Authors:
Mohammed Khalil El Kouifat Rabat National School of Mines (ENSMR), BP: 753 Agdal-Rabat, Morocco

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Houcine Zniker Faculty of Sciences, Ibn Tofaïl University, Kenitra, Morocco

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Ikram Feddal Department of Industrial and Civil Sciences and Technologies, Abdelmalek Essadi Tetouan, Morocco

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Bennaceur Ouaki Rabat National School of Mines (ENSMR), BP: 753 Agdal-Rabat, Morocco

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Abstract

Aim

The occlusion of the teeth is affected due to the appearance of micro-cracks resulting from maximum stresses in the contact zones between the wire and the bracket under normal and tangential loading. The objective of this study is to evaluate the surface and volume constraints in the presence of bonding and partial sliding zones on the contact surface between wires and supports. Knowledge of these stress fields will make it possible to better limit the surfaces where most of the micro-cracks occur. Indeed, the evaluation of the stress will facilitate the modelling or application of established micro crack models on this subject, because the initiation of micro-cracks often appears on the contact surface or just below it.

Materials and methods

In this study, the two most common situations of contact between the wire and the bracket were studied; the first corresponds to the situation where the wire is positioned in the center of the support (classic friction), and the second corresponds to the situation where the inclined wire touches the ends of the supports (critical contact angle).The MATHCAD software was used to simulate the damage zones for normal loading in the two cases studied (classic friction, critical contact angle). We proposed a Hertzian loading for the first case and a linear loading for the second case. Also, the effect of the additional load during wire tightening applied by the orthodontist was studied.

Results

The charge concentration is located above the contact zone, of the order of 0.3P0 (pressure per unit of arbitrary normal length), according to Mathcad simulation results. The adhesion zone/micro-slip zone contact generates the largest tangential load, which is directed towards the side experiencing the most stress. We also observed that the stick area shifts towards the recessed side when the additional load is applied. Additionally, comparing the configurations, the critical contact angle resulted in a higher maximum shear stress.

Abstract

Aim

The occlusion of the teeth is affected due to the appearance of micro-cracks resulting from maximum stresses in the contact zones between the wire and the bracket under normal and tangential loading. The objective of this study is to evaluate the surface and volume constraints in the presence of bonding and partial sliding zones on the contact surface between wires and supports. Knowledge of these stress fields will make it possible to better limit the surfaces where most of the micro-cracks occur. Indeed, the evaluation of the stress will facilitate the modelling or application of established micro crack models on this subject, because the initiation of micro-cracks often appears on the contact surface or just below it.

Materials and methods

In this study, the two most common situations of contact between the wire and the bracket were studied; the first corresponds to the situation where the wire is positioned in the center of the support (classic friction), and the second corresponds to the situation where the inclined wire touches the ends of the supports (critical contact angle).The MATHCAD software was used to simulate the damage zones for normal loading in the two cases studied (classic friction, critical contact angle). We proposed a Hertzian loading for the first case and a linear loading for the second case. Also, the effect of the additional load during wire tightening applied by the orthodontist was studied.

Results

The charge concentration is located above the contact zone, of the order of 0.3P0 (pressure per unit of arbitrary normal length), according to Mathcad simulation results. The adhesion zone/micro-slip zone contact generates the largest tangential load, which is directed towards the side experiencing the most stress. We also observed that the stick area shifts towards the recessed side when the additional load is applied. Additionally, comparing the configurations, the critical contact angle resulted in a higher maximum shear stress.

1 Introduction

Malocclusion is the misalignment of teeth, or when the association between the upper and lower dental arches is incorrect. Orthodontics is the discipline that consists in promoting better dental occlusion by correcting the defects of the positioning of the teeth. For this purpose, orthodontics uses wires and orthodontic brackets which are fixed on the external face of the teeth. When the wire is engaged in the slot of the brackets it generates the necessary forces for orthodontic tooth movement [1–4].

During the metallurgical examination of the contact zone between two surfaces, it was often noticed that the morphology of these surfaces mainly depends on the loading mode imposed. Referring to the various (fatigue induced by small deflection) simulation tests [5], it has been noticed that under a given normal load P, the application of cyclic stress generates a certain asymmetry of the facies characterizing the micro-sliding generated on both sides. Thus, if the load is high enough that macro-sliding does not occur, the area located on the side of the eccentric will be more stressed than that located on the embedded side [6, 7]. Under these conditions, the alternating deformation will therefore be weaker if not zero on the side of the embedding, and consequently the micro-sliding can only occur on the side most stressed.

In this context, the roughness of the contact surface has an important effect on a variety of elements such as friction, wear, and other potential failures [8, 9]. For various dental materials, the coefficient of friction in various dental materials varies greatly depending on the surface roughness [10, 11]. A good understanding of this interaction is essential in dental applications because it affects how materials interact as well as their overall performance and durability provides an in-depth explanation of the complex interplay of forces and stresses that compose the behavior of contact zones by carefully examining the different loading directions given to the system.

Different numerical approaches exist in the literature to simulate the behavior of the archwire in contact with the bracket [12–15]. Similar geometries have been recreated in a variety of applications, including seal simulations [15] and coil springs [16]. As a result, Xinwen et al. created a finite element approach for calculating orthodontic force in the entire dentition utilizing a three-dimensional mandible, brackets, and archwire model. The simulation results showed higher accuracy with absolute force differences ranging from 0.5 to 22.7 cN and relative differences ranging from 2.5 to 11. 0%. To investigate support wire and support wire interactions, Jaeger et al. [17] used stainless steel and titanium-molybdenum alloy wires in their three support systems. The contact configurations are obtained by experimental and numerical investigations, they involve transitions that cause large variations in the effective wire stiffness (EWS). EWS is at its lowest when the wire touches one wing and increases by up to 300% when the wire touches two wings on the opposite side. This study improves the basic knowledge and has clinical implications for multi-support-wire contact arrangements.

