Effects of elastic indenter deformation on spherical instrumented indentation tests: the reduced elastic modulus

Although the Hertz theory is not applicable in the analysis of the indentation of elastic-plastic materials, it is common practice to incorporate the concept of indenter/specimen combined modulus to consider indenter deformation. The appropriateness was assessed of the use of reduced modulus to incorporate the effect of indenter deformation in the analysis of the indentation with spherical indenters. The analysis based on finite element simulations considered four values of the ratio of the indented material elastic modulus to that of the diamond indenter, E/E(i) (0, 0.04, 0.19, 0.39), four values of the ratio of the elastic reduced modulus to the initial yield strength, E(r)/Y (0, 10, 20, 100), and two values of the ratio of the indenter radius to maximum total displacement, R/delta(max) (3, 10). Indenter deformation effects are better accounted for by the reduced modulus if the indented material behaves entirely elastically. In this case, identical load-displacement (P - delta) curves are obtained with rigid and elastic spherical indenters for the same elastic reduced modulus. Changes in the ratio E/E(i), from 0 to 0.39, resulted in variations lower than 5% for the load dimensionless functions, lower than 3% in the contact area, A(c), and lower than 5% in the ratio H/E(r). However, deformations of the elastic indenter made the actual radius of contact change, even in the indentation of elastic materials. Even though the load dimensionless functions showed only a little increase with the ratio E/E(i), the hardening coefficient and the yield strength could be slightly overestimated when algorithms based on rigid indenters are used. For the unloading curves, the ratio delta(e)/delta(max), where delta(e) is the point corresponding to zero load of a straight line with slope S from the point (P(max), delta(max)), varied less than 5% with the ratio E/E(i). Similarly, the relationship between reduced modulus and the unloading indentation curve, expressed by Sneddon`s equation, did not reveal the necessity of correction with the ratio E/E(i). The most affected parameter in the indentation curve, as a consequence of the indentation deformation, was the ratio between the residual indentation depth after complete unloading and the maximum indenter displacement, delta(r)/delta(max) (up to 26%), but this variation did not significantly decrease the capability to estimate hardness and elastic modulus based on the ratio of the residual indentation depth to maximum indentation depth, h(r)/h(max). In general, the results confirm the convenience of the use of the reduced modulus in the spherical instrumented indentation tests.

Effects of mechanical properties, residual stress and indenter tip geometry on instrumented indentation data in thin films

In this work, an axisymmetric two-dimensional finite element model was developed to simulate instrumented indentation testing of thin ceramic films deposited onto hard steel substrates. The level of film residual stress (sigma(r)), the film elastic modulus (E) and the film work hardening exponent (n) were varied to analyze their effects on indentation data. These numerical results were used to analyze experimental data that were obtained with titanium nitride coated specimens, in which the substrate bias applied during deposition was modified to obtain films with different levels of sigma(r). Good qualitative correlation was obtained when numerical and experimental results were compared, as long as all film properties are considered in the analyses, and not only sigma(r). The numerical analyses were also used to further understand the effect of sigma(r) on the mechanical properties calculated based on instrumented indentation data. In this case, the hardness values obtained based on real or calculated contact areas are similar only when sink-in occurs, i.e. with high n or high ratio VIE, where Y is the yield strength of the film. In an additional analysis, four ratios (R/h(max)) between indenter tip radius and maximum penetration depth were simulated to analyze the combined effects of R and sigma(r) on the indentation load-displacement curves. In this case, or did not significantly affect the load curve exponent, which was affected only by the indenter tip radius. On the other hand, the proportional curvature coefficient was significantly affected by sigma(r) and n. (C) 2010 Elsevier B.V. All rights reserved.

