that by increasing the spinning solution concentration, the diameter of the resultant nanofibers increased which further increased the tensile strength of the nanofibrous mats. The results of the three-point bending test indicated that FS, EY, WOF of the nanofiber reinforced composites were all significantly increased by the addition of nylon 66 nanofibers; as an illustration, the addition of 6% nanofibrous mats (23% wt) improved FS of the Microhybrid composite by 68.08%, EY of the Nanohybrid composite by 509%, and WOF of the Microfill composite by 106.08%, as compared to those of the pure dental composite. Furthermore, the incorporation of the nanofibers within the resin matrix increased the microhardness value of the reinforced resin, as compared to the unreinforced resin, for all three different dental composites.

Simulation of Marine Bio-Composite Using Empirical Data Combined with Finite Element Technique

After development of world-first marine bio-composite from 100% waste materials, the necessity of obtaining a simulation tool to predict the performance of this novel material under different conditions has arisen. This study examines the combination of empirical optimization and finite element simulation method as an economic and time-effective tool to predict the mechanical performance of novel complex bio-composite mixtures at the design phase. Bio-composite panels were manufactured introducing marine bio-fillers as secondary reinforcements in a wood–polypropylene particulate blend, from 100% waste resources. The particulate panels were subject to tensile test for mechanical characterization. Based on these results, some of the necessary parameters for finite element simulation has defined empirically and a finite element model was developed utilizing ANSYS software, performing a simulation series. Post-processing of the simulation results was carried out to predict the deformation behavior of the material during the three-point bending test. To validate this technique of material definition, the simulated static bending test results were verified with factual physical tests, and both techniques were well in accordance with each other. This simulation method demonstrated reliable feedback on the behavior of materials for the development of innovative complex materials. Therefore, the time invested, materials used and experimental procedures can be significantly reduced, having significant economic benefits for research and industrial projects.

Resveratrol and puerarin on peak bone mass in young rats

To compare effects of resveratrol, puerarin and the compounds on peak bone mass in rats. Forty SPF Wistar rats weighed 109.45 g to 119.44 g with an average of 115.87 g were selected. After 3 days' adaption, rats were divided into control group (the same volume of distilled water per day), puerarin group(15.4 mg/kg puerarin daily), resveratrol group (8.4 mg/kg resveratrol daily), compound drug group (daily dose of 8.4 resveratrol added 15.4 mg/kg of puerarin) and 10 in each group. The body weight of the rats was monitored at every 7 days and body bone density was measured at every month. All rats were sacrificed after 3 months. The bone mineral density of femur and vertebrae was detected by dual energy X-ray absorptiometry; bone biomechanics, VG staining was used to analyze bone histomorphometry;ELISA was used to detect serum bone metabolic index and microstructure of femur were scanned with Micro-CT scanner. There were no significant differences in body weight among groups during exoeriment. Bone mineral density results showed BMD of femur and vertebrae in the other three groups were significantly increased, and R+P group was significantly higher than PR group and RES group(P<0.05) by compared with CON group;three-point bending and compression test results showed compared with CON group, other three groups of femoral and vertebral maximum load values were significantly increased, and P+R group was higher than PR group and RES group, but elastic modulus was not statistically significant. Bone histomorphometry showed that number of trabecular bone in other three groups were significantly increased compared with CON group, separation of trabecular bone were significantly reduced, continuity was improved, and R+P group was significantly better than RES and PR group. The results of Micro-CT scan showed that separation of trabecular bone were significantly reduced, continuity were improved in other three groups, and R+P group was significantly better than RES and PR group. The numbers of trabecular bone (Tb.N), trabecular bone thickness (Tb.Th), volume of trabecular bone (BV/TV) in PR group, RES group and R+P group were significantly higher than CON group, but trabecular bone separation (Tb.Sp) was significantly reduced. Serum levels results showed, level of OC in the other three groups were higher than control group(P<0.05), content of TRACP 5b decreased, and level of OC in P+R group was significantly higher than PR group and RES group, content of TRACP 5b was no significant change. Compound of puerarin and resveratrol assigned in a 1:1 ratio could improve bone mineral density and bone mass in young rats, enhance biomechanical properties of bone, promote mineralization and maturation of osteoblasts, inhibit osteoblastic bone resorption, and is better than the role of their respective monomers. The paper showed that traditional Chinese medicine compound medicine will be used as a new way to prevent and treat osteoporosis.

