- Email: [email protected]
A methodology for fracture strength evaluation of complete denture
Engineering Failure Analysis 18 (2011) 1253–1261
Contents lists available at ScienceDirect
Engineering Failure Analysis journal homepage: www.elsevier.com/locate/engfailanal
Review
A methodology for fracture strength evaluation of complete denture A. Cernescu a,⇑, N. Faur a, C. Bortun b, M. Hluscu a a b
Mechanics and Strength of Materials Department, Politehnica University of Timisoara, Romania Department of Dental Technology, ‘’Victor Babes’’ University of Medicine and Pharmacy of Timisoara, Romania
a r t i c l e
i n f o
Article history: Received 22 December 2010 Received in revised form 3 March 2011 Accepted 4 March 2011 Available online 12 March 2011 Keywords: Complete denture Reverse engineering FEM–XFEM Structural integrity Stress intensity factors
a b s t r a c t Objective: This paper presents a methodology for evaluating the mechanical strength and structural integrity of complete denture based on a thorough study on the mechanical properties of dental material and numerical FEM analysis. Methods: A light curing composite resin, Eclipse (Dentsply International Inc.,– DeguDent GmbH, Hanau, Germany) was tested to evaluate the mechanical properties. According to standards recommendations were performed tensile and bending tests, fracture mechanics and fatigue crack growth rate tests. Using ABAQUS software, was performed a complex FEM analysis on a denture model obtained by 3D scanning and reverse engineering techniques, which may reveal if the applied load can initiate a crack or not. For if a crack is initiated, based on the methodology presented in this study, is analyzed the effect it has on complete denture. Results: For a pressure load of 1.5 MPa, applied on palatal cusps of the upper teeth, we identified the stress concentrations areas, the values of maximum principal stress and strain, and were observed that a crack is initiated. Based on XFEM analysis were evaluated the stress intensity factors at the crack tip and was determined an equivalent stress intenp mm. The value of K eq sity factor, K eq I ¼ 7:42 MPa I is lower than the threshold stress intensity factor range, DKth (resulted from experimental tests), which means that the crack initiated is a stationary crack. Based on results, was calculated a risk factor, which give the fracture probability of the complete denture. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction The loss of teeth impairs patients’ appearance, masticatory ability and speech, thus upsetting the quality of their social and personal life [1]. To restore these functions, removable and complete dentures are often used. The selection of materials for the construction of dentures is crucial because this directly relates to the performance and life span of the appliance during service in the oral cavity. Generally, the complete dentures are made of acrylic composite resins, as basis, and artificial teeth. Acrylic composite resins consist of three primary ingredients: an organic resin matrix, inorganic filler particles and a coupling agent [2,5]. Due, to the brittle fracture behavior and sometimes the processing technology of these materials, there can be obtained complete dentures with small defects which can initiate cracks and resulting in failure of total denture before the expected life time. Among the prevalent fracture types, 29% was a mid-line fracture, in which 68% were observed in maxillary complete dentures and 28% in mandibular complete dentures [4]. The longevity of the maxillary complete dentures for patients with occlusion against mandibular natural dentitions is about 21 months, whereas the average denture life time for those with occlusion against artificial mandibular teeth is of about 10 years [6]. Dorner and all pointed out that the
⇑ Corresponding author. E-mail address: [email protected] (A. Cernescu). 1350-6307/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.engfailanal.2011.03.004
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A. Cernescu et al. / Engineering Failure Analysis 18 (2011) 1253–1261
denture base fractures were reported in 5.8% patients with one complete denture in each arch and tended to occur more frequently if patients had only one denture and that is maxillary complete denture [7]. The relative short life time of the maxillary dentures has led researchers [8,9] to investigate the causes of fracture by studying the stress distribution upon mastication and to find ways to improve their mechanical performance. Different methods such as electrical resistance strain gage [10,11], brittle lacquer [9,12], photoelasticity [13,14] and finite element analysis [15,16] have been used for investigating strain or stress distribution during deformation of dentures. The strain gage and brittle lacquer methods are used to measure stress developed on the surface of dentures and to locate the area of maximum stress where failure occurs. The locations selected for placement of the strain gages depend on the researchers’ experience and the recorded locations of denture fracture. If wrongly placed, they may not provide the most useful results. Brittle lacquer coating can only provide primitive and qualitative information about the stress distribution [17]. The finite element method (FEM) has been used for five decades for numerical stress analysis [18]. 2D FEM can be applied to analyze structures with 2D plane symmetry [19]. It complements or even eliminates the use of complicated experimental methods. The advent of 3D FEM further enables researchers to perform stress analysis on complicated geometries such as complete dentures, and provides a more detailed evaluation of the complete state of stress in the structures. The aims of this paper were to investigate the stress distribution and structural integrity of a maxillary complete denture based on a proposed methodology involving FEM analysis, a thorough knowledge of the mechanical properties of the material and good knowledge of Fatigue and Fracture Mechanics. 2. Materials and methods 2.1. Methodology for fracture strength evaluation To assess the mechanical strength and structural integrity of the analyzed complete denture there was proposed a methodology of calculation based on numerical analysis with finite element method, which is outlined in Fig. 1. This methodology allows rapid and efficient assessment of complete denture durability. Assessment methodology, requires first, a detailed experimental analysis of the denture material, then based on loading and boundary conditions similar to those in the mouth is evaluated the stress and strain fields in complete denture.
