Ti Grade Research Articles

Grain refinement effect on fatigue life of two grades of commercially pure titanium

The fatigue life and fatigue limit of commercially pure Ti grade 2 and 4 in coarse-grained and ultrafine-grained states were experimentally determined. Ultrafine structures were prepared by Conform severe plastic deformation method and by conventional Equal channel angular pressing, respectively. The differences in the improvement of fatigue life and the influence of both procedures on the fatigue limit based on 107 cycles to fracture are discussed in terms of grain refinement, microstructure, differences in fatigue damage mechanism and influence of surface roughness on the initiation of fatigue cracks. Improvement in fatigue life was observed for both materials, however, the improvement of the fatigue limit was found only for Ti grade 2.

A New Method of Predicting the Parameters of the Rotational Friction Welding Process Based on the Determination of the Frictional Heat Transfer in Ti Grade 2/AA 5005 Joints.

The article presents an original approach to determining the basic parameters of rotational friction welding (RFW) based on the analysis of friction heat transfer at the faying surfaces. Dissimilar Ti Grade 2/AA 5005 joints were used to demonstrate the method. The work established that for the analyzed joint, the optimum temperature at the faying surface that allow for a good quality weld to be obtained should be ~505 °C. On this basis, a map of optimal parameters was developed to achieve this temperature. This approach could potentially allow for more precise control of the welding process, leading to better joint quality and performance. The paper includes both a description of the technological process of friction welding and an attempt to explain the mechanism of the phenomena occurring in the welding area. The numerical calculations presented in the article were carried out using the ADINA System v. 9.8.2, which allows for the consideration of heat friction in the axial symmetric thermo-mechanical model. Frictional resistance was determined by the temperature-dependent friction coefficient. The assumed thermo-mechanical model required the determination of elastic-plastic properties versus temperature for the analyzed materials. The simulations of the friction welding were carried out for the different welding parameters and time. The different variants of friction welding were modelled.

Effect of Enterococcus faecalis Biofilm on Corrosion Kinetics in Titanium Grade 4 Alloys with Different Surface Treatments.

E. faecalis has been associated with bacteremia, sepsis, and bacterial endocarditis and peri-implantitis. This microorganism can remain in the alveolus even after extraction of the root remnant. This study aimed to evaluate the corrosion on different surfaces of commercially pure titanium (Ti) grade 4 (Ticp-G4) as a function of the bacterial biofilm effect of Enterococcus faecalis. A total of 57 discs were randomly divided according to their surface finish (n = 19). For microbiological analysis (n = 9), the discs were placed in 12-well plates containing E. faecalis culture and incubated at 37 °C for 7 days. The results show that for the intergroup analysis, considering the "electrolyte" factor, there was a difference between the groups. There was greater biofilm formation for the D.A.Zir group, with greater electrochemical exchange for Biofilm, and the presence of biofilm favored greater electrochemical exchange with the medium.

Surface treatment of Ti and Ti composites using concentrating solar power and laser

Titanium and its composites are widely used in implants of bones and teeth. Besides mechanical properties also surface characteristics are very important in these biomaterials. Very important are properties such as surface topography, roughness, chemistry, and surface energy, wettability, and Ti oxides or Ti nitride layers thickness. The concentrated solar power was used successfully to nitride Ti Grade 2 and powder metallurgical Ti prepared from hydrogenated dehydrogenated Ti powder. The nitriding experiments were performed under nitrogen atmosphere at different temperatures and time in SF40 (40kW horizontal solar furnace) at PSA, Spain. Concentrated solar energy has been shown to be an economical alternative to conventional gas nitriding techniques in electric furnaces, CVD, PVD, plasma nitriding, or laser treatments. It has been observed that the solar process represents a significant reduction of the heating time to several minutes (up to 5 minutes at temperature range 500-1000 °C), a clean and non-polluting high-temperature process. The formation of continuous and homogeneous surface layers of TiN, Ti2N and their mixture according to the nitriding temperature was investigated using X-ray diffraction and electron microscopy. Laser surface treatment is of great significance in modifying surface morphology and surface and near-surface region microstructures. Effects of lase treatment parameters on machined surface morphology, surface roughness and chemistry are analyzed in this study and discussed from the point of view of application in dental implantology. The current advances of our research group in application of laser-treated powder metallurgy prepared Ti-based materials are analyzed and discussed.

