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.

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.

Quasiharmonic elastic constants corrected for deviatoric thermal stresses

The quasiharmonic approximation (QHA), in its simplest form also called the statically constrained (SC) QHA, has been shown to be a straightforward method to compute thermoelastic properties of crystals. Recently we showed that for noncubic solids SC-QHA calculations develop deviatoric thermal stresses at high temperatures. Relaxation of these stresses leads to a series of corrections to the free energy that may be taken to any desired order, up to self-consistency. Here we show how to correct the elastic constants obtained using the SC-QHA. We exemplify the procedure by correcting to first order the elastic constants of MgSiO(3) perovskite and MgSiO(3) postperovskite, the major phases of the Earth's lower mantle. We show that this first-order correction is quite satisfactory for obtaining the aggregated elastic averages of these minerals and their velocities in the lower mantle. This type of correction is also shown to be applicable to experimental measurements of elastic constants in situations where deviatoric stresses can develop, such as in diamond-anvil cells.

On the mass determination of super-Earths orbiting active stars: the CoRoT-7 system

Context. Star activity makes the mass determination of CoRoT-7b and CoRoT 7c uncertain. Investigators of the CoRoT team proposed several solutions, but all but one of them are larger than the initial determinations of 4.8 +/- 0.8 M(Earth) for CoRoT-7b and 8.4 +/- 0.9 M(Earth) for CoRoT 7c. Aims. This investigation uses the excellent HARPS radial velocity measurements of CoRoT-7 to redetermine the planet masses and to explore techniques for determining mass and orbital elements of planets discovered around active stars when the relative variation in the radial velocity due to the star activity cannot be considered as just noise and can exceed the variation due to the planets. Methods. The main technique used here is a self-consistent version of the high-pass filter used by Queloz et al. (2009, A&A, 506, 303) in the first mass determination of CoRoT-7b and CoRoT-7c. The results are compared to those given by two alternative techniques: (1) the approach proposed by Hatzes et al. (2010, A&A, 520, A93) using only those nights in which two or three observations were done; (2) a pure Fourier analysis. In all cases, the eccentricities are taken equal to zero as indicated by the study of the tidal evolution of the system. The periods are also kept fixed at the values given by Queloz et al. Only the observations done in the time interval BJD 2 454 847-873 are used because they include many nights with multiple observations; otherwise, it is not possible to separate the effects of the rotation fourth harmonic (5.91 d = P(rot)/4) from the alias of the orbital period of CoRoT-7b (0.853585 d). Results. The results of the various approaches are combined to give planet mass values 8.0 +/- 1.2 M(Earth) for CoRoT-7b and 13.6 +/- 1.4 M(Earth) for CoRoT 7c. An estimation of the variation of the radial velocity of the star due to its activity is also given. Conclusions. The results obtained with three different approaches agree to give higher masses than those in previous determinations. From the existing internal structure models they indicate that CoRoT-7b is a much denser super-Earth. The bulk density is 11 +/- 3.5 g cm(-3), so CoRoT-7b may be rocky with a large iron core.

Transiting exoplanets from the CoRoT space mission XIII. CoRoT-13b: a dense hot Jupiter in transit around a star with solar metallicity and super-solar lithium content

We announce the discovery of the transiting planet CoRoT-13b. Ground-based follow-up in CFHT and IAC80 confirmed CoRoT's observations. The mass of the planet was measured with the HARPS spectrograph and the properties of the host star were obtained analyzing HIRES spectra from the Keck telescope. It is a hot Jupiter-like planet with an orbital period of 4.04 days, 1.3 Jupiter masses, 0.9 Jupiter radii, and a density of 2.34 g cm(-3). It orbits a G0V star with T(eff) = 5 945 K, M(*) = 1.09 M(circle dot), R(*) = 1.01 R(circle dot), solar metallicity, a lithium content of +1.45 dex, and an estimated age of between 0.12 and 3.15 Gyr. The lithium abundance of the star is consistent with its effective temperature, activity level, and age range derived from the stellar analysis. The density of the planet is extreme for its mass, implies that heavy elements are present with a mass of between about 140 and 300 M(circle plus).

