Numerical Simulation of Crack Formation in All Ceramic Dental Bridge

Ceramics have rapidly emerged as one of the major dental biomaterials in prosthodontics due to exceptional aesthetics and outstanding biocompatibility. However, a challenging aspect remaining is its higher failure rate due to brittleness, which has to a certain extent prevented the ceramics from fully replacing metals in such major dental restorations as multi-unit bridges. This paper aims at simulating the crack initiation and propagation in dental bridge. Unlike the existing studies with prescriptions of initial cracks, the numerical model presented herein will predict the progressive damage in the bridge structure which precedes crack initiation. This will then be followed by automatic crack insertion and subsequent crack growth within a continuum to discrete framework. It is found that the numerical simulation correlates well to the clinical and laboratory observations. Introduction As a relatively new technique, all-ceramic dental bridges exhibit outstanding aesthetics and excellent biocompatibility. In contrast to metal restoration, ceramics are recognized as superior in translucency and shape resemblances, which are particularly attractive to the patients who have a high esthetic requirement. For this reason, ceramics have emerged as one of the major dental biomaterials in the start-of-the-art prosthonontic clinic. However, a problematic aspect of such ceramic materials is their limited loading capability due to the relatively low fracture toughness [1] and time-dependent strength decrease caused by progressive crack growth [2]. This has become a major barrier limiting the exploitation of ceramic materials to fully replace metals in such major dental restorations as bridges, where tensile stress levels are sizeable. It would be perferred if the crack initiation and growth in the bridge can be predicted and assessed prior to the bridge construction, thus providing criteria for an improved design. From a biomechanical point of view, the all-ceramic bridge exhibits a new stress status and complex damage mode, which drastically challenge the strength theory and design principles established in traditional prosthetic dentistry. In the context of structural analysis, experimental and numerical approaches have been adopted. Kelly et al reported a series of in-vitro and in-vivo test results in the mid 1990’s [3]. They showed that the failures likely occurred in bridge connectors that link the pontic to the abutment, with approximately 70 to 78% originating from the interface between the core and aesthetic ceramics [3]. More recently, Oh et al [4] investigated the effect of bridge design on the fracture resistance, where a range of connector radii is experimentally tested. Substantial effort has also been devoted to the study of fracture mechanism of dental ceramic structures and materials [5]. Rekow et al analysed crack growth and damage accumulation in dental restorations [6]. Baran et al examined the fatigue characteristics of ceramics in various conditions [7]. To monitor the damage process of bridges, Fischer et al adopted a non-destructive means to material testing [8]. Recently Lohbauer et al explored the fatigue life and failure probability of dental ceramics, where fracture mechanics and statistical methods were employed [9]. Key Engineering Materials Vol. 312 (2006) pp. 293-298 online at http://www.scientific.net © 2005 Trans Tech Publications, Switzerland All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of the publisher: Trans Tech Publications Ltd, Switzerland, www.ttp.net. (ID: 141.212.55.228-05/07/06,16:02:11) As a powerful numerical tool, the linear finite element (FE) method has been employed to reveal detailed stress distributions in bridges [10-12]. Pospiech’s work [13] clearly demonstrated that the peak tensile stress occurs in the connector region, and showed further evidence for dentists to improve the bridge design. Lang et al [14] adopted a simplified FE model to predict the load to fracture of an all-ceramic bridge and also validated the numerical results via laboratory tests. However, until now there are no published data available in simulating the crack formation in the dental bridges by making use of nonlinear finite/discrete element methods. From a fracture mechanics perspective, there are two important hypotheses that are conventionally adopted to enable various crack-induced numerical simulations; firstly, the prescription of initial cracks and secondly the adoption of linear elastic fracture mechanics theory. This paper will attempt to explore the possibility of not relying on a priori prescription of a preliminary crack. Rather, the numerical modelling will predict the progressive damage which precedes crack initiation. This will then be followed by automatic crack insertion and subsequent crack growth within a continuum-to-discrete framework. The proposed study is expected to model more realistically the crack formation mechanism in an all-ceramic bridge structure. Materials and Methods Fracture Model. The fracture in such brittle materials as ceramics is generally related to anisotropic phenomenon [15]. The formation and growth of micro-cracks within a brittle solid occur in directions that attempt to maximize the subsequent energy release rate and also minimize the strain energy density [16]. For this purpose, the Rankine rotating crack model has been developed for computing the tensile failure in brittle materials [16]. For mode I dominated fracture problems, the initial failure surface for Rankine rotating crack model can be defined by a tensile failure surface as in Fig. 1a).