As a result, in order to evaluate the volume stress and the surface stress in the presence or absence of an additional loading during contact between the cylindrical wire of diameter 0.4572 mm and the square slot bracket of 0.5588 mm, a simulation using Mathcad version 14 was carried out for two imposed normal loads, we have studied two of the most encountered cases of the contact between the wire and the bracket, the first case where the wire is located in the middle of the bracket, and the second case where the inclined wire touches the extremes of the brackets [18]. We have proposed a Hertzian loading for the first case and a linear loading for the second case. Also, we have studied the effect of the additional load during the tightening of wires applied by the orthodontist.

2 Materials and methods

2.1 Materials

We have modelled the contact between a wire with a diameter of 0.4572 mm made of 304L stainless steel in accordance with the ASTM A240 [19] standard and a support with a slot of 0.5588 mm for the two most frequent cases [20]. The simulation of the contact between the orthodontic wire and the bracket is performed using Mathcad 14 software (Fig. 1a and b).

Fig. 1.
Fig. 1.

Classical friction (a) and critical contact angle (b)

Citation: International Review of Applied Sciences and Engineering 2024; 10.1556/1848.2024.00764

Since the wire has a circular section, while the slot is with a rectangular form, we can see a contact between a plane and a cylinder as shown in Fig. 2.

Fig. 2.
Fig. 2.

Contact between wire and bracket (cylinder/plane)

Citation: International Review of Applied Sciences and Engineering 2024; 10.1556/1848.2024.00764

2.2 Methods

2.2.1 Volume stress

The study consists in evaluating the surface stress, volume stress, and more particularly the maximum shear stress, as well as in the presence of an additional tangential load at the level of the contact between the wire and the brackets. For the case of classic friction, the critical contact angle is obtained in a partial slip condition, when the tangential load never exceeds the product of the normal force P by the coefficient of friction (Q < µP) [21]. Note that the preload applied by the orthodontist placing the bracket in contact with the wire is the source of the initial stress.

The contact modelling for the two configurations mentioned above are shown in Fig. 3.

Fig. 3.
Fig. 3.

Modelling of the contact for classical friction (a) and critical contact angle (b)

Citation: International Review of Applied Sciences and Engineering 2024; 10.1556/1848.2024.00764

Equations ((1)(3)) theoretically demonstrated provide a basis for determining the state of stress induced in a body under a given pressure p (x) and for a shear distribution q (x). For an infinitesimal element dξ located on the contact surface, xthe stresses σxx,σyy,τxyandτxymax generated below the contact can be expressed by K.L. Johnson [22].
σxx=2πy(aap(ξ)(xξ)2dξy2[(xξ)2+y2]2+aaq(ξ)(xξ)3dξy[(xξ)2+y2]2)
σyy=2πy(aap(ξ)dξy4[(xξ)2+y2]2+aaq(ξ)(xξ)dξy3[(xξ)2+y2]2)
τxy=2πy(aap(ξ)(xξ)dξy3[(xξ)2+y2]2+aaq(ξ)(xξ)2dξy2[(xξ)2+y2]2)

2.2.2 Surface stress without additional loading

Initially, we recall that in the presence of a micro-sliding zone, the pressure and stress distributions on the surface (Fig. 4) are given by:

Fig. 4.
Fig. 4.

Micro-slip zone (a) and stick zone (b)

Citation: International Review of Applied Sciences and Engineering 2024; 10.1556/1848.2024.00764

  1. -For |x| ≤ a:
p(x)Normalloaddistribution
  1. -For − a ≤ x ≤ a1 and a1 ≤ x ≤ a:
q(x)=q(x)=μp(x)
  1. -For |x| ≤ a1:
q(x)=q(x)+q(x)=μp(x)μa1ap1(x)
Where a1 represents the limit of the stick area and p1(x) is the normal load for the a1 such as:
a1=a1QµP

Q and P respectively represent the tangential force and the normal force applied to the contact.

2.2.3 Formulations of the Surface stress with additional loading

Therefore, by taking as a starting point the model established by D. Nowell and DA Hills [23], one can consider the two-dimensional problem of a simple contact between a cylinder and a half-plane as schematized on Fig. 5a and b.

Fig. 5.
Fig. 5.

Cylinder-half-plane contact whether or not there is additional loading

Citation: International Review of Applied Sciences and Engineering 2024; 10.1556/1848.2024.00764

If, under the effect of the stresses σ1 and σ2 applied on both sides of the contact (Fig. 5b), the limits c1 and c2 of the stick zone have the same value e, these will no longer be symmetrical with respect to the center of the contact and the additional tangential load is given by:
|σ1σ2|=σ0
c1=a1+e
c2=a1+e
Where –a1 and a1 represent the limits of this zone in the absence of the additional loading as shown in Fig. 6).
Fig. 6.
Fig. 6.

Action of a normal and tangential load distributed on an infinite half-plane, case of the Hertzian load

Citation: International Review of Applied Sciences and Engineering 2024; 10.1556/1848.2024.00764

The distribution of the contact pressure on the contact zone is given by:
q(x)For|x|a:
Where p0 is given by:
p0=2Pµa
In this case, the distribution of the shear stresses generated on the contact surface is such that:
q(x)=q(x)=µq(x)Foraxc1andc1xa
q(x)=q(x)+q(x)Forc2xc2
Where q’’(x) is to be determined in this particular case and μ represents the coefficient of friction.
The evaluation of the function q’’(x) is solved by N.I. Muskhelishvilli et al. [24] and is in the following form:
q(x)=(xc2)(c1x)πc2c1(μp0a)ξ(σ04)(ξc2)(c1ξ)(ξx)dξ
And will require the consistency of the integral between c1 and, c2 namely:
c2c1(μp0t/a)(σ0/4)(tc2)(c1t)dt=0
On the other hand, the evaluation of equation (16) is reduced to:
c1+c2=σ0a2µσ0
We are, thereafter, led to establish another equation taking into account the total tangential load applied to the contact imprint (-a, a). Thus, we have:
Q=a+aq(x)dx=μP+C2C1q(x)dx
Q=μPμP(c1c22a)2
Is:c1c2=2a1QμP
From equations (15) and (17) we deduce the formulated result for this proposal by D. Nowell and D.A. Hills, namely:
c1=σ0a4μP0+a1QμP
c2=σ0a4μP0a1QμP
  • The first case: classical friction

