Predicting fatigue damage in intact and restored teeth Sam Evans Sam Smith School of Engineering, Cardiff University PO Box 925, The Parade, Cardiff CF24 0YF

Introduction Tooth fracture or cracking is a common cause of clinical failure The cause of this problem is not well understood Cracks occur in the tooth due to cavity preparation Abfraction may involve fatigue

Typical tooth damage Reproduced from:- me/bsms/dental.html

Abfraction Typical non- carious cervical lesions (Rees 1998)

Introduction The aim of this study was to model fatigue crack growth using computational fracture mechanics models This could provide insights into the mechanisms of abfraction and post- restoration cracking

The problem A typical molar with an amalgam restoration was modelled A 114 m crack was introduced at the region of maximum stress, as found by Xu et al after preparation with a diamond burr Xu, H. H. K., Kelly, J. R., Jahanmir, S., Thompson, V. P., Enamel subsurface damage due to tooth preparation with diamonds. J. Dent. Res. 76(10) (1997):

Finite element model A 2D finite element model was developed, based on Arola et al 2. Modelled in plane strain, using Franc2D (Cornell Fracture Group, edu) Linear interface elements were used- mostly in compression 2. Arola, D., Huang, M. P. and Sultan, M. B., The failure of amalgam dental restorations due to cyclic fatigue crack growth J. Mat. Sci.: Materials in Medicine 10(1999):

Initial mesh, showing dentine, enamel and restoration

Initial 114 m crack

Crack region remeshed

Crack propagated in 50 m steps up to 1.6mm

Fatigue life prediction Preliminary fatigue crack growth data by Arola et al 3 was used to predict the crack growth rate A simple Paris Law model fits the data well Variable amplitude loading etc will affect crack growth in practice 3.

Stiffness of side much reduced

Crack length vs time Crack length (mm) Time (years)

Discussion Stresses in the tooth are in the right range to cause clinical fractures in a typical clinical timescale Crack may become dormant due to load redistribution Tooth is then left vulnerable to unusual loads, decay etc

Abfraction

Crack propagation

Crack length Figure The number of cycles for the crack to grow to a given length under a 10N load for the first and final models Crack length (mm) Cycles 50N load 20N load

Discussion Propagation of cracks is likely at typical physiological loads Crack growth likely from small (50µm) initial cracks Possible formation of deep rounded lesions inside the PDL Interaction with erosion during initiation and propagation

Conclusions These models predict crack propagation at relevant rates under typical physiological loads Fatigue seems likely to be a factor in abfraction damage Possible to avoid fatigue damage through improved restorations?

Acknowledgements The abfraction model was developed by Sam Smith The Franc software is provided by the Cornell Fracture Group