Cone Cracks Research Articles

Characterization of quasi-plastic deformation of WC–Co composite using Hertzian indentation technique

Abstract Using the Hertzian indentation technique, the evolution of the WC–Co composite from plastic deformation to final fracture was studied. Loaded with a spherical indenter, the material underwent initial elastic, elastic–plastic, and fully plastic deformations, finally ended with macrocracks, namely cone cracks and radial cracks. The behaviors of both WC grains and cobalt binder phase during each step of the deformation process was studied including the slip of WC grains, the formation of microcracks, the apparent strain hardening of the WC–Co composite, and the evolution from quasi-plastic deformation to the formation of macro-rings cracks and radial cracks. The correlation between microcracks and the quasi-plastic deformation, apparent strain hardening, and macrocracks are examined.

Design maps for failure of all-ceramic layer structures in concentrated cyclic loading

A study is made of the competition between failure modes in ceramic-based bilayer structures joined to polymer-based substrates, in simulation of dental crown-like structures with a functional but weak “veneer” layer bonded onto a strong “core” layer. Cyclic contact fatigue tests are conducted in water on model flat systems consisting of glass plates joined to glass, sapphire, alumina or zirconia support layers glued onto polycarbonate bases. Critical numbers of cycles to take each crack mode to failure are plotted as a function of peak contact load on failure maps showing regions in which each fracture mode dominates. In low-cycle conditions, radial and outer cone cracks are competitive in specimens with alumina cores, whereas outer cone cracks prevail in specimens with zirconia cores; in high-cycle conditions, inner cone cracks prevail in all cases. The roles of other factors, e.g. substrate modulus, layer thickness, indenter radius and residual stresses from specimen preparation, are briefly considered.

Torsion of an elastic space with a semi-infinite conical crack

The axisymmetric problem of stress concentration near a conical crack in an infinite elastic space with a rotation center is addressed. The problem is reduced to an integro-differential equation. Its exact solution is obtained. An expression for the stress intensity factor in crack neighborhood is derived and numerically analyzed for different positions of the rotation center and the crack opening angles

Multi-crack analysis of hydraulically pumped cone fracture in brittle solids under cyclic spherical contact

The evolution of surface damage in bilayers due to cyclic spherical indentation in the presence of incompressible lubricant is studied using an all-transparent glass/polycarbonate system as a model for more practical applications such as dental crowns and rolling contact fatigue. In situ observations and post-mortem material sectioning reveal that inner cone cracks evolve sequentially from the contact edge inward by slow growth in a process controlled by stress shielding from preceding cracks. The embryonic cracks are then accelerated by the action of fluid pressure into the flexural tensile stress at the lower part of the coating, where crossover fracture leading to delamination between the coating and substrate may ensue.

On internal cone cracks induced by conical indentation in brittle materials

The conditions for cone cracks to develop due to a conical indentation are investigated. Axisymmetric numerical simulations, based on the finite element method, are conducted, assuming a linear-elastic, perfectly plastic material. A superposition scheme is employed to simulate a range of crack geometries, including various lengths and orientations. The results indicate that the class of cracks investigated is prone to develop internally in brittle materials. Based on a reversed analysis, a new technique is proposed for measuring the fracture toughness in bulk material and thick coatings through one simple indentation test when the cone crack appears.

Contact damage in an yttria stabilized zirconia: Implications

This paper presents the results of a combined experimental and computational study of contact damage in a 3 mole% yttria partially stabilized zirconia (3-YSZ) that is relevant to hip implants and dental restorations. Contact-induced loading in real applications is idealized using Hertzian contact model to explain plasticity phenomena and failure mechanisms observed under monotonic and cyclic loading. Under monotonic loading, the elastic moduli increase with increasing loading levels. Under cyclic loading, the ceramic specimens fail with progressive cone cracking. X-ray analyses reveal that stress-induced phase transformation (from tetragonal to monoclinic phases) occurs under cyclic contact loading above the critical load levels (approximately 8.5 kN). Furthermore, when the cyclic loading level (5.0 kN) is less than a critical load levels (7.5 kN) that is required to induce surface cone cracks, significant plastic damage is observed in the subsurface zone underneath the contact area. These suggest that the cyclic contact loading induce both plastic damage and tetragonalto-monoclinic phase transformation in the 3-YSZ, leading to significant degradation in long-term strength. The implications of the results are discussed for the design of zirconia femoral heads in total hip replacements and zirconia crowns in dental restoration.