In this application we choose the load as a maximum in the middle and it tends towards zero in the edges of the contact, The possible load to model in this distribution is the normal Hertzian load expressed in the form [25]:
p(x)=p01(xa)2
Where a is the half-width of the contact and p0 the maximum load in the middle of the contact given by:
p0=2Pπa

An example of this Herz distribution is given in Fig. 6 [26].

  • The second case: Critical contact angle

For the case where the wire is inclined (critical contact angle), we choose the load in which its value is maximum at the edges of the half contact widths, and decreases when the contact area decreases while moving away. The normal load is in a form taking into account the low forces applied with no concavity and convexity. This type of distribution is given in Fig. 7.
p(x)=p0(1+xa)
Fig. 7.
Fig. 7.

Distribution of a linear load

Citation: International Review of Applied Sciences and Engineering 2024; 10.1556/1848.2024.00764

3 Results

3.1 Experimental results

We performed fretting experiments regarding the interaction of dental wire and brackets in our previous experimental research [27, 28]. Using scanning electron microscopy (SEM) and energy-dispersive X-ray spectroscopy (EDS), significant results were obtained. When we looked at these results, we found some interesting data regarding the contact area on the eccentric side of the beam. It was about 0.02 mm2.This contact zone has diverse characteristics that are worth discussing. The results indicate the presence of two unique zones: a stick zone (zone 1) and a micro-slip zone (zone 2), as shown in Fig. 8.

Fig. 8.
Fig. 8.

The contact area between wire and bracket, stick zone (1), micro-slip (2). Outside the contact (3) [27 (CC BY-NC 4.0)]

Citation: International Review of Applied Sciences and Engineering 2024; 10.1556/1848.2024.00764

3.2 Simulations results

We will give the analytical results for the proposed models for the two dental positions in this section. To validate the presence of the experimentally observed micro-slip and stick zone.

3.2.1 The first case: classical friction

  • Stresses of volume: Hertzien load

In this configuration we have plotted the contours of the volume stresses of σxxp0, σyyp0, τxyp0 and τxymaxp0 in the plane (x, y) for a coefficient of friction of 0.3, a half-width of 0.25 mm, with a normal load of 5 N mm−1. The graphical representation of stress distribution is shown in Figs 9a, 9b, and 9c [17].

Fig. 9a.
Fig. 9a.

Iso-stresses σxxP0 in the case of Hertzien loading for µ = 0.3

Citation: International Review of Applied Sciences and Engineering 2024; 10.1556/1848.2024.00764

Fig. 9b.
Fig. 9b.

Iso-stresses σyyP0inthecaseof Hertzien loading for µ = 0.3

Citation: International Review of Applied Sciences and Engineering 2024; 10.1556/1848.2024.00764

Fig. 9c.
Fig. 9c.

Iso-stresses τxyP0inthecaseof Hertzien loading for µ = 0.3

Citation: International Review of Applied Sciences and Engineering 2024; 10.1556/1848.2024.00764

Furthermore, we conducted comprehensive simulations using Mathcad to generate iso-stress plots for volumes σxx,P0, σyyP0 and τxyP0 under Hertzian loading conditions. For a coefficient of friction of 0.3 and a width of 0.5 mm, our analysis revealed noteworthy observations. Notably, σxx, closely approximated P0 and exhibited concentration at a depth of approximately 0.2 mm. In contrast, the maximal value of σyy,P0, around 0.8 was situated at a depth of 0.18 mm. τxyP0 exhibited a peak value of 0.3, as illustrated in Fig. 10.

Fig. 10.
Fig. 10.

Maximum shear iso-stresses τxymaxP0inthecaseof Hertzien loading for µ = 0 (a) and µ = 0.3 (b)

Citation: International Review of Applied Sciences and Engineering 2024; 10.1556/1848.2024.00764

τxymaxP0 is a fundamental parameter that was introduced to evaluate the maximum shear stress (Fig. 11). This parameter is given:
τxymax=(σxx+σyy2)2+τxy2
Fig. 11.
Fig. 11.

The distribution of the tangential load along the contact for the case of a coefficient of friction of µ = 0.3 for σ0 = 0 MPa (a) and σ0 = 7.316 MPa (b)

Citation: International Review of Applied Sciences and Engineering 2024; 10.1556/1848.2024.00764

Significantly, the absence of tangential loading led to maximum shear iso-stresses symmetrically centered at a depth of 0.2 mm. On the other hand, in the presence of tangential loading, the maximum shear stress underwent a shift of 0.3 units towards the most stressed side.

  • Surface stress: Hertzien load

In this part of the paper, we provide the findings of our research into the deterioration modes caused by the interplay of a tangential load and stress on the wire in contact with the bracket. For this purpose, we used a Mathcad algorithm based on experimental data from wire-bracket contact. The specific parameters adopted for the analysis are as follows:

  • Half-width of the contact: a = 0.25 mm (Half of 0.4572 mm)

  • Load per unit of total tangential length: Q = 1.2 N

  • Pressure per unit of arbitrary normal length: P0 = 12.7 N

  • Coefficient of friction: µ = 0.3

  • Additional tangential load: σ0 = 7.316 MPa.