Evaluation of superficial microhardness in dental enamel with different eruptive ages

This study evaluated the superficial microhardness of enamel in teeth at different posteruptive ages (before eruption in the oral cavity, 2-3 years after eruption, 4-10 years after eruption and more than 10 years after eruption). The study sample was composed of 134 specimens of human enamel. One fragment of each tooth was obtained from the flattest central portion of the crown to produce specimens with 3 x 3 mm. The enamel blocks were minimally flattened out and polished in order to obtain a flat surface parallel to the base, which is fundamental for microhardness testing. Microhardness was measured with a microhardness tester and a Knoop diamond indenter, under a static load of 25 g applied for 5 seconds. Comparison between the superficial microhardness obtained for the different groups was performed by analysis of Student's t test. The results demonstrated that superficial microhardness values have a tendency to increase over the years, with statistically significant difference only between unerupted enamel and that with more than 10 years after eruption. According to the present conditions and methodology, it was concluded that there were differences between the superficial micro-hardness of specimens at different eruptive ages, revealing an increasing mineralization. However, this difference was significant only between unerupted specimens and those with more than 10 years after eruption.

Study of the surface hardness and modulus of elasticity of conventional and microwave-cured acrylic resins

The aim of this study was to evaluate the following acrylic resins: Clássico®, QC-20® and Lucitone®, recommended specifically for thermal polymerization, and Acron MC® and VIPI-WAVE®, made for polymerization by microwave energy. The resins were evaluated regarding their surface nanohardness and modulus of elasticity, while varying the polymerization time recommended by the manufacturer. They were also compared as to the presence of water absorbed by the samples. The technique used was nanoindentation, using the Nano Indenter XP®, MTS. According to an intra-group analysis, when using the polymerization time recommended by the manufacturer, a variation of 0.14 to 0.23 GPa for nanohardness and 2.61 to 3.73 GPa for modulus of elasticity was observed for the thermally polymerized resins. The variation for the resins made for polymerization by microwave energy was 0.15 to 0.22 GPa for nanohardness and 2.94 to 3.73 GPa for modulus of elasticity. The conclusion was that the Classico® resin presented higher nanohardness and higher modulus of elasticity values when compared to those of the same group, while Acron MC® presented the highest values for the same characteristics when compared to those of the same group. The water absorption evaluation showed that all the thermal polymerization resins, except for Lucitone®, presented significant nanohardness differences when submitted to dehydration or rehydration, while only Acron MC® presented no significant differences when submitted to a double polymerization time. Regarding the modulus of elasticity, it was observed that all the tested materials and products, except for Lucitone®, showed a significant increase in modulus of elasticity when submitted to a lack of hydration.

Aplicação de indentação instrumentada na caracterização mecânica de poliuretana derivada de óleo de mamona

Neste trabalho são investigadas as propriedades mecânicas de poliuretana derivada do óleo de mamona, utilizando a técnica de indentação instrumentada com penetradores de geometrias piramidal e esférica. Foi analisada a influência da forma do penetrador utilizado nos ensaios de indentação instrumentada para se obter valores das propriedades mecânicas de polímero derivado de óleo de mamona. Os penetradores utilizados são de pontas piramidais dos tipos Berkovich e canto de cubo e esférico de raio igual a 150 μm em um Nanoindenter XP TM com cargas aplicadas entre 1 e 200 mN. As penetrações variam de acordo com o formato do penetrador, sendo maiores para pontas agudas. A dureza e o módulo de elasticidade foram determinados, utilizando o método de Oliver e Pharr. Verificou-se que os valores medidos para a dureza são maiores para penetradores mais agudos. Os valores obtidos com a ponta piramidal Berkovich foram de 0,14 GPa para pequenas penetrações e 0,12 GPa para maiores penetrações. Já os valores obtidos com ponta canto de cubo foram 25 a 30% maiores. Isso está relacionado com os volumes das regiões que apresentam deformações plásticas elevadas, no caso de penetradores agudos comparados com os volumes das regiões que sofrem deformações viscoelásticas. A viscosidade aparente determinada, utilizando penetrador esférico em testes de força aplicada constante, é igual a (22 ± 2) × 10(12) Pa.s.