Mechanical Properties and Contact Damages of Nanostructured Silicon Carbide Ceramics

Three types of nanostructured silicon carbide ceramics were prepared with additives of Al2O3 and Y2O3 as the primary sintering additives, together with 1 mass% CaO, 1 mass% MgO or 0.73 mass% AlN. The silicon carbides (SiC) containing tens of nanometers of grains were successfully fabricated using a two-step sintering process. The mechanical properties and contact damages of the nanostructured SiC ceramics were investigated in this study. The nanostructured SiC ceramics exhibited a hardness of~20 GPa, a strength of 400-700 MPa, and a toughness of 3.0 MPa•m1/2. The nature of the contact damage exhibited classical ring or cone cracks formed in a region of weak tension outside the contact rather than microcracks in the diffuse quasi-plastic zones as observed in heterogeneous microstructures consisting of micron-sized elongated grains.

Failure mode of dental restorative materials under Hertzian indentation

Objective To explore the application of Hertzian indentation testing to amalgam and GIC; study the failure behavior of the bi-layer structure of each material on a relatively soft substrate; and investigate the effect of thickness. Methods Amalgam (Lojic+, SDI, Bayswater, Australia) and ceramic-reinforced GIC (Advanced Healthcare, Tonbridge, UK) discs, 10 mm diameter, thicknesses ranging from 0.4 to 8.0 mm, were tested resting freely on a substrate (30% glass fibre-reinforced polyamide; E = 10 GPa, 10 mm diameter and 5 mm thick). Increasing load was applied to the center of the disc by a 20 mm-diameter hard steel ball until fracture occurred. Acoustic emission sensing was used as a supplemental method for crack detection. The load at the first crack was recorded. Fracture surfaces were observed under SEM to identify the crack initiation site and the failure mode. Results The main failure mode of both materials shifted from bottom-initiated radial cracking to near-contact cone cracking or subsurface plastic deformation as the thickness was increased. There was a wide thickness range for the transition of the failure mode for amalgam. Failure load was proportional to the square of thickness for amalgam, except for deviations at small and very large thickness; for the GIC, it was proportional to the thickness to the power ∼1.6, except for thin layers. Significance The Hertzian indentation test can be applied to investigate the failure behavior of amalgam and GIC in addition to ceramics, for which purpose it may have value as a routine test. Failure mode changed with specimen thickness. The importance of considering both failure mode and failure load or strength is emphasized.

Onset of Cone Cracking in Ion-Exchanged Glass

A simple fracture mechanics approach is used to predict the critical crack size required to initiate Hertzian cracks in a brittle material in the absence and presence of a residual surface stress. To test the approach, the load and location of ring/cone cracks are measured in a silicate glass before and after ion exchange. The crack sizes estimated by this technique are, however, different before and after the ion-exchange process. It is concluded that the ion-exchange process changes the nature of the surface flaws, which is a key assumption in previous theoretical analyses in using Hertzian contacts as a means to estimate surface stress.

Numerical analysis of the contact stresses developed during the indentation of coated systems with substrates with orthotropic properties

Many works in the literature have analyzed the contact stresses developed during the indentation of coated systems. In general, the damage observed in systems with soft substrates is characterized by circular cone cracks that propagate at the edge of the indentations. In systems with soft substrates, recent works have also shown that the amount of substrate indentation pile-up presents direct relationship with a peak in radial stresses at film surface and, consequently, with the amount of indentation circular cracks. In this work, a series of finite element analyses was conducted to simulate the indentation of systems with an elastic film and an elastic-plastic substrate. Two values of film thickness were selected and, in each simulation, substrates were divided into two layers with different plastic properties. The layer on the bottom was considered isotropic and the layer attached to the film presented plastic properties along the loading direction ( z) that were different from the plastic properties along the radial and tangential directions. Different ratios between axial and radial/tangential properties were considered. Results indicated that the amount of substrate pile-up and, consequently, the peak in radial stresses at film surface, could be significantly reduced in coated systems with substrates with orthotropic plastic properties.

Effect of loading method on the fracture mechanics of two layered all-ceramic restorative systems

Objective The aim of this research was to evaluate both the fracture and impact strength of two core veneered all-ceramic systems and to reveal whether the speed of loading affects fracture mechanism. Methods The absorbed energy by IPSEmpress-Eris crowns and Cercon-Ceram S crowns in a fracture strength test was compared by the energy absorbed in an impact strength test. The principles of fractography were used to identify fracture origin and dimensions and to calculate the stress at failure. Finite element analysis (FEA) was used to rationalize the results. Results For the IPSEmpress 2-Eris crowns, there was a significant difference in the energy absorbed for the fracture test and the impact test, where for the Cercon-Ceram S, there was no significant difference. Despite the high strength of the zirconia cores there was no significant difference in the energy absorbed between the two systems in the impact strength test. The dominant mode of failure of layered all-ceramic restorations under occlusal loading is cone cracking in the veneering ceramic. Significance It was concluded that to exploit the high strength of the zirconia cores the strength of the veneering ceramic has to improve as delamination and cone cracking of the veneer are the most expected failure modes.