To be able to highlight these degradation modes generated under the effect of the tangential load in the presence of an additional load on the wire in contact with the bracket, we use the Mathcad program that has been developed with the experimental data adopted during the wire-bracket contact [29], namely:

  • Half-width of the contact: a = 0.25 mm (Half of 0.4572 mm)

  • Load per unit of total tangential length: Q = 1.2 N

  • Pressure per unit of arbitrary normal length: P0 = 12.7 N

  • Coefficient of friction: µ = 0.3

  • Additional tangential load: σ0 = 7.316 MPa.

3.2.2 The second case: critical contact angle

We have also plotted the contours of the volume stresses of σxxp0, σyyp0, τxyp0 and τxymaxp0 for this linear normal load with the same conditions described above and with a critical contact angle θc=3°. The results are shown in Figs 12a, 12b, 12c, and 13.

Fig. 12a.
Fig. 12a.

Iso-stresses σxxP0inthecaseof linear loading for µ = 0.3

Citation: International Review of Applied Sciences and Engineering 2024; 10.1556/1848.2024.00764

Fig. 12b.
Fig. 12b.

Iso-stresses σyyP0inthecaseof linear loading for µ = 0.3

Citation: International Review of Applied Sciences and Engineering 2024; 10.1556/1848.2024.00764

Fig. 12c.
Fig. 12c.

Iso-stresses τxyP0inthecaseof linear loading for µ = 0.3

Citation: International Review of Applied Sciences and Engineering 2024; 10.1556/1848.2024.00764

Fig. 13.
Fig. 13.

Iso-stresses τxymaxP0inthecaseof linear loading for µ = 0 (a) and µ = 0.3 (b)

Citation: International Review of Applied Sciences and Engineering 2024; 10.1556/1848.2024.00764

We have simulated on Mathcad, the Iso-stresses of volumes σxxp0 , in the first case of a linear loading with a coefficient of friction of 0.3 for a width of 0.5 mm. Note that σxxp0 max reaches the value 1.6 P0 (pressure per unit of arbitrary normal length).

For σyyP0 the maximum value is 1.4 and located around 0.1 mm in depth. Shear stress τxyP0 reaches the maximum value of 0.6, located at the edges of the contact 0.25 mm.

On the maximum shear load in the absence of tangential loading, we note that the value of 0.5 is concentrated at the edge 0.25 mm. On the other hand, in the presence of friction, the value reaches 0.7. This explains the noticeable degradation that is often observed at the edge of the bracket as reported in many research [14].

4 Discussions

4.1 Experimental results

The stick zone (Zone 1) plays an important role in understanding the fretting behaviour of the dental wire and the bracket surface. This zone provides a significant interaction between the two materials as it maintains the stability of the system under the fretting circumstances. The ability of the stick zone to restrict relative motion between the wire and the bracket helps to prevent extreme wear and possible failure.

The micro-slip zone (Zone 2), which is close to the stick-zone, on the other hand, exhibits a different element of the fretting phenomena. The specific feature of oxides inside this zone shows that material deterioration is restricted. This degradation is most likely the result of cyclic loading and relative movement, which causes surface layer disintegration and probable chemical interactions between the materials involved.

The appearance of a stick zone and a micro-slip zone within the contact zone emphasizes the friction problems between the wire and the brackets. This interaction illustrates the stability between sticky and abrasive wear mechanisms. Although the bonding zone protects by reducing relative movement, the deterioration of the micro-slip zone demonstrates the potential difficulties in preserving the integrity of the material over time.

The observations of this study have an impact on the design and performance of dental brackets and wires. The results revealed a complex interplay that combines a stick zone and a micro-slip zone, as established by SEM and EDS analysis. Hence, it may be possible to mitigate fretting effects by improving the composition and surface treatment of materials in the contact area, especially in cyclic load conditions. Future research could examine the chemical and mechanical complexities of these zones, potentially leading to measures to improve the longevity and dependability of dental orthodontic systems.

4.2 Analytical prevention results

4.2.1 The first case: classical friction

  1. Stresses of volume: Hertzien load

The analysis of our results provides good knowledge of the stress distribution within the system studied, particularly under specific loading conditions. The contour plots and iso-stress simulations provide valuable visual insights into how distinct parameters influence the distribution of stresses. Valuable visual information was obtained through contour plots and iso-stress simulations on how different parameters affect the stress distribution.

The dominance of σxx over σyy highlights the important influence of the applied normal load on the stress distribution along the x-axis. The location of σ_xx at a shallow depth of approximately 0.2 mm highlights the importance of surface stresses and its possible influence on the behaviour of the material.

The presence of the micro-sliding zone, represented by τxyp0, reflects the importance of the effect of frictional stresses. The displacement of peak shear stress due to tangential loading emphasizes the critical interaction between friction and stress models, particularly in scenarios involving relative motion.

Practical implications for design and engineering considerations were obtained from these identified models and stress variations. Information from this analysis can be used to control material selection, geometry, and loading conditions to reduce stress concentrations and improve overall system durability.

  • Surface stress: Hertzien load

Mathcad software results produced using the specified parameters provide insight into the different degradation modes that manifest due to the combined impacts of tangential loading and additional loading on the wire/bracket contact. We can further explore the implications of the chosen circumstances by applying these parameters to the analysis.

The half-width of the contact (a = 0.25 mm) is essential to establish the extent of contact between the wire and the support. This parameter affects the stress and deformation distribution in the contact region, which can affect wear patterns and material reactions.

Friction-induced stresses are produced when the load per unit total tangential length (Q = 1.2 N) interacts with the coefficient of friction (= 0.3). The importance of this load regarding the friction coefficient influences the friction forces at work, which in turn influence the wear and deformation mechanisms.

The normal forces experienced within the contact are influenced by the pressure per unit of arbitrary normal length (= 12.7 N). This parameter, associated with the additional tangential load (= 7.316 MPa), modifies the stress distribution, which can lead to localized degradation of the material.

