P-h Curves and Hardness Value Prediction for Spherical Indentation Based on the Representative Stress Approach

2014 ◽  
Vol 493 ◽  
pp. 628-633 ◽  
Author(s):  
I. Nyoman Budiarsa ◽  
Mikdam Jamal
Keyword(s):  
Experimental Data ◽  
Direct Analysis ◽  
Model Material ◽  
Spherical Indentation ◽  
Fe Model ◽  
Fe Modelling ◽  
Plastic Materials ◽  
Wide Range ◽  
Elastic Plastic Materials ◽  
Hardness Values

In this work, finite element (FE) model of spherical indentation has been developed and validated. The relationships between constitutive materials parameters (σy and n) of elastic-plastic materials, indentation P-h curves and hardness on spherical indenters has been systematically investigated by combining representative stress analysis and FE modelling using steel as a typical model material group. Parametric FE models of spherical indentation have been developed. Two new approaches to characterise the P-h curves of spherical indentation have been developed and evaluated. Both approaches were proven to be adequate and effective in predicting indentation P-h curves. The concept and methodology developed is to be used to predict Rockwell hardness value of materials through direct analysis and validated with experimental data on selected sample of steels. The Hardness predicted are compared with the experimental data and showed a good agreement. The approaches established was successfully used to produce hardness values of a wide range of material properties, which is then used to establish the relationship between the hardness values with representative stress.

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.

scholarly journals Finite Element Studies of the Influence of Pile-up on the Analysis of Nanoindentation Data

1996 ◽  
Vol 436 ◽  
Author(s):  
A. Bolshakov ◽  
W. C. Oliver ◽  
G. M. Pharr
Keyword(s):  
Finite Element ◽  
Contact Area ◽  
Peak Load ◽  
Soft Materials ◽  
Modulus Ratio ◽  
Hard Materials ◽  
Plastic Materials ◽  
Wide Range ◽  
Pile Up ◽  
Elastic Plastic Materials

AbstractMethods currently used for analyzing nanoindentation load-displacement data give good predictions of the contact area in the case of hard materials, but can underestimate the contact area by as much as 40% for soft materials which do not work harden. This underestimation results from the pile-up which forms around the hardness impression and leads to potentially significant errors in the measurement of hardness and elastic modulus. Finite element simulations of conical indentation for a wide range of elastic-plastic materials are presented which define the conditions under which pile-up is significant and determine the magnitude of the errors in hardness and modulus which may occur if pile-up is ignored. It is shown that the materials in which pile-up is not an important factor can be experimentally identified from the ratio of the final depth after unloading to the depth of the indentation at peak load, a parameter which also correlates with the hardness-to-modulus ratio.

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.

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.

Hardness Prediction Based on P-h Curves and Inverse Material Parameters Estimation

2015 ◽  
Vol 776 ◽  
pp. 233-238
Author(s):  
I. Nyoman Budiarsa
Keyword(s):  
Material Properties ◽  
Element Model ◽  
Parameters Estimation ◽  
Spherical Indentation ◽  
Vickers Indentation ◽  
Material Parameters ◽  
Wide Range ◽  
Constitutive Material ◽  
The Relationship ◽  
Hardness Values

The Finite Element model of Vickers indentation has been developed. The model was validated against published testing data. An approach to predict the P-h curves from constitutive material properties has been developed and evaluated based the relationship between the curvature and material properties and representative stress. The equation and procedure established was then successfully used in predict the full Vickers indentation P-h curve. FE Spherical indentation models of different radius have been developed and replay file model was developed that is able to produce data of different materials properties. Two new approaches to characterise the P-h curves of spherical indentation have been developed and evaluated. One is the full curve fitting approach while the other is depth based approach. Both approaches were proven to be adequate and effective in predicting indentation P-h curves. The concept and methodology developed is successfully used to predict hardness values (HV and HRB) of materials through direct analysis and validated with experimental data on selected sample of steels. The approaches (i.e. predict hardness from P-h curves) established was successfully used to produce hardness values of a wide range of material properties, which is then used to establish the relationship between the hardness values (HV and/or HRB) with representative stress. This provided a useful tool to evaluate the feasibility of using hardness values in predicting the constitutive material parameters with reference to accuracy and uniqueness by mapping through all potential materials ranges

A review of the determination of energy release rates for strips in tension and bending. Part I – static solutions

1993 ◽  
Vol 28 (4) ◽  
pp. 237-246 ◽  
Author(s):  
J G Williams
Keyword(s):  
Energy Release ◽  
Release Rates ◽  
Elastic Plastic ◽  
Plastic Materials ◽  
Wide Range ◽  
Static Solutions ◽  
Energy Release Rates ◽  
Elastic Plastic Materials ◽  
Peel Tests

It is shown that solutions for the energy release rate G may be obtained for a uniform strip by simply considering the change in length. The simplicity of the system enables a wide range of boundary conditions and material properties to be incorporated into the analysis and G may be computed for elastic and elastic-plastic materials. Inextensible flexible strips are considered first as they are useful for modelling peel tests and these results are developed to cover elastic and elastic-plastic behaviour. Elastic strips in tension are also considered and the analysis is developed to include transverse loading which induces bending. General considerations of path and loading history dependence are also included.

scholarly journals Representative Stress-Strain Curve by Spherical Indentation on Elastic-Plastic Materials

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Chao Chang ◽  
M. A. Garrido ◽  
J. Ruiz-Hervias ◽  
Zhu Zhang ◽  
Le-le Zhang
Keyword(s):  
Strain Curve ◽  
Stress Constraint ◽  
Spherical Indentation ◽  
Stress Strain Curve ◽  
Constraint Factor ◽  
Stress Strain ◽  
Constraint Factors ◽  
Plastic Materials ◽  
Elastic Plastic Materials ◽  
The Relationship

Tensile stress-strain curve of metallic materials can be determined by the representative stress-strain curve from the spherical indentation. Tabor empirically determined the stress constraint factor (stress CF), ψ, and strain constraint factor (strain CF), β, but the choice of value for ψ and β is still under discussion. In this study, a new insight into the relationship between constraint factors of stress and strain is analytically described based on the formation of Tabor’s equation. Experiment tests were performed to evaluate these constraint factors. From the results, representative stress-strain curves using a proposed strain constraint factor can fit better with nominal stress-strain curve than those using Tabor’s constraint factors.

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