A Laboratory Experiment Using Nanoindentation to Demonstrate the Indentation Size Effect

A laboratory experiment using nanoindentation to demonstrate the indentation size effect is described. This laboratory introduces students to sophisticated instrumentation at low cost and low risk and utilizes recent research in the materials community as its foundation. The motivation, learning objectives, experimental details, data, and data analysis are presented. This experiment is intended for use in an upper-division materials science elective at the university level and has been successfully used in laboratory courses for senior undergraduates and first-year graduate students at Stanford University and Santa Clara University.

The correlation of indentation size effect experiments with pyramidal and spherical indenters

Experiments were conducted in annealed iridium using pyramidal and spherical indenters over a wide range of load. For a Berkovich pyramidal indenter, the hardness increased with decreasing depth of penetration. However, for spherical indenters, hardness increased with decreasing sphere radius. Based on the number of geometrically necessary dislocations generated during indentation, a theory that takes into account the work hardening differences between pyramidal and spherical indenters is developed to correlate the indentation size effects measured with the two indenters. The experimental results verify the theoretical correlation.

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.

Particle size effect on abrasion resistance of mottled cast iron with different retained austenite contents

Effects of particle abrasive sizes on wear resistance of mottled cast iron with different retained austenite contents were studied. Abrasive wear tests using a pin test on alumina paper were carried out, using abrasive sizes between 16 mu m and 192 mu m. Retained austenite content of the matrix was determined by X-ray diffraction. The wear surface of samples and the alumina paper were examined by scanning electron microscopy for identifying the wear micromechanism. The results show that at lower abrasive sizes the mass loss was similar for the iron with different austenite contents. However, at higher abrasive sizes the samples with higher retained austenite content presented higher abrasion resistance. For lower abrasive sizes tested, samples with higher and lower retained austenite content both presented microcutting. On the other hand, the main wear micromechanism for the samples with higher retained austenite content and higher abrasive sizes was microploughing. The samples with lower retained austenite content presented microcutting and wedge formation at higher abrasive sizes. Higher abrasive size induced more microcutting in samples with lower retained austenite. The iron with lower retained austenite content presented wider grooves for the different abrasive sizes measured. SEM on the abrasive paper used on samples with higher retained austenite showed continuous and discontinuous microchips and the samples with lower retained austenite showed discontinuous microchips at 66 and 141 mu m. This research demonstrates the relation between abrasive size, wear resistance, groove width and wear micromechanism for mottled cast iron with different retained austenite contents. (C) 2009 Elsevier B.V. All rights reserved.

Size Effect and Notch Size Effect in Metal Fatigue

It is a well known phenomenon that the constant amplitude fatigue limit of a large component is lower than the fatigue limit of a small specimen made of the same material. In notched components the opposite occurs: the fatigue limit defined as the maximum stress at the notch is higher than that achieved with smooth specimens. These two effects have been taken into account in most design handbooks with the help of experimental formulas or design curves. The basic idea of this study is that the size effect can mainly be explained by the statistical size effect. A component subjected to an alternating load can be assumed to form a sample of initiated cracks at the end of the crack initiation phase. The size of the sample depends on the size of the specimen in question. The main objective of this study is to develop a statistical model for the estimation of this kind of size effect. It was shown that the size of a sample of initiated cracks shall be based on the stressed surface area of the specimen. In case of varying stress distribution, an effective stress area must be calculated. It is based on the decreasing probability of equally sized initiated cracks at lower stress level. If the distribution function of the parent population of cracks is known, the distribution of the maximum crack size in a sample can be defined. This makes it possible to calculate an estimate of the largest expected crack in any sample size. The estimate of the fatigue limit can now be calculated with the help of the linear elastic fracture mechanics. In notched components another source of size effect has to be taken into account. If we think about two specimens which have similar shape, but the size is different, it can be seen that the stress gradient in the smaller specimen is steeper. If there is an initiated crack in both of them, the stress intensity factor at the crack in the larger specimen is higher. The second goal of this thesis is to create a calculation method for this factor which is called the geometric size effect. The proposed method for the calculation of the geometric size effect is also based on the use of the linear elastic fracture mechanics. It is possible to calculate an accurate value of the stress intensity factor in a non linear stress field using weight functions. The calculated stress intensity factor values at the initiated crack can be compared to the corresponding stress intensity factor due to constant stress. The notch size effect is calculated as the ratio of these stress intensity factors. The presented methods were tested against experimental results taken from three German doctoral works. Two candidates for the parent population of initiated cracks were found: the Weibull distribution and the log normal distribution. Both of them can be used successfully for the prediction of the statistical size effect for smooth specimens. In case of notched components the geometric size effect due to the stress gradient shall be combined with the statistical size effect. The proposed method gives good results as long as the notch in question is blunt enough. For very sharp notches, stress concentration factor about 5 or higher, the method does not give sufficient results. It was shown that the plastic portion of the strain becomes quite high at the root of this kind of notches. The use of the linear elastic fracture mechanics becomes therefore questionable.

