Mechanical Strength Analysis of Extracoronal Magnetic Attachment
by Three-Dimensional Finite Element Method-Report II Introduction of elasto-plastic analysisA. Otoda, Yo. Ohno, K. Shiraishi, T. Masuda, K. Okamoto, T. Itakura, Y. Nakamura, Y. Takada 1,Yu. Ohno, Y. Tanaka.
Department of Removable Proshodontics, School of Dentistry Aichi-Gakuin University
1
Division of Dental Biomaterials, Tohoku University Graduate School of Dentistry

Introduction
We have developed extracoronal magnetic attachments for vital teeth, and they are widely used in clinicalpractice. However, the mechanical strength of such magnetic attachments is not fully confirmed. Ohno
from our department reported the mechanical strength analysis of an extracoronal magnetic attachment
using Au-Ag-Pd alloy by three-dimensional finite element method in the 21st Conference on MagneticApplications in Dentistry. However, platinum gold alloy is more frequently used than Au-Ag-Pd alloy inclinical practice.
In the present study, we focused on heat treatment of platinum gold alloy, and mechanical strength
analysis of an extracoronal magnetic attachment was performed.

ObjectiveThe purpose of the present study was to investigate mechanical strength of platinum gold extracoronalmagnetic attachment up to the elastic limit.

Materials and Methods
As a preliminary experiment, the stress-strain curve of dental gold casting alloy (PGA-3, ISHIFUKUMetal Industry Co., Ltd(Fig.1) after heat treatment was calculated, followed by the elasto-plastic analysis
of a simple-shaped sample based on the stress-strain curve. The finite element model of an extracoronalmagnetic attachment was fabricated, and elasto-plastic analysis was performed to examine mechanicalstrength of extracoronal magnetic attachments.

Fig. 1 Use metal:PGA-3(ISHIFUKU)
1. Preliminary experiment1) Stress-strain curve
The size of a sample was 2 mm in diameter (parallel area), 25 mm in the distance between marks, and 55
mm in full length. PGA-3 (ISHIFUKU Metal Industry Co., Ltd) suitable for milling and applied toabutment teeth of extracoronal magnetic attachments in our university was used for the study (Fig. 2).

Fig. 2 Sample fabrication
Samples were invested, cast, and heat treated under the manufacturer’s instructions. Samples withhardening heat treatment, no heat treatment, and softening heat treatment were prepared (7 each).
Stress-strain measurement was performed using the Instron Universal Tester (Instron Japan) with acrosshead speed of 0.5 mm / min (Fig. 3).

Fig. 3 Tensile test
The slopes of the strain amount in the elastic region were calculated. An inflection point and the following
behavior in the plastic region were plotted to complete the stress-strain curve. The stress-strain curve wasintroduced to the exploratory analysis to examine the consistency of the elasto-plastic analysis.
2) Load displacement curve
The size of a sample was 7.0 mm in minor axis, 35.0 mm in diameter, and 1.6 mm in thickness (Fig. 4).

Fig. 4 Sample size and Sample

Samples were invested, cast, and heat treated under the manufacturer’s instructions. Seven samples wereprepared for each treatment. Load displacement was measured using the Instron Universal Tester with acrosshead speed of 0.5 mm / min.
2. Exploratory analysis
Fig. 5 shows the size of an exploratory analysis model.

Fig. 5 Size of an exploratory analysis model
Elements and nodes were 5,164 and 23,288, respectively.
Constraint condition was applied in one direction to Z axis, and a rigid body simulating an indenter wasplaced at the center of a plate at 0.5 mm / min.
For material constants, the elastic coefficient of platinum gold alloy and material property in the plastic
region were introduced from the stress-strain curve of the preliminary experiment for the analysis.
3. Actual analysis
Fig. 6 shows elements and nodes, and boundary condition of the present analysis.

Fig.6 Analysis model and boundary condition
The base and extracoronal model were fabricated together. A model was fabricated by cementing a keeper
and attaching a housing on top of it.
A complete constraint was applied to the top, bottom, and back surfaces in the X, Y, and Z directions.
A load was applied at the center of the extracoronal attachment in the Z axis direction for 5 minutes at arate of 0.5 mm / min (Fig. 7).

