Materials Science Elastic Modulus of a Triple-stranded Stainless Steel Arch Wire via Three- and Four-point Bending

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Abstract
The modulus of elasticity (E) was determined in simple three- and four-point bending for an 0.0175" (3 X 0.008") stainless steel arch wire. Using variable light loads (10-160 g) to limit the elastic deflection of a wire to less than 5% of its beam length, the force-deflection profiles were determined for three nominal span lengths (L = 0.35", 0.75", and 1.00") in three-point bending and three nominal inner span lengths (L2 = 0.17", 0.40", and 0.50") in four-point bending (single outer span length, L = 1.00"). By assuming that each wire could be considered as a bundle of frictionless, tightly wound helical springs (i.e., strands), in which both the Young's modulus (E) and the shear modulus (G) contribute to the overall stiffness, values for E equaled 28.6 +/- 0.6 X 10(6) and 29.6 +/- 0.9 X 10(6) psi in three- and four-point bending, respectively. In addition, by using simple beam theory, the values of E for the 0.010" and 0.018" single-stranded wires were measured and equaled 27.2 +/- 0.3 X 10(6) and 27.8 +/- 0.7 X 10(6) psi in three-point bending, and 27.9 +/- 0.7 and 27.8 +/- 1.2 X 10(6) psi in four-point bending, respectively. Despite the fact that the elastic moduli of all three wires were significantly different (p less than 0.001), the results corroborated the metallurgical literature in which E spanned 27.8-30.2 X 10(6) psi. This was in contrast to the dental literature, in which a broader range of values has been reported, i.e., 18.3-38.0 X 10(6) psi.

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