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Pre-overloading to Extend Fatigue Life of Cast ClaspsDepartment of Conservative Dentistry and Prosthodontics, Dental School, University of Jordan, Amman 11942, Jordan; anabtawime{at}yahoo.com
Permanent deformation in bending is associated with the development of residual stresses. The objective of this study was to characterize those residual stresses and test whether they can be manipulated to extend the fatigue lives of cast clasps. Simulations with validated non-linear finite element models were used to characterize the residual stresses in clasps cast from Ti-6Al-7Nb, Co-Cr, and Type IV gold alloys. In addition, two groups of as-cast and pre-overloaded (subjected to a load that produced 20 µm of permanent deformation) Ti-6Al-7Nb clasps (10 specimens each) were subjected to cyclic 0.5-mm deflections at 5 Hz until fatigue. Pre-overloaded specimens demonstrated significantly longer fatigue lives (32,200 ± 17,300 cycles) than did those tested in the as-cast condition (17,900 ± 7600 cycles), consistent with the maximum tensile stress values revealed by finite element analysis.
Key Words: fatigue • finite element analysis • non-linear analysis • residual stresses • clasp
Among many other metals, Ti-6Al-7Nb and Type IV gold alloys offer flexible alternatives to the conventional Co-Cr alloy for fabrication of removable partial denture frameworks. Because of the reduced possibility of traumatic overloading, clasps made from flexible materials can be designed to engage deeper undercuts on abutment teeth than is conventionally accepted for Co-Cr alloys (Mahmoud et al., 2005). This is preferable when esthetics or periodontal health is of primary concern. However, the high strains associated with engaging deeper undercuts can increase the possibility of permanent deformation and fatigue fracture (Mahmoud et al., 2005). Approaches—including the development of new materials (Lin et al., 2005), heat or chemical treatment (Akahori et al., 2002), and the optimization of clasp designs (Sato et al., 1995)—have been undertaken to reduce the possibilities of such failures. It is also widely accepted that the formation of favorable compressive residual stresses at the surface can improve fatigue resistance. In the industrial field, shot peening and surface rolling are practical examples of such mechanical treatment (Dieter, 1986).(AQ) Permanent deformation in bending is also associated with residual stresses (Beer et al., 2002). Using the same logic, we hypothesized that deliberate induction of minute permanent deformations can be used to increase fatigue resistance. To test the hypothesis, we conducted a bending test with finite element simulation for cast clasps made from Co-Cr, Type IV gold, and Ti-6Al-7Nb alloys. The residual stress patterns associated with different levels of permanent deformation were characterized from experimentally verified mathematical models. The stress analysis results were used for the design of a fatigue test for Ti-6Al-7Nb clasps, as a test of the hypothesis that residual stresses accompanying minute permanent deformations can extend the fatigue lives of cast clasps.
Bending and Fatigue Test Specimens The basic test specimen was a cast clasp adapted in one plane to a cylinder having a 5-mm radius. The angle subtended by the clasp was 120 degrees (Fig. 1  ). Similar to a previous report, casting patterns for test specimens were made in a duplicating mold (Mahmoud et al., 2005). The average width and thickness of the casting patterns at 30 and 120 degrees were 0.75/1.01 mm and 0.54/0.65 mm, respectively.
The materials and equipment used in investing and casting are summarized in the Table . The manufacturer’s instructions were followed strictly, and the specimens were finished and treated as indicated in the Table (Mahmoud et al., 2005).
Bending Test Three clasp specimens for each alloy were subjected to a bending test. As described in a previous report (Mahmoud et al., 2007), each specimen was fixed to the testing machine (MMT, 250N, Shimadzu, Kyoto, Japan) with screws, and was subjected to a sinusoidal cyclic deflection by force at the tip of each clasp arm at a frequency of 0.5 Hz. Specimens were loaded radially to the outside in a direction that makes a 30-degree angle with the cylinder’s cross-sectional plane (Sato et al., 1997). Each specimen was deflected incrementally with 25-µm steps. At each increment, loading was carried out for 10 cycles, and the resulting permanent deformation was measured. Permanent deformation was recorded as the difference in the piston tip-loading sphere distance between the position at the beginning of each cycle and the position at the first cycle.