Fig. 1. Procedure for assessing structural integrity and mechanical strength of dental prosthesis, where E – tensile Young’s modulus; ruts – ultimate tensile strength; A – total elongation; KIC – fracture toughness; da/dN – fatigue crack growth rate; DK – stress intensity factor range; DKth – threshold stress intensity factor range; c – safety factor; K eq I - equivalent stress intensity factor.
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2.2. Experimental evaluation of the denture material For this study a light curing composite resin Eclipse (Dentsply International Inc. – DeguDent GmbH, Hanau, Germany), was tested to evaluate the mechanical properties. This resin has an elastic behavior followed by a brittle fracture, Fig. 2. For this analysis there were made tensile and bending tests on samples from Eclipse resin, prepared according to the manufacturer’s recommendations. The tests were carried out on a Zwick/Roell ProLine 5 kN testing machine according to ISO 527 [20] (tensile tests) and ASTM D 790 [21] (bending tests) standard and were evaluated the following mechanical properties: – – – –
Ultimate tensile strength: ruts = 76.655 MPa. Tensile Young’s modulus: E = 2900 MPa. Total elongation: At = 2.83 %. Flexural strength: rf = 92 MPa.
The fracture toughness of the Eclipse resin, was determined based on critical stress intensity factor, Kc, on SENB samples, p according to ASTM D5045 [22] standard. Thus, fracture toughness was evaluate as KIC = 100.655 MPa mm. In general, the fatigue loadings in the mouth can be equivalent with a constant amplitude spectrum with stress ratio R = 0. For this type of loading, were performed fatigue crack growth rate tests, according to ASTM D647 [23] standard. The results were expressed in terms of da/dN = f(Kmax) diagram, Fig. 3. Also, were determined the material constants in Paris’ law, p C = 4 1025 and n = 17.844 and the threshold value of the stress intensity factor range, DKth = 14.228 MPa mm. The crack propagation tests were carried out on a servo-hydraulic testing machine (Multipurpose Dynamic Test System, LFV-10-HM, Walter + Baiag, Switzerland), using CT specimens. 2.3. Geometric modeling of the maxillary complete denture Reverse engineering technology was employed to convert a real maxillary complete denture, made of light curing resin Eclipse, into a virtual numerical model [3]. A thin layer of green dye (Okklean, Occlusion spray, DFS, Germany) was sprayed onto the surface of the denture to increase its contrast for scanning. The denture was positioned on a rotating table of a Roland 3D scanner, model LPX-1200, and scanned with a scanning pitch of 0.1 0.1 mm. The scanned surfaces of the denture, Fig. 4, were then imported to the software Pixform Pro (INUS Technology, Seoul, Korea), which combined the surfaces and repaired any defects to create a fully closed surface. The hollow denture was exported in initial graphics exchange specification (IGES) format and then imported into Solid Works 2007 for conversion into a solid model, Fig. 5. 2.4. The FEM and XFEM analysis Using the FEM software package, ABAQUS v6.9.3, on the geometric model of the complete denture was performed an analysis of the stress and strain field. The maximum force of mastication in a patient with complete denture is between 60 and 80 N [24]. For this loading case was considered a mastication force of 70 N distributed on palatal cusps of the upper
Fig. 2. Stress–strain diagram of the Eclipse material.
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ΔK = (1 − R ) ⋅ K max = K max
Fig. 3. The crack propagation diagram for stress ratio R = 0.
