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)].

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. 1205-1207 ◽  
Author(s):  
Karsten Durst ◽  
Hamad ur Rehman ◽  
Benoit Merle
Keyword(s):  
Finite Element ◽  
Penetration Depth ◽  
Correction Factor ◽  
Elastic Material ◽  
Contact Area ◽  
Contact Stiffness ◽  
Fe Analysis ◽  
Tip Radius ◽  
True Contact Area ◽  
True Contact

[Meza et al. J. Mater. Res.23(3), 725 (2008)] recently claimed that the correction factor beta for the Sneddon equation, used for the evaluation of nanoindentation load-displacement data, is strongly depth- and tip-shape-dependent. Meza et al. used finite element (FE) analysis to simulate the contact between conical or spheroconical indenters, and an elastic material. They calculated the beta factor by comparing the simulated contact stiffness with Sneddon’s prediction for conical indenters. Their analysis is misleading, and it is shown here that by applying the general Sneddon equation, taking into account the true contact area, an almost constant and depth-independent beta factor is obtained for conical, spherical and spheroconical indenter geometries.

Penetration depth and tip radius dependence on the correction factor in nanoindentation measurements

2008 ◽  
Vol 23 (3) ◽  
pp. 725-731 ◽  
Author(s):  
J.M. Meza ◽  
F. Abbes ◽  
M. Troyon
Keyword(s):  
Penetration Depth ◽  
Correction Factor ◽  
Contact Stiffness ◽  
Nanoindentation Test ◽  
Simple Analytical Model ◽  
Element Analysis ◽  
Maximum Penetration Depth ◽  
Maximum Penetration ◽  
Tip Radius ◽  
Indenter Geometry

Dimensional analysis is used to show that the maximum penetration depth and the tip radius affect the β correction factor appearing in the Sneddon relationship between unloading contact stiffness, contact area, and elastic modulus. A simple analytical model based on elasticity theory is derived that predicts the variation of β with penetration depth. This model shows that β increases at low penetration depth and decreases with the tip radius. The β(h) curve given by the model is compared with that calculated by finite element analysis for an elastic material and also with that deduced from experimental measurements performed on fused quartz with two Berkovich indenters: a sharp one and a blunted one. It is also demonstrated that the correction factor can be expressed as two multiplicative contributions, a contribution related to the mechanical properties of the material and a contribution related to the indenter geometry. Implications of these findings on nanoindentation test are also discussed.

Correction factor for contact area in nanoindentation measurements

2005 ◽  
Vol 20 (3) ◽  
pp. 610-617 ◽  
Author(s):  
Michel Troyon ◽  
Liye Huang
Keyword(s):  
Elastic Modulus ◽  
Correction Factor ◽  
Contact Area ◽  
Basic Equation ◽  
Elastic Moduli ◽  
Contact Stiffness ◽  
Factor Α ◽  
Tip Radius ◽  
The Relationship ◽  
Indenter Shape

In the relationship between unloading contact stiffness, elastic modulus, and contact area, which is the fundamental basic equation for nanoindentation analysis, a multiplicative correction factor is generally needed. Sometimes this correction factor is called γ to take into account the elastic radial inward displacements, and sometimes it is called β to correct for the fact that the indenter shape is not a perfect cone. In reality, these two effects simultaneously coexist and thus it is proposed that this correction factor is α = βγ. From nanoindentation data measured on three materials of different elastic moduli with a sharp Berkovich indenter and a worn one, the tip of which was blunt, it is demonstrated that the correction factor α does not have a constant value for a given material and indenter type but depends on the indenter tip rounding and also on the deformation of the indenter during indentation. It seems that α increases with the tip radius and also with the elastic modulus of the measured materials.

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.

Critical Examination of the Two-slope Method in Nanoindentation

2005 ◽  
Vol 20 (8) ◽  
pp. 2194-2198 ◽  
Author(s):  
M. Troyon ◽  
L. Huang
Keyword(s):  
Correction Factor ◽  
Contact Area ◽  
Contact Stiffness ◽  
Critical Examination ◽  
Slope Method ◽  
Loading And Unloading ◽  
Factor Α ◽  
Analytical Expressions ◽  
Good Agreement

In this paper, we derive corrected analytical expressions for calculating the hardness and modulus by the two-slope method. This method relies on the determination of the slopes of the loading and unloading curves rather than the indenter displacement as an input. These expressions take into account the correction factor α in the fundamental relations among contact stiffness, elastic modulus, and contact area, which is frequently forgotten or misused in the literature. It is shown that these corrected expressions allow measurements of the hardness and modulus in very good agreement with the commonly used technique based on the determination of the contact area. Additionally, the correction factor α can be easily determined if Young's modulus of the material is known.

scholarly journals Study on Model of Penetration into Thick Metallic Targets with Finite Planar Sizes by Long Rods

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Juan Wang ◽  
Junhai Zhao ◽  
Jianhua Zhang ◽  
Yuan Zhou
Keyword(s):  
Penetration Depth ◽  
High Speed ◽  
Strength Theory ◽  
Unified Strength Theory ◽  
Cylindrical Cavity Expansion ◽  
Plastic Materials ◽  
Long Rod ◽  
Expansion Model ◽  
Elastic Plastic Materials ◽  
The Impact

A finite cylindrical cavity expansion model for metallic thick targets with finite planar sizes, composed of ideal elastic-plastic materials, with penetration of high-speed long rod is presented by using the unified strength theory. Considering the lateral boundary and mass abrasion of the target, the penetration resistance and depth formulas are proposed, solutions of which are obtained by MATLAB program. Then, a series of different criteria-based analytical solutions are obtained and the ranges of penetration depth of targets with different ratios of target radius to projectile radius (rt/rd) are predicted. Meanwhile, the numerical simulation is performed using the ANSYS/LS-DYNA finite element code to investigate the variations in residual projectile velocity, length, and mass abrasion. It shows that various parameters have influences on the antipenetration performance of the target, such as the strength coefficient b, rt/rd, the shape of the projectile nose, and the impact velocity of the projectile, among which the penetration depth has increased by 18.95% as b = 1 decreases to b = 0 and has increased by 32.28% as rt/rd = 19.88 decreases to rt/rd = 4.9.

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