The reduced modulus in the analysis of sharp instrumented indentation tests

In the analysis of instrumented indentation data, it is common practice to incorporate the combined moduli of the indenter (E-i) and the specimen (E) in the so-called reduced modulus (E-r) to account for indenter deformation. Although indenter systems with rigid or elastic tips are considered as equivalent if E-r is the same, the validity of this practice has been questioned over the years. The present work uses systematic finite element simulations to examine the role of the elastic deformation of the indenter tip in instrumented indentation measurements and the validity of the concept of the reduced modulus in conical and pyramidal (Berkovich) indentations. It is found that the apical angle increases as a result of the indenter deformation, which influences in the analysis of the results. Based upon the inaccuracies introduced by the reduced modulus approximation in the analysis of the unloading segment of instrumented indentation applied load (P)-penetration depth (delta) curves, a detailed examination is then conducted on the role of indenter deformation upon the dimensionless functions describing the loading stages of such curves. Consequences of the present results in the extraction of the uniaxial stress-strain characteristics of the indented material through such dimensional analyses are finally illustrated. It is found that large overestimations in the assessment of the strain hardening behavior result by neglecting tip compliance. Guidelines are given in the paper to reduce such overestimations.

Numerical analysis of different methods to calculate residual stresses in thin films based on instrumented indentation data

In this work, different methods to estimate the value of thin film residual stresses using instrumented indentation data were analyzed. This study considered procedures proposed in the literature, as well as a modification on one of these methods and a new approach based on the effect of residual stress on the value of hardness calculated via the Oliver and Pharr method. The analysis of these methods was centered on an axisymmetric two-dimensional finite element model, which was developed to simulate instrumented indentation testing of thin ceramic films deposited onto hard steel substrates. Simulations were conducted varying the level of film residual stress, film strain hardening exponent, film yield strength, and film Poisson's ratio. Different ratios of maximum penetration depth h(max) over film thickness t were also considered, including h/t = 0.04, for which the contribution of the substrate in the mechanical response of the system is not significant. Residual stresses were then calculated following the procedures mentioned above and compared with the values used as input in the numerical simulations. In general, results indicate the difference that each method provides with respect to the input values depends on the conditions studied. The method by Suresh and Giannakopoulos consistently overestimated the values when stresses were compressive. The method provided by Wang et al. has shown less dependence on h/t than the others.

Relationship between elastic and mechanical properties of dental ceramics and their index of brittleness

The purpose of the study was to verify the effects of a number of materials' parameters (crystalline content; Young's modulus, E; biaxial flexure strength, sigma(i); Vickers hardness, VH; fracture toughness, K-Ic; fracture surface energy, gamma(f); and index of brittleness, B) on the brittleness of dental ceramics. Five commercial dental ceramics with different contents of glass phase and crystalline particles were studied: a vitreous porcelain (VM7/V), a porcelain with 16 vol% leucite particles (d.Sign/D), a glass-ceramic with 29 vol% leucite particles (Empress/E1), a glass-ceramic with 58 vol% lithium-disilicate needle-like particles (Empress 2/E2), and a glass-infiltrated alumina composite with 65 vol% crystals (In-Ceram Alumina/IC). Discs were constructed according to manufacturers' instructions, ground and polished to final dimensions (12 mm x 1.1 mm). Elastic constants were determined by ultrasonic pulse-echo method. sigma(i) was determined by piston-on-3-balls method in inert condition. VH was determined using 19.6 N load and K-Ic was determined by indentation strength method. gamma(f) was calculated from the Griffith-Irwin relation and B by the ratio of HV to K-Ic. IC and E2 showed higher values of sigma(i), E, K-Ic and gamma(f), and lower values of B compared to leucite-based glass-ceramic and porcelains. Positive correlations were observed for sigma(i) versus K-Ic, and K-Ic versus E-1/2, however, E did not show relationship with HV and B. The increase of crystalline phase content is beneficial to decrease the brittleness of dental ceramics by means of both an increase in fracture surface energy and a lowering in index of brittleness. (C) 2012 Elsevier Ltd and Techna Group Sri. All rights reserved.

