Document Type : Research Paper


1 Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Khorasan Razavi, 9177948944, Iran

2 Dental Research Center, Faculty of Dentistry, Mashhad University of Medical Sciences, Mashhad, Khorasan Razavi, 9138813944, Iran


The aim of the study was to find the optimum combination of materials and thicknesses to provide a tough, damage resistant multi-layer system with numerical methods to restore the damaged teeth. Extended Finite Element Method (XFEM) was used to assess the critical loads for the onset of damage modes such as radial cracks and plastic deformation in dental prostheses, which consist of a brittle outerlayer (porcelain)/ metal (Au, Pd, Co)-core/ substrate (dentin) trilayer system. XFEM not only has the ability to model crack initiation process, but also could solve crack propagation problems. Generally speaking, porcelain layer shouldn't be thinner than 0.5 mm, as the stresses due to bending become tensile critically in porcelain undersurfaces and radial cracks would occur in low loads. Also, it could be concluded that XFEM in axisymmetric model could properly estimate crack initiation and propagation path. Yielding of metal core makes additional flexural stress at overlaying brittle surface and consequently, facilitates radial cracks. In dental applications, the optimum porcelain thickness would be between 0.75 and 1.25 mm. Furthermore, yield strength and stiffness of metal is better to be high sufficiently to prevent it from plastic deformation and ensuing radial cracks.

