Hertzian Indentation Research Articles

Contact damage of silicon carbide ceramics with different grain structures measured by Hertzian and Vickers indentation

We have used Hertzian and Vickers indentation to investigate contact damage in sintered SiC ceramics, one consisting of uniform, fine-grains and the other a coarse, elongated grain structure. Cracking-resistance measured by Hertzian indentation, showed no discernible difference, nor did the Vickers hardness. However, numerical analysis of the Vickers indentation size effect, performed using the proportional specimen resistance model, indicates 77.3% greater surface energy, mostly realised through cracking, is experienced by heterogeneous SiC per unit area of indentation impression. This is typified by an observable increase in the number of radial cracks generated around Vickers impressions, which has been found to artificially increase the KIC determined by Vickers indentation fracture. Quantitative measurements of pre-existing flaws by Hertzian indentation show that heterogeneous SiC retains a higher density of larger flaws. Relationships between the differences in cracking around Vickers indents and the pre-existing flaw populations of these two SiC ceramics are discussed.

유리/다공성 알루미나의 접촉하중에 의한 기계적 거동

Porous alumina with different porosities, 5.2 - 47.5%, were coated with cover-glass having a thickness of 160 μm, using epoxy adhesive. We investigated the effect of the porosity of the substrate layer on the crack initiation load, and the size of cracks propagated in the coating layer. Hertzian indentations were used to evaluate the damage behavior under a constrained loading condition. Typically, two types of cracks, ring cracks and radial cracks, were observed on the surface of the glass/porous alumina structure. Indentation stress-strain curves, crack initiation loads, crack propagation sizes, and flexural strengths were investigated as a function of porosities. The results indicated that a porosity of less than 30% and a higher substrate elastic modulus were beneficial at suppressing cracks occurrence and propagation. We expect lightweight mechanical components with high strength can be successfully fabricated by coating and controlling porosities in the substrate layer.

Hertzian Indentation Stress Field Equations

Indentation with hard spherical indenters (so called Hertzian indentation) is a well‐known technique to probe the mechanical properties of ceramics and other brittle materials. Using contact mechanics, it is possible to calculate the stress distribution in the sample and use it to express maximum tensile or compressive stresses as a function of load and contact radius. The equations describing the full stress distribution are not usually mentioned in the literature, and surprisingly most of the classical references disclosing them are either mistaken or incomplete. We recovered the full and detailed equations for the stress field distribution and numerically implemented them using the computer language Python. We point out the relationships between the different expressions that have been published, check the consistency with existing results, and discuss the sources of confusion.

Fracture toughness of cemented carbides: Testing method and microstructural effects

Fracture toughness is one the most important parameters for design applications and performance assessment of WC–Co cemented carbides (hardmetals). Different from hardness, fracture toughness is commonly a property more difficult to evaluate, particularly in brittle materials. A large number of different testing methods have been introduced to evaluate toughness of hardmetals, but in general all of them have either theoretically debatable issues or important experimental difficulties. In this study, three different fracture toughness testing methodologies are investigated: three-point bending on Chevron notched specimen (“reference” baseline), Palmqvist indentation test, and Hertzian indentation method. The work is conducted in several cemented carbide grades with different microstructures, in terms of both WC grain size and Co binder content. It is found that Chevron-notched three-point bending test yields suitable fracture toughness values for a wide range of cemented carbide grades with varying hardness. Concerning indentation methods, the Hertzian one may be particularly recommended, as compared to Palmqvist method, as far as hardness (HV30) drops below 1300. On the other hand, if HV30 is higher than 1300 Palmqvist indentation procedure yields reliable fracture toughness measurements. Experimental findings are finally analyzed and discussed on the basis of two theoretical models proposed in the literature.

The Excellent Mechanical Properties of Cork: A Novel Approach through the Analysis of Contact Stress

In many technological applications of cork, this biomaterial is under strongly localized contact stresses, which largely differ from the homogeneous distribution of stresses of the typical uniaxial compression tests. Indentation tests constitute an excellent form of determining the behavior of the materials under localized stresses. In the present study, the applicability of Hertzian and Brinell indentation tests to the evaluation of the mechanical properties of cork is tested. One of the main conclusions of the study is that the elastic anisotropy of the material is related to the anisotropic structure of the different sections cut from a cork sample, a clear difference between the back tangential section and the other sections being observed.

