31 MICRODEFECTS ANALYSIS OF DENTAL CONTACT SURFACES Gheorghe FRUNZA1, Mihai Cătălin FRUNZA, Cornel SUCIU1 1 University of Suceava, Faculty of Mechanical Engineering, Mechatronics and Management, ROMANIA, University of Medicine and Pharmacy, Bucharest, Faculty of Dental Medicine, ROMANIA frunza@fim.usv.ro ABSTRACT The tribological processes influence the behaviour of the biocontacts between biological bodies, between biomaterials or between biological bodies and biomaterials. Whether natural or artificial, any biocontact is the locus of biophysical, biochemical, and metabolic mechanisms taking place on both the molecular and the supramolecular levels. The first mechanism is influenced by biomechanical and bioelectric changes, the second comprises biochemical reactions that depend on the nature of interface materials, and the third manifests itself by the action of the enzymes that hold the potential of degrading all components of the extracellular matrix. These mechanisms mutually interact and may yield complex interface phenomena within the stomatognatic system. This paper presents a tribological model concerning dental contacts deterioration, based on contact mechanics elements, fracture mechanics and on the actual topography of the tooth surface. Keywords: dental contacts, surface topography, microcracks, biomechanical fatigue NOMENCLATURE general stress,, ; where - normal stress, - shear stress; C, m are experimentally determined scaling constants; K K max K min K max 1 R ; where R 1,1 ; K c fracture toughness; geometric parameter which depends on enamel surface stress and crack tip type; ao initial crack length; a f final crack length; o contact general stresses in dental enamel, which can be computed with contact mechanics equations [1]. BIOTRIBOLOGICAL MOTIVATION Teeth are the hardest biological solids in the human body. The reason is the external layer, which is about mm thick, called enamel. Teeth fit in elastic, solid structures (the maxillary bones), are surrounded by soft elements (gingiva, tongue, cheeks, lips) and operate in a fluid medium, called saliva. In this biosystem, teeth establish various contacts between them, which can be divided into two categories: passive and active (Fig. 1). ACTIVE Static Dynamic PASSIVE Static DENTALCONTACTS Fig. 1. Dental contacts classification. The passive contacts are represented by the lateral contacts between neighbouring teeth. The configuration of these contacts undergoes some changes, because initially they are point contacts, which enlarge themselves in time, due to tribological processes. Active contacts appear both in static and dynamic regime, during mandible movements, when the two arcades are in contact. Contacts between opposed teeth appear when physiological functions are exerted (mastication, swallowing) or when abnormal acts take place, like bruxism or teeth grinding, clenching.
3 Mastication forces Normal load in contact F Material parameters Defects in subsurface 1 Q Defects on surface Phenomenons at the biocontact interface F Fig.. A dental tribological model There are other circumstances, when although teeth do not touch, they receive great forces: nail biting, pencil biting or dental trauma. The oral cavity functioning involves chewing. This occurs through the contact of opposite teeth from both jaws, interposition of food bowl which causes a degree of friction at the interface and, physical, appears tooth wear. Dental contacts are usually nonconform, linear in frontal area and punctual in lateral area, or conform, when after a long process of occlusal wear, the two surfaces are almost perfectly joined. Such contacts are loaded with an average force of 75 N. The consequences of dental contacts are: stress development, wear, crack initiation and propagation, fractures, tooth position modification and eventually tooth destruction. DENTAL TRIBOLOGICAL MODEL The oral tribological system is mainly characterised by teeth wear and friction, saliva lubrication and food adhesion on teeth. Every single one of these processes can be normal (physiologic) or abnormal (pathologic). Thus, saliva facilitates contacts between teeth, but also when it is reduced in quantity, increases the wear. Food adhesion stimulates the salivary glands and the gustative papillae, but also it can lead to decays. The dental surfaces present a particular wear depending on their localization. The proximal surfaces which provide the contacts between neighbouring teeth have a limited wear, as the greatest wear exists on the occlusal surfaces which participate in mastication. Teeth wear is influenced by: masticatory system state (existing forces, teeth number, dental contacts, filling materials, etc), abrasive or acid diet, tooth brushing, saliva, age, gender etc. The occlusal surface wear correlates with the active tooth eruption, and so, as the wear proceeds, the tooth is slightly pushed out of its alveolar bone by the formation of a micro layer of dental cement. The moderate wear of dental cusps is beneficial, permitting a more freely movement of the mandible and thereby the reduction of the lateral forces. The surface microwear analysis is useful in correlation with diet or teeth brushing method, but also for the study of biomechanical factors within dental contacts. The microwear is influenced moreover by the characteristics of the material itself: the general shape of enamel surface, the architecture of enamel rods, enamel hardness. The phenomena which take place at the interface of two elements in a biocontact, but also in their interior are profoundly influenced (as it is sustained in []) by the stresses state. The dental contacts can be assimilated with hertz contacts (linear or punctual), non-hertz contacts, surface contacts or multicontacts. Such biocontacts are charged, mainly in the mastication process, with any kind of loads, which generate in the body of the tooth a complex-3d state of tension [3]. The pressure from the interface of the contact varies concordantly with the normal load in contact Q, the geometric configuration, the nature of teeth material and of the interface contact conditions (Fig. ). This pressure at the interface of the biocontact has a spatial state of stress, which can be calculated with the relations from the contact mechanics [1]. Both dental layers, enamel and dentine, are formed by an organic matrix filled with mineral content. Moreover, each of them has an independent structure, which varies concordantly with the topography, tooth type, ageing, wear and pathological events. Accordingly, the measurements of their mechanical properties, including the elastic and fracture ones, are very hard to obtain. The Young s module for enamel can be determined through classic invasive methods, considering the material: linear elastic, uniform and isotropic. But the values obtained in different experiments varied a lot, from 9. to 84. GPa, depending upon the orientation of enamels rods (the basic units of enamel). Basically, the Young s module on the rods direction is much greater than perpendicularly on them. Thus, the hypothesis of the isotropic material is not accurate and is applicable only for tooth general assessment.
