Analysis of Indentation Size Effect of Vickers Hardness Tests of Steels.
Advanced Materials Research Vols. 652-654 (2013) pp 1307-1310
Online available since 2013/Jan/25 at www.scientific.net
© (2013) Trans Tech Publications, Switzerland
doi:10.4028/www.scientific.net/AMR.652-654.1307
Analysis of Indentation Size Effect of Vickers Hardness Tests of Steels
Nyoman Budiarsa, Andrew Norbury, Xiaoxiang Su, Gareth Bradley
and Xuejun Ren
School of Engineering, Liverpool John Moores University, L3 3AF, UK
Keywords: Vickers hardness, indentation size effect, H/E.
Abstract. In this work, the indentation size effect (ISE) in Vickers hardness tests of steel with
selected heat treatments (annealed or tempered) has been investigated and analysed. Systematical
hardness tests were performed within a commonly used micro-load range. The experimental data was
analysed according to the Meyer power-law and the proportional specimen resistance (PSR) models
and the link between ISE and material properties was discussed. The results showed that the
experimental data fitted well with the Mayers power-law (P = A.dn) and the PSR (P/d = al + a2d)
models. The ISE index (n) showed a good correlation with the hardness-elastic modulus ratio (H/E),
which potentially could be used to predict the relative contributions of the elastic and plastic
deformation contact area under indentation load and to normalize the hardness values for inverse
material properties .
Introduction
Vickers microhardness testing is widely used in testing different types of materials. It requires only a
small amount of material and is convenient to use. In some cases, the property distributions over a
wide area can be mapped, which is particularly useful for situations such as welded joints, surface
integrities of machined surfaces or gradient materials. Recent developments in inverse FE modelling
could potentially extend the use of hardness tests to a new area of predicting the constitutive plastic
properties (e.g. yield strength and work hardening coefficients). This is particular appealing to
situations such as heat treatments of steels where hardness tests are routinely used for process
developments and/or quality control. However, the results of a hardness test can be influenced by
many factors, among which ISE, i.e. observation of the phenomena that the hardness is dependent on
the applied load [1], is the most significant issue. ISE could directly influence the analysis of hardness
results, in particular when comparing data from different sources. This has to be investigated to be
able to accurately predict/compare the material properties from hardness tests.
ISE has been studied extensively for indenters of various shapes including both sharp (conical or
pyramidal) and spherical indenters over different material groups [2-5]. The source of ISE is still a
subject of study, which has been attributed to a number of phenomena and mechanisms, including:
elastic recovery, work hardening during indentation and strain gradients associated with dislocations
[5-8]. The scale of ISE has been correlated to different material properties such as elastic modules,
dislocation density, etc. [2, 5-7]. Previous work by Ren et al [3] on Knoop hardness tests of single
crystal ceramics showed the ISE coefficients exhibited a good correlation with the hardness to
modulus ratio (H/E) of the materials. It is of interest to extend the work to steels with different teat
treatments due to their widespread applications.
In this work, the ISE of steels with selected heat treatments (annealed or tempered) has been
investigated and analysed. Systematical hardness tests were performed within a commonly used
micro-load range. The experimental data was analysed according to the Meyer power-law and the
PSR models and the link between ISE to material properties is explored.
All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP,
www.ttp.net. (ID: 180.254.211.210, Liverpool John Moores University, United Kingdom-12/08/13,01:53:57)
1308
Advances in Materials and Materials Processing
Materials and Experimental
The sample material used was a medium carbon steel with 0.54 % C (0.54 C; 0.9 Mn, 0.055 P, 0.014
S, 0.19 Si, 0.014Ni) in the form of steel rods (5 mm in diameter). The hardnesses of samples under
annealed or quenched and tempered (200°C, 400°C and 600°C) conditions were compared to
establish the ISE over a load range commonly used in testing heat-treated components. The samples
were sectioned, mounted in resin before being polished with diamond paste. The hardness tests were
undertaken carried out on a Duramin Vickers microhardness tester and the experimental data
analysed utilising the power law and PSR models.
Results and Discussions
Fig. 1 shows the variation in the Vickers hardness of the materials with respect to applied load. Each
data point represents the mean value of six measurements. As shown in the figure, there is a clear
variation in the ISE of the Vickers hardness on steel with different heat-treatment conditions. The
hardness of the annealed sample is much lower than the other tempered samples, with the hardness
value decreasing with increasing tempering temperature. In all the cases, within the testing load used,
the data clearly showed that increasing the applied load resulted in decreased hardness values. As the
tempering temperature increased, the variations of hardness with respect to load became less
significant.