Improved strength-impairing contact damage resistance of Ti 3Si(Al)C 2/SiC composites

The resistance of Ti 3Si(Al)C 2-based materials to strength-impairing contact damage was investigated using the Hertzian indentation method. Microstructural analysis indicated that for the three types of testing materials the contact damage was governed by multiple grain slip, crushed grains, and intergranular shear failure. No cone cracking or other macro-cracks were visible on or beneath the contact damage surfaces. Bending tests on the specimens containing single-cycle contact damage revealed that the resistance of Ti 3Si(Al)C 2 to strength degradation was significantly improved by incorporating SiC particles into the matrix. The mechanism of the improvement is ascribed to the increased shear resistance and the fact that the hard SiC particles inhibit the downward extent of the contact damage through restricting the slip and deformation of the Ti 3Si(Al)C 2 grains.

Statistical failure analysis of brittle coatings by spherical indentation: theory and experiment

The mode of failure and failure probability of a brittle coating on a compliant substrate subjected to a static load through a spherical indenter is investigated experimentally and theoretically. We extend our recent study (2003, J Mat Sci 38:1589) of surface crack initiation in a monolithic solid to the layered system, and account for the multi axial stress state of the indentation in the failure probability analysis. Two modes of failure, a Hertzian cone crack initiating from the contacting surface and a half-penny-shaped crack initiating from the interface, are investigated and the probability of failure initiation for both surfaces are theoretically predicted and compared with experimental data.The effect of interface debonding on failure phenomena is investigated. For a given load the failure probability for debonded specimens is significantly higher than that of well-bonded samples. For the debonded case the theoretical failure probability curve falls within the 90% confidence interval of the experimental data, while the experimental values for the completely bonded case show somewhat lower failure probabilities than that predicted. This may be attributed to the possible bridging effect by the adhesive on interfacial surface defects in the ceramic that is not accounted for in our model.

Sphere contact fatigue of a coarse‐grained Al2O3 ceramic

ABSTRACTThe opposite sphere test is an appropriate tool to determine crack‐growth exponents for fatigue under repeated contact loading. Lifetime measurements for a coarse‐grained Al2O3 are reported. To explain the fatigue exponents that strongly deviated from those obtained in cyclic bending tests, a fracture mechanics analysis was carried out. It was aimed at determining the correct stress intensity factor solution for the tests, including limited dimensions of test specimens deviating from the case of a cone crack in a half space. Cone crack development was observed microscopically and the related stress intensity factors were computed for the observed crack shape.For modelling the fatigue behaviour, it is assumed that the fatigue effect is influenced by a reduction of the shielding term of crack growth resistance due to periodical friction between the grain‐interlock bridges in coarse‐grained alumina. This results in a loss of traction at the junctions, crack tip shielding is reduced, and the effective load at the crack tip is increased.

Hertzian fracture at unloading

Hertzian fracture through indentation of flat float glass specimens by steel balls has been examined experimentally. Initiation of cone cracks has been observed and failure loads together with contact and fracture radii determined at monotonically increasing load but also during unloading phases. Contact of dissimilar elastic solids under decreasing load may cause crack inception triggered by finite interface friction and accordingly the coefficient of friction was determined by two different methods. In order to make relevant predictions of experimental findings, a robust computational procedure has been developed to determine global and local field values in particular at unloading at finite friction. It was found that at continued loading it is possible to specify in advance how the contact domain divides into invariant regions of stick and slip. The maximum tensile stress was found to occur at the free surface just outside the contact contour, the relative distance depending on the different elastic compliance properties and the coefficient of friction. In contrast, at unloading invariance properties are lost and stick/slip regions proved to be severely history dependant and in particular with an opposed frictional shear stress at the contact boundary region. This causes an increase of the maximum tensile stress at the contour under progressive unloading. Predictions of loads to cause crack initiation during full cycles were made based on a critical stress fracture criterion and proved to be favourable as compared to the experimental results.

Effect of temperature on hardness and indentation cracking of fused silica

The fracture behavior induced by Vickers indentations in fused silica was investigated as a function of temperature. Indentations were performed from room temperature to 400°C in air. The indentations and the crack pattern formed were analyzed by optical and scanning electron microscopy. The hardness at room temperature was 7.3±0.3GPa and decreased to 4.2±0.1GPa at 400°C. Cone and radial cracks were observed at all temperatures. The radial crack length increased with temperature for a constant load. Lateral and median cracks were present under the indenter, and their expansion was constrained by cone cracks nucleated during the loading-unloading cycle. The threshold loads for cone and radial crack nucleation increased with temperature. The results are discussed in terms of the elastic modulus/hardness ratio variation with temperature.

