Moment-curvature relations for a pseudoelastic beam

Predicting in vivo failure of rotary nickel-titanium endodontic instruments under cyclic fatigue

“…Results showed that the curvature of root canal had a major infl uence on bending stress, and thus on instrument lifespan. However, results obtained from the relations formulated by Atanackovic and Achenbach 7) and Zbiciak 9) indicated that maximum stress might not necessarily occur at the outer layer of Ni-Ti instruments. On the basis of this observation, we modifi ed the Coffi n-Manson relation 8) .…”

“…However, it does not return along the same path in the σ-ε plane, exhibiting the pseudoelastic hysteresis effect shown in Fig. 3 6,7,9,14) . Further, the rotary Ni-Ti instrument functions as a rotating rod.…”

“…In our development of a mathematical model for the bending deformation of rotary Ni-Ti endodontic instruments, we leveraged on an equation which determined the maximum normal stress in Ni-Ti wires in pure bending 7) . Results showed that the curvature of root canal had a major infl uence on bending stress, and thus on instrument lifespan.…”

“…On the basis of this observation, we modifi ed the Coffi n-Manson relation 8) . Nickel-titanium alloy is a pseudoelastic material 6,7,13,14) . It deforms with the application of forces and torques and returns to the original shape after the forces and torques are removed (elastic property).…”

“…Therefore, the purpose of this study was to examine the lifespan of rotary Ni-Ti endodontic instruments via simulated root canals with different curvatures. By connecting experimental data to relations formulated by Achenbach et al 6) , Atanackovic and Achenbach 7) , Meyers and Kumar 8) and Zbiciak 9) to simulate the pseudoplastic behaviour of Ni-Ti shape memory alloys when under cyclic loading, a novel mathematical model was derived which could be used to predict the bending fatigue life of rotary Ni-Ti endodontic instruments.…”