Hertzian Indentation Research Articles

Failure behavior of glass ionomer cement under Hertzian indentation

Objective To investigate the load-bearing capacity and failure mode of various types of glass ionomer cement (GIC) under Hertzian indentation, exploring the relationship between the failure behavior and formulation, and examining claims of filler-reinforcement of GIC. Methods Discs 2 mm thick, 10 mm diameter, 8–18 replicates, were fabricated for two filler-reinforced GICs, four unmodified and unreinforced GICs, and four resin-modified GICs, with a dental silver amalgam and a filled-resin restorative material for comparison. Testing was at 23 °C, wet, after 7 d storage at 37 °C in artificial saliva at pH 6, using a 20 mm diameter hard steel ball and filled-nylon substrate ( E: 10 GPa). First failure was detected acoustically; mode was determined visually. At least 1/3 of specimens in each case were examined under scanning electronic microscope for corroboration. Results Reinforced and unmodified-unreinforced GICs were indistinguishable by failure load (one-way analysis of variance, P = 0.425, overall 260 ± 70 N) and mode. Failure loads for resin-modified GICs were 360–1150 N, amalgam ∼680 N, and filled resin ∼1200 N. Resin-modified GICs tended to be tougher (incomplete fracture), all others gave complete fracture (radial cracking). The stronger materials (two resin-modified GICs and filled resin) showed some cone cracking. Significance While resin-modified GICs showed various extents of increase of failure load over that of the plain GICs, consistent with the hybrid chemistry, filler-reinforcement was not evident for the two claimed products, consistent with structural and theoretical expectations.

Theoretical analysis of Hertzian contact fracture: Ring crack

The axisymmetric fracture behavior of brittle materials under an applied indentation force is investigated by considering the pile-up of Somigliana ring dislocations. For such a mixed-mode crack problem, the stress intensity factors (SIFs) and strain energy release rate are obtained by solving a system of Cauchy singular integral equations. The Auerbach range is extensively studied during the formation of a shallow ring crack. The Auerbach constant is also determined from the exact solutions, enabling the prediction of surface energy from Hertzian indentation tests. The obtained results can be used to extract the fracture parameters of brittle materials by using the indentation technique.

Photoelastic effects in Pb(Mg1/3Nb2/3)O3−29%PbTiO3 single crystals investigated by Hertzian contact experiments

Photoelastic effects in small single-crystal Pb(Mg1/3Nb2/3)O3−29%PbTiO3 (PMN–29%PT) samples were investigated by Hertzian contact experiments. The experiments were performed on samples having various crystallographic orientations. The resulting photoelastic fringe patterns were observed to be strongly dependent on the orientation of the samples, showing that pseudocubic unpoled PMN–29%PT single crystals have highly anisotropic elastic properties. Annealing above the Curie temperature was found to completely remove the fringe patterns created by the Hertzian indentation experiments. In addition, three-dimensional simulations of the Hertzian contact experiments were performed using ANSYS®. The simulations used cubic-form elastic constants calculated from data on poled PMN–30%PT single crystals. The ANSYS® modeling results were comparable to the experimentally observed fringe patterns, suggesting that the elastic properties of pseudocubic unpoled PMN–PT single crystals may resemble those of pseudotetragonal poled PMN–PT single crystals. This resemblance is considered significant because of the uniqueness of the growth direction during seeded crystal growth. ANSYS® provided a reliable method for qualitative simulation of photoelastic effects in unpoled PMN–PT single crystals under mechanical loading.

Dependence of adhesion and friction on porosity in porous anodic alumina films

We explore, using atomic force microscopy, adhesion and friction characteristics of porous anodic alumina (PAA) films as the porosity varies. Pore formation greatly reduces the adhesive force, by as much as 30 times, but the porosity of PAA films has little influence on its adhesion properties, showing good agreement with the relative contact area estimated by the Hertzian model and indentation theory. Frictional coefficients vary nonlinearly with the porosity of the PAA films due to intrinsic characteristics of the surface morphology of PAA films.

Brittle wear of silicate materials by Hertzian rubbing contact

We studied the tribological properties of a structural series of 11 silicate materials to identify the main physical parameters that control the brittle wear of these materials. First, for each material we characterized Young's modulus E by ultrasonic microscopy, roughness σ by atomic force microscopy and crack pressure Pc by Hertzian indentation testing. Second, we measured the static and dynamic friction coefficients μS and μD, respectively, with a ball probe tribometer for each material and for three hardnesses of the ball probe. The experiments showed that crack density, which quantified the brittle wear of the materials, was controlled by an adimensional number, Cr = Pc/μSE. We show in this paper how this number takes into account the combined effects of the mechanical properties, the lubricating coating layer and the residual internal stresses of these materials.