Tailoring Ti Grade 2 and TNTZ alloy surfaces in a two-step mechanical–chemical modification

ABSTRACT The aim of this work was to improve the surface properties of cp-Ti Grade 2 and β-Ti alloy TNTZ (Ti-29Nb-13Ta-4.6Zr) for biomedical applications. A hybrid surface treatment consisting of shot peening and chemical etching was conducted. Subsequently, the physicochemical properties and topography of the modified surfaces were analysed. Microhardness measurements of the shot-peened samples revealed a great increase in the surface hardness to the similar level as can be achieved for the ultrafine-grained and nanostructured materials. Roughness tests and microscopic observations showed significant topographical differences, depending on the material and modification process involved. Moreover, in this paper we demonstrate the influence of the substrate and treatments on the wettability. Obtained results confirmed that designed hybrid modification of Ti Grade 2 and TNTZ has significant potential for biomedical applications.

High Adherence of Oral Streptococcus to Polylactic Acid Might Explain Implant Infections Associated with PLA Mesh Implantation.

The aim of this study was to evaluate and compare the biofilm formation properties of common pathogens associated with implant-related infections on two different implant material types. Bacterial strains tested in this study were Staphylococcus aureus, Streptococcus mutans, Enterococcus faecalis, and Escherichia coli. Implant materials tested and compared were PLA Resorb × polymer of Poly DL-lactide (PDLLA) comprising 50% poly-L-lactic acid and 50% poly-D-lactic acid) and Ti grade 2 (tooled with a Planmeca CAD-CAM milling device). Biofilm assays were done with and without saliva treatment to evaluate the effect of saliva on bacterial adhesion and to mimic the intraoral and extraoral surgical routes of implant placement, respectively. Five specimens of each implant type were tested for each bacterial strain. Autoclaved material specimens were first treated with 1:1 saliva-PBS solution for 30 min, followed by washing of specimens and the addition of bacterial suspension. Specimens with bacterial suspension were incubated for 24 h at 37 °C for biofilm formation. After 24 h, non-adhered bacteria were removed, and specimens were washed, followed by removal and calculation of adhered bacterial biofilm. S. aureus and E. faecalis showed more attachment to Ti grade 2, whereas S. mutans showed higher adherence to PLA in a statistically significant manner. The salivary coating of specimens enhanced the bacterial attachment by all the bacterial strains tested. In conclusion, both implant materials showed significant levels of bacterial adhesion, but saliva treatment played a vital role in bacterial attachment, therefore, saliva contamination of the implant materials should be minimized and considered when placing implant materials inside the body.

Effect of Laser Treatment on Intrinsic Mechanical Stresses in Titanium and Some of Its Alloys

Laser surface treatment conducted at different power levels is an option to modify titanium bone implants to produce nano- and microtopography. However, such processing can lead to excess mechanical stress within the surface layer. This research aims to calculate the level of such residual stresses after the surface processing of Ti grade IV, Ti15Mo, and Ti6Al7Nb alloys with an Nd:YAG laser. Light and scanning electron microscopies (SEM), energy-dispersive X-ray spectroscopy (EDS), X-ray diffractometry (XRD), optical profilography, and nano-indentation tests were applied to characterize the surface zone. The laser processing resulted in a distinct surface pattern and the formation of remelted zones 66–126 µm thick, with roughness values ranging between 0.22 and 1.68 µm. The mechanical properties were weakly dependent on the material composition. The residual stresses caused by the laser treatment were moderate, always tensile, increasing with loading, and was the highest for the Ti15Mo alloy.

Microstructure and properties of AlCr and AlCrFe coatings deposited by magnetron sputtering

In this work, AlCr and AlCrFe coatings were deposited via magnetron sputtering on technical substrates of carbon steel C45 and titanium grade 2. The coatings feature an amorphous structure, a thickness of 3–4 μm, and are uniform in terms of thickness and chemical composition. No major defects were visible at the interface; however, there is no diffusion at the interface, which indicates the adhesive type of bonding and results in relatively low adhesion. The coatings are characterized by a hardness of about 8–10 GPa and a Young modulus above 150 GPa. Both values are slightly higher for steel substrate. The coatings assure good corrosion resistance for steel substrate while underperforming those of Ti grade 2.

The influence of microstructure and texture on the hardening by annealing effect in cold-rolled titanium

The purpose of this study was to compare the influence of microstructural and textural changes on the hardening by annealing effect in cold-rolled titanium. Ultrafine-grained (UFG) Ti Grade 2 was produced by multi-pass cold rolling (or warm rolling at 400 °C at the final stage) to different thickness reductions (90%, 95% and 97%) aimed at varying both the microstructural features of the material (dislocation density, grain size distribution and grain boundary characteristics) and its texture (the intensity and volume fraction of texture components). The hardening effect of UFG Ti Grade 2 sheets was obtained by a short-time annealing at 250 °C for 15 min. The highest strengthening, of about 4–5%, was observed for the UFG Ti Grade 2 sheet rolled to 90%; the strengthening gradually decreased for higher thickness reductions (down to ∼ 2% for 97%). The texture intensity and volume fractions of texture components for the annealed UFG Ti Grade 2 sheets were very close to their as-rolled counterparts, so this did not demonstrate any clear reason for the hardening effect. Instead, the dislocation substructure recovered during annealing at 250 °C, i.e. the dislocation density declined significantly, the remaining dislocations became rearranged, and it was easier to differentiate more nanosized subgrains of about 50–150 nm. The hardening by annealing effect was a result of the annihilation of mobile dislocations and the ordering of the dislocation substructure, mostly within coarse grains (>500 nm). The level of strengthening by low-temperature annealing was mainly affected by the fraction of coarse grains with a tangled-dislocation substructure in the as-rolled state, i.e. a higher fraction of coarse grains favored more pronounced strengthening. These observations seem to be very promising for optimizing the cold rolling process and short-time annealing of the UFG Ti Grade 2 sheets, which could be a simple and cost-effective way of enhancing their mechanical properties.

Numerical Simulation of Temperature Fields during Laser Welding-Brazing of Al/Ti Plates.

The formation of dissimilar weld joints, including Al/Ti joints, is an area of research supported by the need for weight reduction and corrosion resistance in automotive, aircraft, aeronautic, and other industries. Depending on the cooling rates and chemical composition, rapid solidification of Al/Ti alloys during laser welding can lead to the development of different metastable phases and the formation of brittle intermetallic compounds (IMCs). The effort to successfully join aluminum to titanium alloys is associated with demands to minimize the thickness of brittle IMC zones by selecting appropriate welding parameters or applying suitable filler materials. The paper is focused on the numerical simulation of the laser welding-brazing of 2.0 mm thick titanium Grade 2 and EN AW5083 aluminum alloy plates using 5087 aluminum filler wire. The developed simulation model was used to study the impact of laser welding-brazing parameters (laser power, welding speed, and laser beam offset) on the transient temperature fields and weld-pool characteristics. The results of numerical simulations were compared with temperatures measured during the laser welding-brazing of Al/Ti plates using a TruDisk 4002 disk laser, and macrostructural and microstructural analyses, and weld tensile strength measurements, were conducted. The ultimate tensile strength (UTS) of welded-brazed joints increases with an increase in the laser beam offset to the Al side and with an increase in welding speed. The highest UTS values at the level of 220 MPa and 245 MPa were measured for joints produced at a laser power of 1.8 kW along with a welding speed of 30 mm·s-1 and a laser beam offset of 300 μm and 460 μm, respectively. When increasing the laser power to 2 kW, the UTS decreased. The results exhibited that the tensile strength of Al/Ti welded-brazed joints was dependent, regardless of the welding parameters, on the amount of melted Ti Grade 2, which, during rapid solidification, determines the thickness and morphology of the IMC layer. A simple formula was proposed to predict the tensile strength of welded-brazed joints using the computed cross-sectional Ti weld metal area.

Thermal Stability and Mechanical Behavior of Ultrafine-Grained Titanium with Different Impurity Content

Ultrafine-grained (UFG) commercially pure (Ti Grade 2) and high-purity (Ti 99.99%) titanium can be a good alternative to less biocompatible Ti alloys in many biomedical applications. Their severe plastic deformation may lead to a substantial increase of strength, but their highly refined microstructure show a lower thermal stability which may limit their range of applications. The purpose of this study was to investigate the effect of interstitial elements on the thermal stability of UFG Ti Grade 2 and high-purity Ti 99.99% processed by a multi-pass cold rolling to the total thickness reduction of 90%. The severely cold rolled Ti sheets were annealed at temperature in the range of 100-600 °C for 1 h and, subsequently, they were evaluated in terms of microstructure stability, mechanical performance as well as heat effects measured by differential scanning calorimetry (DSC). It was found that the microstructure and mechanical properties were relatively stable up to 200 and 400 °C in the case of UFG Ti 99.99% and Ti Grade 2, respectively. DSC measurements confirmed the aforementioned results about lower temperature of recovery and recrystallization processes in the high-purity titanium. Surprisingly, the discontinuous yielding phenomenon occurred in both investigated materials after annealing above their thermal stability range, which was further discussed based on their microstructural characteristics. Additionally, the so-called hardening by annealing effect was observed within their thermal stability range (i.e., at 100-400 °C for UFG Ti Grade 2 and 100 °C for UFG Ti 99.99%).

Tool wear and surface roughness evaluation of mill insert tools in high-speed machining of Ti-6Al-4 V

The experiment carried out using high-speed machining (HSM) in this study is primarily focused on producing high-quality products and lowering the cost of production. To increase tool life and surface quality, HSM is a metal cutting method that priorities quick speeds and feed rates. Determining the appropriate machining and cutting settings that can produce the best results in terms of tool performance and surface qualities becomes essential in this way. Experiments using the L9 orthogonal array were conducted to determine the ideal responses for the Ti grade −5 alloy using a variety of variables, including cutting speed, feed rate, depth of cut, and stepover. By machining at a fast speed, the ultimate goal is to provide a superior surface finish and lengthen the tool life. According to the results of the machining, the cutting speed and stepover have a significant impact on the machining outcome. The optimal value of surface roughness Ra = 0.51 m is achieved with the following parameters: speed = 450 m/min, feed rate = 2100 mm/min, depth of cut = 0.3 mm, and stepover = 60 %. Confirmatory tests with a value of less than 10 % have verified the results. The conclusion being drawn that it is in strong agreement with the experimental results. The findings of this research reveal that the Taguchi technique is capable of analysing the advanced features of boundaries in HSM. This demonstrates the validity of the Taguchi methodology as a specialized model for addressing the issue of high-speed machining settings for titanium grade 5 alloy.

Synthesis of Hard Layer by Titanium Addition During Welding Process and Quenched Directly

Enhance the surface hardness of materials usually conducted through a hardfacing technique. Hardfacing is popular, whereby materials with better properties are deposited over cheaper bulk material. This work fabricated hard layers by adding titanium (Ti) wire during the welding process. This research used low-carbon steel as the base material, wire optime Ti grade 1 for Ti addition, and an HV 600 electrode with a diameter of 3.2 mm for filler metal. A single-layer weld was conducted with SMAW (positive polarity and 90 A). The samples were directly quenched in a different solution after welding. The properties of the weld layer were examined phase, structure, microstructure, macrostructure, and hardness using optical emission spectroscopy (OES), x-ray diffraction (XRD), an optical microscope, a digital camera, and a hardness device, respectively. Adding titanium (Ti) to the weld layer and quenching the samples after welding in the solution enhances the hardness. This phenomenon is attributed to different phase compositions, oxides, and microstructures. A fine dispersion of small particles and oxide amount is important in increasing hardness. There is no cracking in the weld and base metal. In conclusion, samples BNTiO and BNTiM are recommended for lathe-cutting tools.

DEVELOPMENT OF AN EXPERIMENTAL TECHNIQUE FOR THE ESTIMATION OF FATIGUE CRACK EVOLUTION IN TITANIUM ALLOYS BASED ON AN ENERGY APPROACH

This paper presents an experimental study of energy dissipation caused by fatigue crack growth in titanium alloys Ti Grade 2, Ti-1.1Al-0.9Mn, and Ti-4.6Al-1.77V using an original heat flux measurement technique. It is shown that significant structural changes occur in the material under plastic deformation, leading to internal energy evolution. As is known, a large part of the deformation energy is dissipated as heat. The developed experimental technique allows high-accuracy measurements of the heat flux caused by plastic zone development at the crack tip directly in the fatigue experiment. Simultaneous measurements of the crack length and displacements in the stress concentration zone allow estimating the energy balance of the tested specimens. Analysis of the obtained data confirms that the stored strain energy reflecting the structural state of the material can be used as a fracture criterion. A kinetic equation is derived for predicting the fatigue crack growth rate in the Paris regime by energy dissipation rate on the basis of heat flux data.

Atomic–scale investigations of passive film formation on Ti-Nb alloys

This study extensively investigates the passive film formation mechanisms on Ti-xNb alloys by using several electrochemical techniques, including electrochemical impedance spectroscopy (EIS) before and after potentiostatic polarization at the passive zone, and Mott-Schottky (MS) measurements in 9 g/l NaCl electrolyte at 37 °C, together with X-ray photoelectron spectroscopy (XPS) and transmission electron microscopy (TEM) analysis. Overall, the Ti40Nb presented lower corrosion resistance due to a thinner passive film as compared to commercial pure Ti (grade 2) and Ti12Nb. The passive film formed on Ti12Nb and Ti40Nb alloys at a steady-state condition (+0.5 VAg/AgCl for 60 min) is composed of amorphous phases of TiO, Ti2O3, TiO2, Nb2O5, and crystalline phases of TiO2 (anatase) and Nb2O5.

Innovative application of two-stage sulfuric acid leaching for efficient recovery of Ti from titanium-bearing electric furnace slag

A two-stage sulfuric acid leaching process was developed to efficiently recover Ti from a titanium-bearing electric furnace slag (TEFS) made from V-Ti magnetite, which has a high content of impurities and low Ti content. The efficiency of the recovery mechanism was investigated. Anosovite and gangue minerals in the TEFS reacted with sulfuric acid and generated several solid substances such as TiOSO4, CaSO4, sulfates of Mg and Al, and silicate in the first-stage of the acidolysis, which formed the product layer and hindered the diffusion of sulfuric acid. Moreover, a high content of the impurities caused the gangue minerals to closely wrap around the anosovite, which hindered the acidolysis. By adopting a two-stage acid-leaching process, soluble sulfates, which are the most abundant product of acidolysis, were dissolved in water during the first-stage of the water leaching, which exposed the unreacted anosovite, diopside, and spinel. Accordingly, sulfuric acid completely reacted with the unreacted minerals during the second-stage acidolysis. The Si- and Ca-containing products of the acidolysis mainly existed in the form of silicate and CaSO4 and were later converted to silica gel and gypsum, respectively, after the second-stage water leaching. With this innovative process, the leaching rate of Ti improved significantly, achieving a 99.33% total leaching rate. Moreover, lowering the initial sulfuric acid concentration to 48% still yielded a total leaching rate of 98.04%, with the Ti grade of the final residue dropped to 3.14%.

Influence of Neutron Irradiation on Microstructure and Mechanical Properties of Coarse- and Ultrafine-Grained Titanium Grade 2

The influence of neutron irradiation on the microstructure and related mechanical properties of Ti Grade 2 in coarse- and ultrafine-grained conditions was investigated. It was found that mechanical properties of the coarse-grained (CG) state were significantly affected by neutron irradiation. At room temperature (RT), the yield stress increased by more than 30%, whereas the ductility decreased by more than 50%. An even bigger difference in the mechanical properties between irradiated and non-irradiated states was observed at a temperature of 300 °C. Changes in the mechanical properties can be attributed to the high density of defect clusters/dislocation loops induced by neutron irradiation. On the other hand, the ultrafine-grained (UFG) state is more resistant to radiation damage. The mechanical properties at RT did not change upon neutron radiation, while at a temperature of 300 °C, the yield stress increased only by about 10%. Enhanced radiation resistance of the UFG state can be attributed to the presence of a high density of dislocations and dense network of high-angle grain boundaries, which act as traps for radiation-induced defects and, thus, prevent the accumulation of these defects in the microstructure.

Corrosion mechanism of Ti-6Al-4V morse taper dental implants connected to 316 L stainless steel prosthetic abutment

The aim of this work was to investigate the effect of galvanic coupling between stainless steel AISI 316 L abutment type Morse taper and implant made of ASTM F1108–14 Ti-6Al-4V alloy. The assembly of the two alloys was carried out using mechanical imbrication by means of successive strikes at 0.05 J force onto the abutment inserted in the implant along the centerline. Corrosion attack at the interface of the alloys was evaluated according to the number of strikes used for joining the parts. Corrosion resistance was evaluated for the samples by open circuit potential measurements as function of time and scanning vibrating electrode technique (SVET) and scanning ion selective electrode technique (SIET) in phosphate buffer solution with pH adjusted to 3.0, and into which hydrogen peroxide was added to simulate tissue inflammatory conditions. Samples were evaluated at the cross and longitudinal sections. Results indicated that the number of strikes used in assembling affected corrosion susceptibility. The lowest amount of corrosion products was associated to the highest number of strikes used. The corrosion resistance was related to the characteristics of the crevice between the implant and the abutment. • Galvanic corrosion between Ti grade V dental implants and AISI 316 L prosthetic abutment was investigated. • Localized attack susceptibility increased with the number of strikes to connect the Ti grade V dental implant and the AISI 316 L abutment. • Local electrochemical techniques were very useful in evaluating the corrosion of the coupled dental implant and prosthetic abutment.

Bio-Tribocorrosion of Titanium Dental Implants and Its Toxicological Implications: A Scoping Review.

Bio-tribocorrosion is a phenomenon that combines the essentials of tribology (friction, wear, and lubrication) and corrosion with microbiological processes. Lately, it has gained attention in implant dentistry because dental implants are exposed to wear, friction, and biofilm formation in the corrosive oral environment. They may degrade upon exposure to various microbial, biochemical, and electrochemical factors in the oral cavity. The mechanical movement of the implant components produces friction and wear that facilitates the release of metal ions, promoting adverse oro-systemic reactions. This review describes the bio-tribocorrosion of the titanium (Ti) dental implants in the oral cavity and its toxicological implications. The original research related to the bio-tribo or tribocorrosion of the dental implants was searched in electronic databases like Medline (Pubmed), Embase, Scopus, and Web of Science. About 34 studies included in the review showed that factors like the type of Ti, oral biofilm, acidic pH, fluorides, and micromovements during mastication promote bio-tribocorrosion of the Ti dental implants. Among the various grades of Ti, grade V, i.e., Ti6Al4V alloy, is most susceptible to tribocorrosion. Oral pathogens like Streptococcus mutans and Porphyromonas gingivalis produce acids and lipopolysaccharides (LPS) that cause pitting corrosion and degrade the TiO2. The low pH and high fluoride concentration in saliva hinder passive film formation and promote metal corrosion. The released metal ions promote inflammatory reactions and bone destruction in the surrounding tissues resulting in peri-implantitis, allergies, and hyper-sensitivity reactions. However, further validation of the role of bio-tribocorrosion on the durability of the Ti dental implants and Ti toxicity is warranted through clinical trials.

Finite element analysis of stress-strain state of the deformation zone of a UFG TI Grade 4 workpiece subjected to abrasive-free ultrasonic finishing

An effective approach to increasing the fatigue resistance of metal products is to create compressive residual stresses on the surface of the product using surface plastic deformation (SPD) processing. One of the effective SPD methods is the process of abrasive-free ultrasonic finishing (AFUF). Another well-known approach to improving mechanical properties including fatigue resistance is to create an ultrafinegrained (UFG) structural state in the product. This research focuses on the finite-element study of the stress-strain state of a UFG workpiece subjected to SPD by the AFUF method. Commercially pure Grade 4 titanium in the UFG state obtained by the ECAP-Conform method was chosen as a workpiece material. In the course of the study, the stress-strain state of the deformation zone was analyzed after a single indentation with subsequent unloading under the elastic-plastic scenario. The effect of the indenter oscillation amplitude and its geometry on radial residual stresses including their depth of occurrence, average normal stress and strain intensity was analyzed. It was found that as the indenter radius increases, the strain intensity (e) value decreases. The e parameter distribution has a gradient nature with a decrease in values from the surface to the center of the workpiece. An analysis of simulation results shows that radial residual stresses in the deformation zone are predominantly compressive, and, accordingly, they will increase the fatigue resistance of the finished product. It was established that as the indenter oscillation amplitude increases, the values of compressive radial residual stresses also increase. Their maximum values reach 540 MPa at an amplitude of 75 μm with the depth of these stresses up to 0.3 mm. An increase in the indenter radius, i.e. in fact the contact area, leads to an increase in the magnitude of compressive radial residual stresses with an almost linear behavior.