Simple solutions of multilayered discs subjected to biaxial moment loading

Objectives: The purpose of this study was to derive a simple closed-form solution for the stress distribution through the thickness of multilayered discs subjected to biaxial moment loading, such that it can be used readily to evaluate the biaxial strength of multilayered dental ceramics using biaxial flexure tests. Methods: A simple analytical model was developed to derive the stress distribution through the thickness of multilayered discs subjected to biaxial moment loading. The accuracy of the solution was verified by comparing with previous rigorous analytical solutions and finite element results. The results obtained from Roark's formulas for bilayered discs were also included for comparison. Results: Examples of porcelain/zirconia bilayered discs subjected to ring-on-ring and piston-on-ring loadings were used for comparison among different analyses. Despite the simplicity in deriving the present solution, it is sufficiently accurate in comparing with previous rigorous solutions and finite element results. Also, if the biaxial stresses on the top and the bottom surfaces of the disc can be measured during testing, the biaxial stress/strain through the entire thickness of the multilayered disc can be determined using equations derived in the present model. Significance: International Organization for Standardization has selected piston-on-three-ball tests to establish ISO 6872 for dentistry-ceramic materials. However, monolayered specimens are considered in tests for this standard. While dental materials are usually fabricated into layered structures, modification of the current standard is essential. Our simple closed-form solution serves as a basis for extending the current standard to multilayered systems. ? 2008 Academy of Dental Materials.