Analysis of the tip roundness effects on the micro- and macroindentation response of elastic-plastic materials

In this work, the effects of indenter tip roundness oil the load-depth indentation curves were analyzed using finite element modeling. The tip roundness level was Studied based on the ratio between tip radius and maximum penetration depth (R/h(max)), which varied from 0.02 to 1. The proportional Curvature constant (C), the exponent of depth during loading (alpha), the initial unloading slope (S), the correction factor (beta), the level of piling-up or sinking-in (h(c)/h(max)), and the ratio h(max)/h(f) are shown to be strongly influenced by the ratio R/h(max). The hardness (H) was found to be independent of R/h(max) in the range studied. The Oliver and Pharr method was successful in following the variation of h(c)/h(max) with the ratio R/h(max) through the variation of S with the ratio R/h(max). However, this work confirmed the differences between the hardness values calculated using the Oliver-Pharr method and those obtained directly from finite element calculations; differences which derive from the error in area calculation that Occurs when given combinations of indented material properties are present. The ratio of plastic work to total work (W(p)/W(t)) was found to be independent of the ratio R/h(max), which demonstrates that the methods for the Calculation of mechanical properties based on the *indentation energy are potentially not Susceptible to errors caused by tip roundness.

Analysis of the effects of conical indentation variables on the indentation response of elastic-plastic materials through factorial design of experiment

In this work, the effects of conical indentation variables on the load-depth indentation curves were analyzed using finite element modeling and dimensional analysis. A factorial design 2(6) was used with the aim of quantifying the effects of the mechanical properties of the indented material and of the indenter geometry. Analysis was based on the input variables Y/E, R/h(max), n, theta, E, and h(max). The dimensional variables E and h(max) were used such that each value of dimensionless Y/E was obtained with two different values of E and each value of dimensionless R/h(max) was obtained with two different h(max) values. A set of dimensionless functions was defined to analyze the effect of the input variables: Pi(1) = P(1)/Eh(2), Pi(2) = h(c)/h, Pi(3) = H/Y, Pi(4) = S/Eh(max), Pi(6) = h(max)/h(f) and Pi(7) = W(P)/W(T). These six functions were found to depend only on the dimensionless variables studied (Y/E, R/h(max), n, theta). Another dimension less function, Pi(5) = beta, was not well defined for most of the dimensionless variables and the only variable that provided a significant effect on beta was theta. However, beta showed a strong dependence on the fraction of the data selected to fit the unloading curve, which means that beta is especially Susceptible to the error in the Calculation of the initial unloading slope.

The role of crystalline anisotropy in mechanical property extractions through Berkovich indentation

This work uses crystal plasticity finite element simulations to elucidate the role of elastoplastic anisotropy in instrumented indentation P-h(s) curve measurements in face-centered Cubic (fcc) crystals. It is shown that although the experimental fluctuations in the loading stage of the P-h(s) curves can be attributed to anisotropy, the variability in the unloading stage of the experiments Is much greater than that resulting from anisotropy alone. Moreover, it is found that the conventional procedure used to evaluate the contact variables ruling the unloading P-h(s) curve introduces all uncertainty that approximates to the more fundamental influence of anisotropy. In view of these results, a robust procedure is proposed that uses contact area measurements in addition to the P-h(s) curves to extract homogenized J(2)-Plasticity-equivalent mechanical properties from single crystals.

The influence of crystallographic orientation on the generation of multiple structural phases generation in Silicon by cyclic microindentation

A Raman scattering study on multiple phase generation in silicon submitted to successive Vickers microindentation cycles, in different crystallographic orientations, was performed. The microindentations were perfon-ned in a virgin single crystal (100)-oriented surface, in the [001] and [011] directions. The results indicated that the formation of multiple phases by cyclic microindentation may depend on the crystallographic direction and number of successive cycles: the onset of several different structural phases was detected after the third cycle for the [001] direction and only after 15 cycles for the [011] direction, indicating that there is a crystallographic orientation dependence for multiple phase generation. (C) 2007 Elsevier B.V. All rights reserved.

