applied fracture mechanics

Fracture of Dental Materials 125cracking, and quasi-plasticity at the top surfaces and radial cracking at the lower (inner)surfaces are measured as a function of ceramic-layer thickness. The characteristic features ofthese were;i. Cone cracks initiate from the top surface outside the contact circle, where the Hertziantensile stress level reaches its maximum [40, 41]. The crack first grows downward as ashallow, stable surface ring, resisted by the material toughness T (KIC), before poppinginto full cone geometry at loadPC = A(T 2 /E)rwith A = 8.6x10 3 from fits to data from monolithic ceramics with known toughness [42]ii. Quasiplasticity initiates when the maximum shear stress in the Hertzian near fieldexceeds Y/2, with yield stress Y ~ H/3 determined by the material hardness H(load/projected area, Vickers indentation)[43].The critical load is PY = DH(H/E) 2 r 2with D = 0.85 from fits to data for monolithic ceramics with known hardness [42].iii. Radial cracks initiate spontaneously from a starting flaw at the lower ceramic surfacewhen the maximum tensile stress in this surface equals the bulk flexure strength σF, atloadPR = BσFd 2 /log(EC/ES)with d being the ceramic layer thickness and B = 2.0 from data fits to well-characterizedceramic-based bilayer systems [38].Thus, given basic material parameters, one can in principal make priori predictions of thecritical loads for any given bilayer system. Note that PC and PY are independent of layerthickness d, whereas PR is independent of sphere radius r. These relations, within the limitsof certain underlying assumptions, have been verified for model ceramic/substrate bilayersystems [38, 44]. They claimed that these damage modes, especially radial cracking, weredirectly relevant to the failure of all-ceramic dental crowns. The critical load data were analyzedwith the use of explicit fracture-mechanics relations, expressible in terms of routinelymeasurable material parameters (elastic modulus, strength, toughness, hardness) and essentialgeometrical variables (layer thickness, contact radius).Lawn et al. [45] conducted tests on model flat-layer specimens fabricated from various dentalceramic combinations bonded to dentin-like polymer substrates in bilayer (ceramic/polymer)and trilayer (ceramic/ceramic/polymer) configurations. The specimens wereloaded at their top surfaces with spherical indenters, simulating occlusal function. The onsetof fracture was observed in situ using a video camera system mounted beneath the transparentpolymer substrate. Critical loads to induce fracture and deformation at the ceramictop and bottom surfaces were measured as functions of layer thickness and contact duration.Radial cracking at the ceramic undersurface occurred at relatively low loads, especiallyin thinner layers. Fracture mechanics relations were used to confirm the experimental datatrends, and to provide explicit dependencies of critical loads in terms of key variables (material—elasticmodulus, hardness, strength and toughness; geometric—layer thicknesses andcontact radius). Tougher, harder and (especially) stronger materials show superior damage