Fig. 4. The scanned surfaces of the denture.
teeth, Fig. 6. The areas with distributed force are about 46.666 mm2 and the result is a normal pressure of 1.5 MPa. To fix the model, there have been applied supports on surfaces shown in Fig. 7. The supports from denture channel allow a 0.2 mm displacement in vertical direction and stop the displacements in horizontal plane. Also, the supports from palatal vault allow a 0.1 mm displacement in vertical direction and stop the displacements in horizontal plane. Allowed displacements were considered to replace the deformations of the oral mucosa. The geometric model was meshed in tetrahedral finite elements, C3D8 (154,742 elements) and based on FEM simulation were determined the maximum principal stress (Fig. 8) and Maximum Principal Strain (Fig. 9). Using the XFEM procedure [25] (Extended Finite Element Method), incorporated in ABAQUS, can determine whether to applied load, a crack is initiated or not, where it is initiated and the stress intensity factors at the crack tip. If the applied pressure does not cause a crack initiation, a safety factor (c) is calculated as shown in Fig. 1. If the pressure cause a crack initiation (Fig. 10), then we calculate the values of stress intensity factors at the crack tip, to determine an equivalent stress intensity factor, K eq I , and compare with fracture toughness, KIC. The XFEM method is based on the enrichment of the FE model with additional degrees of freedom (DOFs) that are tied to the nodes of the elements intersected by the crack [26]. In this manner, the discontinuity is included in the numerical model
A. Cernescu et al. / Engineering Failure Analysis 18 (2011) 1253–1261
Fig. 5. The solid model of a real maxillary complete denture.
Normal pressure
Normal pressure
Fig. 6. Areas with normal pressure applied on palatal cusps of teeth.
u1=0,u2=0,u3= -0.2
u1=0,u2=0,u3= -0.1 Fig. 7. Applied boundary conditions on maxillary complete denture model.
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The point with maximum value
Fig. 8. The maximum principal stress distribution (max. value is 72.5 MPa).
The point with maximum value
Fig. 9. The maximum principal strain distribution (max. value is 0.0265 mm/mm).
without modifying the numerical discretization, as the mesh is generated without taking into account the presence of the crack. Therefore, only a single mesh is needed for any crack length and orientation. In addition, nodes surrounding the crack tip are enriched with DOFs associated with functions that reproduce the asymptotic LEFM fields. This enables the modeling of the crack discontinuity within the crack-tip element and substantially increases the accuracy in the computation of the stress intensity factors (SIFs). The nodal displacement for crack modeling in the extended finite element method is given by the following relationship:
uXFEM ðxÞ ¼
X i2C
Ni ðxÞui þ
X i2K
Ni ðxÞHðxÞai þ
X i2K
" Ni ðxÞ
4 X
a¼1
# F a ðxÞbia
ð1Þ
A. Cernescu et al. / Engineering Failure Analysis 18 (2011) 1253–1261
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Fig. 10. The Heaviside function of enriched nodes, crack location, enriched element and surface crack (medallion).
½F a ðr; hÞ; a ¼ 1 4 ¼
pffiffiffi pffiffiffi h pffiffiffi h pffiffiffi h h r sin ; r cos ; r sin sin h; r cos sin h 2 2 2 2
ð2Þ
where C is the set of all nodes in the mesh, Ni(x) is the nodal shape function and ui is the standard DOF of nodes i (ui represents the physical nodal displacement for non-enriched nodes only). The subsets K and K contain the nodes enriched with Heaviside function H(x) or crack-tip functions Fa(x), respectively, and ai, bia are the corresponding DOFs, and r, h are local polar co-ordinates defined at the crack tip [26–33]. Once the nodal displacements obtained for the crack-tip nodes with XFEM procedure, and applying the post-processing subroutines, described in Refs. [26,27] and adapted for our case, were obtained values of stress intensity factors KI and KII and that K eq I [33]:
hc ¼ 2 tan
1
2 0 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi13 2 41 @ K I þ signðK II Þ 8 þ K I A5 4 K II K II
3 K eq I ¼ K I cos
hc 3 hc K II cos sin hc 2 2 2
ð3Þ
ð4Þ
3. Results and conclusions After processing all the data and calculations, the values of stress intensity factors were determined as KI = 2.0121 p p p MPa mm, KII = -10.996 MPa mm, hc = 67.076° (crack propagation direction) and the corresponding K eq mm. I ¼ 7:42 MPa eq The value of equivalent stress intensity factor, K I , is less than DKth and according to proposed methodology it is considered that the initiated crack does not propagate and becomes a stationary crack. In this study, the maximum principal stress criterion for brittle fracture was used for evaluation the stress distribution in complete denture. Next, the fracture risk must be analyzed, considering that a crack is initiated. Also, must be analyzed which are the factors with highest weight in the fracture risk of the denture – the crack initiated or the maximum principal stress. The FAD approach was used to evaluate the fracture risk of the analyzed complete denture. The Failure Assessment Diagram is a concept of a two failure criteria to describe the interaction between fracture and collapse. This diagram is defined in terms of two parameters [34]: Kr – the ratio of the applied linear elastic stress intensity factor, KI, to the materials fracture toughness, KC; Sr – the ratio of the applied stress to the stress to cause collapse of the cracked structure. For construction of the FAD diagram, Fig. 11, was used the following relationship [34]:
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Fig. 11. The FAD diagram and corresponding point (A) of the analyzed complete denture.
