Determination of Young's modulus by spherical indentation

1997 ◽  
Vol 12 (9) ◽  
pp. 2459-2469 ◽  
Author(s):  
N. Huber ◽  
D. Munz ◽  
Ch. Tsakmakis
Keyword(s):  
Finite Element ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Indentation Test ◽  
Spherical Indentation ◽  
Plastic Materials ◽  
Finite Element Calculations ◽  
Loading And Unloading ◽  
Elastic Plastic Materials

In this paper we consider elastic plastic materials that are tested by spherical indentation. Finite element calculations, which take into account nonlinear geometry properties, are carried out in order to determine the influence of the plastic history on the unloading response of the material. Two different iterative methods are proposed for determining Young's modulus under the assumption of a bilinear plasticity law. The first method deals with loading and unloading parts of the indentation test, whereas the second one deals only with unloading parts of the indentation test.

A New Method Developed for Brittle and Ductile Materials to Evaluate Mechanical Properties of a Lump Specimen in the Use of Indentation Test

2006 ◽  
Vol 129 (2) ◽  
pp. 284-292 ◽  
Author(s):  
Pal Jen Wei ◽  
Jen Fin Lin
Keyword(s):  
Yield Strength ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Elastic Recovery ◽  
Indentation Test ◽  
New Method ◽  
Ductile Materials ◽  
Conventional Material ◽  
Loading And Unloading ◽  
Logarithm Function

In this study, the load-depth (P‐h) relationships matching the experimental results of the nanoindentation tests exhibited at the subregions of small and large depths are obtained, respectively. The relationships associated with these two subregions are then linked by the hyperbolic logarithm function to attain a single expression that is applied in the evaluation of the specimen’s elastic recovery ability, as shown in the unloading process. A new method is developed in the present study to evaluate both Young’s modulus and the yield strength of either a ductile or brittle material through the uses of the appropriate P‐h relationships developed in the load and unloading processes. The results of the Young’s modulus and the yield strength achieved by the present method are compared to those obtained from the conventional material tests for a lump material. The scattering of the experimental data shown in the loading and unloading processes are also interpreted by different causes.

Nanoindentation by Multiple Loads Methodology: A Pile Up Correction Procedure

2007 ◽  
Vol 345-346 ◽  
pp. 805-808 ◽  
Author(s):  
Miguel Angel Garrido ◽  
Jesus Rodríguez
Keyword(s):  
Element Model ◽  
Spherical Indentation ◽  
Correction Procedure ◽  
Elastic Plastic ◽  
Multiple Loads ◽  
Plastic Materials ◽  
Wide Range ◽  
Pile Up ◽  
Elastic Plastic Materials

Young’s modulus and hardness data obtained from nanoindentation are commonly affected by phenomena like pile up or sink in, when elastic-plastic materials are tested. In this work, a finite element model was used to evaluate the pile up effect on the determination of mechanical properties from spherical indentation in a wide range of elastic-plastic materials. A new procedure, based on a combination of results obtained from tests performed at multiple maximum loads, is suggested.

Determination of Poisson’s Ratio of Articular Cartilage by Indentation Using Different-Sized Indenters

2004 ◽  
Vol 126 (2) ◽  
pp. 138-145 ◽  
Author(s):  
Hui Jin ◽  
Jack L. Lewis
Keyword(s):  
Finite Element ◽  
Articular Cartilage ◽  
Nonlinear Equation ◽  
Young’S Modulus ◽  
Poisson’S Ratio ◽  
Young's Modulus ◽  
Indentation Test ◽  
Test Method ◽  
Poisson's Ratio ◽  
Unconfined Compression

Articular cartilage is often characterized as an isotropic elastic material with no interstitial fluid flow during instantaneous and equilibrium conditions, and indentation testing commonly used to deduce material properties of Young’s modulus and Poisson’s ratio. Since only one elastic parameter can be deduced from a single indentation test, some other test method is often used to allow separate measurement of both parameters. In this study, a new method is introduced by which the two material parameters can be obtained using indentation tests alone, without requiring a secondary different type of test. This feature makes the method more suitable for testing small samples in situ. The method takes advantages of the finite layer effect. By indenting the sample twice with different-sized indenters, a nonlinear equation with the Poisson’s ratio as the only unknown can be formed and Poisson’s ratio obtained by solving the nonlinear equation. The method was validated by comparing the predicted Poisson’s ratio for urethane rubber with the manufacturer’s supplied value, and comparing the predicted Young’s modulus for urethane rubber and an elastic foam material with modulii measured by unconfined compression. Anisotropic and nonhomogeneous finite-element (FE) models of the indentation were developed to aid in data interpretation. Applying the method to bovine patellar cartilage, the tissue’s Young’s modulus was found to be 1.79±0.59MPa in instantaneous response and 0.45±0.26MPa in equilibrium, and the Poisson’s ratio 0.503±0.028 and 0.463±0.073 in instantaneous and equilibrium, respectively. The equilibrium Poisson’s ratio obtained in our work was substantially higher than those derived from biphasic indentation theory and those optically measured in an unconfined compression test. The finite element model results and examination of viscoelastic-biphasic models suggest this could be due to viscoelastic, inhomogeneity, and anisotropy effects.