Grain size effect on the electrical response of SnO2 thin and thick film gas sensors

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Size effect on structure and dielectric properties of Nb-doped barium titanate

It is known that the dielectric properties of BaTiO3 (BT) are strongly dependent on its grain size. Coarse-grained ceramics of pure BT showed lower dielectric constant at room temperature then fine grained. Many authors considered that when the grain size is lower than 700 nm, the lattice of BT changes from tetragonal to pseudocubic, and the dielectric constant value is very low. In the doped BT this effect is more complex, because it is necessary to consider also the influence of dopants. The grain size effect on the structure and dielectric properties of niobium-doped barium titanate was investigated. Niobium-doped barium titanate was prepared from powders obtained by doping of commercial barium titanate and from organometallic complex using citrates as precursors (Pechini procedure). The crystal and microstructure of sintered niobium-doped barium titanate were determined. Dielectric constant and dissipation factor were measured. The observation confirmed that the structure and properties are strongly dependent on grain size. (C) 2003 Elsevier B.V. B.V. All rights reserved.

Grain size effect on the structural and dielectric properties of Pb0.85La0.15TiO3 ferroelectric ceramic compound

This paper presents a study of the influence of particle size on the structural and dielectric properties of Pb0.85La0.15TiO3 (PLT15) ferroelectric ceramic samples. The samples were prepared with average grain size of 1.69 +/- 0.08 mu m and 146 +/- 8 nm using, respectively, conventional and spark plasma sintering techniques. A decrease in the tetragonality degree as the crystallite size decreased was explained by an internal stress caused by the existence of a large amount of grain boundaries. The local structure exhibited no significant modification and the dielectric measurements showed a diffuse phase transition and a reduction in the permittivity magnitude at T-m as the average grain size decreased. The nanostructured ceramic sample prepared at a relatively lower temperature and sintering time presented a dielectric constant value of approximately 2000 at room temperature. (c) 2012 Elsevier Ltd and Techna Group S.r.l. All rights reserved.

Latent hardening size effect in small-scale plasticity

We aim at understanding the multislip behaviour of metals subject to irreversible deformations at small-scales. By focusing on the simple shear of a constrained single-crystal strip, we show that discrete Dislocation Dynamics (DD) simulations predict a strong latent hardening size effect, with smaller being stronger in the range [1.5 µm, 6 µm] for the strip height. We attempt to represent the DD pseudo-experimental results by developing a flow theory of Strain Gradient Crystal Plasticity (SGCP), involving both energetic and dissipative higher-order terms and, as a main novelty, a strain gradient extension of the conventional latent hardening. In order to discuss the capability of the SGCP theory proposed, we implement it into a Finite Element (FE) code and set its material parameters on the basis of the DD results. The SGCP FE code is specifically developed for the boundary value problem under study so that we can implement a fully implicit (Backward Euler) consistent algorithm. Special emphasis is placed on the discussion of the role of the material length scales involved in the SGCP model, from both the mechanical and numerical points of view.

Latent hardening size effect in small-scale plasticity

We aim at understanding the multislip behaviour of metals subject to irreversible deformations at small-scales. By focusing on the simple shear of a constrained single-crystal strip, we show that discrete Dislocation Dynamics (DD) simulations predict a strong latent hardening size effect, with smaller being stronger in the range [1.5 µm, 6 µm] for the strip height. We attempt to represent the DD pseudo-experimental results by developing a flow theory of Strain Gradient Crystal Plasticity (SGCP), involving both energetic and dissipative higher-order terms and, as a main novelty, a strain gradient extension of the conventional latent hardening. In order to discuss the capability of the SGCP theory proposed, we implement it into a Finite Element (FE) code and set its material parameters on the basis of the DD results. The SGCP FE code is specifically developed for the boundary value problem under study so that we can implement a fully implicit (Backward Euler) consistent algorithm. Special emphasis is placed on the discussion of the role of the material length scales involved in the SGCP model, from both the mechanical and numerical points of view.

A survey of the literature on the size effect on material strength /

"Final report for period 1 August 1972 to 30 September 1976."