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.

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.

Indentation of elastically anisotropic half-spaces by cones and parabolae of revolution

Indentation of ceramic materials with smooth indenters such as parabolae of revolution and spheres can be conducted in the elastic regime to relatively high loads. Ceramic single crystals thus provide excellent calibration media for load-and depth-sensing indentation testing; however, they are generally anisotropic and a complete elastic analysis is cumbersome. This study presents a simplified procedure for the determination of the stiffness of contact for the indentation of an anisotropic half-space by a rigid frictionless parabola of revolution which, to first order, approximates spherical indentation. Using a similar approach, a new procedure is developed for analysing conical indentation of anisotropic elastic media. For both indenter shapes, the contact is found to be elliptical, and equations are determined for the size, shape and orientation of the ellipse and the indentation modulus.

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.

The correlation of the indentation size effect measured with indenters of various shapes

Experimental results are presented which show that the indentation size effect for pyramidal and spherical indenters can be correlated. For a pyramidal indenter, the hardness measured in crystalline materials usually increases with decreasing depth of penetration, which is known as the indentation size effect. Spherical indentation also shows an indentation size effect. However, for a spherical indenter, hardness is not affected by depth, but increases with decreasing sphere radius. The correlation for pyramidal and spherical indenter shapes is based on geometrically necessary dislocations and work-hardening. The Nix and Gao indentation size effect model (J. Mech. Phys. Solids 46 (1998) 411) for conical indenters is extended to indenters of various shapes and compared to the experimental results. © 2002 Elsevier Science Ltd. All rights reserved.

Assessment Of The Fixation Of Mandibular Symphysis Fractures Using Conical Cannulated Screws: Mechanical And Photoelastic Tests.

The aim of this study was to use mechanical and photoelastic tests to compare the performance of cannulated screws with other fixation methods in mandibular symphysis fractures. Ten polyurethane mandibles were allocated to each group and fixed as follows: group PRP, 2 perpendicular miniplates; group PLL, 1 miniplate and 1 plate, parallel; and group CS, 2 cannulated screws. Vertical linear loading tests were performed. The differences between mean values were analyzed with the Tukey test. The photoelastic test was carried out using a polariscope. The results revealed differences between the CS and PRP groups at 1, 3, 5, and 10 millimeters of displacement. The photoelastic test confirmed higher stress concentration in all groups close to the mandibular base, whereas the CS group showed it throughout the region assessed. Conical cannulated screws performed well in mechanical and photoelastic tests.

Using the ultrasound and instrumented indentation techniques to measure the elastic modulus of engineering materials

Currently, the acoustic and nanoindentation techniques are two of the most used techniques for material elastic modulus measurement. In this article fundamental principles and limitations of both techniques are shown and discussed. Last advances in nanoindentation technique are also reviewed. An experimental study in ceramic, metallic, composite and single crystals was also done. Results shown that ultrasonic technique is capable to provide results in agreement with those reported in literature. However, ultrasonic technique does not allow measuring the elastic modulus of some small samples and single crystals. On the other hand, the nanoindentation technique estimates the elastic modulus values in reasonable agreement with those measured by acoustic methods, particularly in amorphous materials, while in some policristaline materials some deviation from expected values was obtained.

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.

Indications of Conical Emission of Charged Hadrons at the BNL Relativistic Heavy Ion Collider

Three-particle azimuthal correlation measurements with a high transverse momentum trigger particle are reported for pp, d + Au, and Au + Au collisions at root(S)NN = 200 GeV by the STAR experiment. Dijet structures are observed in pp, d + Au and peripheral Au + Au collisions. An additional structure is observed in central Au + Au data, signaling conical emission of correlated charged hadrons. The conical emission angle is found to be theta = 1.37 +/- 0.02(stat)(-0.07)(+0.06)(syst), independent of p perpendicular to.

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.

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.