Effects of post-weld heat treatment on the microstructural evolution and mechanical properties of dissimilar friction stir welded AA6061+SiCp/AA6061-O joint

Abstract A research on the microstructure and mechanical properties of the dissimilar joint was carried out so as to understand the effects of post-weld heat treatment (PWHT) on microstructural evolution, microhardness, tensile and flexural properties of the dissimilar friction stir welded (FSWed) joint. The results showed that there is a sufficient and rather complicated material mixing in the nugget zone (NZ). After PWHT, the grains in the joint area except for the NZ demonstrated a grain refinement with more homogeneous and equiaxed grains. Fine and clustered SiC particles in the NZ are confirmed by scanning electron microscope (SEM). In addition, the microhardness values of nugget zones both in as-welded and PWHT condition exhibited a higher Vickers compared to that of AA6061-O. Furthermore, a mean tensile strength of 183.30 MPa that demonstrates a 52.22% increase in tensile strength is also observed in the transverse tensile tests subsequent to PWHT. Considering the three-point bending test results, it is explicit that an increase of 121.96% in the bending extension is obtained as there is no significant increase in maximum bending force after the PWHT.

3D printing of materials with spatially non-linearly varying properties

Functionally graded materials (FGMs) with spatially varying material properties in 3D space are highly desired for a wide range of applications. Although FGMs are ubiquitous in biological materials, the fabrication of FGMs with continuous non-linear spatial variation of material properties remains a great challenge. Here we present a self-developed extrusion-based additive manufacturing system capable of fabricating FGMs with sophisticated material property distributions. The workflow involves property function modeling, gray-scale representation and control codes generation, digital material feeding and active multi-material mixing. The effectiveness of the technology is demonstrated by the successful printing of a diverse range of objects with complex spatial variations in color and Al2O3 concentration. In addition, by controlling the dynamic change of the different components during reactive 3D printing process, we can fabricate polyurethane (PU) objects with various gradient patterns in material mechanical properties. The results of the cantilever bending test and simulation show that the material gradient can effectively relieve the stress concentration. The proposed gradient 3D printing system opens a new avenue for manufacturing FGMs with exquisite material property distributions thus far only accessible by biological materials grown in nature.

Synthesis and characterization of functionally graded nickel‐nickel coated ZrO2 composite coating

AbstractElectroless‐nickel plated ZrO2 (NCZ) particles have been used to produce a functionally graded nickel‐electroless‐nickel plated ZrO2 composite coating. So, electroless‐nickel plated ZrO2 particles concentration was continuously increased from 0 to an optimum value in the electroplating bath (Watt's bath). The substrate was ST37 steel and the thickness of the coating was approximately 50 μm. Also a uniformly distributed nickel‐electroless‐nickel plated ZrO2 composite coating has been manufactured as comparison. The composite coatings were characterized by scanning electron microscopy and energy‐dispersive X‐ray spectroscopy. Structure and phase composition were identified by X‐ray diffraction analysis. Microhardness of the coatings was evaluated by employing a Vickers instrument. Three‐point bend test was carried out to compare the adhesion strength of the coatings. Dry sliding wear tests were performed using a pin‐on‐disk wear apparatus. The electrochemical behavior of the coatings was studied by electrochemical impedance spectroscopy. The microhardness measurements showed that, with increasing the co‐electrodeposited electroless‐nickel plated ZrO2 particle content in the nickel matrix, the microhardness increases from interface towards the surface of the functionally graded composite coating. Bend, wear and electrochemical test results confirmed that the functionally graded composite coating has higher adhesion, wear resistance and corrosion resistance as compared with the uniformly distributed coating. This has been attributed to lower mechanical mismatch between coating and substrate in functionally graded composite coating with respect to the uniformly distributed one.