Studying SiC/SiC Composites by X-Ray Tomography

Continuous SiC fiber reinforced SiC matrix composites (SiC/SiC) have been studied and developed for high temperature applications and nuclear applications. In this study, SiC/SiC composites were fabricated via polymer impregnation and pyrolysis (PIP) process and studied by X-ray tomography. The SiC/SiC composites were first scanned using a Metris X-tek 320 kV source at the Henry Moseley X-ray Imaging Facility at the University of Manchester, the closed porosities were investigated after three dimensional (3D) imaging of the samples. Furthermore, high-resolution synchrotron X-ray tomography was applied to the SiC/SiC composite at Diamond Light Source. Digital volume correlation was employed for Hertzian indentation testing of the SiC/SiC composite, quantifying damage by measurement of the displacement fields within the material. A Cellular Automata integrated with Finite Elements (CAFE) method was developed to account for the effect of microstructure on the fracture behavior of the SiC/SiC composite. Graded microstructures, textures and multiple phases were simulated and a mesh-free framework was developed to compute the damage development through the microstructure. The results indicated that we could study the development of discontinuous cracking and damage coalescence, and its sensitivity to microstructure with this method.

Contact-mechanical properties at pre-creep temperatures of fine-grained graphene/SiC composites prepared in situ by spark-plasma sintering

Hertzian indentation was used to investigate for the first time the elastic–plastic behavior and contact damage evolution with temperature (in the 25–850 °C range) in air of different in situ grown graphene/SiC composites. Three SiC starting powders differing in polytypes and particle sizes were liquid-phase densified by spark-plasma sintering, thus producing ceramic composites that contain about 4 vol.% of epitaxial grown graphene flakes at the grain boundaries and have interesting differences in their microstructure. The general trend in the contact mechanical behavior is qualitatively similar among the different composites, with the elastic modulus, yield stress, and critical loads for the onset of quasi-plasticity and ring/cone cracking all decreasing with increasing temperature, with the differences at the quantitative level being explained in terms of the particular microstructure of each graphene/SiC composite.

3D Studies of Indentation by Combined X-Ray Tomography and Digital Volume Correlation

Hardness testing obtains material properties from small specimens via measurement of load-displacement response to an imposed indentation; it is a surface characterisation technique so, except in optically transparent materials, there is no direct observation of the assumed damage and deformation processes within the material. Three-dimensional digital image correlation (digital volume correlation) is applied to study deformation beneath indentations, mapping the relative displacements between high-resolution synchrotron X-ray computed tomographs (0.9 μm voxel size). Two classes of material are examined: ductile aluminium-silicon carbide composite (Al-SiC) and brittle alumina (Al2O3). The measured displacements for Hertzian indentation in Al-SiC are in good agreement with an elastic-plastic finite element simulation. In alumina, radial cracking is observed beneath a Vickers indentation and the crack opening displacements are measured, in situ under load, for the first time. Potential applications are discussed of this characterization technique, which does not require resolution of microstructural features.

Hertzian indentation testing of glass-ionomer restoratives: A reliable and clinically relevant testing approach

