Modeling conical indentation in homogeneous materials and in hard films on soft substrates

2005 ◽  
Vol 20 (2) ◽  
pp. 521-528 ◽  
Author(s):  
Wangyang Ni ◽  
Yang-Tse Cheng
Keyword(s):  
Indentation Depth ◽  
Total Work ◽  
Instrumented Indentation ◽  
Solid Materials ◽  
Reduced Modulus ◽  
Homogeneous Materials ◽  
Von Mises ◽  
Reversible Work ◽  
Incremental Theory Of Plasticity ◽  
Conical Indentation

Dimensional analysis and finite element modeling were conducted to examine conical indentation in homogeneous materials and in hard films on soft substrates. In this paper, the solid materials modeled follow the incremental theory of plasticity with a von-Mises yield surface. The validity of the Oliver–Pharr method was examined. It was found that, for hard films on soft substrates, the Oliver–Pharr method is applicable only when the indentation depth is less than 10% of the film thickness. A linear relationship between the ratio of hardness to reduced modulus and the ratio of reversible work to total work was observed for conical indentation in homogeneous materials and in hard films on soft substrates. This relationship can be used to analyze instrumented indentation experiments.

A study of indentation work in homogeneous materials

2006 ◽  
Vol 21 (6) ◽  
pp. 1363-1374 ◽  
Author(s):  
Mengxi Tan
Keyword(s):  
Plastic Deformation ◽  
Elastic Modulus ◽  
Elastic Energy ◽  
Size Effects ◽  
Unit Volume ◽  
Plastic Work ◽  
Total Work ◽  
Indentation Size ◽  
Scaling Relationships ◽  
Homogeneous Materials

The work of indentation is investigated experimentally in this article. A method of using the elastic energy to extract the elastic modulus is proposed and verified. Two types of hardness related to the work of indentation are defined and examined: Hwtis defined as the total work required creating a unit volume of contact deformationand Hwp is defined as the plastic work required creating a unit volume of plastic deformation; experiments show that both hardness definitions are good choices for characterizing hardness. Several features that may provide significant insights in understanding indentation measurements are studied. These features mainly concern some scaling relationships in indentation measurements and the indentation size effects.

Overstraining of flush plain cross-bored cylinders

2004 ◽  
Vol 218 (2) ◽  
pp. 143-153 ◽  
Author(s):  
J M Kihiu ◽  
G O Rading ◽  
S M Mutuli
Keyword(s):  
Finite Element Method ◽  
Yield Criterion ◽  
Three Dimensional ◽  
Yield Condition ◽  
Solution Technique ◽  
Stress Distributions ◽  
Dimensional Finite Element ◽  
Von Mises ◽  
Three Dimensional Finite Element ◽  
Incremental Theory Of Plasticity

A three-dimensional finite element method computer program was developed to establish the elastic-plastic, residual and service stress distributions in thick-walled cylinders with flush and non-protruding plain cross bores under internal pressure. The displacement formulation and eight-noded brick isoparametric elements were used. The incremental theory of plasticity with a 5 per cent yield condition (an element is assumed to have yielded when the effective stress is within 5 per cent of the material yield stress) and von Mises yield criterion were assumed. The frontal solution technique was used. The incipient yield pressure and the pressure resulting in a 0.3 per cent overstrain ratio were established for various cylinder thickness ratios and cross bore-main bore radius ratios. For a thickness ratio of 2.25 and a cross bore-main bore radius ratio of 0.1, the stresses were determined for varying overstrain and an optimum overstrain ratio of 37 per cent was established. To find the accuracy of the results, the more stringent yield condition of 0.5 per cent was also considered. The benefits of autofrettage were presented and alternative autofrettage and yield condition procedures proposed.