K r ¼ Sr
8
p2
ln sec
p 12 Sr 2
ð5Þ
This analysis was represented in the FAD diagram by point A. The coordinates of point A are:
Kr ¼
K eq MPS I ¼ 0:945 ¼ 0:0737 and Sr ¼ UTS KC
MPS – Maximum Principal Stress, UTS – Ultimate Tensile Stress. In FAD diagram, point A is in the safe area but too close to the limit of Sr, indicating a high risk of fracture and that failure is controlled by maximum principal stress. The fracture probability of the denture is very high, 94.5% (Sr = 0.945) and in this case, should be made improvements to reduce the stress field around the crack. This paper presents a particular case in assessing the mechanical strength of the dentures. The study is based on a methodology that requires a thorough knowledge of material properties and a good knowledge of the concepts of Fracture Mechanics and FEM analysis, Fatigue of Materials and Damage Tolerance. The method presented can form the basis of strength calculations for both dentures are in design stage and for those that are in use and after the examination was observed defects or cracks. Acknowledgements This work was supported by the strategic Grant POSDRU/89/1.5/S/57649, Project ID-57649 (PERFORM-ERA), co-financed by the European Social Fund-Investing in People, within the Sectoral Operational Programme Human Resources Development 2007-2013 and by the IDEAS Grant CNCSIS, 1878/2008, Contract No. 1141/2009. References [1] Mack F, Schwahn C, Feine JS, et al. The impact of tooth loss on general health related to quality of life among elderly Pomeranians: results from the study of health in Pomerania (SHIP-O). Int J Prosthodont 2005;18:414–9. [2] David G. Charlton, Resin composites. [3] Cheng YY, Li YJ, Fok SL, Cheung WL, Chow TW. 3D FEA of high-performance polyethylene fiber reinforced maxillary dentures. Dental Mater; 2010, article in press. [4] Darbar UR, Huggett R, Harrison A. Denture fracture – a survey. Br Dent J 1994;176:342–5. [5] Jagger DC, Harrison A, Jandt KD. The reinforcement of dentures. J Oral Rehabil 1999;26:185–94. [6] Hargreaves AS. The prevalence of fractured dentures. A survey. Br Dent J 1969;126:451–5. [7] Dorner S, Zeman F, Koller M, Lang R, Handel G, Behr M. Clinical performance of complete denture: a retrospective study. Int J Prosthodont 2010;23(5):410–7. [8] Horton E. Experimental investigation of internal strains in polimerised metyl methacrylate as revealed by polarized light. Br Dent J 1949;86:176–80. [9] Matthews E, Wain EA. Stresses in denture bases. Br Dent J 1956;100:167–71. [10] Stafford GD, Griffiths DW. Investigation of the strain produced in maxillary complete dentures in function. J Oral Rehabil 1979;6:241–56. [11] Prombonas A, Vlissidis D. Effects of the position of artificial teeth and load levels on stress in the complete maxillary denture. J Prosthet Dent 2002;88:415–22. [12] Wain EA. A method of measuring stress in dentures. Nature 1955;175:1082–3. [13] Craig RG, Farah JW, El-Tahawi HM. Three-dimensional photoelastic stress analysis of maxillary complete dentures. J Prosthet Dent 1974;31:122–9.
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[14] Fernandes CP, Glantz P-OJ, Svensson SA, Bergmark A. Reflection photoelasticity: a new method for studies of clinical mechanics in prosthetic dentistry. Dent Mater 2003;19:106–10. [15] Rees Js, Huggett R, Harrison A. Finite element analysis of the stress-concentrating effect of fraenal notches in complete dentures. Int J Prosthodont 1990;3:238–40. [16] Darbar UR, Hugget R, Harrison A, Williams K. Finite element analysis of stress distribution at the tooth-denture base interface of acylic resin teeth debonding from the denture base. J Prosthet Dent 1995;74:591–4. [17] Jonson W. A study of stress distribution in complete upper dentures. Dent Pract 1965;15:374–9. [18] Turner MJ, Clough RW, Martin HC, Topp LJ. Stiffness and deflection analysis of complex structures. J Aero Sci 1956;23:805–24. [19] Clough RW, The finite element method in plane stress analysis. In: Proceedings, American Society of civil engineers 2nd conference on electronic computation, 1960. p. 345-78. [20] SR. EN ISO 527, Standard test method for tensile properties of plastic materials. [21] ASTM D790. Standard test methods for flexural properties of unreinforced and reinforced plastics and electrical insulating materials. [22] ASTM D5045. Standard test methods for plane-strain fracture toughness and strain energy release rate of plastic materials. [23] ASTM D647. Standard test method for measurement of fatigue crack growth rates. [24] Zarb G, Bolender CH. Carlsson G, Boucher’s prosthodontic treatment for edentulous patients, Mosby, 1997. [25] ABAQUS Version 6.9.3, – documentation manual. [26] Giner E, Sukumar N, Tarancon JE, Fuenmayor FJ. An Abaqus implementation of the extended finite element method. Eng Frac Mech 2009;76:347–68. [27] T.P. Fries, RWTH Aachen University, Germany
Contents lists available at ScienceDirect
Engineering Failure Analysis journal homepage: www.elsevier.com/locate/engfailanal
Review
A methodology for fracture strength evaluation of complete denture A. Cernescu a,⇑, N. Faur a, C. Bortun b, M. Hluscu a a b
Mechanics and Strength of Materials Department, Politehnica University of Timisoara, Romania Department of Dental Technology, ‘’Victor Babes’’ University of Medicine and Pharmacy of Timisoara, Romania
a r t i c l e
i n f o
Article history: Received 22 December 2010 Received in revised form 3 March 2011 Accepted 4 March 2011 Available online 12 March 2011 Keywords: Complete denture Reverse engineering FEM–XFEM Structural integrity Stress intensity factors
a b s t r a c t Objective: This paper presents a methodology for evaluating the mechanical strength and structural integrity of complete denture based on a thorough study on the mechanical properties of dental material and numerical FEM analysis. Methods: A light curing composite resin, Eclipse (Dentsply International Inc.,– DeguDent GmbH, Hanau, Germany) was tested to evaluate the mechanical properties. According to standards recommendations were performed tensile and bending tests, fracture mechanics and fatigue crack growth rate tests. Using ABAQUS software, was performed a complex FEM analysis on a denture model obtained by 3D scanning and reverse engineering techniques, which may reveal if the applied load can initiate a crack or not. For if a crack is initiated, based on the methodology presented in this study, is analyzed the effect it has on complete denture. Results: For a pressure load of 1.5 MPa, applied on palatal cusps of the upper teeth, we identified the stress concentrations areas, the values of maximum principal stress and strain, and were observed that a crack is initiated. Based on XFEM analysis were evaluated the stress intensity factors at the crack tip and was determined an equivalent stress intenp mm. The value of K eq sity factor, K eq I ¼ 7:42 MPa I is lower than the threshold stress intensity factor range, DKth (resulted from experimental tests), which means that the crack initiated is a stationary crack. Based on results, was calculated a risk factor, which give the fracture probability of the complete denture. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction The loss of teeth impairs patients’ appearance, masticatory ability and speech, thus upsetting the quality of their social and personal life [1]. To restore these functions, removable and complete dentures are often used. The selection of materials for the construction of dentures is crucial because this directly relates to the performance and life span of the appliance during service in the oral cavity. Generally, the complete dentures are made of acrylic composite resins, as basis, and artificial teeth. Acrylic composite resins consist of three primary ingredients: an organic resin matrix, inorganic filler particles and a coupling agent [2,5]. Due, to the brittle fracture behavior and sometimes the processing technology of these materials, there can be obtained complete dentures with small defects which can initiate cracks and resulting in failure of total denture before the expected life time. Among the prevalent fracture types, 29% was a mid-line fracture, in which 68% were observed in maxillary complete dentures and 28% in mandibular complete dentures [4]. The longevity of the maxillary complete dentures for patients with occlusion against mandibular natural dentitions is about 21 months, whereas the average denture life time for those with occlusion against artificial mandibular teeth is of about 10 years [6]. Dorner and all pointed out that the
⇑ Corresponding author. E-mail address: [email protected] (A. Cernescu). 1350-6307/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.engfailanal.2011.03.004
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denture base fractures were reported in 5.8% patients with one complete denture in each arch and tended to occur more frequently if patients had only one denture and that is maxillary complete denture [7]. The relative short life time of the maxillary dentures has led researchers [8,9] to investigate the causes of fracture by studying the stress distribution upon mastication and to find ways to improve their mechanical performance. Different methods such as electrical resistance strain gage [10,11], brittle lacquer [9,12], photoelasticity [13,14] and finite element analysis [15,16] have been used for investigating strain or stress distribution during deformation of dentures. The strain gage and brittle lacquer methods are used to measure stress developed on the surface of dentures and to locate the area of maximum stress where failure occurs. The locations selected for placement of the strain gages depend on the researchers’ experience and the recorded locations of denture fracture. If wrongly placed, they may not provide the most useful results. Brittle lacquer coating can only provide primitive and qualitative information about the stress distribution [17]. The finite element method (FEM) has been used for five decades for numerical stress analysis [18]. 2D FEM can be applied to analyze structures with 2D plane symmetry [19]. It complements or even eliminates the use of complicated experimental methods. The advent of 3D FEM further enables researchers to perform stress analysis on complicated geometries such as complete dentures, and provides a more detailed evaluation of the complete state of stress in the structures. The aims of this paper were to investigate the stress distribution and structural integrity of a maxillary complete denture based on a proposed methodology involving FEM analysis, a thorough knowledge of the mechanical properties of the material and good knowledge of Fatigue and Fracture Mechanics. 2. Materials and methods 2.1. Methodology for fracture strength evaluation To assess the mechanical strength and structural integrity of the analyzed complete denture there was proposed a methodology of calculation based on numerical analysis with finite element method, which is outlined in Fig. 1. This methodology allows rapid and efficient assessment of complete denture durability. Assessment methodology, requires first, a detailed experimental analysis of the denture material, then based on loading and boundary conditions similar to those in the mouth is evaluated the stress and strain fields in complete denture.
Fig. 1. Procedure for assessing structural integrity and mechanical strength of dental prosthesis, where E – tensile Young’s modulus; ruts – ultimate tensile strength; A – total elongation; KIC – fracture toughness; da/dN – fatigue crack growth rate; DK – stress intensity factor range; DKth – threshold stress intensity factor range; c – safety factor; K eq I - equivalent stress intensity factor.
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2.2. Experimental evaluation of the denture material For this study a light curing composite resin Eclipse (Dentsply International Inc. – DeguDent GmbH, Hanau, Germany), was tested to evaluate the mechanical properties. This resin has an elastic behavior followed by a brittle fracture, Fig. 2. For this analysis there were made tensile and bending tests on samples from Eclipse resin, prepared according to the manufacturer’s recommendations. The tests were carried out on a Zwick/Roell ProLine 5 kN testing machine according to ISO 527 [20] (tensile tests) and ASTM D 790 [21] (bending tests) standard and were evaluated the following mechanical properties: – – – –
Ultimate tensile strength: ruts = 76.655 MPa. Tensile Young’s modulus: E = 2900 MPa. Total elongation: At = 2.83 %. Flexural strength: rf = 92 MPa.
The fracture toughness of the Eclipse resin, was determined based on critical stress intensity factor, Kc, on SENB samples, p according to ASTM D5045 [22] standard. Thus, fracture toughness was evaluate as KIC = 100.655 MPa mm. In general, the fatigue loadings in the mouth can be equivalent with a constant amplitude spectrum with stress ratio R = 0. For this type of loading, were performed fatigue crack growth rate tests, according to ASTM D647 [23] standard. The results were expressed in terms of da/dN = f(Kmax) diagram, Fig. 3. Also, were determined the material constants in Paris’ law, p C = 4 1025 and n = 17.844 and the threshold value of the stress intensity factor range, DKth = 14.228 MPa mm. The crack propagation tests were carried out on a servo-hydraulic testing machine (Multipurpose Dynamic Test System, LFV-10-HM, Walter + Baiag, Switzerland), using CT specimens. 2.3. Geometric modeling of the maxillary complete denture Reverse engineering technology was employed to convert a real maxillary complete denture, made of light curing resin Eclipse, into a virtual numerical model [3]. A thin layer of green dye (Okklean, Occlusion spray, DFS, Germany) was sprayed onto the surface of the denture to increase its contrast for scanning. The denture was positioned on a rotating table of a Roland 3D scanner, model LPX-1200, and scanned with a scanning pitch of 0.1 0.1 mm. The scanned surfaces of the denture, Fig. 4, were then imported to the software Pixform Pro (INUS Technology, Seoul, Korea), which combined the surfaces and repaired any defects to create a fully closed surface. The hollow denture was exported in initial graphics exchange specification (IGES) format and then imported into Solid Works 2007 for conversion into a solid model, Fig. 5. 2.4. The FEM and XFEM analysis Using the FEM software package, ABAQUS v6.9.3, on the geometric model of the complete denture was performed an analysis of the stress and strain field. The maximum force of mastication in a patient with complete denture is between 60 and 80 N [24]. For this loading case was considered a mastication force of 70 N distributed on palatal cusps of the upper
Fig. 2. Stress–strain diagram of the Eclipse material.
