In this study, a numerical approach to the fracture behavior in a three-unit zirconia-based fixed partial denture (FPD) framework was made under mechanical loading using a newly developed three-dimensional (3D) numerical modeling code. All the materials studied were treated heterogeneously and Weibull distribution law was applied to describe the heterogeneity. The Mohr-Coulomb failure criterion with tensile strength cut-off was utilized to judge whether the material was in an elastic or failed state. For validation, the fracture pattern obtained from the numerical modeling was compared with a laboratory test; they largely correlated with each other. Similar fracture initiation sites were detected both in the numerical simulation and in an earlier fractographic analysis. The numerical simulation applied in this study clearly described the stress distribution and fracture process of zirconia-based FPD frameworks, information that could not be gained from the laboratory tests alone. Thus, the newly developed 3D numerical modeling code seems to be an efficient tool for prediction of the fracture process in ceramic FPD frameworks.

Finite element analysisFixed partial denture Fracture process Numerical simulationOblique loading a b s t r a c t Using a newly developed three-dimensional (3D) numerical modeling code, an analysis was performed of the fracture behavior in a three-unit ceramic-based fixed partial denture (FPD) framework subjected to oblique loading. All the materials in the study were treated heterogeneously; Weibull's distribution law was applied to the description of the heterogeneity. The Mohr-Coulomb failure criterion with tensile strength cut-off was utilized in judging whether the material was in an elastic or failed state. The simulated loading area was placed either on the buccal or the lingual cusp of a premolar-shaped pontic with the loading direction at 301, 451, 601, 751 or 901 angles to the occlusal surface. The stress distribution, fracture initiation and propagation in the framework during the loading and fracture process were analyzed. This numerical simulation allowed the cause of the framework fracture to be identified as tensile stress failure. The decisive fracture was initiated in the gingival embrasure of the pontic, regardless of whether the buccal or lingual cusp of the pontic was loaded. The stress distribution and fracture propagation process of the framework could be followed step by step from beginning to end. The bearing capacity and the rigidity of the framework vary with the loading position and direction. The framework loaded with 901 towards the occlusal surface has the highest bearing capacity and the greatest rigidity. The framework loaded with 301 towards the occlusal surface has the least rigidity indicating that oblique loading has a major impact on the fracture of ceramic frameworks.& 2015 Elsevier Ltd. All rights reserved. IntroductionCeramics are among the most inert biomaterials known. Their advantages include high biocompatibility (Depprich et al., 2008), good esthetic appearance (Ghazal et al., 2008), low solubility and low thermal conductivity (Chai et al., 2007). Among the crucial problems for ceramics, however, are low fracture resistance and brittleness and, consequently, no or little apparent plastic deformation can occur before fracture (Munz and Fett, 1999 j o u r n a l o f t h e m e c h a n i c a l b e h a v i o r o f b i o m e d i c a l m a t e r i a l s 5 0 ( 2 0 1 5 ) 2 0 6 -2 1 4

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