A critical reassessment of elastic unloading in sharp instrumented indentation experiments and the extraction of mechanical properties

This work examines the extraction of mechanical properties from instrumented indentation P-h(s) curves via extensive three-dimensional finite element analyses for pyramidal tips in a wide range of solids under frictional and frictionless contact conditions. Since the topography of the imprint changes with the level of pile-up or sink-in, a relationship is identified between correction factor beta in the elastic equation for the unloading indentation stage and the amount of surface deformation effects. It is shown that the presumption of a constant beta significantly affects mechanical property extractions. Consequently, a new best-fit function is found for the correlation between penetration depth ratios h(e)/h(max), h(r)/h(max) and n, circumventing the need for the assumption of a constant value for beta, made in our prior investigation [Acta Mater. 53 (2005) pp. 3545-3561]. Simulations under frictional contact conditions provide sensible boundaries for the influence of friction on both h(e)/h(max) and h(r)/h(max). Friction is essentially found to induce an overestimation in the inferred n. Instrumented indentation experiments are also performed in three archetypal metallic materials exhibiting distinctly different contact responses. Mechanical property extractions are finally demonstrated in each of these materials.

An experimental and numerical investigation on tyre impact

A key issue in the design of tyres is their capability to sustain intense impact loads. Hence, the development of a reliable experimental data basis is important, against which numerical models can be compared. Experimental data on tyre impact in the open literature is somewhat rare. In this article, a specially design rig was developed for tyre impact tests. It holds the test piece in a given position, allowing a drop mass with a round indenter to hit pressurised tyres with different impact energies. A high-speed camera and a laser velocimeter were used to track the impact event. From the laser measurement it was possible to obtain the impact force and the local indentation. A finite element study was then conducted using material properties from the open literature. By comparing the experimental measurements with the numerical results, it became evident that the model was capable of predicting the major features of the impact of a mass on a tyre. This model is therefore of value for the assessment of the performance of a tyre in extreme cases of mass impact. (C) 2009 Elsevier Ltd. All rights reserved.

Subcritical crack growth in porcelains, glass-ceramics, and glass-infiltrated alumina composite for dental restorations

The objective was to compare fracture toughness (K(Ic)), stress corrosion susceptibility coefficient (n), and stress intensity factor threshold for crack propagation (K(I0)) of two porcelains [VM7/Vita (V) and d.Sign/Ivoclar (D)], two glass-ceramics [Empress/Ivolcar (E1) and Empress2/Ivlocar (E2)] and a glass-infiltrated alumina composite [In-Ceram Alumina/Vita (IC)]. Disks were constructed according to each manufacturer`s processing method, and polished before induction of cracks by a Vickers indenter. Crack lengths were measured under optical microscopy at times between 0.1 and 100 h. Specimens were stored in artificial saliva at 37A degrees C during the whole experiment. K(Ic) and n were determined using indentation fracture method. K(I0) was determined by plotting log crack velocity versus log K(I). Microstructure characterization was carried out under SEM, EDS, X-ray diffraction and X-ray fluorescence. IC and E2 presented higher K(Ic) and K(I0) compared to E1, V, and D. IC presented the highest n value, followed by E2, D, E1, and V in a decreasing order. V and D presented similar K(Ic), but porcelain V showed higher K(I0) and lower n compared to D. Microstructure features (volume fraction, size, aspect ratio of crystalline phases and chemical composition of glassy matrix) determined K(Ic). The increase of K(Ic) value favored the increases of n and K(I0).