Through the combination of these parameters simulated via the Mathcad program, we can observe and analyse the degradation modes that develop under the specified conditions. The interaction of tangential and normal loads, together with the coefficient of friction, shows the complex nature of wear, deformation and material behaviour upon contact with the support wire.

4.2.2 The second case: critical contact angle

The results of our investigation provide important insights into the stress distribution under linear normal loading. Volume stress plots provide a visual picture of how several parameters influence stress patterns.

Under linear loading, the significant increase in σxxp0, reaches 1.6 P0 (pressure per unit of arbitrary normal length), indicating increased stress concentration along the x-axis. This concentration of stresses, particularly at the edge of the support, can have consequences on the deformation of the material and wear at this location.

The presence of a maximum value of 1.4 for σyyp0, at a shallow depth of 0.1 mm shows the importance of normal loading to influence the stress distribution. This observation is relevant for understanding the behavior of the system at applied loads.

The apparent shear stress τxyp0 at the edges of the contact zone, which reaches 0.6, indicates the possibility of local material deterioration due to shear forces. This phenomenon can participate to wear and material degradation, especially in areas experiencing higher stress concentrations.

The difference between the maximum shear stresses in the absence and presence of transverse loading highlights the important effect of friction on the evolution of stress patterns. The increase in frictional shear stress helps explain the pronounced deterioration reported at the support edge in previous research. The increase in frictional shear stress helps explain the pronounced degradation reported by Khan et al. at the edge of the support [30] in previous research

5 Conclusion

In this study, we carried out a simulation on MATHCAD14 for a better understanding of the concentration of the maximum shear load for the case of a Hertzian load, which models the case of classical friction, and a linear load allowing us to model the real case of a critical contact angle.

The simulations showed that the concentration of the load is located above the contact; it is of the order of 0.3P0 (pressure per unit of arbitrary normal length). Moreover, we have simulated the contact between the wire and bracket in Mathcad14 using the Johnson formulations for the case of a linear and Hertzian loading with an additional tangential load, we clearly see that the maximum tangential load is obtained at the interface between the stick-zone and the micro-slip zone and is oriented towards the most stressed side. We also note that the stick zone is shifted towards the recessed side when the additional load was applied and for comparison between the two configurations studied, we found that the maximum shear stress is greater in the case of the critical angle contact.

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    • Export Citation
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    S. Sangral and M. Jayaprakash, “Evaluating the effect of contact pad geometry on the fretting fatigue behavior of titanium alloy by experimental and finite element analysis,” J. Fail. Anal. Prev., vol. 22, no. 2, pp. 773784, 2022.

    • Search Google Scholar
    • Export Citation
  • [12]

    B. Tran, D. S. Nobes, P. W. Major, J. P. Carey, and D. L. Romanyk, “The three-dimensional mechanical response of orthodontic archwires and brackets in vitro during simulated orthodontic torque,” J. Mech. Behav. Biomed. Mater., vol. 114, 2021, Art no. 104196.

    • Search Google Scholar
    • Export Citation
  • [13]

    J. Kawamura and N. Tamaya, “A finite element analysis of the effects of archwire size on orthodontic tooth movement in extraction space closure with miniscrew sliding mechanics,” Prog. Orthod., vol. 20, pp. 16, 2019.

    • Search Google Scholar
    • Export Citation
  • [14]

    Y.-F. Liu, P.-Y. Zhang, Q.-F. Zhang, J.-X. Zhang, and J. Chen, “Digital design and fabrication of simulation model for measuring orthodontic force,” Biomed. Mater. Eng., vol. 24, no. 6, pp. 22652271, 2014.

    • Search Google Scholar
    • Export Citation
  • [15]

    J. Grün, S. Feldmeth, and F. Bauer, “The sealing mechanism of radial lip seals: a numerical study of the tangential distortion of the sealing edge,” Tribol Mater., vol. 1, no. 1, pp. 110, 2022.

    • Search Google Scholar
    • Export Citation
  • [16]

    M. Sreenivasan, M. D. Kumar, R. Krishna, T. Mohanraj, G. Suresh, D. H. Kumar, and A. S. Charan, “Finite element analysis of coil spring of a motorcycle suspension system using different fibre materials,” Mater. Today Proc., vol. 33, pp. 275279, 2020.

    • Search Google Scholar
    • Export Citation
  • [17]

    R. Jaeger, F. Schmidt, K. Naziris, and B. G. Lapatki, “Evaluation of orthodontic loads and wire–bracket contact configurations in a three-bracket setup: comparison of in-vitro experiments with numerical simulations,” J. Biomech., vol. 121, 2021, Art no. 110401.

    • Search Google Scholar
    • Export Citation
  • [18]

    H. Hertz and H. Hertz, “Über die Berührung fester elastischer Körper, Journal für die reine und angewandte Mathematik 92, 156-171 (1881),” J. Für Reine Angew. Math., vol. 171, pp. 156171, 1881.

    • Search Google Scholar
    • Export Citation
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    ASTM International, West Conshohocken, PA, Standard No., ASTM A240/A240M-16a., and American Society for Testing & Mater, “ASTM, ‘standard specification for chromium and chromium-nickel stainless steel plate, sheet, and strip for pressure vessels and for general applications’,” 2016.

    • Search Google Scholar
    • Export Citation
  • [20]

    W. A. Brantley and T. Eliades, “Orthodontic materials: scientific and clinical aspects,” Am. J. Orthod. Dentofacial Orthop., vol. 119, no. 6, pp. 672673, 2001.

    • Search Google Scholar
    • Export Citation
  • [21]

    B. Podgornik, “Adhesive wear failures,” J. Fail. Anal. Prev., vol. 22, no. 1, pp. 113138, 2022.

  • [22]

    K. L. Johnson, “Contact mechanics cambridge univ,” Press Camb., vol. 95, no. 365, p. 922, 1985.

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    A. Sackfield, D. A. Hills, and D. Nowell, Mechanics of Elastic Contacts. Elsevier, 2013.