Study on the embrittlement of flash annealed Fe85.2B9.5P4Cu0.8Si0.5 metallic glass ribbons

Nanocrystalline Fe-based alloys have excellent soft magnetic properties, but their application is limited due to annealing induced embrittlement. In this work the embrittlement of flash annealed Fe85.2Si0.5B9.5P4Cu0.8 (at.%) ribbons was investigated using two-point bending and tensile tests as well as nanoindentation testing. In addition, fracture surfaces of notched tensile specimens were analyzed in dependence on annealing temperature and correlated to mechanical and structural transitions.The amorphous ribbons have been flash annealed for 10 s at temperatures between 330 °C and 540 °C under an applied tensile stress of 20 MPa. X-ray diffraction and atom probe tomography were used to analyze the phase formation, microstructure and elemental partitioning. The results of two-point bending tests show a sharp transition from ductile to brittle behavior at annealing temperatures between 330 °C and 350 °C. The stress intensity factor is decreasing from 70.4 MPam to 3.2MPam. Thus, embrittlement takes place before the onset of crystallization at 400 °C. This embrittlement is related to a reduced shear band activity as a more localized shear activity during two-point bending. Nanoindentation results suggest a slight increase in the shear transformation zone volume, which could be related to a relaxation of free volume.

Moisture barrier and bending properties of silicon nitride films prepared by roll-to-roll plasma enhanced chemical vapor deposition

In this study, we demonstrated a single-layer silicon nitride (SiNx) film deposited on polyethyleneterephthalate substrate as a moisture permeation barrier film that reduced the water vapor transmission rate (WVTR). The SiNx film was fabricated by roll-to-roll, plasma-enhanced chemical vapor deposition (R2R-PECVD) in widths as large as 500 mm. The effects of the NH3/SiH4 flow ratio on the SiNx properties were investigated according to their refractive index, optical characteristics, film density, WVTR, and chemical composition. The durability of the flexibility of the SiNx film was investigated via outer/inner bending test and cyclic bending fatigue test. The SiNx film showed excellent thickness uniformity and optical properties. At the NH3/SiH4 flow ratio of 3, the SiNx film exhibited the highest film density and the best moisture barrier performances of 1.67 × 10−3 g/m2·day. The results of the inner bending test showed that the flexibility of the SiNx film was excellent. The test results showed that the failure bending radius was 2 mm. The durable flexibility of the SiNx film was influenced by the internal residual stress and microstructure. After 10,000 cyclic inner-bending fatigue tests, no crack was observed, and the WVTR values were maintained below 2.0 × 10−3 g/m2·day. These results indicate that the single-layer SiNx film fabricated with a simple R2R PECVD has a high potential as a moisture barrier film for future flexible electronic applications.

A review of EBSD: from rudimentary on line orientation measurements to high resolution elastic strain measurements over the past 30 years.

Considering that the Electron Back Scatter Diffraction technique, EBSD, features in more than 60% of the papers published in the current conference proceedings, this review concentrates on the most recent development in the last ten years, that is, High Resolution EBSD. An outline of the theory is presented and four-point bend test results are shown proving the sensitivity of the technique for measuring elastic strain is 1 part in 10000. Other examples of its use included here are strains surrounding indents in silicon, mapping the stress concentration at grain boundaries ahead of dislocation pile ups and dislocation generation at grain boundaries due to strain ahead of nano indentations. An application is presented to distinguish the c axis direction in slightly tetragonal PZT crystals and developments in obtaining absolute strain measurement as opposed to the relative strain measurement currently the norm are discussed.

Experimental study on the flexural behaviour of notched steel beams strengthened by prestressed CFRP plate with an end plate anchorage system

Strengthening deficient steel structures using prestressed bonded Carbon Fibre Reinforced Polymer (CFRP) plate could be a promising technology, but has not been well developed yet due to the lack of a proper CFRP prestressing device. In this study, notched steel beams strengthened with prestressed CFRP plate with end anchorage systems were designed and experimentally studied. The prestress loss and flexural behaviour of the strengthened steel beams were investigated. With the aid of strain gauges and Fibre Bragg Grating (FBG) sensors, the prestress loss in specimens with prestress levels of 20% and 40% were monitored during tensioning, release and a mid-long period after release. There is almost no prestress loss for specimens after 30 days of release, which indicates that the end anchorage system can effectively impede prestress loss. From the four-point bending test results, the bearing capacity and utilization ratio of the CFRP plate, effect of prestress on the flexural performance and failure modes were discussed. The prestressed strengthening can improve the bearing capacity and ductility of deficient steel beams, and increases the utilizationrate of CFRP plate, while the enhancement of the stiffness is not obvious. Additionally, the bearing capacity of the specimens and utilization rate of the CFRP increase with the prestress level. More importantly, the prestressed strengthening can delay debonding propagation of the strengthened beams, preventing premature failure.