Influence of leucite content on slow crack growth of dental porcelains

Objectives. To determine the stress corrosion susceptibility coefficient, n, of seven dental porcelains (A: Ceramco I; B: Ceramco-II; C: Ceramco-III; D: d.Sign; E: Cerabien; F: Vitadur-Alpha; and G: Ultropaline) after aging in air or artificial saliva, and correlate results with leucite content (LC). Methods. Bars were fired according to manufacturers` instructions and polished before induction of cracks by a Vickers indenter (19.6 N, 20 s). Four specimens were stored in air/room temperature, and three in saliva/37 degrees C. Five indentations were made per specimen and crack lengths measured at the following times: similar to 0; 1; 3; 10; 30; 100; 300; 1000 and 3000 h. The stress corrosion coefficient n was calculated by linear regression analysis after plotting crack length as a function of time, considering that the slope of the curve was (2/(3n + 2)]. Microstructural analysis was performed to determine LC. Results. LC of the porcelains were 22% (A and B); 6% (C); 15% (D); 0% (E and F); and 13% (G). Except for porcelains A and D, all materials showed a decrease in their n values when stored in artificial saliva. However, the decrease was more pronounced for porcelains B, F, and G. Ranking of materials varied according to storage media (in air, porcelain G showed higher n compared to A, while in saliva both showed similar coefficients). No correlation was found between n values and LC in air or saliva. Significance. Storage media influenced the n value obtained for most of the materials. LC did not affect resistance to slow crack growth regardless of the test environment. (c) 2008 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

Short-term in situ/ex vivo study of the anticariogenic potential of a resin-modified glass-ionomer cement associated with adhesive systems

Objective: As resin-modified glass-ionomer cement (RMGIC) is an adhesive material, its association to dentin bonding agents (DBAs) was previously proposed. This study investigated the adjunctive behavior of an RMGIC with etch-and-rinse bonding systems under in situ/ex vivo cariogenic challenge. Method and Materials: Bovine enamel blocks (3 3 2 mm) were randomly assigned to group VP, Vitremer + its own primer (3M ESPE); group VSB, Vitremer + Single Bond (3M ESPE); and group VPB, Vitremer + Prime & Bond 2.1 (Dentsply). Two blocks of each group were randomly placed in an acrylic palatal appliance, so each appliance included six blocks. Volunteers (n = 10) wore these appliances according to given instructions to promote a sucrose challenge eight times/day for 15 days. After this period, the blocks were removed from the devices and cleaned, and demineralization was assessed through longitudinal microhardness analysis (Knoop indenter, 25 g/5 s). Data were submitted to three-way ANOVA and Tukey test (P < .05). Results: No treatment was able to completely avoid demineralization. All materials showed a statistically significant difference in mineral loss when the microhardness on the outer enamel was compared with deeper regions (P < .05). Conclusion: Association of the tested RMGICs with etch-and-rinse DBAs did not seem to be more beneficial against caries than the conventional treatment with RMGIC. (Quintessence Int 2010; 41: e192-e199)

Fatigue life and failure modes of crowns systems with a modified framework design

Objectives: To evaluate the effect of framework design on the fatigue life and failure modes of metal ceramic (MC, Ni-Cr alloy core, VMK 95 porcelain veneer), glass-infiltrated alumina (ICA, In-Ceram Alumina/VM7), and veneered yttria-stabilized tetragonal zirconia polycrystals (Y-TZP, IPSe.max ZirCAD/IPS e.max,) crowns. Methods: Sixty composite resin tooth replicas of a prepared maxillary first molar were produced to receive crowns systems of a standard (MCs, ICAs, and Y-TZPs, n = 10 each) or a modified framework design (MCm, ICAm, and Y-TZPm, n = 10 each). Fatigue loading was delivered with a spherical steel indenter (3.18 mm radius) on the center of the occlusal surface using r-ratio fatigue (30-300 N) until completion of 10(6) cycles or failure. Fatigue was interrupted every 125,000 cycles for damage evaluation. Weibull distribution fits and contour plots were used for examining differences between groups. Failure mode was evaluated by light polarized and SEM microscopy. Results: Weibull analysis showed the highest fatigue life for MC crowns regardless of framework design. No significant difference (confidence bound overlaps) was observed between ICA and Y-TZP with or without framework design modification. Y-TZPm crowns presented fatigue life in the range of MC crowns. No porcelain veneer fracture was observed in the MC groups, whereas ICAs presented bulk fracture and ICAm failed mainly through the veneer. Y-TZP crowns failed through chipping within the veneer, without core fractures. Conclusions: Framework design modification did not improve the fatigue life of the crown systems investigated. Y-TZPm crowns showed comparable fatigue life to MC groups. Failure mode varied according to crown system. (C) 2010 Elsevier Ltd. All rights reserved.