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    N. I. Muskhelishvili and N. I. Muskhelishvili, “Effective solution of the principal problems of the static theory of elasticity for the half-plane, circle and analogous regions,” Singul. Integral Equ. Bound. Probl. Funct. Theor. Their Appl. Math. Phys., pp. 282322, 1958.

    • Search Google Scholar
    • Export Citation
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    A. Qazi, “Numerical modeling of the coupling between wheelset dynamics and wheel-rail contact.” Université Gustave Eiffel, 2022.

  • [26]

    H. Wu, A. Jagota, and C.-Y. Hui, “Lubricated sliding of a rigid cylinder on a viscoelastic half space,” Tribol. Lett., vol. 70, no. 1, p. 1, 2022.

    • Search Google Scholar
    • Export Citation
  • [27]

    M. K. El Kouifat and B. Ouaki, “Fretting-corrosion of orthodontic arch-wire/bracket contacts in saliva environment,” World J. Dent., vol. 9, no. 5, pp. 387393, 2018.

    • Search Google Scholar
    • Export Citation
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    E. K. Mk, “Corrosion of orthodontic arch-wires in artificial saliva environment,” J. Int. Dent. Med. Res., vol. 11, no. 3, 2018.

  • [29]

    R. H. Higa, N. T. Semenara, J. F. C. Henriques, G. Janson, R. Sathler, and T. M. F. Fernandes, “Evaluation of force released by deflection of orthodontic wires in conventional and self-ligating brackets,” Dent. Press J. Orthod., vol. 21, pp. 9197, 2016.

    • Search Google Scholar
    • Export Citation
  • [30]

    H. Khan, S. Mheissen, A. Iqbal, A. R. Jafri, and M. K. Alam, “Bracket failure in orthodontic patients: the incidence and the influence of different factors,” Biomed. Res. Int., vol. 2022, p. 2022.

    • Search Google Scholar
    • Export Citation
  • [1]

    J. Tominaga, H. Ozaki, P. C. Chiang, M. Sumi, M. Tanaka, Y. Koga, C. Bourauel, and N. Yoshida, “Effect of bracket slot and archwire dimensions on anterior tooth movement during space closure in sliding mechanics: a 3-dimensional finite element study,” Am. J. Orthod. Dentofacial Orthop., vol. 146, no. 2, pp. 166174, 2014.

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    P. Venkatesh, “Evaluation of tooth movement with dual slot bracket system in lingual biomechanics-A 3D finite element model analysis,” 2018.

    • Search Google Scholar
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    N. Daratsianos, C. Bourauel, R. Fimmers, A. Jäger, and R. Schwestka-Polly, “In vitro biomechanical analysis of torque capabilities of various 0.018 ″lingual bracket–wire systems: total torque play and slot size,” Eur. J. Orthod., vol. 38, no. 5, pp. 459469, 2016.

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    Z. Zhou and J. Zheng, “Tribology of dental materials: a review,” J. Phys. Appl. Phys., vol. 41, no. 11, 2008, Art no. 113001.

  • [5]

    A. G. Basha, R. Shantaraj, and S. B. Mogegowda, “Comparative study between conventional en-masse retraction (sliding mechanics) and en-masse retraction using orthodontic micro implant,” Implant Dent, vol. 19, no. 2, pp. 128136, 2010.

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    F. Farzanegan, H. Shafaee, H. Norouzi, H. Bagheri, and A. Rangrazi, “Comparison of the high cycle fatigue behavior of the orthodontic NiTi wires: an in vitro study,” Pesqui. Bras. Em Odontopediatria E Clínica Integrada, vol. 22, 2022.

    • Search Google Scholar
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  • [7]

    L. Li, T. Yu, B. Shang, B. Song, and Y. Chen, “Analysis of contact stress and fatigue crack growth of transmission shaft,” J. Fail. Anal. Prev., pp. 119, 2023.

    • Search Google Scholar
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  • [8]

    S. Vulović, I. Stančić, A. Popovac, and A. Milić-Lemić, “Surface roughness evaluation of different novel CAD/CAM dental materials”.

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  • [9]

    S. Vulović, A. Todorović, I. Stančić, A. Popovac, J. N. Stašić, A. Vencl, and A. Milić‐Lemić, “Study on the surface properties of different commercially available CAD/CAM materials for implant‐supported restorations,” J. Esthet. Restor. Dent., vol. 34, no. 7, pp. 11321141, 2022.

    • Search Google Scholar
    • Export Citation
  • [10]

    F. S. Martínez-Cruz, M. Vite-Torres, A. Moran-Reyes, and J. A. Bravo-Mejía, “Wear and friction characterisation of some restorative dental materials,” Tribol. Mater., vol. 1, no. 1, pp. 2734, 2022.

    • Search Google Scholar
    • Export Citation
  • [11]

    S. Sangral and M. Jayaprakash, “Evaluating the effect of contact pad geometry on the fretting fatigue behavior of titanium alloy by experimental and finite element analysis,” J. Fail. Anal. Prev., vol. 22, no. 2, pp. 773784, 2022.

    • Search Google Scholar
    • Export Citation
  • [12]

    B. Tran, D. S. Nobes, P. W. Major, J. P. Carey, and D. L. Romanyk, “The three-dimensional mechanical response of orthodontic archwires and brackets in vitro during simulated orthodontic torque,” J. Mech. Behav. Biomed. Mater., vol. 114, 2021, Art no. 104196.

    • Search Google Scholar
    • Export Citation
  • [13]

    J. Kawamura and N. Tamaya, “A finite element analysis of the effects of archwire size on orthodontic tooth movement in extraction space closure with miniscrew sliding mechanics,” Prog. Orthod., vol. 20, pp. 16, 2019.