Flexible transparent conductive film based on silver nanowires and reduced graphene oxide

Silver nanowires (AgNWs) with diameter of 90—150 nm and length of 20—50 μm were successfully synthesized by a polyol process. Graphene oxide (GO) was prepared by Hummers method, and was reduced with strong hydrazine hydrate at room temperature. The flexible transparent conductive films (TCFs) were fabricated using the mixed cellulose eater (MCE) as matrix and AgNWs and reduced graphene oxide (rGO) as conductive fillers by the improved vacuum filtration process. Then, the optical, electrical and mechanical properties of the AgNWs-rGO films were investigated. The results show that for the AgNWs-rGO film produced with the deposition densities of AgNWs and rGO as 110 mg·m-2 and 55 mg·m-2, the optical transmission at 550 nm is 88.4% with Rs around 891 Ω·sq-1, whereas the optical transmission for the AgNWs-rGO film with deposition densities of AgNWs and rGO of 385 mg·m-2 and 55 mg·m-2 is 79.0% at 550 nm with Rs around 9.6 Ω·sq-1. There is little overt increase in Rs of the AgNWS-rGO film after tape tests for 200 times. The bending test results indicate that the change in Rs of AgNWs-MCE film is less than 2% even after 200 cycles of compressive or tensile bending. The excellent mechanical properties of the AgNWs-rGO film can be attributed to the burying of AgNWs and rGO at the surface of MCE.

54‐2: Flexible a‐IGZO TFT for Large Sized OLED TV

Flexible a‐IGZO TFTs have been developed on transparent PI substrate with multi‐buffer for large sized OLED TV. It was carefully considered and designed to meet the electrical properties of oxide TFTs and specific needs for flexible display. We achieved high performance of device on PI substrate, which shows 0.34 V of threshold voltage, 10.25 cm2/Vs of field effect mobility, and 0.22 V/dec of sub‐threshold swing on average. The electrical and mechanical reliability of PI‐based oxide TFTs were verified by the results of Bias Temperature Stability (BTS) and bending test, showing no significant device degradation. This work should contribute to commercialize large sized flexible OLED TV.

Evaluation of a highly-modified asphalt binder for field performance

This paper deals with laboratory and field evaluation of pure and polymer-modified asphalts (PMAs), in which one bitumen and one polymer type of different contents were used. Styrene-butadiene-styrene (SBS) modified asphalts were selected to evaluate which polymer concentration could offer cost-effective solutions on heavily trafficked highways. Polymer concentrations used were 0%, 3%, and 6% SBS by weight of binder. Asphalt cement containing 6% SBS was referred to as a highly-modified binder in this study. An in-service test road was constructed in 2012 to compare the performance of asphalt pavements built with PMAs while all other variables were held constant as possible. The results of laboratory testing indicated that the morphology of SBS modified binders was influenced by storage temperature and polymer content. The formation of an interlocked continuous network was shown to enhance the rheological properties of PMAs. Significant differences in resistance to rutting and cracking were noted between highly-modified and control asphalt mixtures. This observation was attributed to increased modulus and enhanced critical strain energy release rate of polymer-modified asphalt mixtures. Preliminary performance evaluations showed that none of the test sections evaluated exhibited obvious rutting. Notable differences were, however, observed in the cracking behavior. The test section with the highly-modified binder had a much better resistance to cracking. The field measurements on cracking corresponded well with the test results of the semi-circular bend test in the laboratory. The experimental results of the highly-modified asphalt were in good agreement with field performance. Future monitoring is needed to evaluate long-term trends in performance.