Transiting exoplanets from the CoRoT space mission VIII. CoRoT-7b: the first super-Earth with measured radius

Aims. We report the discovery of very shallow (Delta F/F approximate to 3.4 x 10(-4)), periodic dips in the light curve of an active V = 11.7 G9V star observed by the CoRoT satellite, which we interpret as caused by a transiting companion. We describe the 3-colour CoRoT data and complementary ground-based observations that support the planetary nature of the companion. Methods. We used CoRoT colours information, good angular resolution ground-based photometric observations in- and out- of transit, adaptive optics imaging, near-infrared spectroscopy, and preliminary results from radial velocity measurements, to test the diluted eclipsing binary scenarios. The parameters of the host star were derived from optical spectra, which were then combined with the CoRoT light curve to derive parameters of the companion. Results. We examined all conceivable cases of false positives carefully, and all the tests support the planetary hypothesis. Blends with separation >0.40 '' or triple systems are almost excluded with a 8 x 10(-4) risk left. We conclude that, inasmuch we have been exhaustive, we have discovered a planetary companion, named CoRoT-7b, for which we derive a period of 0.853 59 +/- 3 x 10(-5) day and a radius of R(p) = 1.68 +/- 0.09 R(Earth). Analysis of preliminary radial velocity data yields an upper limit of 21 M(Earth) for the companion mass, supporting the finding. Conclusions. CoRoT-7b is very likely the first Super-Earth with a measured radius. This object illustrates what will probably become a common situation with missions such as Kepler, namely the need to establish the planetary origin of transits in the absence of a firm radial velocity detection and mass measurement. The composition of CoRoT-7b remains loosely constrained without a precise mass. A very high surface temperature on its irradiated face, approximate to 1800-2600 K at the substellar point, and a very low one, approximate to 50 K, on its dark face assuming no atmosphere, have been derived.

The CoRoT-7 planetary system: two orbiting super-Earths

We report on an intensive observational campaign carried out with HARPS at the 3.6 m telescope at La Silla on the star CoRoT-7. Additional simultaneous photometric measurements carried out with the Euler Swiss telescope have demonstrated that the observed radial velocity variations are dominated by rotational modulation from cool spots on the stellar surface. Several approaches were used to extract the radial velocity signal of the planet(s) from the stellar activity signal. First, a simple pre-whitening procedure was employed to find and subsequently remove periodic signals from the complex frequency structure of the radial velocity data. The dominant frequency in the power spectrum was found at 23 days, which corresponds to the rotation period of CoRoT-7. The 0.8535 day period of CoRoT-7b planetary candidate was detected with an amplitude of 3.3 m s(-1). Most other frequencies, some with amplitudes larger than the CoRoT-7b signal, are most likely associated with activity. A second approach used harmonic decomposition of the rotational period and up to the first three harmonics to filter out the activity signal from radial velocity variations caused by orbiting planets. After correcting the radial velocity data for activity, two periodic signals are detected: the CoRoT-7b transit period and a second one with a period of 3.69 days and an amplitude of 4 m s(-1). This second signal was also found in the pre-whitening analysis. We attribute the second signal to a second, more remote planet CoRoT-7c. The orbital solution of both planets is compatible with circular orbits. The mass of CoRoT-7b is 4.8 +/- 0.8 (M(circle plus)) and that of CoRoT-7c is 8.4 +/- 0.9 (M(circle plus)), assuming both planets are on coplanar orbits. We also investigated the false positive scenario of a blend by a faint stellar binary, and this may be rejected by the stability of the bisector on a nightly scale. According to their masses both planets belong to the super-Earth planet category. The average density of CoRoT-7b is rho = 5.6 +/- 1.3 g cm(-3), similar to the Earth. The CoRoT-7 planetary system provides us with the first insight into the physical nature of short period super-Earth planets recently detected by radial velocity surveys. These planets may be denser than Neptune and therefore likely made of rocks like the Earth, or a mix of water ice and rocks.

Elastic Maier-Saupe-Zwanzig model and some properties of nematic elastomers

We introduce a simple mean-field lattice model to describe the behavior of nematic elastomers. This model combines the Maier-Saupe-Zwanzig approach to liquid crystals and an extension to lattice systems of the Warner-Terentjev theory of elasticity, with the addition of quenched random fields. We use standard techniques of statistical mechanics to obtain analytic solutions for the full range of parameters. Among other results, we show the existence of a stress-strain coexistence curve below a freezing temperature, analogous to the P-V diagram of a simple fluid, with the disorder strength playing the role of temperature. Below a critical value of disorder, the tie lines in this diagram resemble the experimental stress-strain plateau and may be interpreted as signatures of the characteristic polydomain-monodomain transition. Also, in the monodomain case, we show that random fields may soften the first-order transition between nematic and isotropic phases, provided the samples are formed in the nematic state.