Fig. 7 Constraint condition of the present analysis model
The same method was employed for material constants, and the elastic coefficient of platinum gold alloyand material property in the plastic region were introduced from the stress-strain curve of the preliminary
experiment for the analysis.
Patran, a general purpose pre/post processor and Mark, a general purpose finite element program, andMSC were used for explanatory and actual analyses.

Results
1. Preliminary experiment1) Stress-strain curve
Fig. 8 shows the results of stress-strain curves.

Fig. 8 Stress strain curves

A known value was substituted. Elastic coefficients were 82 G Pa in hardening heat treatment, 94 G Pa as
cast, and 98 G Pa in softening heat treatment. Plastic region remain unchanged for all treatments.
A SEM image (Fig. 9) showed ductile fracture.

Fig. 9 SEM image2) Load-displacement curve
Fig. 10 shows the results of load-displacement curves of measurement and analysis values.

Fig. 10 Load-displacement curves
2. Explanatory analysis
The agreement rate between measurement and analysis values was the highest as cast, followed bysoftening heat treatment and hardening heat treatment.
3. Actual analysis
Fig. 11 shows the von Mises stress distribution chart of the present analysis.

Fig. 11 von Mises stress distribution chart
The stress distribution chart indicated stress concentration of the stress applied on the top surface of an
attachment on the neck part of an attachment.
Fig. 12 shows the load-displacement curves of the present analysis.

Fig. 12 Load-displacement curves
Elastic limit was 1.5 mm at 1100 N loading for hardening heat treatment, 1.3 mm at 800 N as cast, and 1.1mm at 600 N loading for soft heat treatment.

Discussion
1. Stress-strain curve
Stress-strain curves were measured using finite element analysis to investigate mechanical strength of an
extracoronal magnetic attachment. Actual measurement allowed to know material properties specific to themetal, and to introduce proper mechanical properties to the finite element model. The fracture cross-section
after the tensile test was observed by SEM. The images indicated that samples were fractured in a ductile
manner, not due to twist or strain by a machine.
2. Preliminary experiment
Although the elasto-plastic analysis is rarely introduced in the medical field, it is actively introduced in theindustrial field and its credibility has been established. In the present study, actual measurement of thepreliminary experiment and comparison with the explanatory analysis were performed before the analysisof an extracoronal magnetic attachment to confirm practicality and credibility. The results of thepreliminary experiment and explanatory analysis showed approximate values in extracoronal magneticattachments with hardening and softening heat treatment. Errors were confirmed in the actual measurement
and analysis values of samples with hardening heat treatment. It is considered that measurement error
increased with each heat treatment.
3. Analysis model
A finite element model of the present study was fabricated by constructing an extracoronal attachment
model based on the commercialized and normalized CAD data. A housing and the base were fabricated tofit the model. The size of the model was meticulously reproduced.
A model with tetrahedral elements was fabricated. Although it is said that calculation accuracy decreases
in tetrahedral elements compared with hexahedral elements, the present model was subdivided to make all
elements approximately the same shape, and, therefore, inaccurate stress concentration and reaction force
due to the insufficient elements could be avoided.
Stress distribution was evaluated using von Mises stress. Although compression and tensile properties
cannot be evaluated in von Mises stress, this method can easily exhibit stress concentration. The results
showed stress concentration at the superior margin of an extracoronal magnetic attachment groove, andstress transmission in the upper and lower parts of the base. The similar results were obtained in the break
test. Crowns and abutment teeth were simulated for the base. It was pointed out that high stressconcentration may arise at the margin line by applying stress to an extracoronal magnetic attachment.

Conclusions
Practicality and credibility were reconfirmed by performing preliminary experiment of elasto-plasticanalysis.
Three-dimensional finite element analysis showed that the elastic limit of an extracoronal magnetic
attachment fabricated with platinum gold alloy exists around 1,000 N.

References
1. Nakamura Y.: Prosthetic case report using extracoronal magnetic attachments
2. Okada M., Nakamura Y., Tanaka Y.: Application of extracoronal attachments on vital teeth,
The Journal of the Japanese Society of Magnetic Applications in Dentistry
3. Shoji K., Nakamura Y., Tanaka Y.: Strength of the neck part of and extracoronal magnetic attachment
4. Dental precious metal products, ISHIFUKU Metal Industry Co., Ltd