Numerical study on the dynamic fracture behavior of 3D heterogeneous rocks using General Particle Dynamics

The General Particle Dynamics code (GPD) is developed to simulate initiation, propagation and coalescence of cracks in 3D brittle rock specimens subjected to dynamic loads. In GPD, fractures of particles are determined through a damage evolution law of brittle rock materials. An elasto-brittle damage model is employed to reflect the initiation and growth of cracks and the macro-failure of brittle rocks. Numerical examples, including pre-notched semi-circular bending and uniaxial compression testing, have been carried out to verify the applicability of GPD to simulate the dynamic failure of rocks. Results of pre-notched semi-circular bend test show that GPD is capable of realistically simulating the mechanical behavior of rock materials subjected to dynamic loads. Under dynamic uniaxial loadings, the dynamic increment factor increases with increasing strain rate. Failure modes of samples pass from tensile to mixed shear-tension mode with increasing the loading speed. The number of fractions of sample increases with increasing the loading speed. Moreover, the failure mode of samples pass from a typical splitting failure to a mixed mode failure with decreasing heterogeneity coefficient while the number of cracks and fractions increases with decreasing the heterogeneity coefficient. The numerical results obtained from GPD are in excellent agreement with experiments and other numerical methods.

Numerical analysis of reinforced concrete structures with oriented steel fibers and re-bars

In this study, a new strength and stiffness numerical analysis approach of fiber reinforced concrete with oriented fibers and re-bars is proposed. The model is based on discrete lattice simulation that is obtained from standard tetrahedron mesh. Area of cross section of lattice members is obtained by homogenization of each tetrahedron finite element. A non-linear material constitutive model that takes into account fiber orientation, concrete damage and plasticity of re-bars is proposed. Re-bars are embedded in fiber concrete lattice by using a special joint elements that are consistent with re-bar’s surface pattern. The numerical model is validated by using four-point bending test results of high performance fiber concrete with oriented fibers. Moreover, the model showed a good agreement with re-bar pull-out test results for ultra-high performance concrete with oriented fibers. The proposed model is used to analyze a ribbed concrete panel with oriented fibers and best optimal fiber orientation for three-point bending is proposed.

COMPARISON OF RESPONSE SURFACE METHODOLOGY (RSM) AND ARTIFICIAL NEURAL NETWORKS (ANN) TOWARDS EFFICIENT OPTIMIZATION OF FLEXURAL PROPERTIES OF GYPSUM-BONDED FIBERBOARDS

ABSTRACT In this study, the hydration behavior of gypsum paste mixed with bagasse and kenaf fibers as lignocellulosic material and fiberglass as inorganic material is evaluated. Moreover, the properties of gypsum-bonded fiberboard (GBFB) are examined using bagasse fibers (Saccharum officinarum.L), kenaf fibers (Hibiscus cannabinus.L) and industrial fiberglass. The weight ratios of fiberglass (at three levels 0, 3 and 6%), bagasse fiber (at three levels 0, 7.5 and 15%) and kenaf fiber (at three levels 0, 7.5 and 15%) to gypsum are used to make the gypsum-bonded fiberboard with the nominal density 1.10 g.cm-3 . After preparing the fiberboard, its flexural properties were examined. Response surface methodology (RSM) and artificial neural network (ANN) were used to model the bending strength of gypsum-bonded fiberboard. According to the hydration tests, it was determined that as the extractives in the lignocellulosic materials increased, the temperature of the mixture decreased and its setting time increased. According to the bending test results, it was determined that there is an ideal consistency between the predicted values and the observed data, so that as bagasse and kenaf fiber increased, the modulus of rupture (MOR) increased. Maximum MOR of panel was predicted to be 10.81 MPa and 11MPa by RSM and ANN at optimum condition. Based on the statistical analysis, the training and validation data sets of the studied models were compared by the coefficient of determination (R2), root mean squares error (RMSE) and mean absolute error (MAE). ANN model showed a much more accurate prediction than RSM in terms of the values R2, RMSE and MAE.