    • Search Google Scholar
    • Export Citation
  • [14]

    Y.-F. Liu, P.-Y. Zhang, Q.-F. Zhang, J.-X. Zhang, and J. Chen, “Digital design and fabrication of simulation model for measuring orthodontic force,” Biomed. Mater. Eng., vol. 24, no. 6, pp. 22652271, 2014.

    • Search Google Scholar
    • Export Citation
  • [15]

    J. Grün, S. Feldmeth, and F. Bauer, “The sealing mechanism of radial lip seals: a numerical study of the tangential distortion of the sealing edge,” Tribol Mater., vol. 1, no. 1, pp. 110, 2022.

    • Search Google Scholar
    • Export Citation
  • [16]

    M. Sreenivasan, M. D. Kumar, R. Krishna, T. Mohanraj, G. Suresh, D. H. Kumar, and A. S. Charan, “Finite element analysis of coil spring of a motorcycle suspension system using different fibre materials,” Mater. Today Proc., vol. 33, pp. 275279, 2020.

    • Search Google Scholar
    • Export Citation
  • [17]

    R. Jaeger, F. Schmidt, K. Naziris, and B. G. Lapatki, “Evaluation of orthodontic loads and wire–bracket contact configurations in a three-bracket setup: comparison of in-vitro experiments with numerical simulations,” J. Biomech., vol. 121, 2021, Art no. 110401.

    • Search Google Scholar
    • Export Citation
  • [18]

    H. Hertz and H. Hertz, “Über die Berührung fester elastischer Körper, Journal für die reine und angewandte Mathematik 92, 156-171 (1881),” J. Für Reine Angew. Math., vol. 171, pp. 156171, 1881.

    • Search Google Scholar
    • Export Citation
  • [19]

    ASTM International, West Conshohocken, PA, Standard No., ASTM A240/A240M-16a., and American Society for Testing & Mater, “ASTM, ‘standard specification for chromium and chromium-nickel stainless steel plate, sheet, and strip for pressure vessels and for general applications’,” 2016.

    • Search Google Scholar
    • Export Citation
  • [20]

    W. A. Brantley and T. Eliades, “Orthodontic materials: scientific and clinical aspects,” Am. J. Orthod. Dentofacial Orthop., vol. 119, no. 6, pp. 672673, 2001.

    • Search Google Scholar
    • Export Citation
  • [21]

    B. Podgornik, “Adhesive wear failures,” J. Fail. Anal. Prev., vol. 22, no. 1, pp. 113138, 2022.

  • [22]

    K. L. Johnson, “Contact mechanics cambridge univ,” Press Camb., vol. 95, no. 365, p. 922, 1985.

  • [23]

    A. Sackfield, D. A. Hills, and D. Nowell, Mechanics of Elastic Contacts. Elsevier, 2013.

  • [24]

    N. I. Muskhelishvili and N. I. Muskhelishvili, “Effective solution of the principal problems of the static theory of elasticity for the half-plane, circle and analogous regions,” Singul. Integral Equ. Bound. Probl. Funct. Theor. Their Appl. Math. Phys., pp. 282322, 1958.

    • Search Google Scholar
    • Export Citation
  • [25]

    A. Qazi, “Numerical modeling of the coupling between wheelset dynamics and wheel-rail contact.” Université Gustave Eiffel, 2022.

  • [26]

    H. Wu, A. Jagota, and C.-Y. Hui, “Lubricated sliding of a rigid cylinder on a viscoelastic half space,” Tribol. Lett., vol. 70, no. 1, p. 1, 2022.

    • Search Google Scholar
    • Export Citation
  • [27]

    M. K. El Kouifat and B. Ouaki, “Fretting-corrosion of orthodontic arch-wire/bracket contacts in saliva environment,” World J. Dent., vol. 9, no. 5, pp. 387393, 2018.

    • Search Google Scholar
    • Export Citation
  • [28]

    E. K. Mk, “Corrosion of orthodontic arch-wires in artificial saliva environment,” J. Int. Dent. Med. Res., vol. 11, no. 3, 2018.

  • [29]

    R. H. Higa, N. T. Semenara, J. F. C. Henriques, G. Janson, R. Sathler, and T. M. F. Fernandes, “Evaluation of force released by deflection of orthodontic wires in conventional and self-ligating brackets,” Dent. Press J. Orthod., vol. 21, pp. 9197, 2016.

    • Search Google Scholar
    • Export Citation
  • [30]

    H. Khan, S. Mheissen, A. Iqbal, A. R. Jafri, and M. K. Alam, “Bracket failure in orthodontic patients: the incidence and the influence of different factors,” Biomed. Res. Int., vol. 2022, p. 2022.

    • Search Google Scholar
    • Export Citation
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Editor-in-Chief: Ákos, Lakatos University of Debrecen (Hungary)

Founder, former Editor-in-Chief (2011-2020): Ferenc Kalmár University of Debrecen (Hungary)

Founding Editor: György Csomós University of Debrecen (Hungary)

Associate Editor: Derek Clements Croome University of Reading (UK)

Associate Editor: Dezső Beke University of Debrecen (Hungary)

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  • Mohammad Nazir AHMAD Institute of Visual Informatics, Universiti Kebangsaan Malaysia, Malaysia

    Murat BAKIROV Center for Materials and Lifetime Management Ltd. Moscow Russia

    Nicolae BALC Technical University of Cluj-Napoca Cluj-Napoca Romania

    Umberto BERARDI Ryerson University Toronto Canada

    Ildikó BODNÁR University of Debrecen Debrecen Hungary

    Sándor BODZÁS University of Debrecen Debrecen Hungary

    Fatih Mehmet BOTSALI Selçuk University Konya Turkey

    Samuel BRUNNER Empa Swiss Federal Laboratories for Materials Science and Technology