Instrumented indentation probing of laser surface-refined cast Al alloy

2004 ◽  
Vol 19 (1) ◽  
pp. 202-207 ◽  
Author(s):  
S. Nayak ◽  
Laura Riester ◽  
Narendra B. Dahotre
Keyword(s):  
Elastic Modulus ◽  
Indentation Depth ◽  
Laser Energy ◽  
Laser Surface ◽  
Al Alloy ◽  
Hard Phase ◽  
Instrumented Indentation ◽  
Average Hardness ◽  
Melted Layer ◽  
A319 Alloy

The surface layer of A319 alloy was refined by selective remelting using laser energy. Instrumented indentation technique was used to measure hardness (H) and elastic modulus (E) of the laser-melted layer. Berkovich tip was used to indent the material for 100-nm, 200-nm, 500-nm, and 1000-nm depths. The H and the E were found to be 1.22 GPa and 78.2 GPa, respectively, for 1000-nm indentation depths. The variances associated with H and E were minimal, whereas, the same for substrate possessed significant scattering. Also, H and E increased with decreasing depth of indentation. Closer examination suggested that when the heterogeneity in the material was in the scale of indentation depth, significant scattering took place and the hard phase Si influenced the average hardness. However, the influence of indentation depth on elastic modulus was not statistically significant.

scholarly journals Revelation of a functional dependence of the sum of two uniaxial strengths/hardness on elastic work/total work of indentation

2006 ◽  
Vol 21 (4) ◽  
pp. 895-903 ◽  
Author(s):  
Dejun Ma ◽  
Taihua Zhang ◽  
Chung Wo Ong
Keyword(s):  
Functional Relationship ◽  
Functional Dependence ◽  
Indentation Test ◽  
Fatigue Tests ◽  
Total Work ◽  
Finite Element Analyses ◽  
Instrumented Indentation ◽  
The Relationship ◽  
True Hardness ◽  
Instrumented Indentation Test

Dimensional and finite element analyses were used to analyze the relationship between the mechanical properties and instrumented indentation response of materials. Results revealed the existence of a functional dependence of (engineering yield strength σE,y + engineering tensile strength σE,b)/Oliver & Pharr hardness on the ratio of reversible elastic work to total work obtained from an indentation test. The relationship links up the Oliver & Pharr hardness with the material strengths, although the Oliver & Pharr hardness may deviate from the true hardness when sinking in or piling up occurs. The functional relationship can further be used to estimate the sum σE,y + σE,b according to the data of an instrumented indentation test. The σE,y + σE,b value better reflects the strength of a material compared to the hardness value alone. The method was shown to be effective when applied to aluminum alloys. The relationship can further be used to estimate the fatigue limits, which are usually obtained from macroscopic fatigue tests in different modes.

Characterization of NiTi superelastic properties by nano-dynamic modulus analysis and nanoindentation

2017 ◽  
Vol 10 (02) ◽  
pp. 1650071 ◽  
Author(s):  
Meni Kabla ◽  
Doron Shilo
Keyword(s):  
Martensitic Transformation ◽  
Shape Memory Alloys ◽  
Shape Memory ◽  
Dynamic Modulus ◽  
Indentation Depth ◽  
Modulus Analysis ◽  
Reduced Modulus ◽  
Transformation Stress

Nano-dynamic modulus analysis (DMA) is a technique that allows measuring the reduced modulus during nanoindentation. This paper demonstrates the usefulness of nano-DMA in the characterization of superelastic properties of shape memory alloys. Measurements of reduced modulus as a function of the indentation depth reveal a transition, which is associated with the finish of the martensitic transformation at the region right beneath the tip. Further analysis of nanoindentation data at the transition indentation depth allows the evaluation of representative properties which are proportional to the transformation stress and the strain at the end of the martensitic transformation and can be used for comparing between different samples.

Modelling of Nanoindentation of Compliant Layers on Stiffer Substrates using Finite Element Analysis

2007 ◽  
Vol 1025 ◽  
Author(s):  
Charles A Clifford ◽  
Martin P Seah
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Atomic Force Microscope ◽  
Indentation Depth ◽  
Element Analysis ◽  
Depth Data ◽  
Atomic Force ◽  
Reduced Modulus ◽  
Compliant Layer ◽  
Initial Results

AbstractNanoindentation using an Atomic Force Microscope (AFM) or a nanoindenter was modelled using Finite Element Analysis (FEA). Force versus indentation depth data were taken for a system consisting of a compliant layer on a stiffer substrate. It was found that the FEA results may be expressed analytically by a simple function that describes the reduced modulus value obtained with Oliver and Pharr's method for any moduli values, thickness of layer or radius of the indenter tip. Initial results obtained by varying the Poisson's ratio of the layer and substrate are also presented.

