Estimating material elasticity by spherical indentation load-relaxation tests on viscoelastic samples of finite thickness

A two-step viscoelastic spherical indentation method is proposed to compensate for 1) material relaxation and 2) sample thickness. In the first step, the indenter is moved at a constant speed and the reaction force is measured. In the second step, the indenter is held at a constant position and the relaxation response of the material is measured. Then the relaxation response is fit with a multi-exponential function which corresponds to a three-branch general Maxwell model. The relaxation modulus is derived by correcting the finite ramp time introduced in the first step. The proposed model takes into account the sample thickness, which is important for applications in which the sample thickness is less than ten times the indenter radius. The model is validated numerically by finite element simulations. Experiments are carried out on a 10% gelatin phantom and a chicken breast sample with the proposed method. The results for both the gelatin phantom and the chicken breast sample agree with the results obtained from a surface wave method. Both the finite element simulations and experimental results show improved elasticity estimations by incorporating the sample thickness into the model. The measured shear elasticities of the 10% gelatin sample are 6.79 and 6.93 kPa by the proposed finite indentation method at sample thickness of 40 and 20 mm, respectively. The elasticity of the same sample is estimated to be 6.53 kPa by the surface wave method. For the chicken breast sample, the shear elasticity is measured to be 4.51 and 5.17 kPa by the proposed indentation method at sample thickness of 40 and 20 mm, respectively. Its elasticity is measured by the surface wave method to be 4.14 kPa. © 2011 IEEE.

Size effects in the conical indentation of an elasto-plastic solid

The size effect in conical indentation of an elasto-plastic solid is predicted via the Fleck and Willis formulation of strain gradient plasticity (Fleck, N.A. and Willis, J.R., 2009, A mathematical basis for strain gradient plasticity theory. Part II: tensorial plastic multiplier, J. Mech. Phys. Solids, 57, 1045-1057). The rate-dependent formulation is implemented numerically and the full-field indentation problem is analyzed via finite element calculations, for both ideally plastic behavior and dissipative hardening. The isotropic strain-gradient theory involves three material length scales, and the relative significance of these length scales upon the degree of size effect is assessed. Indentation maps are generated to summarize the sensitivity of indentation hardness to indent size, indenter geometry and material properties (such as yield strain and strain hardening index). The finite element model is also used to evaluate the pertinence of the Johnson cavity expansion model and of the Nix-Gao model, which have been extensively used to predict size effects in indentation hardness. © 2012 Elsevier Ltd.

Insight into differences in nanoindentation properties of bone.

Nanoindentation provides the ideal framework to determine mechanical properties of bone at the tissue scale without being affected by the size, shape, and porosity of the bone. However, the values of tissue level mechanical properties vary significantly between studies. Since the differences in the bone sample, hydration state, and test parameters complicate direct comparisons across the various studies, these discrepancies in values cannot be compared directly. The objective of the current study is to evaluate and compare mechanical properties of the same bones using a broad range of testing parameters. Wild type C56BL6 mice tibiae were embedded following different processes and tested in dry and rehydrated conditions. Spherical and Berkovich indenter probes were used, and data analysis was considered within the elasto-plastic (Oliver-Pharr), viscoelastic and visco-elastic-plastic frameworks. The mean values of plane strain modulus varied significantly depending on the hydration state, probe geometry and analysis method. Indentations in dry bone analyzed using a visco-elastic-plastic approach gave values of 34 GPa. After rehydrating the same bones and indenting them with a spherical tip and utilizing a viscoelastic analysis, the mean modulus value was 4 GPa, nearly an order of magnitude smaller. Results suggest that the hydration state, probe geometry and the limitations and assumptions of each analysis method influence significantly the measured mechanical properties. This is the first time that such a systematic study has been carried out and it has been concluded that the discrepancies in the mechanical properties of bone measured by nanoindentation found in the literature should not be attributed only to the differences between the bones themselves, but also to the testing and analysis protocols.

Multi-scale permeability of murine bone measured by nanoindentation

The determination of lacunar-canalicular permeability is essential to understand the mechano-transduction mechanism of bone. Murine models are widely used to investigate skeletal growth and regulation, but the value of lacunar-canalicular permeability is still unclear. To address this question, a poroelastic analysis based on nanoindentation data was used to calculate the lacunar-canalicular permeability of wild type C57BL/6 mice of 12 months. Cross-sections of three tibiae were indented using spherical fluid cell indenter tips of two sizes. Results suggest that the value of lacunar-canalicular intrinsic permeability of B6 female murine tibia is in the order of 10 -24 m2. The distribution of the values of intrinsic permeability suggests that with larger contact sizes, nanoindentation alone is capable of capturing the multi-scale permeability of bone. Multi-scale permeability of bone measured by nanoindentation will lead to a better understanding of the role of fluid flow in mechano-transduction. © 2013 American Society of Civil Engineers.

Age-related changes in mouse bone permeability.