Fig. 1 Variation of the Vickers microhardness
data for steel (0.54%C) under different heattreatment conditions.
Fig. 2 Indentation data for steel plotted
according to the Meyer power
law in logarithmic form.
The ISE has traditionally been described in terms of the Meyer power law and the proportional
specimen resistance model [6-7]. The power law described relationships between the applied load
(P), and the resulting indentation size (d):
P = A d
(1)
Log P = log A + n log d
(2)
where P is the applied load, d is the diagonal length and, A and n are constants. The exponent n, is a
measure of the ISE behaviour, which has been experimentally observed between 1.5 and 2.0 [5-6].
When n > 2, there is reverse ISE behaviour, whilst when n=2, the hardness is independent of the
applied test load, and is given by Kick’s law:
Advanced Materials Research Vols. 652-654
P = A d
Where A0 is geometric conversion factor for the indenter used.
1309
(3)
Fig. 2 plots the indentation data according to the Meyer power law in logarithmic form. It is evident
from the figure, that this equation describes the data well for all samples. The slope, which represents
the ISE index n, was higher for the tempered condition than the annealed condition and exhibited an
increasing trend with increasing tempering temperature indicating less significant ISE over the load
range used. This suggested that ISE increased with increasing nominal hardness values.
Proportional specimen resistance (PSR) approaches resulted in a relationship between the applied
load (P) and the resulting indentation size d (µm) with which, the normal ISE behaviour could be
described by the relation [6]:
P = a d + a d
= a + a d
(4)
(5)
Where the parameter a1 characterises the load dependence of hardness and a2 is a load-independent
constant. a1 represents the energy consumed in creating new surface and a2 represents the work of
permanent deformation or the volume energy of deformation. Equation (5) could be used to describe
the measured data as depicted in Fig. 3. The correlation coefficients were again greater than 0.99 in all
cases. There was a clear difference between the slope of data for the annealed condition and the
tempered conditions, which increased as the hardness of the samples increased.
Fig. 3 Indentation data for steel plotted
according to the PSR model.
Fig. 4 Power-law index n and PSR a1 vs. the
hardness-to-modulus ratio H/E.
The hardness test results showed that in all the cases, there was a clear ISE in the heat-treated steel
samples tested. Both power law and PSR model could accurately depict the ISE observed. Previous
work has linked the ISE to the Young’s modulus, but it is commonly accepted that the Young’s
modulus of steels does not vary significantly with heat treatments, so elastic resistance could not be
the main cause of ISE observed over the load range employed. Fig. 4 depicts the power-law index n
against the hardness-to-modulus ratio H/E. It is clearly shown that the ISE parameters exhibited a
reasonable agreement with the H/E values. This suggests, similar to the Knoop hardness in single
crystals of ceramics [6], that the ISE could be linked to the hardness-Elastic modulus. This potentially
could provide a method to normalise ISE in order to inversely predict the plastic material parameters
of metals with different heat treatment conditions. Further work is required to study this trend with a
more comprehensive set of data.
1310
Advances in Materials and Materials Processing
Summary
In this work, the indentation size effect (ISE) in hardness tests of steel with selected heat treatments
(annealed or tempered) was investigated and analysed. Systematical hardness tests were performed
within a commonly used micro-load range. The experimental data was analysed according to the
Meyer power-law and the proportional specimen resistance (PSR) models and the link between ISE
to material properties was also discussed. The results showed that the experimental data fitted well
with the Mayers power-law (P = A.dn) and the PSR (P/d = al + a2d) models. The Mayers index (n)
showed a good correlation with hardness-elastic modulus ratio (H/E), which potentially could be used
to predict the relative contributions of elastic and plastic deformation contact area under indentation
load. Further work, with a more comprehensive set of data, is required to study this trend and
establish a procedure to normalize the data in order to predict the constitutive materials properties
inversely from hardness tests.
References
[1] X. Kong, Q. Yang , B. Li , G. Rothwell, R. English and X.J. Ren: Materials & Design Vol 29(8)
(2008), p.1554.
[2] M. Atkinson: Journal Mech. Sci. Vol. 33 (1991), p.843.
[3] X.J. Ren, R.M. Hooper, C. Griffiths, J.L. Henshall: J Materials science Vol. 22 (2003), p.1105.
[4] Y.V. Milman, A.A. Golubenko, S.N. Dub: Acta Materialia Vol.59 (2011), p.7480.
[5] G.M. Pharr, E.G. