| Abstract|| |
Aim: Thermal analysis of the temperature and stress distribution of parallel sided, threaded and non-threaded dowels and core materials under thermal loading within a maxillary central incisor using a three dimensional finite element study.
Materials and Methods: 3D models of endodontically treated maxillary central incisor with parallel sided, threaded and non- threaded post and core materials were simulated using the ANSYS software. Materials simulated were parallel sided cast gold post and core, parallel sided fibre reinforced composite (FRC) post and core, and parallel sided, threaded, prefabricated stainless steel post and amalgam core. Thermal loads simulating hot (60 degree C/ 333K) and cold (15 degree C/288K) liquid were applied for 15 seconds at the incisal edge. The temperature changes at the selected nodes were obtained on the various post and core materials, interface between post and dentin, interface between core and dentin, within the dentin and within the cement layer.
Results: Temperature and stress distribution pattern were represented in numerical and color coding and results interpreted. Thermal stresses arises as a result of temperature changes. A decreased temperature gradient of the metallic dowels and core (T1 hot - 0.002K, T3 hot - 1.071K, T1 cold -0.99K, T3 cold - 0K) were obtained than that of the FRC dowel and core of 1.982K(hot) and1.55K(cold) respectively due to the higher thermal conductivity of the metals. Higher thermal stress values of 3.567 Mpa(hot) and 3.092 Mpa(cold) respectively were obtained for the FRC dowels and higher stress values of 39.679 Mpa(hot) and 57.855 Mpa(cold) respectively were also obtained for the FRC cores. These values indicated that thermal stresses of the FRC dowel and core were greater than that of cast gold dowel and core and prefabricated stainless steel dowel and amalgam core due to its high coefficient of thermal expansion. Maximum stress values of the FRC dowel and core of 1.87 Mpa(hot) and 2.57 Mpa(cold) respectively were also generated in the cement layer, core and metal ceramic crown. The junction of the metal ceramic crown and dentin demonstrated the maximum stress. Higher thermal stress values of 59.162 ± 10 Mpa were obtained in the restoration and the coronal portion of the dentin than the stress levels of .0039 ± 10Mpa in the supporting bone due to an increased thermal expansion.
Conclusion: Non-metallic dowel and core materials such as fibre reinforced composite dowels (FRC) generate greater stress than metallic dowel and core materials. This emphasized the preferable use of the metallic dowel and core materials in the oral environment.
Keywords: Finite element thermal analysis, temperature changes, thermal analysis of dowel and core materials, thermal stress distribution
|How to cite this article:|
Varghese S, Ariga P, Padmanaban T V, Subramanian R. A finite element thermal analysis of various dowel and core materials. Indian J Dent Res 2012;23:176-81
|How to cite this URL:|
Varghese S, Ariga P, Padmanaban T V, Subramanian R. A finite element thermal analysis of various dowel and core materials. Indian J Dent Res [serial online] 2012 [cited 2021 Oct 28];23:176-81. Available from: https://www.ijdr.in/text.asp?2012/23/2/176/100422
| Introduction|| |
When a large portion of the clinical crown has been lost due to damage, it is often impossible to achieve sufficient anchorage of a restoration in the remaining dentin. The clinician may choose from cast post and cores, corono-radicular core build-ups to prefabricated posts.
Thermal loads in the oral environment range from zero degree C to 67 degree C.  Dentin being a fundamental substrate, its properties and characteristics like thermal insulation and fluid exchange are key determinants. , During restorative procedures, natural tooth tissues are replaced by a host of restorative materials. The efficiency of these restorative materials as acceptable substitutes, with respect to the properties of natural tooth tissues has to be determined.  Likewise, the response of these restorative materials to thermal stresses caused by temperature changes also has to be investigated. During a change in temperature, tooth restorations may expand or contract more than the tooth depending upon their thermal expansion coefficients, creating either tangential tensile or compressive stresses in the natural tooth. The clinical significance would be in terms of the fracture of the restoration, poor marginal adaptation and marginal leakage.
So far, the work carried out on this subject was considered to be inconclusive. In vitro studies conducted by De Vree,  Spierings et al, , using the finite element method on heat transport problems, resulted in a linear function of temperature to time. On the contrary, in vivo studies conducted by Spieringset al, , resulted in a non - linear function of temperature to time.
Hence, the aim of this study was to investigate the distribution of the thermal stresses resulting from temperature changes:
- On the various post and core materials,
- Interface between post and dentin,
- Interface between core and dentin,
- Within the dentin, and
- Within the cement layer, using 3D FE model of a maxillary central incisor.
| Materials and Methods|| |
In this investigation, a 3Dmodel of a block section of the maxilla, that included a central incisor and its supporting structures were analyzed using ANSYS finite element software. A maxillary central incisor with its internal anatomy and morphology was modeled with the geometric data. ,,, The mesiodistal and labiopalatal measurements of an extracted tooth were obtained by cutting the tooth at various sections.  The measurements obtained correlated with the data given in the literature. ,,,, The unrestored tooth model was then modified as an endodontically treated maxillary central incisor, restored with a post and core and porcelain fused to metal crown 23.5mm long with a root length of 13.5mm and a diameter of 7mm at the cervical margin.
The supporting tissues consisted of a cylindrical section of bone with its soft tissues 20mm in height and 10mm in diameter. The tooth was invested in a socket of 0.5mm cortical bone with uniform periodontal ligament 0.2mm. , A 2mm thick layer of soft tissue covered a 2mm thick cortical layer of the bone. The remaining bone was trabecular bone. Data for the supporting structures were obtained from the literature , and mechanical drawings created. Each entity of the model was designed as a separate layer using lines and arc segments. Volumes were generated for each of these layers and attached to one another. The model was subdivided into 67,286 ten node tetrahedral axisymmetric finite elements defined by 90,756 nodes. [Figure 1].With the incorporation of elastic and thermal properties, the model simulated the natural tooth.
T1 (First model) -Parallel sided cast gold post and core
T2 (Second model) -Parallel sided fibre reinforced composite (FRC) post and core
T3 (Third model) - Parallel sided, threaded, pre-fabricated stainless steel post and amalgam core.
All the three models had a post length of 10.5mm, post diameter of 2.3mm with 3mm guttapercha at the apex.  The elliptical shape of the post space obtained by flaring the occlusal 2 to 3mm of post space during the canal enlargement, strengthened the post and also served as an anti rotational feature.  Luting agent was glass ionomer cement for T1and T3 models and flowable composite for T2 after the tooth was etched, bonded and silanized;  modeled to a uniform thickness of 35 microns. The respective cores was 6mm in height labially and 4mm in height interproximally.  The tooth preparation for the artificial tooth assumed a uniform incisal reduction of 2mm and 1.5mm reduction of the axial surfaces. A taper of 2 degrees was given on each axial wall. A full shoulder margin was modeled with a 2 mm ferrule of the coronal dentin. ,, The placement of a ferrule (Hemmingset al)  has been considered as the most important anti rotational feature for posts and cores. A 0.3mm thick cast gold coping was veneered with the porcelain for porcelain fused to metal crown.  Glass ionomer cement was used as the luting agent for T1and T3 models and also modeled to a uniform thickness of 35 microns  by offsetting.
Each element was assigned unique elastic and thermal properties to represent the materials modeled. ,,,,, [Table 1]. Homogeneity, iosotrophy, and linear elasticity were assumed for all materials including the continual interfaces between the materials. The model was restrained at all the nodes on the inferior and lateral edges of the trabecular bone, and on the lateral edges of the cortical bone and soft tissues.
Simulating mouth temperature, the initial temperature of 36 degrees C (309K) was given as the base temperature. Thermal loads simulating hot (60 degree C/333K) and cold (15 degrees C/288K) liquid was applied for 15 seconds at the incisal edge of the three models as performed by Spierings et al. The temperature changes at the selected nodes were obtained.
The stress distribution caused by thermal stresses were calculated using the three dimensional Von Mises criteria.
σ1,σ2,σ3 are known as principal stresses and σvm is the Von Mises stress. ThePrincipal stresses are normal stresses acting on the principal planes on which shearing stresses are zero. They are found by using the existing six normal and shearing stress components σx,σy,σz,σxy,σyz,σzy.
Stress distribution was represented both in numerical values and color coding and the results were interpreted after the models were subjected to the analysis.
| Results|| |
Stress distribution was represented in numerical values and color coding and results interpreted. [Table 2]a.
Thermal conductivity of cast gold was 0.710cal/cm and stainless steel was 2.1cal/cm, whereas thermal conductivity of the FRC and dentin was 0.0026 cal/cm and 0.0015 cal/cm respectively. Temperature differences between the coronal portion of the core and the apical tip of the dowel was T1 hot - 0.002K, T2 hot -1.982K, T3 hot - 1.071K, T1 cold - 0.99K, T2 cold - 1.55K,and T3 cold - 0K [Table 2]b. Temperature changes were greater at the coronal portion of the core than the apical section of the dowel, as base temperature was reached at the coronal portion of the dowel [Figure 2].
|Figure 2: Temperature gradient from coronal portion of the core to apical tip of dowel|
Click here to view
The thermal expansion coefficient of dentin, gold alloy, stainless steel and FRC were 8.3 x 10-6/o C, 14.4 x 10-6/oC, 9.9 x 10-6/oC and 27.8 x 10-6/oC respectively. The Von Mises stress within the core were T1 hot - 36.641MPa, T2 hot - 39.679 MPa, T3 hot - 39.292 MPa,T1 cold - 33.192 MPa, T2 cold - 57.855 MPa and T3 cold - 35.622 MPa. The Von Misses stress between the dowel and the dentin were T1 hot - 2.988 Mpa, T2 hot - 3.567Mpa, T3 hot - 2.765Mpa, T1 cold - 2.655 Mpa, T2 cold - 3.092 Mpa, and T3 cold - 2.589 Mpa. Von Mises stresses in the supporting bone was T1 hot - 0.010 MPa, T2 hot - 0.00519MPa, T3 hot - 0.0040MPa, T1 cold - 0.010MPa, T2 cold - 0.014MPa, and T3 cold - 0.0039MPa [Table 3]a.
Von Mises stress levels in the cement layer were T1 hot - 1.064MPa, T2 hot - 1.87MPa, T3 hot - 1.07MPa, T1 cold - 1.953MPa, T2 cold - 2.57MPa, T3 cold - 1.819MPa. Thermal stresses were developed in the cement layer also. T2 hot and T2 cold models showed increased stress levels than T1 and T3 hot and cold models [Figure 3].
| Discussion|| |
This study investigated the distribution of thermal stresses resulting from temperature changes under the thermal loading. The results proved that thermal stress levels were closely related to the temperature gradient. Teeth restored with various dowel and core materials, are subjected to cyclic thermal stresses in the oral cavity with the normal intake of hot and cold food and beverages. Thermal loads in the oral environment range from zero degree C to 67 degree Cas suggested by Palmer et al.
Thermal conductivity, thermal diffusivity and linear coefficient of thermal expansion are important parameters in predicting the transfer of thermal energy through a material since an unsteady state of heat transfer exists during ingestion of hot and cold food and beverages.  When dental structures are replaced with restorative materials, the thermal diffusivity of the tooth changes.  Thermal diffusivity of a material controls the time and rate of the temperature change as heat passes through a material.  It measures the rate at which a body with non-uniform temperature reaches a state of thermal equilibrium.
As proved by Spieringset al,  thermal analysis can be performed by calculation of the temperature changes in a theoretical tooth model by finite element method. Finite element analysis is a computational analysis used extensively in measuring internal stresses which cannot be assessed by other experimental methods. It has also been extensively applied in determining the stress distribution patterns in endodontically treated teeth since stress induced root fractures are common. ,,,, Results are displayed as a color measurement bar in which each color corresponds to a range of stress values. Different shades of color indicates stress with dark red indicating maximum stress and dark blue indicating reduced stress. ,
The results of this study showed that temperature gradient of the metal dowel and the core was smaller than the FRC dowel and core. T1 and T3 hot and cold models showed a decreased temperature gradient in the dowel and core, cement layer and tooth compared to T2 hot and T2 cold models [Figure 2].This could be attributed to the increased thermal conductivity of the metal dowel and core materials compared to the FRC dowel and core materials which correlates to the findings by Braden M. 
The thermal stresses of the resin dowel and core were greater than that of cast gold dowel and core and prefabricated stainless steel dowel and amalgam core. Von Mises stress in the restoration and the coronal portion of the dentin was higher than the stress levels in the supporting bone  [Table 3]a.
Thermal stresses were developed in the cement layer also. T2 hot and T2 cold models showed increased stress levels than T1 and T3 hot and cold models [Figure 3]. This could be attributed to the increased coefficient of thermal expansion levels of FRC dowel and core materials compared to metal dowel and core materials. Concentration of stresses at the apical end of the dowel could lead to failures cohesively within the cement or at its interface within the dentin. This result was similar to previous studies by Braden,  Cohen et al and Hong - So Yang. 
The FRC dowel and core restoration generated high stress in the cement layer, core and metal ceramic crown. The junction of metal ceramic crown and dentin demonstrated the maximum stress. This emphasized the need for a ferrule in the final restoration which has been suggested to improve the integrity of the endodontically treated tooth as it counteracts the functional lever forces, wedging effects and the lateral forces exerted during insertion and function. , Thermal changes had minimal effect on the surrounding bone as concluded by Braden.
The Von Mises stress levels in this study were higher than that conducted by Yang et al. This could be attributed to the fact that a three dimensional model was used unlike a two dimensional model used in the previous studies. The reason for selecting Von Mises criteria which apparently rises in tensile type stresses, lies in the fact that the brittle materials of which tooth is a member, fail primarily to tensile type normal stresses. As stated by Yaman et al,  the samples, as well as the measurement techniques of each conducted measurement may never be identical owing to a large degree of variance of the material properties found in the literature.
The outcome of this study suggested that it was preferable to use the metallic dowel and core materials in the oral environment. Non-metallic dowel and core materials such as FRC dowels produce greater stress than the metallic dowel materials of the stainless steel and gold alloy.
This study was a simulative analysis; long term clinical studies are required to obtain better inferences. Other parameters such as occlusion should be investigated and the combined effects of thermal changes and occlusion evaluated.
| Conclusion|| |
Finite Element Analysis was done to investigate the temperature and stress distribution under thermal loading on the various dowel and core materials using a simulated three dimensional model of a maxillary central incisor.
Within the limitations of this study, the following can be concluded:
- Thermal stress levels were closely related to the temperature gradient.
- Temperature gradient of the metal dowel and core was lesser than that of the non-metal dowel and core because of the higher thermal conductivity of the former materials.
- The thermal stresses of the FRC dowel and core were greater than that of cast gold dowel and core and prefabricated stainless steel dowel and amalgam core due to its high coefficient of thermal expansion.
- FRC dowel and core restoration generated high stress in the cement layer, core and metal ceramic crown.
- The junction of metal ceramic crown and dentin demonstrated the maximum stress.
- Thermal stresses were greater in the restoration and the coronal portion of the dentin than the stress levels in the supporting bone due an increased thermal expansion of the restorative materials.
Hence, the outcome of this study suggests that it is preferable to use the metallic dowel and cores in the oral environment. Non-metallic dowel and core materials such as fibre reinforced composite dowels (FRC) generate greater stress than the metallic dowel and core materials.
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Department of Prosthodontics, Noorul Islam College of Dental Sciences, Aralumoodu P O, Neyattinkara
Source of Support: None, Conflict of Interest: None
[Figure 1], [Figure 2], [Figure 3]
[Table 1], [Table 2], [Table 3]