The determination of lacunar-canalicular permeability is essential for understanding local fluid flow in bone, which may indicate how bone senses changes in the mechanical environment to regulate mechano-adaptation. The estimates of lacunar-canalicular permeability found in the literature vary by up to eight orders of magnitude, and age-related permeability changes have not been measured in non-osteonal mouse bone. The objective of this study is to use a poroelastic approach based on nanoindentation data to characterize lacunar-canalicular permeability in murine bone as a function of age. Nine wild type C57BL/6 mice of different ages (2, 7 and 12 months) were used. Three tibiae from each age group were embedded in epoxy resin, cut in half and indented in the longitudinal direction in the mid-cortex using two spherical fluid indenter tips (R=238 μm and 500 μm). Results suggest that the lacunar-canalicular intrinsic permeability of mouse bone decreases from 2 to 7 months, with no significant changes from 7 to 12 months. The large indenter tip imposed larger contact sizes and sampled larger ranges of permeabilities, particularly for the old bone. This age-related difference in the distribution was not seen for indents with the smaller radius tip. We conclude that the small tip effectively measured lacunar-canalicular permeability, while larger tip indents were influenced by vascular permeability. Exploring the age-related changes in permeability of bone measured by nanoindentation will lead to a better understanding of the role of fluid flow in mechano-transduction. This understanding may help indicate alterations in bone adaptation and remodeling.

Age-related changes in mouse bone permeability

The determination of lacunar-canalicular permeability is essential for understanding local fluid flow in bone, which may indicate how bone senses changes in the mechanical environment to regulate mechano-adaptation. The estimates of lacunar-canalicular permeability found in the literature vary by up to eight orders of magnitude, and age-related permeability changes have not been measured in non-osteonal mouse bone. The objective of this study is to use a poroelastic approach based on nanoindentation data to characterize lacunar-canalicular permeability in murine bone as a function of age. Nine wild type C57BL/6 mice of different ages (2, 7 and 12 months) were used. Three tibiae from each age group were embedded in epoxy resin, cut in half and indented in the longitudinal direction in the mid-cortex using two spherical fluid indenter tips (R=238 μm and 500 μm). Results suggest that the lacunar-canalicular intrinsic permeability of mouse bone decreases from 2 to 7 months, with no significant changes from 7 to 12 months. The large indenter tip imposed larger contact sizes and sampled larger ranges of permeabilities, particularly for the old bone. This age-related difference in the distribution was not seen for indents with the smaller radius tip. We conclude that the small tip effectively measured lacunar-canalicular permeability, while larger tip indents were influenced by vascular permeability. Exploring the age-related changes in permeability of bone measured by nanoindentation will lead to a better understanding of the role of fluid flow in mechano-transduction. This understanding may help indicate alterations in bone adaptation and remodeling. © 2013 Elsevier Ltd.

Mechanical Deformation Behavior of Nonpolar GaN Thick Films by Berkovich Nanoindentation

In this study, the deformation mechanisms of nonpolar GaN thick films grown on m-sapphire by hydride vapor phase epitaxy (HVPE) are investigated using nanoindentation with a Berkovich indenter, cathodoluminescence (CL), and Raman microscopy. Results show that nonpolar GaN is more susceptible to plastic deformation and has lower hardness than c-plane GaN. After indentation, lateral cracks emerge on the nonpolar GaN surface and preferentially propagate parallel to the < 11 (2) over bar0 > orientation due to anisotropic defect-related stresses. Moreover, the quenching of CL luminescence can be observed to extend exclusively out from the center of the indentations along the < 11 (2) over bar0 > orientation, a trend which is consistent with the evolution of cracks. The recrystallization process happens in the indented regions for the load of 500 mN. Raman area mapping indicates that the distribution of strain field coincides well with the profile of defect-expanded dark regions, while the enhanced compressive stress mainly concentrates in the facets of the indentation.

Theoretical analysis of the relationships between hardness, elastic modulus, and the work of indentation for work-hardening materials

In our previous paper, the expanding cavity model (ECM) and Lame solution were used to obtain an analytical expression for the scale ratio between hardness (H) to reduced modulus (E-r) and unloading work (W-u) to total work (W-t) of indentation for elastic-perfectly plastic materials. In this paper, the more general work-hardening (linear and power-law) materials are studied. Our previous conclusions that this ratio depends mainly on the conical angle of indenter, holds not only for elastic perfectly-plastic materials, but also for work-hardening materials. These results were also verified by numerical simulations.

