The Eulerian buckling test for orthodontic wires

Orthodontic treatment is mainly dependent on the loads developed by metal wires. The load developed by a buckled orthodontic wire is of great concern for molar distalization and cannot be simply derived from mechanical properties measured through classical tests (i.e. tensile, torsion, and bending). A novel testing method, based on the Eulerian approach of a simple supported beam, has been developed in order to measure the load due to buckling of orthodontic wires. Elastic titanium molybdenum alloy (TMA; SDS Ormco) and superelastic Nitinol (3M Unitek) and copper nickel-titanium (NiTi; SDS Ormco) wires, each having a rectangular cross section of 0.016 × 0.022 square inches (0.41 × 0.56 mm2), were used. The wires were activated and deactivated by loading and unloading. In order to analyse thermo-mechanical properties in buckling, mechanical tests were assisted by calorimetric measurements through differential scanning calorimetry (DSC). Statistical analysis to determine differences between the samples was undertaken using two-way analysis of variance (ANOVA) and Tukey's post hoc test, and one-way ANOVA to assess differences between the tested wires under similar conditions and different materials. The results suggest that the load due to buckling depends on material composition, wire length, the amount of activation, temperature, and deformation rate. The results can be considered as the lower bound for the loads experienced by teeth as far as a buckled wire is concerned. At a temperature higher than the austenite finish transition temperature, superelastic wires were strongly dependent on temperature and deformation rate. The effect due to an increase of deformation rate was similar to that of a decrease of temperature. Load variations due to temperature of a superelastic wire with a length of 20 mm were estimated to be approximately 4 g/°C. The high performance of an applied superelastic wire may be related to the high dynamics of the load in relation to temperature.