(7,9,10)Be elastic scattering and total reaction cross sections on a (12)C target

Elastic scattering angular distributions for (7)Be, (9)Be, and (10)Be isotopes on (12)C target were measured at laboratory energies of 18.8, 26.0, and 23.2 MeV, respectively. The analysis was performed in terms of optical model potentials using Woods-Saxon and double-folding form factors. Also, continuum discretized coupled-channels calculations were performed for (7)Be and (9)Be + (12)C systems to infer the role of breakup in the elastic scattering. For the (10)Be + (12)C system, bound states coupled-channels calculations were considered. Moreover, total reaction cross sections were deduced from the elastic scattering analysis and compared with published data on other weakly and tightly bound projectiles elastically scattered on the (12)C target, as a function of energy.

Quasi-elastic barrier distribution of the (17)O+(64)Zn system and the derivation of the (17)O nuclear matter diffuseness

The quasi-elastic excitation function for the (17)O+(64)Zn system was measured at energies near and below the Coulomb barrier, at the backward angle theta(lab) = 161 degrees. The corresponding quasi-elastic barrier distribution was derived. The excitation function for the neutron stripping reactions was also measured, at the same angle and energies, and the experimental values of the spectroscopic factors were deduced by fitting the data. A reasonably good agreement was obtained between the experimental quasi-elastic barrier distribution with the coupled-channel calculations including a very large number of channels. Of the channels investigated, three dominated the coupling matrix: two inelastic channels, (64)Zn(2(1)(+)) and (17)O(1/(+)(2)), and one-neutron transfer channel, particularly the first one. On the other hand, a very good agreement is obtained when we use a nuclear diffuseness for the (17)O nucleus larger than the one for (16)O. We verify that quasi-elastic barrier distribution is a sensitive tool for determining nuclear matter diffuseness.

Comparison of (120)Sn((6)He, (6)He)(120)Sn and (120)Sn(alpha,alpha)(120)Sn elastic scattering and signatures of the (6)He neutron halo in the optical potential

Cross sections of (120)Sn(alpha,alpha)(120)Sn elastic scattering have been extracted from the alpha-particle-beam contamination of a recent (120)Sn((6)He,(6)He)(120)Sn experiment. Both reactions are analyzed using systematic double-folding potentials in the real part and smoothly varying Woods-Saxon potentials in the imaginary part. The potential extracted from the (120)Sn((6)He,(6)He)(120)Sn data may be used as the basis for the construction of a simple global (6)He optical potential. The comparison of the (6)He and alpha data shows that the halo nature of the (6)He nucleus leads to a clear signature in the reflexion coefficients eta(L) : The relevant angular momenta L with eta(L) >> 0 and eta(L) << 1 are shifted to larger L with a broader distribution. This signature is not present in the alpha-scattering data and can thus be used as a new criterion for the definition of a halo nucleus.

Elastic scattering and total reaction cross section of (6)He+(120)Sn

The elastic scattering of (6)He on (120)Sn has been measured at four energies above the Coulomb barrier using the (6)He beam produced at the RIBRAS (Radioactive Ion Beams in Brasil) facility. The elastic angular distributions have been analyzed with the optical model and three- and four-body continuum-discretized coupled-channels calculations. The total reaction cross sections have been derived and compared with other systems of similar masses.

Elastic scattering and total reaction cross sections for the (8)Li+(12)C system

The elastic-scattering angular distribution for (8)Li on (12)C has been measured at E(LAB) = 23.9 MeV with (8)Li radioactive nuclear beam produced by the Radioactive Ion Beams in Brazil facility. This angular distribution was analyzed in terms of optical-model with Woods-Saxon and double-folding Sao Paulo potential. The roles of the breakup and inelastic channels were also investigated with cluster folding and deformed potentials, respectively, through coupled-channels calculations. The angular distribution for the proton-transfer (12)C((8)Li, (9)Be)(11)B reaction was also measured at the same energy. The spectroscopic factor for the <(9)Be|(8)Li + p > bound system was obtained and compared with shell-model calculations and with other experimental values. Total reaction cross sections for the present system were also extracted from the elastic-scattering analysis. A systematic of the reduced reaction cross sections obtained from the present and published data on (6,7,8)Li isotopes on (12)C was performed as a function of energy.

Breakup coupling effects on near-barrier quasi-elastic scattering of (6,7)Li on (144)Sm

Excitation functions of quasi-elastic scattering at backward angles have been measured for the (6,7)Li + (144)Sm systems at near-barrier energies, and fusion barrier distributions have been extracted from the first derivatives of the experimental cross sections with respect to the bombarding energies. The data have been analyzed in the framework of continuum discretized coupled-channel calculations, and the results have been obtained in terms of the influence exerted by the inclusion of different reaction channels, with emphasis on the role played by the projectile breakup.