Anisotropic mechanical properties and contact damage in air-plasma-sprayed thermal barrier coatings with bond coating nature and thermal exposure condition

The anisotropic mechanical properties and contact damage of air-plasma-sprayed (APS) zirconia-based thermal barrier coatings (TBCs) have been investigated using Vickers and Hertzian indentation tests as functions of the nature of the bond coating and the degree of thermal exposure. The hardness values of the TBC systems are dependent on the applied load at relatively low loads, and became saturated at a load of 30 N, independent of the nature of the bond coating or the degree of exposure. The values of the top coating obtained on the top surface from the Vickers indentation tests were higher than those on the sectional plane, indicating that there is an anisotropic strain behavior due to the microstructure. The regions near to the interface of the top coating and the thermally grown oxide (TGO) layer show higher values after thermal exposure, whereas the values of the APS bond coating increased and the indentation values of the high-velocity oxygen fuel (HVOF) sprayed bond coating slightly decreased after thermal exposure, owing to resintering and element deficiency during thermal exposure, respectively. In contact damage tests, the TBC system with the HVOF bond coating showed less damage than the TBC system with the APS bond coating. The shape of the damage was different between the two systems. After thermal exposure, the damage was reduced in both TBC systems, and the cracking or delamination formed at the regions near to the interface of the top coating and the TGO layer in both TBC systems.

Hertzian cone crack propagation on polycrystalline materials: Role of R-curve and residual stresses

In this work, the angle of the cone crack produced by Hertzian indentation is studied in relation to the shearing contribution of the crack shielding. This shielding is especially relevant in polycrystalline brittle materials, and may be responsible of the disagreement between previously predicted and actual values of the angle of cone crack. The study was conducted by means of an automated finite-element model of crack propagation, in which an analytical expression of the R-curve was included in the crack path determination. In addition, the influence of extrinsic effects, such as macroscopic residual stresses, was studied. The calculations were compared to crack observations on alumina and alumina-based laminates. Experimental results were in agreement with simulations. Based on this model, a method for quantitative assessment of both mode-I and mode-II crack shielding is proposed.

Contact Properties of Yttria Partially Stabilized Zirconia Up To 1000°C

The mechanical properties of a commercial polycrystalline yttria partially stabilized zirconia (Y‐PSZ) are evaluated as a function of temperature up to the onset of creep. Hertzian indentation tests in combination with finite element modeling (FEM) are used to determine its elastic–plastic properties up to 1000°C. Vickers hardness measurements are also performed at selected temperatures to complement the mechanical characterization. In addition, critical loads for radial and ring crack initiation are determined from postmortem inspection of test surfaces. The results reveal a dramatic hardening and strengthening of Y‐PSZ as the temperature decreases below 600°C, effects that are attributed to the tetragonal‐to‐monoclinic (t→m) transformation. Above the transformation temperature, the material strength continues to decrease with increasing temperature but at a lower rate, an effect that is explained by a gradual grain boundary degradation.

Study of the resistance to crack propagation in alumina by acoustic emission

The resistance to crack propagation or R-curve effect is still extensively studied in polycrystalline ceramic materials. This effect is shown in the literature by the increase of the stress intensity factor K I versus crack extension, or by the decrease of crack velocity versus K I under flexure tests. We have studied this fracture resistance by using the acoustic emission and the Hertzian indentation technique. It was found that the acoustic emission count rate decreases, like crack velocity in conditions of sub-critical crack growth before the failure is reached. Two specimen of alumina, respectively with small and coarse grains, were tested. A high crack extension resistance is obtained for coarse-grained alumina. Mechanisms of crack bridging and crack shielding are responsible for the R-curve effect. These mechanisms are also operating during cyclic loading. The resistance to crack propagation increases more and more after each cycle. Also we obtain R-curve effect during static loading. On the other hand, toluene or silicone oil corrosive environment delays the crack propagation. But water medium has a reverse effect and the apparent toughness is reduced in this case.