Analysis of the practical force accuracy of electromagnet-based nanoindenters

Two important factors that influence the force accuracy of the electromagnet-based nano-indenters but have not yet attracted much attention are analyzed, and a more reasonable way to estimate the force accuracy is presented in this paper. MTS Nano Indenter (R), with the characteristics of a coil suspended in a uniform magnetic field by two sets of springs acting as an actuator and force measuring unit, is used as an example. One of the two factors is the uniformity of the magnetic field. The other is the stiffness of the supporting spring. Consequently, the practical force accuracy varies considerably from test to test because it firmly depends on the working position of the coil and the displacement stroke. A reasonable estimated accuracy value is of the order of 10 degrees mu N for typical indentation tests with a 10(2) nm indentation depth or a 10 degrees mN test force. (C) 2010 Elsevier Ltd. All rights reserved.

Extracting nanobelt mechanical properties from nanoindentation

A three-spring-in-series model is proposed for the nanobelt (NB) indentation test. Compared with the previous two-spring-in-series model, which considers the bending stiffness of atomic force microscope cantilever and the indenter/NB contact stiffness, this model adds a third spring of the NB/substrate contact stiffness. NB is highly flexural due to its large aspect ratio of length to thickness. The bending and lift-off of NB form a localized contact with substrate, which makes the Oliver-Pharr method [W. C. Oliver and G. M. Pharr, J. Mater. Res. 7, 1564 (1992)] and Sneddon method [I. N. Sneddon, Int. J. Eng. Sci. 3, 47 (1965)] inappropriate for NB indentation test. Because the NB/substrate deformation may have significant impact on the force-indentation depth data obtained in experiment, the two-spring-in-series model can lead to erroneous predictions on the NB mechanical properties. NB in indentation test can be susceptible to the adhesion influence because of its large surface area to volume ratio. NB/substrate contact and adhesion can have direct and significant impact on the interpretation of experimental data. Through the three-spring-in-series model, the influence of NB/substrate contact and adhesion is analyzed and methods of reducing such influence are also suggested. (C) 2010 American Institute of Physics. [doi:10.1063/1.3432748]

Mechanical Behavior of Nanometer Ni by Simulating Nanoindentation

An indentation simulation of the crystal Ni is carried out by a molecular dynamics technique (MD) to study the mechanical behavior at nanometer scales. Indenter tips with both sphere shape and conical shape with 60 cone angle are used, and simulation samples with different crystal orientations are adopted. Some defects such as dislocations and point defects are observed. It is found that nucleated defects (dislocations, amorphous atoms) are from the local region near the pin tip or the sample surface. The temperature distribution of the local region is analyzed and it can explain our MD simulation results.

A method to determine fracture toughness using cube-corner indentation

For the cube-corner indenter, an approximate linear relationship between the ratio of hardness (H) to reduced modulus (E-r) and the ratio of unloading work (W-u) to total loading work (W-t) is confirmed by finite-element calculations and by experiments. Based on this relationship a convenient method to determine the fracture toughness (K-IC) of brittle materials, especially for those at small scale, using cube-corner indentations is proposed. Finally, the method is calibrated by indentation experiments on a set of brittle materials. (C) 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

电磁式纳米压入仪的载荷精度研究

纳米压入仪(Nanoindenter)已成为纳米/微米力学测试的基本工具之一,广泛应用于纳米材料、薄膜、MEMS微结构的力学性能测试。目前商业化仪器有MTS NanoIndenter(incorporated into Agi lent in 2008),Hysitron TriboIndenter,CSM NanoHardness Tester,MML NanoTest,and CSIRO UMIS,其中原MTS Nano Indenter、CSMNano Hardness Tester和MML NanoTest都采用电磁驱动兼载荷计量的原理设计。这类仪器主要优点之一是载荷分辨力高,可以达到50nN甚至更小。然而仪器制造商从未明确给出此类仪器的载荷精度。目前对纳米压痕测试技术的研究也主要集中在压头形状、试样表面粗糙度、毛细力等因素对压痕测试结果的影响,尚未见针对仪器载荷精度的研究报道。国际标准ISO 14577-2:2002虽对仪器施加的试验力的允差进行了规定,但由于电磁式纳米压入仪的结构响应和试样力学行为耦合在一起,试样上的载荷并不完全等同于通过电磁转换原理计量的试验力,因此实际测试时试样上的载荷精度仍是未知。

纳米压痕仪的载荷精度研究

<正>以MTS Nano Indenter(?)XP为例,研究发现了影响电磁式纳米压痕仪载荷精度的两个重要因素。其一,磁场的均匀性。在实验位移范围内磁场必须是均匀的,这是电磁计量载荷的理论基础。校准实验结果显示,NanoIndenter(?)XP在0.45mm位移行程内的非均匀性为0.24%。即,在0.45mm位移行程内磁场均匀性给载荷

Mechanical Behavior of Nanometer Ni by MD Simulation

The indention simulation of the crystal Ni is carried out by molecular dynamics technique (MD) to study the mechanical behavior at nanometer scales, the indenter tips with sphere shape is used. Some defects such as dislocations, point defects are observed. It is found that defects (dislocations, amorphous) nucleated is from local region near the pin tip or the sample surface. The temperature distribution of local region is analyzed and it can explain our MD simulation result.