Relation between the ratio of elastic work to the total work of indentation and the ratio of hardness to Young's modulus for a perfect conical tip

2009 ◽  
Vol 24 (3) ◽  
pp. 590-598 ◽  
Author(s):  
J. Chen ◽  
S.J. Bull
Keyword(s):  
Numerical Simulation ◽  
Elastic Modulus ◽  
Linear Relationship ◽  
Young’S Modulus ◽  
Excellent Agreement ◽  
Material Properties ◽  
Experimental Results ◽  
Total Work ◽  
Scaling Relationship ◽  
Reduced Modulus

A linear relationship between the ratio of elastic work to the total indentation work and hardness to reduced modulus, i.e., We/Wt = λ H/Er, has been derived analytically and numerically in a number of studies and has been widely accepted. However, the scaling relationship between We/Wt and H/Er has recently been questioned, and it was found that λ is actually not a constant but is related to material properties. In this study, a new relationship between We/Wt and H/Er has been derived, which shows excellent agreement with numerical simulation and experimental results. We also propose a method for obtaining the elastic modulus and hardness of a material without invoking the commonly used Oliver and Pharr method. Furthermore, it is demonstrated that this method is less sensitive to tip imperfections than the Oliver and Pharr approach is.

A Scaling Approach to Modeling Indentation Measurements

2000 ◽  
Vol 649 ◽  
Author(s):  
Yang-Tse Cheng ◽  
Zhiyong Li ◽  
Che-Min Cheng
Keyword(s):  
Finite Element ◽  
Elastic Modulus ◽  
Dimensional Analysis ◽  
Instrumented Indentation ◽  
Elastic Plastic ◽  
Contact Depth ◽  
Finite Element Calculations ◽  
Conical Indentation ◽  
Interpretation Of Results

ABSTRACTUsing dimensional analysis and finite element calculations, the relationships between hardness, elastic modulus, final contact depth, and the work of indentation are extended to conical indentation in elastic-plastic solids with various cone angles. These relationships provide new insights into indentation measurements. They may also be useful to the interpretation of results obtained from instrumented indentation experiments.

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

2010 ◽  
Vol 25 (11) ◽  
pp. 2072-2077 ◽  
Author(s):  
Rong Yang ◽  
Taihua Zhang ◽  
Yihui Feng
Keyword(s):  
Elastic Modulus ◽  
Work Hardening ◽  
Total Work ◽  
Cavity Model ◽  
Perfectly Plastic ◽  
Plastic Materials ◽  
Reduced Modulus ◽  
Scale Ratio ◽  
Elastic Perfectly Plastic ◽  
General Work

In our previous paper, the expanding cavity model (ECM) and Lamé solution were used to obtain an analytical expression for the scale ratio between hardness (H) to reduced modulus (Er) and unloading work (Wu) to total work (Wt) 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.

Elastic loading and elastoplastic unloading from nanometer level indentations for modulus determinations

1998 ◽  
Vol 13 (2) ◽  
pp. 421-439 ◽  
Author(s):  
W. W. Gerberich ◽  
W. Yu ◽  
D. Kramer ◽  
A. Strojny ◽  
D. Bahr ◽  
...  
Keyword(s):  
Surface Roughness ◽  
Indentation Depth ◽  
Property Values ◽  
Elastic Displacement ◽  
Preliminary Survey ◽  
Rigid Plastic ◽  
Reduced Modulus ◽  
Fused Quartz ◽  
Elastic Loading ◽  
Best Fit

A new method for evaluating modulus and hardness from nanoindentation load/ displacement curves is presented. As a spherical indenter penetrates an elastoplastic half-space, the elastic displacement above the contact line is presumed to diminish in proportion to the total elastic displacement under the indenter. Applying boundary conditions on the elastic and plastic displacements for elastic and rigid plastic contacts leads to an expression that can be best fit to the entire unloading curve to determine E*, the reduced modulus. Justification of the formulation is presented, followed by the results of a preliminary survey conducted on three predominantly isotropic materials: fused quartz, polycrystalline Al, and single crystal W. Diamond tips with radii ranging from 130 nm to 5 μm were used in combination with three different nanoindentation devices. Results indicate that the method gives property values consistent with accepted values for modulus and hardness. The importance of surface roughness and indentation depth are also considered.

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