Finite Element Analysis
Similar to a previous report, a multi-linear material property model was used for each alloy (Mahmoud et al., 2007). Prediction of permanent deformation was based on the von Mises equivalent stress criterion for yielding (Dieter, 1986; Beer et al., 2002), which assumes isotropic behavior independent of loading rate. To account for geometric non-linearity, we used the "large displacement" option (Zeinkiewicz and Taylor, 2000; Zhang, 2004). The multi-linear stress-strain curves for the 3 alloys were based on the results of a previous study (Mahmoud et al., 2007) (Fig. 2A
The incremental bending tests were simulated in non-linear finite element analyses, and the residual stresses were characterized as a function of permanent deformation.
Fatigue Test As in the bending test, each specimen was fixed to the testing machine and subjected to a sinusoidal unidirectional cyclic deflection of 0.5 mm by force at the tip of each clasp arm. The frequency was 5 Hz, and the direction of loading was similar to that of the bending test in a direction that makes a 30-degree angle with the cylinder’s cross-sectional plane. The test was continued until fracture, and a t test was performed for comparison of the mean number of cycles for the two groups.
Mathematical Model Verification The deflection values corresponding to different levels of permanent deformation from 5 µm to 800 µm were recorded for the 9 bending tests and their corresponding simulation models. Linear regression analysis was performed for the real-predicted deflection plot (Fig. 2B  ). The r2 value was 0.983, and the linear regression equation was: DeflectionPredicted (µm) = 0.911 (DeflectionReal) + 85 which approached an ideal (Y = X) relation for the deflection range reported in this study (250 to 1800 µm).
Finite Element Analysis Results
The maximum von Mises stress first exceeded the proportional limit at the inner upper corner of each clasp model; this was associated with the development of plastic strains. As deflections increased further, the plastic strains started to involve the lower outer clasp surface opposing the inner upper corner as well (Fig. 3
Areas undergoing plastic deformation demonstrated residual elastic strains and stresses on unloading that were of opposite sign (compressive or tensile) to the loading stresses. Residual stresses took a four-layer pattern (Fig. 3D ). The two surface layers, described above, were accompanied by two other layers having the same signs of the loading stresses and located deeper on both sides of the neutral plane.
The relationship between changes in permanent deformation, von Mises plastic, and residual elastic strains at the inner upper corner of the models is demonstrated in Figs. 2C and 2D
The ’residual elastic strain increase/plastic strain increase’ ratio was generally higher for the Ti-6Al-7Nb alloy, followed by Gold type IV, and being the least in the Co-Cr alloy (Fig. 2C
Fatigue Test, Rationale behind Design, and Results
In the finite element analyses, similar to the bending test, Ti-6Al-7Nb clasp models were loaded incrementally. After each incremental loading, the models were deflected for 0.5 mm, and the maximum S1 values were plotted as a function of permanent deformation (Fig. 2F
Initially, the maximum tensile stress (S1) was at the surface of the inner upper corner of each clasp and kept decreasing throughout the bending test (Fig. 2F
As permanent deformation increased beyond 50 µm, the rise in maximum S1 could be tracked to the tensile residual stresses developing in the deep layer below the inner upper corner (Fig. 3D The fatigue test was designed based on the bending test and stress analysis results explained above. The mean number of cycles for the pre-overloaded clasps was (32,200 ± 17,300) cycles, which was significantly greater than that for clasps tested in the as-cast condition (17,900 ± 7600) (P < 0.05). There was no significant difference in recorded permanent deformations between the two groups (13 and 11 µm, respectively).