Graphical Abstract

An investigation into finding the optimum combination for dental restorations


Main Subjects

[1]     S. J. Sadowsky, “An overview of treatment considerations for esthetic restorations: a review of the literature”, The Journal of Prosthetic Dentistry, Vol. 96,No. 6, pp. 433-442, (2006).
[2]     S. M. Salazar Marocho, A. R. Studart, M. A. Bottino, and A. Della Bona, “Mechanical strength and subcritical crack growth under wet cyclic loading of glass-infiltrated dental ceramics”, Dental Materials, Vol. 26,No. 5, pp. 483-490, (2010).
[3]     L. A. Bicalho, C. A. R. P. Baptista, R. C. Souza, C. Santos, K. Strecker, and M. J. R. Barboza, “Fatigue and subcritical crack growth in ZrO2–bioglass ceramics”, Ceramics International, Vol. 39,No. 3, pp. 2405-2414, (2013).
[4]     S. K. Vanimisetti and R. Narasimhan, “A numerical analysis of spherical indentation response of thin hard films on soft substrates”, International Journal of Solids and Structures, Vol. 43,No. 20, pp. 6180-6193, (2006).
[5]     C. Ford, M. B. Bush, X.-Z. Hu, and H. Zhao, “Numerical interpretation of cone crack initiation trends in a brittle coating on a compliant substrate”, Materials Science and Engineering: A, Vol. 380,No. 1-2, pp. 137-142, (2004).
[6]     H. Chai, “Fracture mechanics analysis of thin coatings under spherical indentation”, International Journal of Fracture, Vol. 119,No. 3, pp. 263-285, (2003).
[7]     Y. Deng, B. R. Lawn, and I. K. Lloyd, “Characterization of Damage Modes in Dental Ceramic Bilayer Structures”, Journal of Biomedical Materials Research Part A: Applied Biomaterials, Vol. 63,No. 2, pp. 137-145, (2002).
[8]     H. Zhao, X. Hu, M. B. Bush, and B. R. Lawn, “Contact damage in porcelain/Pd-alloy bilayers”, Journal of Materials Research, Vol. 15,No. 3, pp. 676-682, (2000).
[9]     Zhao H, Miranda P, Lawn B R, and Hu X Z, “Cracking in Ceramic/metal/polymer Trilayer Systems”, Journal of Materials Research, Vol. 17,No. 5, pp. 1102-1111, (2002).
[10]   Y. Deng, P. Miranda, A. Pajares, F. Guiberteau, and B. R. Lawn, “Fracture of ceramic/ceramic/polymer trilayers for biomechanical applications”, Journal of biomedical materials research. Part A, Vol. 67,No. 3, pp. 828-33, (2003).
[11]   L. Ma, P. C. Guess, and Y. Zhang, “Load-bearing properties of minimal-invasive monolithic lithium disilicate and zirconia occlusal onlays: finite element and theoretical analyses”, Dental Materials, Vol. 29,No. 7, pp. 742-751, (2013).
[12]   H. Zhao, P. Miranda, B. R. Lawn, and X. Hu, “Cracking in Ceramic/metal/polymer Trilayer Systems”, Journal of Materials Research, Vol. 17,No. 5, pp. 1102-1111, (2002).
[13]   T. Qasim, C. Ford, M. Bongué-Boma, M. B. Bush, and X. Hu, “Effect of coating thickness on crack initiation and propagation in non-planar bi-layers”, Materials Science and Engineering: A, Vol. 419,No. 1-2, pp. 189-195, (2006).
[14]   R. G. Craig and J. M. Powers, Restorative dental materials, 11 ed., Mosby, St. Louis, USA, (2002).
[15]   Y. Zhang and J. W. Kim, “Graded structures for damage resistant and aesthetic all-ceramic restorations”, Dental materials, Vol. 25,No. 6, pp. 781-790, (2009).
[16]   A. Geramy and F. Sharafoddin, “Abfraction: 3D analysis by means of the finite element method”, Quintessence international, Vol. 34,No. 7, pp. 526-533, (2003).
[17]   F. Zarone, D. Apicella, R. Sorrentino, Ferro V, R. Aversa, and A. Apicella, “Influence of tooth preparation design on the stress distribution in maxillary central incisors restored by means of alumina porcelain veneers: a 3D-finite element analysis”, Dental materials, Vol. 21,No. 12, pp. 1178-1188, (2005).
[18]   H. Li, J. Li, Z. Zou, and A. S. Fok, “Fracture simulation of restored teeth using a continuum damage mechanics failure model”, Dental materials, Vol. 27,No. 7, pp. e125-33, (2011).
[19]   S. Mohammadi, Extended nite element method (for fracture analysis of structures). Blackwell, (2008).
[20]   A. Barani, A. J. Keown, M. B. Bush, J. J. W. Lee, H. Chai, and B. R. Lawn, “Mechanics of longitudinal cracks in tooth enamel”, Acta biomaterialia, Vol. 7,No. 5, pp. 2285-2292, (2011).
[21]   A. Barani, A. J. Keown, M. B. Bush, J. J. W. Lee, and B. R. Lawn, “Role of tooth elongation in promoting fracture resistance”, Journal of the mechanical behavior of biomedical materials, Vol. 8,pp. 37-46, (2012).
[22]   B. R. Lawn, H. Chai, A. Barani, and M. B. Bush, “Transverse fracture of canine teeth”, Journal of Biomechanics, Vol. 46,No. 9, pp. 1561-1567, (2013).
[23]   H. Zhao, X. Hu, M. B. Bush, and B. R. Lawn, “Cracking of porcelain coatings bonded to metal substrates of different modulus and hardness”, Journal of Materials Research, Vol. 16,No. 5, pp. 1471-1478, (2001).
[24]   P. Miranda, A. Pajares, F. Guiberteau, F. L. Cumbrera, and B. R. Lawn, “Contact fracture of brittle bilayer coatings on soft substrates”, Journal of Materials Research, Vol. 16,No. 1, pp. 115-126, (2001).
[25]   R. L. Sakaguchi and J. M. Powers, Craig’s restorative dental materials, 13 ed., Mosby, Philadelphia, USA, (2012).
[26]   J. Gong, Y. Chen, and C. Li, “Statistical analysis of fracture toughness of soda-lime glass determined by indentation”, Journal of non-crystalline solids, Vol. 279,No. 2-3, pp. 219-223, (2001).
[27]   T. Qasim, M. B. Bush, and X. Hu, “The influence of complex surface geometry on contact damage in curved brittle coatings”, International Journal of Mechanical Sciences, Vol. 48,No. 3, pp. 244-248, (2006).
[28]   C. Ford, M. B. Bush, and X. Hu, “A numerical study of contact damage and stress phenomena in curved porcelain/glass-filled polymer bilayers”,  Composites Science and Technology, Vol. 64,No. 13, pp. 2207-2212, (2004).
[29]   C. Ford, M. B. Bush, X.-Z. Hu, and H. Zhao, “A numerical study of fracture modes in contact damage in porcelain/Pd-alloy bilayers”, Materials Science and Engineering: A, Vol. 364,No. 1-2, pp. 202-206, (2004).
[30]   J. J. W. Lee, Y. Wang, I. K. Lloyd, and B. R. Lawn, “Joining Veneers to Ceramic Cores and Dentition with”, Journal of Dental Research, Vol. 86,No. 8, pp. 745-748, (2007).