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ΔK = (1 − R ) ⋅ K max = K max
Fig. 3. The crack propagation diagram for stress ratio R = 0.
Fig. 4. The scanned surfaces of the denture.
teeth, Fig. 6. The areas with distributed force are about 46.666 mm2 and the result is a normal pressure of 1.5 MPa. To fix the model, there have been applied supports on surfaces shown in Fig. 7. The supports from denture channel allow a 0.2 mm displacement in vertical direction and stop the displacements in horizontal plane. Also, the supports from palatal vault allow a 0.1 mm displacement in vertical direction and stop the displacements in horizontal plane. Allowed displacements were considered to replace the deformations of the oral mucosa. The geometric model was meshed in tetrahedral finite elements, C3D8 (154,742 elements) and based on FEM simulation were determined the maximum principal stress (Fig. 8) and Maximum Principal Strain (Fig. 9). Using the XFEM procedure [25] (Extended Finite Element Method), incorporated in ABAQUS, can determine whether to applied load, a crack is initiated or not, where it is initiated and the stress intensity factors at the crack tip. If the applied pressure does not cause a crack initiation, a safety factor (c) is calculated as shown in Fig. 1. If the pressure cause a crack initiation (Fig. 10), then we calculate the values of stress intensity factors at the crack tip, to determine an equivalent stress intensity factor, K eq I , and compare with fracture toughness, KIC. The XFEM method is based on the enrichment of the FE model with additional degrees of freedom (DOFs) that are tied to the nodes of the elements intersected by the crack [26]. In this manner, the discontinuity is included in the numerical model
A. Cernescu et al. / Engineering Failure Analysis 18 (2011) 1253–1261
Fig. 5. The solid model of a real maxillary complete denture.
Normal pressure
Normal pressure
Fig. 6. Areas with normal pressure applied on palatal cusps of teeth.
u1=0,u2=0,u3= -0.2
u1=0,u2=0,u3= -0.1 Fig. 7. Applied boundary conditions on maxillary complete denture model.
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The point with maximum value
Fig. 8. The maximum principal stress distribution (max. value is 72.5 MPa).
The point with maximum value
Fig. 9. The maximum principal strain distribution (max. value is 0.0265 mm/mm).
without modifying the numerical discretization, as the mesh is generated without taking into account the presence of the crack. Therefore, only a single mesh is needed for any crack length and orientation. In addition, nodes surrounding the crack tip are enriched with DOFs associated with functions that reproduce the asymptotic LEFM fields. This enables the modeling of the crack discontinuity within the crack-tip element and substantially increases the accuracy in the computation of the stress intensity factors (SIFs). The nodal displacement for crack modeling in the extended finite element method is given by the following relationship:
uXFEM ðxÞ ¼
X i2C
Ni ðxÞui þ
X i2K
Ni ðxÞHðxÞai þ
X i2K
" Ni ðxÞ
4 X
a¼1
# F a ðxÞbia
ð1Þ
A. Cernescu et al. / Engineering Failure Analysis 18 (2011) 1253–1261
1259
Fig. 10. The Heaviside function of enriched nodes, crack location, enriched element and surface crack (medallion).