ObjectivesTo investigate the load to failure of encapsulated posterior glass-ionomer (GI) restoratives tested under Hertzian indentation and to explore the validity and reproducibility of the test results achieved for consideration of inclusion as an ISO testing protocol. MethodsGroups of 20 disc-shaped specimens (10.0±0.1mm diameter, 3.10±0.03mm thickness) were prepared (in batches of four) from three encapsulated posterior GI restoratives. Discs were tested while resting freely on a dentine analogue material at 24h under Hertzian indentation at a rate of 1mm/min delivered through a 20mm diameter hard steel ball. The failure mode and fracture origin of the GI specimens was assessed by fractography. Statistical analyses of the load to failure data were conducted using SPSS software (p<0.05) with the normality and homogeneity of variance of the load to failure data assessed using the Shapiro–Wilk and Levene's test, respectively. Data was also analysed using regression analyses to identify trends within the load to failure data sets. ResultsThe load to failure data for the GI restorative groups investigated were normally distributed (p>0.05), homogenous (p>0.05) and not significantly influenced by batch (p>0.780) or specimen number (p>0.447) although significant differences (p<0.05) between the GI restorative materials were evident. Fractographic analysis identified smooth fracture surfaces parallel to the loading axis where the failure mode was bottom initiated radial cracking. The mean coefficient of variation (CoV) for the GI restorative load to failure data sets achieved using Hertzian indentation testing was 7%. SignificanceThe failure mode and fracture origin of the GI restoratives tested using Hertzian indentation is representative of the clinical situation in vivo. The reliability of the load to failure data sets produced were improved compared with routinely employed mechanical testing approaches suggesting the possibility of inclusion as an ISO testing protocol.

Frictional dissipation in elastically dissimilar oscillating Hertzian contacts

We consider the problem of a cyclic Hertzian indentation between elastically dissimilar materials. In the case of loading, the problem was solved by Spence in a series of seminal papers, where he proved a relationship between the solution for a rigid square-shaped punch, to that for a power-law indenter. For example, the stick area is a constant ratio of the contact area, independently on the shape of the punch. “Unfortunately”, on unloading, many of the simple properties of the self-similar loading case are lost, there is a complicated development of an external region of slip which cycles in the two directions (forward and back-slip), and an inner region which continues to slip in the forward direction of the first loading cycle. However, this inner region gradually disappears, and further cyclic loading generates a convergence to a steady state solution which involves residual “locked-in” tangential slip displacements in a permanent stick zone, provided the contact is not fully unloaded. Dissipation in the steady state therefore occurs only in the external region of slip, and we provide some results for the energy dissipation per cycle, as a function of the governing parameters: coefficient of friction, Dundurs’ dissimilarity constant, normal load amplitude. We also show the likely independence of energy dissipation on initial conditions, limited to the possible scenario of overloading. It is seen that dependence of energy dissipation per cycle on load amplitude is closer to quadratic than to cubic, and this may explain some experimental findings which so far were not expected from oscillatory loading of elastically similar half-spaces.

Study on Mechanical Properties of Cement Clinker and Limestone by Hertzian Indentation Method

The recovery resistance, energy dissipation, and other mechanical properties of cement materials are evaluated based on the Hertzian indentation method in this work. It is significant and efficient for engineering application. In results, the calculated energy dissipation of clinker is higher than that of limestone, which can partially be used to explain why the grinding of clinker consumes a lot of energy in cement industry. The recovery resistance for limestone under the peak load of 100N is almost higher than of clinker. However, in contrast to that of 200N, the recovery resistance for limestone is almost identical to that of clinker. It is indicated that the clinker exhibits better plasticity. and greater energy absorption capacity.

Damage and wear resistance of Al&lt;sub&gt;2&lt;/sub&gt;O&lt;sub&gt;3&lt;/sub&gt;–CNT nanocomposites fabricated by spark plasma sintering

In this study, we prepare Al2O3-CNT (carbon nanotube) composites with different contents of CNT, 1~20vol% into the Al2O3 ceramics, for the purpose of improving damage and wear resistance. Al2O3CNT composites are obtained by spark plasma sintering in conditions of 1400~1600C in vacuum and 30MPa~80MPa. Hardness evaluated by Vickers indentation shows that the hardness of Al2O3-CNT composites can be enhanced when the CNT addition is less than 5vol%. Toughness evaluated by Vickers indentation indicates that the toughness of the composites is comparable with that of an Al2O3 monolith. Hertzian indentations using a spherical indenter indicate the hard and elastic behavior of the composites by the addition of CNT. The wear rate and friction coefficients of the composites evaluated by the ball-on-disk method show that the composites represent low friction and reduced wear loss under constant contact load. The results indicate that the damage and wear resistance of Al2O3 ceramics can be enhanced by the addition of carbon nanotubes in optimum conditions.