Hertzian and Nanoindentations on EBPVD-Coated Gadolinium Zirconate Thermal Barrier Materials

New gadolinium-yttrium zirconate thermal barrier coating(TBC) material is deposited by electron beam PVD method, as an alternative to YSZ TBC layer for gas turbine blade applications. XRD analysis reveals that the new TBC material consists of thermally stable pyrochlore structure. Hertzian and nanoindentation evaluations reveal that gadolinium zirconate materials show superior properties as a TBC candidate material with high mechanical properties. The Y2O3 doping improved hardness and elastic modulus of TBC layers. The indentation stress-strain curves by Hertzian indentation and the load-penetration depth curves by nanoindentation indicate that the new TBC layer has higher damage resistance combined with superior thermal insulation properties rather than commercial YSZ coatings.

Hertzian Indentation Damage Behavior of Highly Porous Silicon Nitrides

Highly porous Si3N4 ceramics in service are usually subjected to continuous impact of solid particles which may give rise to localized damage and consequently to strength degradation. Hertzian indentation and three-point bending tests were conducted to investigate the contact damage behavior of highly porous Si3N4 ceramics in this paper. The Hertzian indentation damage morphologies were examined by using a bonded-interface technique. As a result of intragranular microfracture under Hertzian indentation, a distributed subsurface damage region is developed beneath the indenter. It was shown that, with increasing indentation load, the damage region extends progressively and a quasi-plastic stress-strain response exhibits. Failure sources were observed to be Hertzian indentation sites in three-point bending tests, leading to a gradual strength degradation.

Robust Strategies for Automated AFM Force Curve Analysis—II: Adhesion-Influenced Indentation of Soft, Elastic Materials

In the first of this two-part discourse on the extraction of elastic properties from atomic force microscopy (AFM) data, a scheme for automating the analysis of force-distance curves was introduced and experimentally validated for the Hertzian (i.e., linearly elastic and noninteractive probe-sample pairs) indentation of soft, inhomogeneous materials. In the presence of probe-sample adhesive interactions, which are common especially during retraction of the rigid tip from soft materials, the Hertzian models are no longer adequate. A number of theories (e.g., Johnson-Kendall-Roberts and Derjaguin-Muller-Toporov), covering the full range of sample compliance relative to adhesive force and tip radius, are available for analysis of such data. We incorporated Pietrement and Troyon's approximation (2000, "General Equations Describing Elastic Indentation Depth and Normal Contact Stiffness Versus Load," J. Colloid Interface Sci., 226(1), pp. 166-171) of the Maugis-Dugdale model into the automated procedure. The scheme developed for the processing of Hertzian data was extended to allow for adhesive contact by applying the Pietrement-Troyon equation. Retraction force-displacement data from the indentation of polyvinyl alcohol gels were processed using the customized software. Many of the retraction curves exhibited strong adhesive interactions that were absent in extension. We compared the values of Young's modulus extracted from the retraction data to the values obtained from the extension data and from macroscopic uniaxial compression tests. Application of adhesive contact models and the automated scheme to the retraction curves yielded average values of Young's modulus close to those obtained with Hertzian models for the extension curves. The Pietrement-Troyon equation provided a good fit to the data as indicated by small values of the mean-square error. The Maugis-Dugdale theory is capable of accurately modeling adhesive contact between a rigid spherical indenter and a soft, elastic sample. Pietrement and Troyon's empirical equation greatly simplifies the theory and renders it compatible with the general automation strategies that we developed for Hertzian analysis. Our comprehensive algorithm for automated extraction of Young's moduli from AFM indentation data has been expanded to recognize the presence of either adhesive or Hertzian behavior and apply the appropriate contact model.

Nucleation of Shear Bands on EB-PVD Thermal Barriers Coatings under Hertzian Indentations

In this paper the formation of shear bands in columnar EB-PVD thermal barriers coatings is studied. In particular, critical parameters of nucleation of shear bands, such as contact pressure and initiation of cracks in the columns, are extracted from the experimental results. The pertinence of these parameters is discussed respecting to the stress field induced in the material during the indentation.

Quasi-Plastic Deformation of WC-Co Composites Loaded with a Spherical Indenter

The quasi-plastic deformation behavior of cemented tungsten carbide (WC-Co) materials was studied using Hertzian indentation techniques. The indentation stress-strain curves of three WC-10 wt pct Co alloys with different hardness values demonstrate that WC-Co alloys exhibit “quasi-plasticity” behavior under indentation load and the increase of indentation stress vs indentation strain bears similarity to “strain hardening” in ductile metals. The analysis of the subsurface indentation damage shows that the mechanisms of the quasi-plastic deformation of WC-Co material are the formation of microcracks. Microcracks were found at heavily damaged areas in all three alloys, and the number of microcracks was higher for the sample with the higher apparent quasi-plasticity. The threshold stress values for the onset of quasi-plastic deformation and formation of ring cracks were determined and used to evaluate the brittleness index of these materials. The correlation of the brittleness index with hardness values gives insight with regard to the brittle or quasi-plastic responses of WC-Co materials.