General shell section properties and failure model for cross-laminated timber obtained by numerical homogenization

In this study homogenized mechanical properties are derived for structural finite element analysis of cross-laminated timber (CLT) discretized by means of shell elements. In the first step, based on the results of experimental three-point bending tests on a CLT slab component, a numerical optimization procedure is applied to identify the elastic and plastic properties of the individual spruce wood laminates, considering orthotropic elasticity and Hill’s yield criterion. Taking into account its periodic structure, a repeating unit cell (RUC) of the CLT is defined in the subsequent step. To this RUC specific loading conditions are imposed successively, yielding the entries of the homogenized elastic stiffness matrix of a general shell section. Extending the RUC simulations into the inelastic domain of deformation results in a homogenized failure surface on the structural scale, which is implemented as a postprocessing variable in a commercial finite element program. Throughout all analyses, in sensitivity studies the most decisive material properties are identified. Results of comparative simulations on a homogenized structural model and an elaborate full three-dimensional finite element model of a point-supported CLT slab show the accuracy and efficiency of the proposed approach based on homogenized mechanical properties.

An alternative analysis of indirect tensile test results for evaluating fatigue characteristics of asphalt mixes

Fatigue cracking is one of the major distresses responsible for the failure of asphalt pavements. The widely-accepted Superpave® volumetric mix design method does not consider screening the asphalt mixes based on their fatigue resistance. Based on a survey conducted in this study, it was found that many state Departments of Transportations (DOTs) do not perform a fatigue test during mix design, mainly due to lack of specialized equipment, trained personnel and consensus about the most appropriate test method. This present study was undertaken to suggest a simple, quick and effective fatigue test method and the corresponding data analysis procedure. It was found that the indirect tension test, which is usually conducted in the DOTs on a regular basis, can be used to characterize the fatigue resistance of asphalt mixes as well. A simplified data analysis approach has been proposed. The fatigue resistance of asphalt mixes can be determined by using a newly derived parameter called Fatigue Index (fi). Fatigue resistance of five different asphalt mixes were evaluated using this new parameter, fi. It was found that the fi parameter were able to statistically discriminate five selected asphalt mixes with respect to their fatigue resistance. The effectiveness of the fi parameter was verified by investigating its correlations with the results of the semi-circular bend and four-point beam fatigue test results.

Mixed-mode I/II interlaminar fracture toughness of carbon fiber/epoxy composites with the addition of multiwalled carbon nanotubes by spraying technique

This work reports the effect of multiwalled carbon nanotubes on mixed-mode I/II interlaminar fracture toughness ([Formula: see text]) of unidirectional carbon fiber/epoxy composite laminates made by prepregs. The carbon fiber/epoxy laminates were fabricated in an autoclave with a previous deposition of different multiwalled carbon nanotube contents at their middle plane interface by spraying technique. Mixed-mode bending tests were conducted on carbon fiber/epoxy laminate specimens under different mixed-mode ratios. The results of mixed-mode bending tests showed that the addition of multiwalled carbon nanotubes can effectively improve the [Formula: see text] of carbon fiber/epoxy laminates. With a 0.2 wt.% multiwalled carbon nanotubes content in carbon fiber/epoxy laminates, the [Formula: see text] under mixed-mode ratios of 0.2, 0.5 and 0.8 increased by 25%, 12% and 19%, respectively. These results were explained in terms of the damage mechanisms observed at the fracture surfaces of tested specimens by scanning electron microscopy.

Gradient Elastic–Plastic Properties of Expanded Austenite Layer in 316L Stainless Steel

The gradient mechanical properties, variation of stress with strain and surface cracking behavior of expanded austenite developed on 316L austenitic stainless steel were investigated by nanoindentation tests, X-ray residual stress analysis and scanning electron microscope observation in four-point bending tests. The results show that the plastic properties of the carburizing layer including true initial yield strengths and strain hardening exponents increase significantly from substrate to surface, while the true elastic modulus just improves slightly. Due to the onset of plastic flow, the residual stresses are almost equivalent to the true initial yield strengths from surface to the depth of ~ 10 μm. The results of four-point bending tests show that surface stress increases linearly with the increase in strain until the strain reaches ~ 1.0%, after that the plastic yield happens. The expanded austenite surface layer is brittle, and the cracks will be created at the strain of ~ 1.4%. The cracking stress is about ~ 2.4 GPa.