Energy dissipation in depth-sensing indentation as a characteristic of the nanoscratch behavior of coatings

Wear behavior of coatings has usually been described in terms of mechanical properties such as hardness (H) and effective elastic modulus (E*). Alternatively, an energy approach appears as a promising analysis taking into account the influence of those properties. In a nanoindentation test, the dissipated energy depends not only on the hardness and elastic modulus, but also on the elastic recovery (W(e)). This work aims to establish a relation between plastic deformation energy (E(p)) during depth-sensing indentation method and the grooving resistance of coatings in nanoscratch tests. An energy dissipation coefficient (K(d)) was defined, calculated as the ratio of the plastic to the total deformation energy (E(p)/E(t)), which represents the energy dissipation of materials. Reactive depositions using titanium as the target and nitrogen and methane as reactive gases were obtained by triode magnetron sputtering, in order to assess wear and nanoindentation data. A topographical, chemical and microstructural characterization has been conducted using X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), wave dispersion spectroscopy (WDS), scanning electron (SEM) and atomic force microscopy (AFM) techniques. Nanoscratch results showed that the groove depth was well correlated to the energy dissipation coefficient of the coatings. On the other hand, a reduction in the coefficient was found when the elastic recovery was increased. (C) 2009 Elsevier B.V. All rights reserved.

Instrumented indentation testing of an epoxy adhesive used in automobile body assembling

Instrumented indentation has been used to investigate the mechanical properties of BETAMATE 1496 (R) Epoxy adhesive. The properties of the adhesive were analyzed by measuring its hardness and its Young`s modulus in samples extracted from six different positions of the front door of a commercial passenger vehicle in two phases of processing: after application of the adhesive in the door assembling (""pre-cured"" state) and after final cure in the painting oven (""cured"" state). Special attention was given to setting the optimal parameters (""creep"" time and unloading time step) for the instrumented indentation testing for the present application. Young`s modulus values around 1.1 +/- 0.2 GPa and hardness values around 0.15 +/- 0.05 GPa were obtained for all samples, irrespective of the variation of the indentation parameters in the testing procedure and of the relative position of the adhesive in the door frame in both states. (C) 2008 Elsevier Ltd. All rights reserved.

Surface characterization of 6H-SiC (0001) substrates in indentation and abrasive machining

Surface characterization of 6H-SiC (0001) substrates in indentation and abrasive machining was carried out to investigate microfracture, residual damage, and surface roughness associated with material removal and surface generation. Brittle versus plastic deformation was studied using Vickers indention and nano-indentation. To characterize the abrasive machining response, the 6H-SiC (0001) substrates were ground using diamond wheels with grit sizes of 25, 15 and 7 mum, and then polished with diamond suspensions of 3 and 0.05 mum. It is found that in indentation, there was a scale effect for brittle versus plastic deformation in 6H-SiC substrates. Also, in grinding, the scales of fracture and surface roughness of the substrates decreased with a decrease in diamond grit size. However, in polishing, a reduction in grit size of diamond suspensions gave no significant improvement in surface roughness. Furthermore, the results showed that fracture-free 6H-SiC (0001) surfaces were generated in polishing with the existence of the residual crystal defects, which were associated with the origin of defects in single crystal growth. (C) 2003 Elsevier Ltd. All rights reserved.

Polymer indentation with mesoscopic molecular dynamics

Indentation tests are used to determine the hardness of a material, e.g., Rockwell, Vickers, or Knoop. The indentation process is empirically observed in the laboratory during these tests; the mechanics of indentation is insufficiently understood. We have performed first molecular dynamics computer simulations of indentation resistance of polymers with a chain structure similar to that of high density polyethylene (HDPE). A coarse grain model of HDPE is used to simulate how the interconnected segments respond to an external force imposed by an indenter. Results include the time-dependent measurement of penetration depth, recovery depth, and recovery percentage, with respect to indenter force, indenter size, and indentation time parameters. The simulations provide results that are inaccessible experimentally, including continuous evolution of the pertinent tribological parameters during the entire indentation process.