33 For stress state evaluation, heretofore have been used different numerical and analytical methods, with the assumption that enamel is a thin, but tough layer and is supported by a much more elastic material, called dentin. But, until now, the tooth real geometrical topography could not be integrated. METHODS AND RESULTS From a physical point of view, the tooth can be considered a multilayer biological solid of equal strength, anisotropic, with a hard surface layer, 3D loaded, Figure 3. In the present paper, the 3D analysis of the tooth surface was realized with a Nanofocus system, capable of performing 1,000 steps per mm. The surface topography was obtained through optical 3D scanning profilometry using a confocal sensor with a measuring range of.5 mm, shown in Figure 4. Details upon the employed measuring techniques are presented in [8]. Typical topography measurements obtained by scanning the whole tooth are presented in Figure 5. The digitization of a tooth contact area, obtained through laser profilometry, was used for numeric calculation of stress state and Von Mises equivalent stress, in enamel surface and subsurface. Our computations were based on the conjugate gradient method. The use of spectral methods, like Discrete Convolution Fast Fourier Transform (DCFFT), allows for efficient computation of high resolution grids [4]. Fig. 3. 3D state of stress in enamel layer Fig. 4. Laser profilometer and teeth specimens Fig. 5. Non-contact measurements by profilometry
34 Fig. 5. Non-contact measurements by profilometry (continued) In situ experimental research at micro and nano level with mechatronic devices by AFM and nanoindentation has demonstrated that the elastic, plastic and fracture properties of tooth layers are very differrent, i.e., enamel, enamel-dentin junction, dentine. Accordingly, in any point from enamel surface we can admit a variation of the critic length, regarding the initiation and developing of biomechanical fatigue cracks [9]. The variation of the number of cycles until critical crack initiation can be computed with fracture mechanics equations [5]. The fatigue-crack propagation data thus obtained was expressed in terms of a simple Paris power-law expression: da C K m (1) dn If an initial microcrack length a0 is considered and the critical crack is calculated with the relation: af K c max () then the number of cycles until the critical crack appears is given by: N 1 m / 1 m / af ao (3) Nf m C 1 m / [ 1 R o ] A graphical three-dimensional representation (3D) of equation 1, when a f and o are variable, is shown in Figure. Obviously, the number of cycles depends on dental contact type, material nature, surface topography and contact stresses. If a f cons tan t, (the diagram in Fig. 7) a fatigue typical curve is obtained. For numerical calculations, the following data was used: m., R 1, C.4 10 11 subsurface biocontacts are stresses of contact and interface and initial. Firstly, stress depends on configuration of solids in contact, complex mechanical characteristics of the material and applied loads. Secondly, the type of stresses depends on fluid pressure, surface microtopography, friction forces and pathological effects present at interfaces [7]. Fig.. 3D representation for number of cycles variation, as function of maximum stress and micro cracks length, N f f o, a f 100 80 0 a 40 0, max 139 MPa, K c 5.4 MPa m1 / and (determined for bodies in contact as stated in []). The group of stresses which acted at crack initiation and crack propagation on the surface and 0 0 10 4 10 10 8 10 N ( a) Fig. 7. Number of cycles variation, for a f 1.01 10 m N f f o 4 1 10 7
35 CONCLUSIONS REFERENCES The study of dental contacts deterioration requires an interdisciplinary approach, combining expertise in dentistry and tribology, with an emphasis on the theories of contact and fracture mechanics. The former depend on the configuration of the solids in contact, on the complex mechanical characteristics of the material, and on the loads applied. The latter depend on fluid pressure, surface microtopography, friction forces, and pathological effects at the interfaces. For example, a lack of saliva film or a change of physiological biochemical parameters of the saliva can produce biomechanical fatigue, dental wear and dental caries. The proposed tribological model takes into account the dental surface topography obtained with optical profilometry [7] and the interface biofluid (saliva), computes the contact pressure and predicts the crack propagation using fracture mechanics. 1. Frunză G., Frunza M.C., 008, Stress state in enamel layer of dental contacts, Proc. ESB, Lucerne, Switzerland and J. of Biomechanics, 41, supplement 1.. Natali A.N., 003, Dental Biomechanics, London, UK. 3. Frunză M.C., Frunză G., 005, The effects of stress state in dental biocontacts, Proc., WTC III, Washington DC, USA, pp. 717. 4. Spînu S., Diaconescu, E., 008, Numerical Simulation of Elastic Conforming Contacts under Eccentric Loading, Proc. of the STLE/ASME International Joint Tribology Conference IJTC008, October 0-, 008, Miami, Florida, USA. 5. Anderseson T.L., 1995, Fracture Mechanics, CRC Press, Inc, London, Tokyo.. Frunză G., 00, Theoretical an Experimental Research upon the Influence of Initial Stresses in Biomechanical Fatigue, Technical Report, Grant 91, CNCSIS (in Romanian). 7. Frunză G., 008, Research upon the Effects of Initial Stresses in Dental Biocontacts, Technical Report, Grant 757, CNCSIS, (in Romanian). 8. Suciu C., Diaconescu E.N., 008, Experimental set-up and preliminary results upon a new technique to measure contact pressure, Acta Tribologica, 1, pp. 1-. 9. Kruzic J.J., Nalla R.K., Kinney J.H., Ritchie R.O., 005, Mechanistic aspects of in vitro fatigue-crack growth in dentin, Biomaterials, p. 1195 1.