The mechanism of compressive unloading failure in single crystal quartz and other brittle solids

The phenomenon called unloading failure, in which the initiation and growth of cracks occurs during the removal of compressive stresses, has been observed in both uniaxial compression testing and Hertzian indentation testing of brittle materials. We have conducted finite element simulations of uniaxial compression experiments on single crystal quartz (specimens in which unloading failure was observed) to determine: (1) the mechanism responsible for unloading failure in brittle materials, (2) the dependence of this mechanism on friction between the specimen and loading platens, (3) the cause for the selection of specific fracture planes on which the unloading cracks propagate. The simulation results indicate that a slip-stick mechanism which is highly dependent on interface friction is responsible for the generation of tensile stress states leading to failure during unloading. The results also show that elastic anisotropy of a single crystal specimen leads to the self-selection of preferential failure planes during unloading.

Knoop Hardness–Apparent Yield Stress Relationship in Ceramics

In Tabor's classical studies of the deformation of metals, the yield stress (Y) and hardness (H) were shown to be related according to H/Y ≈ 3 for complete or fully plastic deformation. Since then it has been anecdotally shown for ceramics that this ratio is &lt;3. Interest exists to explore this further so Hertzian indentation was used to measure the apparent yield stress of numerous ceramics and metals and their results were compared with each material's load‐dependent Knoop hardness. The evaluated ceramics included standard reference materials for hardness (silicon nitride and tungsten carbide), silicon carbide, alumina, and glass. Several steel compositions were also tested for comparison. Knoop hardness measurements at 19.6 N (i.e., toward “complete or fully plastic deformation”), showed that 2 &lt; H/Y &lt; 3 for the metals and 0.8 &lt; H/Y &lt; 1.8 for the glasses and ceramics. Being that H/Y ≠ 3 for the ceramics indicates that Tabor's analysis is either not applicable to ceramics or that full plastic deformation is not achieved with a Knoop indentation or both.

Failure and behavior in water of hydroxyapatite whisker-reinforced bis-GMA-based resin composites

Failure mode under Hertzian indentation and the behavior on immersion in water of bis-GMA-based composites with HA whiskers or nanoscopic HA powder as filler were evaluated. Failure load decreased with increase in filler loading, but the decrease was smaller for whiskers, which showed a different failure mode both macroscopically and microscopically. Particle-filled composites failed mainly by radial cracking and cone cracking, with some plastic deformation at low filler loading, with fracture into irregular segments. For whisker-filled materials, crack propagation was inhibited by the well-dispersed whiskers by the usual toughening mechanisms; cone cracking was the dominant failure mode, at higher loads than for the powder, and fracture was incomplete. The filler reduced both water-uptake and elution of soluble materials, as expected, but both were lower for the whisker-filled material. Such composites might form the basis of viable materials for dental load-bearing restorations and other applications.

Qualitative assessment of microstructure and Hertzian indentation failure in biocompatible glass ionomer cements

Discs of biocompatible glass ionomer cements were prepared for Hertzian indentation and subsequent fracture analyses. Specifically, 2 × 10 mm samples for reproducing bottom-initiated radial fracture, complemented by 0.2 × 1 mm samples for optimal resolution with X-ray micro tomography (μCT), maintaining dimensional ratio. The latter allowed for accurate determination of volumetric-porosity of the fully cured material, fracture-branching through three Cartesian axes and incomplete bottom-initiated cracking. Nanocomputed tomography analyses supported the reliability of the μCT results. Complementary 2-dimensional fractographic investigation was carried out by optical and scanning electron microscopies on the larger samples, identifying fracture characteristics. The combined 3-D qualitative assessment of microstructure and fractures, complemented by 2-D methods, provided an increased understanding of the mechanism of mechanical failure in these cements. Specifically, cracks grew to link pores while propagating along glass-matrix interfaces. The methodological development herein is exploitable on related biomaterials and represents a new tool for the rational characterisation, optimisation and design of novel materials for clinical service.