Non-linear finite element analysis provided a powerful tool for study of the stress and strain patterns accompanying permanent deformation. We found that initially developed plastic strains caused almost equal values of residual elastic strains of opposite sign, without appreciable permanent deformation. On load release, the elastic core worked to bring the clasp back to its original position. Resisted by the plastically deformed areas, the structure took a new position, satisfying a new force equilibrium state (Beer et al., 2002). This new position defined the permanent deformation amount. Due to their relative size, areas undergoing initial plastic deformations were too small to change the final position of the structure appreciably, and, when unloaded, were compressed or extended back to their original position before yielding, producing almost equal amounts of elastic strains (Beer et al., 2002). However, as more areas became involved in plastic strain, the ratio of ’permanent deformation increase/plastic strain increase’ started to rise. Simultaneously, the ’residual elastic strain increase/plastic strain increase’ ratio fell. In the fatigue test, clasps subjected to the pre-overloading treatment exhibited significantly longer fatigue lives, satisfying our proposed hypothesis. The influence of pre-overloading on stress distributions demonstrated a directional nature. Being applied in the same direction as the anticipated cyclic loading, areas first showing plastic deformation were the same as those having the highest stress values in the fatigue test. The residual stresses developed in the plastically deformed areas were of opposite sign, and led to a proportional reduction in the maximum and mean stress parameters of the loading cycles, even though the stress amplitude, which is governed by the cyclic deflection amount, was basically the same. The models were assumed to be homogeneous and defect-free. However, it is widely known that fatigue cracks tend to nucleate at stress-raisers like defects and inclusions (Dieter, 1986). In reality, the overloading effect will be specifically greater at those high stress areas, leading to the creation of compressive residual stresses exactly where they are needed. Compressive residual stresses will reduce the crack-driving force (Suresh, 1998), and as the crack advances, the wake of material that has previously been deformed plastically will contribute to crack growth retardation, or even arrest, through plasticity-induced crack closure (Elber, 1970, 1971). Besides their beneficial influence when applied before cyclic loads, transient tensile overloads interrupting cyclic loading also have the potential to retard crack advance or even arrest it completely (Suresh, 1998). Transient tensile overloads are believed to act through their plasticity-induced crack closure (Elber, 1970, 1971), crack-tip blunting (Lankford and Davidson, 1982), residual compressive stresses (Allison, 1979; Taira and Tanaka, 1979), and deflection or bifurcation of the crack (Suresh, 1983), among other fatigue-retardation mechanisms. If the overloading treatment tested in this study is expanded to be applied on a periodic basis during removable partial denture maintenance visits, this might have the potential to extend the fatigue life even more. The same mechanism may work in accidental overloading episodes expected to affect clasps when the prosthesis is dislodged or inserted in a path different from that designed. Fatigue in the oral cavity is expected to be influenced by the corrosive nature of oral fluids (Anusavice and Brantley, 2003). Corrosion works synergistically with loading to accelerate crack growth in corrosion fatigue (Dieter, 1986). Tensile overloading-induced crack closure will reduce the ingress of corrosive materials and reduce their influence at this critical area (Dieter, 1986). Compressive overloading in a direction opposite that of cyclic loading will produce effects opposite to those discussed above (Suresh, 1998). The consequence will be exacerbation of crack growth and apparent shortening of fatigue life. Unfortunately, such compressive overloading happens whenever a clasp is activated by being bent toward the tooth surface, a potentially destructive practice. In conclusion, overloading can lead to the production of residual stresses of high magnitudes before the appearance of significant permanent deformations. In addition to their effect on the mean and maximum nominal stress values, those residual stresses will specifically target stress-raising areas, like defects and cracks. When applied in the same direction as that of cyclic loading, they will exhibit a favorable effect, leading to fatigue life extension. Fractographic analysis and testing of the relative effects of overloading treatments on fatigue resistance under different cyclic-loading levels and scenarios are topics for future research.
Special thanks to Dr. Wakabayashi, Dr. Takahashi, and technician Iwasaki for their help. This study was supported by Grants-in-Aid for Scientific Research, 16591936 (N.W.) and 14571840 (N.W.), from The Ministry of Education, Science, and Culture of Japan, and by Scientific Research Grant (125, 2005–2006), from the University of Jordan, Amman, Jordan. Received for publication January 9, 2006. Revision received April 12, 2007. Accepted for publication May 7, 2007.
Journal of Dental Research, Vol. 86, No. 9,
868-872 (2007)
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ABSTRACT
INTRODUCTION
Permanent deformation/