    István BUDAI University of Debrecen Debrecen Hungary

    Constantin BUNGAU University of Oradea Oradea Romania

    Shanshan CAI Huazhong University of Science and Technology Wuhan China

    Michele De CARLI University of Padua Padua Italy

    Robert CERNY Czech Technical University in Prague Czech Republic

    György CSOMÓS University of Debrecen Debrecen Hungary

    Tamás CSOKNYAI Budapest University of Technology and Economics Budapest Hungary

    Eugen Ioan GERGELY University of Oradea Oradea Romania

    József FINTA University of Pécs Pécs Hungary

    Anna FORMICA IASI National Research Council Rome

    Alexandru GACSADI University of Oradea Oradea Romania

    Eric A. GRULKE University of Kentucky Lexington United States

    Janez GRUM University of Ljubljana Ljubljana Slovenia

    Géza HUSI University of Debrecen Debrecen Hungary

    Ghaleb A. HUSSEINI American University of Sharjah Sharjah United Arab Emirates

    Nikolay IVANOV Peter the Great St.Petersburg Polytechnic University St. Petersburg Russia

    Antal JÁRAI Eötvös Loránd University Budapest Hungary

    Gudni JÓHANNESSON The National Energy Authority of Iceland Reykjavik Iceland

    László KAJTÁR Budapest University of Technology and Economics Budapest Hungary

    Ferenc KALMÁR University of Debrecen Debrecen Hungary

    Tünde KALMÁR University of Debrecen Debrecen Hungary

    Milos KALOUSEK Brno University of Technology Brno Czech Republik

    Jan KOCI Czech Technical University in Prague Prague Czech Republic

    Vaclav KOCI Czech Technical University in Prague Prague Czech Republic

    Imra KOCSIS University of Debrecen Debrecen Hungary

    Imre KOVÁCS University of Debrecen Debrecen Hungary

    Angela Daniela LA ROSA Norwegian University of Science and Technology

    Éva LOVRA Univeqrsity of Debrecen Debrecen Hungary

    Elena LUCCHI Eurac Research, Institute for Renewable Energy Bolzano Italy

    Tamás MANKOVITS University of Debrecen Debrecen Hungary

    Igor MEDVED Slovak Technical University in Bratislava Bratislava Slovakia

    Ligia MOGA Technical University of Cluj-Napoca Cluj-Napoca Romania

    Marco MOLINARI Royal Institute of Technology Stockholm Sweden

    Henrieta MORAVCIKOVA Slovak Academy of Sciences Bratislava Slovakia

    Phalguni MUKHOPHADYAYA University of Victoria Victoria Canada

    Balázs NAGY Budapest University of Technology and Economics Budapest Hungary

    Husam S. NAJM Rutgers University New Brunswick United States

    Jozsef NYERS Subotica Tech College of Applied Sciences Subotica Serbia

    Bjarne W. OLESEN Technical University of Denmark Lyngby Denmark

    Stefan ONIGA North University of Baia Mare Baia Mare Romania

    Joaquim Norberto PIRES Universidade de Coimbra Coimbra Portugal

    László POKORÁDI Óbuda University Budapest Hungary

    Antal PUHL (1950–2023) University of Debrecen Debrecen Hungary

    Roman RABENSEIFER Slovak University of Technology in Bratislava Bratislava Slovak Republik

    Mohammad H. A. SALAH Hashemite University Zarqua Jordan

    Dietrich SCHMIDT Fraunhofer Institute for Wind Energy and Energy System Technology IWES Kassel Germany

    Lorand SZABÓ Technical University of Cluj-Napoca Cluj-Napoca Romania

    Csaba SZÁSZ Technical University of Cluj-Napoca Cluj-Napoca Romania

    Ioan SZÁVA Transylvania University of Brasov Brasov Romania

    Péter SZEMES University of Debrecen Debrecen Hungary

    Edit SZŰCS University of Debrecen Debrecen Hungary

    Radu TARCA University of Oradea Oradea Romania

    Zsolt TIBA University of Debrecen Debrecen Hungary

    László TÓTH University of Debrecen Debrecen Hungary

    László TÖRÖK University of Debrecen Debrecen Hungary

    Anton TRNIK Constantine the Philosopher University in Nitra Nitra Slovakia

    Ibrahim UZMAY Erciyes University Kayseri Turkey

    Tibor VESSELÉNYI University of Oradea Oradea Romania

    Nalinaksh S. VYAS Indian Institute of Technology Kanpur India

    Deborah WHITE The University of Adelaide Adelaide Australia

International Review of Applied Sciences and Engineering
Address of the institute: Faculty of Engineering, University of Debrecen
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2022  
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Materials Science (miscellaneous) Q3)
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2021  
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Scopus
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2020  
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5
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Scopus
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102/116=0,9
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General Engineering 205/297 (Q3)
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Management Science and Operations Research 139/166 (Q4)
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Scopus
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0,26
Scopus
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57
Scopus
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36
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23%

 

2019  
Scimago
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4
Scimago
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0,229
Scimago
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Engineering (miscellaneous) Q2
Environmental Engineering Q3
Information Systems Q3
Management Science and Operations Research Q4
Materials Science (miscellaneous) Q3
Scopus
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46/81=0,6
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General Engineering 227/299 (Q4)
Environmental Engineering 107/132 (Q4)
Information Systems 259/300 (Q4)
Management Science and Operations Research 136/161 (Q4)
Materials Science (miscellaneous) 60/86 (Q3)
Scopus
SNIP
0,866
Scopus
Cites
35
Scopus
Documents
47
Acceptance
Rate
21%

 

International Review of Applied Sciences and Engineering
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International Review of Applied Sciences and Engineering
Language English
Size A4
Year of
Foundation
2010
Volumes
per Year
1
Issues
per Year
3
Founder Debreceni Egyetem
Founder's
Address
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Publisher Akadémiai Kiadó
Publisher's
Address
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Publisher
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ISSN 2062-0810 (Print)
ISSN 2063-4269 (Online)

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