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.

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.

On Determining Elastic Modulus from Instrumented Indentation

2013 ◽  
Vol 668 ◽  
pp. 616-620
Author(s):  
Shuai Huang ◽  
Huang Yuan
Keyword(s):  
Finite Element ◽  
Elastic Modulus ◽  
Plastic Material ◽  
Instrumented Indentation ◽  
Computational Simulations ◽  
Elastic Plastic ◽  
Modified Method ◽  
Plastic Materials ◽  
Elastic Plastic Material ◽  
Elastic Plastic Materials

Computational simulations of indentations in elastic-plastic materials showed overestimate in determining elastic modulus using the Oliver & Pharr’s method. Deviations significantly increase with decreasing material hardening. Based on extensive finite element computations the correlation between elastic-plastic material property and indentation has been carried out. A modified method was introduced for estimating elastic modulus from dimensional analysis associated with indentation data. Experimental verifications confirm that the new method produces more accurate prediction of elastic modulus than the Oliver & Pharr’s method.

A response to—“Comment on the evaluation of the constant β relating the contact stiffness to the contact area in nanoindentation for sphero-conical indenters:” Comment to paper “Penetration depth and tip radius dependence on the correction factor in nanoindentation measurements” by J.M. Meza et al. [J. Mater. Res. 23(3), 725 (2008)]

2012 ◽  
Vol 27 (8) ◽  
pp. 1208-1210
Author(s):  
Juan Manuel Meza ◽  
Fazilay Abbes ◽  
Jaime Alexis Garcia Guzman ◽  
Michel Troyon
Keyword(s):  
Penetration Depth ◽  
Correction Factor ◽  
Contact Area ◽  
Contact Stiffness ◽  
Depth Range ◽  
Dimensionless Analysis ◽  
Plastic Materials ◽  
Variation Range ◽  
Elastic Plastic Materials ◽  
Tip Radius

The signification of the correction factor β that we defined for elastic material [J.M. Meza et al. J. Mater. Res.23(3), 725, (2008)] does not correspond to that of factor β in the Sneddon relationship between unloading contact stiffness, elastic modulus, and contact area as remarked by Durst et al. in their Comment (doi:10.1557/jmr.2012.41). To complete the results of Durst et al., the calculation of β is extended to a larger penetration depth range. It is shown that β depends on the depth to tip radius ratio, h/R, and on the Poisson’s ratio according to dimensionless analysis. The variation range of β is about 1.02–1.09 for 0.3 < h/R < 3 for purely elastic materials but can be much larger in case of elastic–plastic materials as shown [F. Abbes et al. J. Micromech. Microeng.20, 65003 (2010)].

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.

Nanomechanical Effects

2021 ◽  
pp. 253-272
Author(s):  
C. Julian Chen
Keyword(s):  
Barrier Height ◽  
Contact Area ◽  
Soft Materials ◽  
Sample Surface ◽  
Soft Material ◽  
Measurable Effect ◽  
Tunneling Barrier ◽  
Hard Materials ◽  
Small Force ◽  
The Stability

This chapter discusses the effect of force and deformation of the tip apex and the sample surface in the operation and imaging mechanism of STM and AFM. Because the contact area is of atomic dimension, a very small force and deformation would generate a large measurable effect. Three effects are discussed. First is the stability of the STM junction, which depends on the rigidity of the material. For soft materials, hysterisis is more likely. For rigid materials, the approaching and retraction cycles are continuous and reproducible. Second is the effect of force and deformation to the STM imaging mechanism. For soft material such as graphite, force and deformation can amplify the observed corrugation. For hard materials as most metals, force and deformation can decrease the observed corrugation. Finally, the effect of force and deformation on tunneling barrier height measurements is discussed.

Solid Formulation, Comparison of Two Formulations, and Concluding Remarks

1989 ◽  
Author(s):  
Shiro Kobayashi ◽  
Soo-Ik Oh ◽  
Taylan Altan
Keyword(s):  
Finite Element ◽  
Field Equation ◽  
Boundary Value Problem ◽  
Metal Forming ◽  
Large Strain ◽  
Boundary Value ◽  
Elastic Plastic ◽  
Plastic Materials ◽  
Elastic Plastic Materials ◽  
Selection Of

In the previous chapters we have discussed only the applications of flow formulation to the analysis of metal-forming processes. Lately, elastic-plastic (solid) formulations have evolved to produce techniques suitable for metal-forming analysis. This evolution is the result of developments achieved in large-strain formulation, beginning from the infinitesimal approach based on the Prandtl–Reuss equation. A question always arises as to the selection of the approach—“flow” approach or “solid” approach. A significant contribution to the solution of this question was made through a project in 1978, coordinated by Kudo, in which an attempt was made to examine the comparative merits of various numerical methods. The results were compiled for upsetting of circular solid cylinders under specific conditions, and revealed the importance of certain parameters used in computation, such as mesh systems and the size of an increment in displacement. This project also showed that the solid formulation needed improvement, particularly in terms of predicting the phenomenon of folding. For elastic-plastic materials, the constitutive equations relate strain–rate to stress–rates, instead of to stresses. Consequently, it is convenient to write the field equation in the boundary-value problem for elastic-plastic materials in terms of the equilibrium of stress rates. In this chapter, the basic equations for the finite-element discretization involved in solid formulations are outlined both for the infinitesimal approach and for large-strain theory. Further, the solutions obtained by the solid formulation are compared with those obtained by the flow formulation for the problems of plate bending and ring compression. A discussion is also given concerning the selection of the approach for the analysis. In conclusion, significant recent developments in the role of the finite-element method in metal-forming technology are summarized. The field equation for the boundary-value problem associated with the deformation of elastic-plastic materials is the equilibrium equation of stress rates. As stated in Chap. 1 (Section 1.3), the internal distribution of stress, in addition to the current states of the body, is supposed to be known, and the boundary conditions are prescribed in terms of velocity and traction-rate.

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.

Analysis of sharp-tip-indentation load–depth curve for contact area determination taking into account pile-up and sink-in effects

2004 ◽  
Vol 19 (11) ◽  
pp. 3307-3315 ◽  
Author(s):  
Yeol Choi ◽  
Ho-Seung Lee ◽  
Dongil Kwon
Keyword(s):  
Finite Element ◽  
Elastic Modulus ◽  
Contact Area ◽  
Indentation Depth ◽  
Indentation Load ◽  
Real Contact Area ◽  
Elastic Deflection ◽  
Contact Depth ◽  
Real Contact ◽  
Pile Up

Hardness and elastic modulus of micromaterials can be evaluated by analyzing instrumented sharp-tip-indentation load–depth curves. The present study quantified the effects of tip-blunting and pile-up or sink-in on the contact area by analyzing indentation curves. Finite-element simulation and theoretical modeling were used to describe the detailed contact morphologies. The ratio f of contact depth, i.e., the depth including elastic deflection and pile-up and sink-in, to maximum indentation depth, i.e., the depth measured only by depth sensing, ignoring elastic deflection and pile-up and sink-in, was proposed as a key indentation parameter in evaluating real contact depth during indentation. This ratio can be determined strictly in terms of indentation-curve parameters, such as loading and unloading slopes at maximum depth and the ratio of elastic indentation energy to total indentation energy. In addition, the value of f was found to be independent of indentation depth, and furthermore the real contact area can be determined and hardness and elastic modulus can be evaluated from f. This curve-analysis method was verified in finite-element simulations and nanoindentation experiments.

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