Relationship between Indenter Calibration and Measured Mechanical Properties of Elastic-Plastic Materials

2015 ◽  
Vol 662 ◽  
pp. 27-30 ◽  
Author(s):  
Jaroslav Čech ◽  
Petr Haušild ◽  
Jiri Nohava
Keyword(s):  
Young’S Modulus ◽  
Young's Modulus ◽  
Plastic Behavior ◽  
Calibration Function ◽  
Simple Method ◽  
Area Function ◽  
Elastic Plastic ◽  
Plastic Materials ◽  
Pile Up ◽  
Elastic Plastic Materials

Calibration of Berkovich indenter area function was performed on materials with different elastic-plastic behavior resulting in pile-up and sink-in, respectively. Experimentally obtained results were compared with the results obtained by the application of theoretical area function. The values of Young’s modulus and hardness were significantly affected by the calibration function used. Since the effects of pile-up and sink-in are already included in the used area function, this simple method can lead to more accurate results of Young’s modulus and hardness measurements.

Determination of the Young’s modulus of porous ß-type Ti–40Nb by finite element analysis

2014 ◽  
Vol 64 ◽  
pp. 1-8 ◽  
Author(s):  
K. Zhuravleva ◽  
R. Müller ◽  
L. Schultz ◽  
J. Eckert ◽  
A. Gebert ◽  
...  
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Element Analysis

Analysis of the tip roundness effects on the micro- and macroindentation response of elastic–plastic materials

2009 ◽  
Vol 24 (3) ◽  
pp. 1037-1044 ◽  
Author(s):  
Sara Aida Rodríguez Pulecio ◽  
María Cristina Moré Farias ◽  
Roberto Martins Souza
Keyword(s):  
Finite Element ◽  
Material Properties ◽  
Total Work ◽  
Plastic Materials ◽  
Maximum Penetration Depth ◽  
Finite Element Calculations ◽  
Maximum Penetration ◽  
Elastic Plastic Materials ◽  
Tip Radius ◽  
Hardness Values

In this work, the effects of indenter tip roundness on 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/hmax), which varied from 0.02 to 1. The proportional curvature constant (C), the exponent of depth during loading (α), the initial unloading slope (S), the correction factor (β), the level of piling-up or sinking-in (hc/hmax), and the ratio hmax/hf are shown to be strongly influenced by the ratio R/hmax. The hardness (H) was found to be independent of R/hmax in the range studied. The Oliver and Pharr method was successful in following the variation of hc/hmax with the ratio R/hmax through the variation of S with the ratio R/hmax. 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 (Wp/Wt) was found to be independent of the ratio R/hmax, 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.

Evaluation of Indentation Test for Measuring Young’s Modulus of Cancellous Bone

2007 ◽  
Vol 544-545 ◽  
pp. 307-310
Author(s):  
Moon Kyu Lee ◽  
Kui Won Choi ◽  
Tae Soo Lee ◽  
H.N. Lim
Keyword(s):  
Porous Materials ◽  
Young’S Modulus ◽  
Cancellous Bone ◽  
Indentation Depth ◽  
Young's Modulus ◽  
Indentation Test ◽  
Spherical Indentation ◽  
Uniaxial Compression Test ◽  
Displacement Curve ◽  
Fe Model

The indentation test has been in the spotlight due to easy and non-destructive testing characteristics. However, there are little studies for the indentation test of porous materials in the evaluation aspect of methodology. The goal of this study was to evaluate a spherical indentation test in the aspect of indenter-size and indentation depth by measuring elastic modulus of porous materials such as a cancellous bone using a FEM. We developed a microstructure-based FE model of cancellous bone with apparent density 0.2~0.8 g/cm3 in order to simulate uniaxial compression test and indentation test in the light of anatomical observation with a scanning electron microscope (SEM). We obtained a load-displacement curve through the indentation simulation and calculated the Young’s modulus of cancellous structure based on Pharr's hypothesis. The result indicated that indenter diameter has to be more than five times of pore size and indentation depth should be about 8% of indenter diameter at least to obtain the appropriate result of the indentation test. It is expected that this result may guide to the design and the simulation of indentation test for porous materials

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