½F a ðr; hÞ; a ¼ 1 4 ¼
pffiffiffi pffiffiffi h pffiffiffi h pffiffiffi h h r sin ; r cos ; r sin sin h; r cos sin h 2 2 2 2
ð2Þ
where C is the set of all nodes in the mesh, Ni(x) is the nodal shape function and ui is the standard DOF of nodes i (ui represents the physical nodal displacement for non-enriched nodes only). The subsets K and K contain the nodes enriched with Heaviside function H(x) or crack-tip functions Fa(x), respectively, and ai, bia are the corresponding DOFs, and r, h are local polar co-ordinates defined at the crack tip [26–33]. Once the nodal displacements obtained for the crack-tip nodes with XFEM procedure, and applying the post-processing subroutines, described in Refs. [26,27] and adapted for our case, were obtained values of stress intensity factors KI and KII and that K eq I [33]:
hc ¼ 2 tan
1
2 0 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi13 2 41 @ K I þ signðK II Þ 8 þ K I A5 4 K II K II
3 K eq I ¼ K I cos
hc 3 hc K II cos sin hc 2 2 2
ð3Þ
ð4Þ
3. Results and conclusions After processing all the data and calculations, the values of stress intensity factors were determined as KI = 2.0121 p p p MPa mm, KII = -10.996 MPa mm, hc = 67.076° (crack propagation direction) and the corresponding K eq mm. I ¼ 7:42 MPa eq The value of equivalent stress intensity factor, K I , is less than DKth and according to proposed methodology it is considered that the initiated crack does not propagate and becomes a stationary crack. In this study, the maximum principal stress criterion for brittle fracture was used for evaluation the stress distribution in complete denture. Next, the fracture risk must be analyzed, considering that a crack is initiated. Also, must be analyzed which are the factors with highest weight in the fracture risk of the denture – the crack initiated or the maximum principal stress. The FAD approach was used to evaluate the fracture risk of the analyzed complete denture. The Failure Assessment Diagram is a concept of a two failure criteria to describe the interaction between fracture and collapse. This diagram is defined in terms of two parameters [34]: Kr – the ratio of the applied linear elastic stress intensity factor, KI, to the materials fracture toughness, KC; Sr – the ratio of the applied stress to the stress to cause collapse of the cracked structure. For construction of the FAD diagram, Fig. 11, was used the following relationship [34]:
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A. Cernescu et al. / Engineering Failure Analysis 18 (2011) 1253–1261
Fig. 11. The FAD diagram and corresponding point (A) of the analyzed complete denture.
K r ¼ Sr
8
p2
ln sec
p 12 Sr 2
ð5Þ
This analysis was represented in the FAD diagram by point A. The coordinates of point A are:
Kr ¼
K eq MPS I ¼ 0:945 ¼ 0:0737 and Sr ¼ UTS KC
MPS – Maximum Principal Stress, UTS – Ultimate Tensile Stress. In FAD diagram, point A is in the safe area but too close to the limit of Sr, indicating a high risk of fracture and that failure is controlled by maximum principal stress. The fracture probability of the denture is very high, 94.5% (Sr = 0.945) and in this case, should be made improvements to reduce the stress field around the crack. This paper presents a particular case in assessing the mechanical strength of the dentures. The study is based on a methodology that requires a thorough knowledge of material properties and a good knowledge of the concepts of Fracture Mechanics and FEM analysis, Fatigue of Materials and Damage Tolerance. The method presented can form the basis of strength calculations for both dentures are in design stage and for those that are in use and after the examination was observed defects or cracks. Acknowledgements This work was supported by the strategic Grant POSDRU/89/1.5/S/57649, Project ID-57649 (PERFORM-ERA), co-financed by the European Social Fund-Investing in People, within the Sectoral Operational Programme Human Resources Development 2007-2013 and by the IDEAS Grant CNCSIS, 1878/2008, Contract No. 1141/2009. References [1] Mack F, Schwahn C, Feine JS, et al. The impact of tooth loss on general health related to quality of life among elderly Pomeranians: results from the study of health in Pomerania (SHIP-O). Int J Prosthodont 2005;18:414–9. [2] David G. Charlton, Resin composites. [3] Cheng YY, Li YJ, Fok SL, Cheung WL, Chow TW. 3D FEA of high-performance polyethylene fiber reinforced maxillary dentures. Dental Mater; 2010, article in press. [4] Darbar UR, Huggett R, Harrison A. Denture fracture – a survey. Br Dent J 1994;176:342–5. [5] Jagger DC, Harrison A, Jandt KD. The reinforcement of dentures. J Oral Rehabil 1999;26:185–94. [6] Hargreaves AS. The prevalence of fractured dentures. A survey. Br Dent J 1969;126:451–5. [7] Dorner S, Zeman F, Koller M, Lang R, Handel G, Behr M. Clinical performance of complete denture: a retrospective study. Int J Prosthodont 2010;23(5):410–7. [8] Horton E. Experimental investigation of internal strains in polimerised metyl methacrylate as revealed by polarized light. Br Dent J 1949;86:176–80. [9] Matthews E, Wain EA. Stresses in denture bases. Br Dent J 1956;100:167–71. [10] Stafford GD, Griffiths DW. Investigation of the strain produced in maxillary complete dentures in function. J Oral Rehabil 1979;6:241–56. [11] Prombonas A, Vlissidis D. Effects of the position of artificial teeth and load levels on stress in the complete maxillary denture. J Prosthet Dent 2002;88:415–22. [12] Wain EA. A method of measuring stress in dentures. Nature 1955;175:1082–3. [13] Craig RG, Farah JW, El-Tahawi HM. Three-dimensional photoelastic stress analysis of maxillary complete dentures. J Prosthet Dent 1974;31:122–9.
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