Analysis, manufacture and characterization of Ni/Cu functionally graded structures

In this work, an experimental and numerical analysis and characterization of functionally graded structures (FGSs) is developed. Nickel (Ni) and copper (Cu) materials are used as basic materials in the numerical modeling and experimental characterization. For modeling, a MATLAB finite element code is developed, which allows simulation of harmonic and modal analysis considering the graded finite element formulation. For experimental characterization, Ni-Cu FGSs are manufactured by using spark plasma sintering technique. Hardness and Young's modulus are found by using microindentation and ultrasonic measurements, respectively. The effective gradation of Ni/Cu FGS is addressed by means of optical microscopy, energy dispersive spectrometry, scanning electron microscopy and hardness testing. For the purpose of comparing modeling and experimental results, the hardness curve, along the gradation direction, is used for identifying the gradation profile; accordingly, the experimental hardness curve is used for approximating the Young's modulus variation and the graded finite element modeling is used for verification. For the first two resonance frequency values, a difference smaller than 1% between simulated and experimental results is obtained. (C) 2012 Elsevier Ltd. All rights reserved.

Evaluation of the micro-hardness and fracture toughness of amorphous and partially crystallized 3CaO center dot P2O5-SiO2-MgO bioglasses

In this work, the effect of the indentation load on the results of hardness and fracture toughness, determined by Vickers micro-hardness measurements, of some glasses and glass-ceramics has been investigated. Furthermore, in order to verify the effect of crystallinity on the results, glasses of composition 52.75 wt.% 3CaO center dot P2O5, 30 wt.% SiO2 and 17.25 wt.% MgO were fused at 1600 degrees C for 4 h and annealed at 700 degrees C for 2h, and further heat-treated at 700, 775, 800 and 900 degrees C for 4h. The obtained materials were analyzed by high resolution X-ray diffraction, HRXRD, to determine the crystallization degree in function of the heat-treatment temperature. The hardness of the different specimens was determined by Vickers' micro-hardness measurements under various loads. It has been observed that with increasing crystallization of the materials their hardness increased. Furthermore, it has been possible to verify the so-called indentation size effect (ISE), i.e. hardness decreases as the indentation depth, under higher loads, increases. This effect has been more pronounced in the glass-ceramic samples. Fracture toughness has been determined by the crack length induced by the Vickers indentations and relating them to the applied loads. Glass materials presented a fracture pattern with characteristics of cleavage, forming cracks of the half-penny shaped type, while the glass-ceramic materials exhibited crack bridging effects and Palmqvist type cracks. (C) 2011 Elsevier B.V. All rights reserved.

Dependence of brittle-to-ductile transition on crystallographic direction in diamond turning of single-crystal silicon

The objective of this paper is to show the dependence relationship between the crystallographic orientations upon brittle-to-ductile transition during diamond turning of monocrystalline silicon. Cutting tests were performed using a -5 degrees rake angle round nose diamond tool at different machining scales. At the micrometre level, the feedrate was kept constant at 2.5 micrometres per revolution (mu m/r), and the depth of cut was varied from 1 to 5 mu m. At the submicrometre level, the depth of cut was kept constant at 500 nm and the feedrate varied from 5 to 10 mu m/r. At the micrometre level, the uncut shoulder generated with an interrupted cutting test procedure provided a quantitative measurement of the ductile-to-brittle transition. Results show that the critical chip thickness in silicon for ductile material removal reaches a maximum of 285 nm in the [100] direction and a minimum of 115 nm in the [110] direction, when the depth of cut was 5 mu m. It was found that when a submicrometre depth of cut was applied, microcracks were revealed in the [110] direction, which is the softer direction in silicon. Micro Raman spectroscopy was used to estimate surface residual stress after machining. Compressive residual stress in the range 142 MPa and smooth damage free surface finish was probed in the [100] direction for a depth of cut of 5 mu m, whereas residual stresses in the range 350 MPa and brittle damage was probed in the [110] direction for a depth of cut of 500 nm.