Effect of elastic modulus mismatch on failure behaviour of glass ionomer cement under Hertzian indentation

ObjectiveTo investigate the effect of the substrate: coating elastic modulus ratio on the failure behaviour of glass ionomer cement (GIC) under Hertzian indentation. MethodsGIC (Amalgomer CR, Advanced Healthcare, Tonbridge, Kent, UK) discs, 2mm thick and 10mm diameter, were randomly divided into 11 groups, 10–22 specimens for each group, and stored at 37°C in artificial saliva for 7days. Discs were tested resting freely on 11 substrate materials at 23°C in air by loading centrally through a 20mm diameter hard steel ball at a crosshead speed of 0.2mm/min. The elastic moduli of the substrates (Es) and the coating GIC (Ec) were first measured with a method similar to that of the Hertzian indentation, except for the three harder materials: amalgam, Al6061 and stainless steel 304. The failure load at the first crack was recorded with the aid of acoustic emission detection. Fracture surfaces were observed by SEM. ResultsEs values ranged from 0.09 to 210GPa; Ec was 7.7GPa. Failure load generally increased with Es at first and then became relatively stable; the turning point occurred for Es/Ec=1. Bottom surface-initiated radial cracking was the principal failure mode on softer substrates (Es/Ec<1), while top surface conical cracking usually occurred on harder substrates (Es/Ec≥1). ConclusionThe elastic modulus ratio, substrate: coating, is a controlling factor for both the failure mode and load for the coating material under Hertzian indentation.

High strain rate indentation-induced deformation in alumina ceramics measured by Cr 3+ fluorescence mapping

Alumina materials with a range of grain sizes and purities were subjected to small-scale dynamic impact by sharpened tungsten carbide projectiles at sub-ballistic velocities. The resistance of the materials to fracture was recorded by visual examination of the cracking on the impacted surface and the damage in the subsurface region. The residual stress and plastic deformation induced in each material were examined using Cr 3+ fluorescence mapping. A modified Hertzian indentation model of the stress state in the material with the addition of a blister field representing the stress induced by the presence of the subsurface plastic zone was found accurately describe the observed cracks beneath the surface of the material, as well as the radial cracks on the surface.

Designing the fiber volume ratio in SiC fiber-reinforced SiC ceramic composites under Hertzian stress

Finite element method (FEM) analysis and experimental studies are undertaken on the design of the fiber volume ratio in silicon carbide (SiC) fiber-reinforced SiC composites under indentation contact stresses. Boron nitride (BN)/Pyrocarbon (PyC) are selected as the coating materials for the SiC fiber. Various SiC matrix/coating/fiber/coating/matrix structures are modeled by introducing a woven fiber layer in the SiC matrix. Especially, this study attempts to find the optimum fiber volume ratio in SiC fiber-reinforced SiC ceramics under Hertzian stress. The analysis is performed by changing the fiber type, fiber volume ratio, coating material, number of coating layers, and stacking sequence of the coating layers. The variation in the stress for composites in relation to the fiber volume ratio in the contact axial or radial direction is also analyzed. The same structures are fabricated experimentally by a hot process, and the mechanical behaviors regarding the load–displacement are evaluated using the Hertzian indentation method. Various SiC matrix/coating/fiber/coating/matrix structures are fabricated, and mechanical characterization is performed by changing the coating layer, according to the introduction (or omission) of the coating layer, and the number of woven fiber mats. The results show that the damage mode changes from Hertzian stress to flexural stress as the fiber volume ratio increases in composites because of the decreased matrix volume fraction, which intensifies the radial crack damage. The result significantly indicates that the optimum fiber volume ratio in SiC fiber-reinforced SiC ceramics should be designed for inhibiting the flexural stress.

An Assessment of the Effectiveness of the Hertzian Indentation Technique for Determining the Fracture Toughness of Brittle Materials

Ring crack initiation loads on glass using a spherical WC indenter were measured, and the methodology proposed by Warren and Hills and Warren was used to estimate glass toughness (KIC). The values obtained were overestimates of KIC, primarily because the methodology does not account for friction correctly. Corrected results that show that the stress‐intensity factor at the surface crack tip is extremely sensitive to the friction coefficient, μ and to Poisson's ratio, ν of the substrate are presented. This sensitivity and an inability to obtain the minimum load for crack initiation despite numerous experimental trials, cast doubt on the utility of the technique to measure KIC.