Thin‐wall ceramic CAD/CAM crown copings: strength and fracture pattern

The strength and fracture pattern of posterior CAD/CAM-generated crown copings with 0.4 mm wall thickness were evaluated in vitro hypothesizing that fracture resistance of YTZP-zirconia copings might be independent of mode of cementation whether resin-bonded or cemented because of the high strength of YTZP-zirconia. Two sets of copings (n = 15) each were fabricated using CEREC inLab CAD/CAM from (i) lithiumdisilicate glass-ceramic, (ii) infiltration ceramic as controls and (iii) YTZP-zirconia. Copings (n = 15) of ceramics (i), (ii) and (iii) each were (a) zinc-phosphate cemented, (b) adhesively seated on resin-based composite dies and loaded until fracture. Load (N) data was analysed using anova and Scheffé tests. Crack pattern was evaluated on additional three sample cross-sections for each group at fracture-start. Radial cracks originated early at the cementation interfaces and cone cracks were observed finally at the loading sites. Mean load (N) values (+/-s.d.) of A-copings at fracture-start/-end (i) 804 +/- 195/862 +/- 162, (ii) 923 +/- 180/975 +/- 147, (iii) 697 +/- 110/1607 +/- 145, were all significantly (P < 0.01) lower when compared with their B-crown coping analogs (i) 1183 +/- 318/1919 +/- 326, (ii) 1621 +/- 165/1820 +/- 211, (iii) 731 +/- 115/1973 +/- 287 except for A3 and B3 at fracture-start. This confirmed our hypothesis at fracture-start (P > 0.05) but rejected it at fracture-end (P < 0.01). The A3 fracture-end data, even if significantly (P < 0.01) lower, came close to the B3 values by 18%. A3 was significantly (P < 0.001) stronger by 86/74% than A1/A2 at fracture-end. The data indicates that YTZP-zirconia copings have the potential to provide support for all-ceramic core crowns, which may be adequate for non-adhesive cementation.

Hydraulically pumped cone fracture in bilayers with brittle coatings

An earlier finite element modeling analysis of inner cone cracks in monolithic brittle solids subject to cyclic indentation in liquids is extended to include the case of a brittle layer bonded to a compliant substrate, using a model glass/polycarbonate bilayer system as an illustrative case study. Provision is made for incorporation of plate flexure stresses, along with hydraulic pumping stresses, into the Hertzian contact field. Tensile flexure stresses ultimately accelerate inner cone cracks through the lower halves of the glass plates to unstable failure. The analysis accounts for the experimentally observed trends in the inner cone crack evolution in cyclic contact fatigue.

Numerical simulation of matrix micro-cracking in short fiber reinforced polymer composites: Initiation and propagation

This paper presents a numerical simulation based analysis of micro-cracking in short fiber reinforced polymer composites. For this case, the conventional linear elastic fracture mechanics approach is shown not to be useful; instead, the Rice–Tracey ductile fracture model is shown to work well in the framework of the local approach to fracture. The model is first applied to the case of matrix cracking from the broken fiber end in a fiber fragmentation test of a single-fiber reinforced composite. The model predicts the measured conical crack path successfully, including the crack initiation angle and the kink formation as the crack propagates away from the fiber. Furthermore, the predicted dependence of the crack length on the nominal strain is found to be in qualitative agreement with measured data. Next the model is applied to micro-cracking in an aligned short fiber composite. The analysis predicts propagation of a matrix crack from the debonded fiber end towards the neighboring fiber at an oblique angle to the fiber axis. Before reaching the neighboring fiber, the crack is found to divert gradually towards the fiber axis. This behavior explains the so-called fiber-avoidance cracking mode reported in the literature. A parametric study is performed to reveal the dependence of the locally-averaged failure stress/strain on the fiber length and volume fraction.

Friction and wear behavior of dental feldspathic porcelain

The friction and wear behavior of dental feldspathic porcelains against uniform Si 3N 4 balls has been investigated using a small amplitude reciprocating apparatus under simulated oral conditions. The variables of load (10–40 N), reciprocating amplitude (100–500 μm), frequency (1–4 Hz) and use of artificial saliva lubrication were selected. Tests lasting up to 10,000 cycles were conducted. The bonded-interface technique was introduced into the wear test for the subsurface damage evaluation. Special attention was paid to the effects of friction conditions of tests, material properties and wear mechanism of dental porcelains. The results show Vita VMK95 possesses a lower friction coefficient and better wear resistance than Cerec Vitablocs MarkII. Among three parameters of the tests on the friction coefficient and wear depth of dental porcelains, the load effect is prominent. Artificial saliva plays an important role in lowering the friction coefficient and wear loss of dental porcelains. Abrasive wear is the main wear mechanism for both, but brittle cracks and delaminations are more frequent for Cerec Vitablocs MarkII, especially under non-lubricated friction. Surface brittle cracks are more dominant in low sliding cycles while subsurface cone or lateral cracks are prominent in high sliding cycles.