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.

Fracture toughness and residual stress measurements in tempered glass by Hertzian indentation

Hertzian indentation was used to assess the fracture toughness ( K Ic) and the surface residual stresses of tempered soda lime glass. Although such measurements are usually performed on chemically strengthened glasses, where the thickness of the layer under compression is limited to several micrometres, our study considers the most useful case of thermally quenched glass, widely used in industry and where the compressed layer is several hundred micrometres thick. Measurements were performed on annealed and thermally quenched samples and residual stresses were calculated using two different models of the literature. Results were compared to stress measurements performed by a conventional photoelasticimetry technique. It is shown that Hertzian indentation gives qualitatively correct results which are comparable for each of the literature models used, provided that interfacial friction between the spherical indenter and substrate is correctly taken into account in the calculations. It is shown that a scratch tester used to perform sliding indentation onto the surface of the samples is a suitable tool for assessing the friction coefficient value.

Li2ZrO3분리막의 제조와 이산화탄소 선택투과 전후의 기계적 특성 평가

In this study, we investigated Li₂ZrO₃ membrane as a candidate material for high-temperature CO₂ separation and evaluated mechanical property. Li₂ZrO₃ powder was synthesized by solid state reaction of Li₂CO₃ and ZrO₂. Then we fabricated Li₂ZrO₃ tape using tape casting method. Dense Li₂ZrO₃ membrane prepared by sintering at 1600℃ for 2 h after pressing Li₂ZrO₃ tape using lamination machine. Mechanical properties before and after CO₂ absorption of fabricated Li₂ZrO₃ membrane such as Hertzian indentation, Vickers hardness and 3-point bending testing were evaluated.

Contact damage initiation in silicon nitride in Hertzian indentation: role of microstructure

A bearing-grade silicon nitride with fine microstructure and a turbine-grade silicon nitride with coarse microstructure were studied with respect to the influence of their microstructures on (a) crack-growth-resistance behavior, (b) strength degradation due to Vickers indentation, and (c) crack initiation in quasi-static indentation with WC spheres. The turbine grade exhibited strong rising crack-growth resistance and less strength degradation due to Vickers indentation as compared to the bearing grade. Partial-ring or C cracks initiated in Hertzian indentation and the critical loads exhibited linear (Auerbach) variation with indenter radius above a critical value. For smaller radius, indentation plasticity preceded C-crack initiation. The bearing grade exhibited higher critical loads for C-crack initiation, but showed greater extension toward a ring crack than the turbine grade. These differences in crack initiation and growth were consistent with the differences in crack initiation and propagation toughness of the two grades. A ball-on-ball impact analysis was used to predict the critical velocities for initiating C cracks in the impact of silicon nitride surfaces with WC spheres.

Hardness degradation in liquid-phase-sintered SiC with prolonged sintering

The effect of the sintering time on the Vickers hardness of liquid-phase-sintered SiC with 10 wt% YAG additives was studied for materials fabricated in Ar and N 2 atmospheres. The hardness of the Ar-sintered materials was found to decrease markedly with increasing sintering time, whereas, in contrast, the decrease was only marginal for the N 2-sintered materials. Berkovich nanoindentation tests showed that the softening could not be attributed in either case to degradation of the SiC grains, thereby pointing to the intergranular YAG phase as the responsible. That the cause was degradation of the YAG phase was confirmed by X-ray energy-dispersive spectrometry and Hertzian indentation tests. The far more pronounced softening observed for the Ar-sintered materials reflects the more severe degradation that the YAG phase undergoes during sintering in this atmosphere.

Temperature dependence of mechanical properties of alumina up to the onset of creep

Mechanical properties of a commercial polycrystalline alumina are evaluated as a function of temperature up to the onset of creep. Hertzian indentation tests in combination with finite element modelling (FEM) are used to determine its elastic and plastic properties from the corresponding indentation stress–strain curves at prescribed temperatures up to 1200 °C. The results reveal a strong decline in the Young's modulus and the yield stress of the material at about 600 °C that is attributed to grain boundary degradation occurring around that temperature. The results are compared with dynamic Young's modulus and Vickers hardness measurements from the literature. The practical interest of measuring the mechanical properties of ceramics at intermediate temperatures is discussed and a general guideline to retain optimum elastic and plastic properties at intermediate temperatures is outlined.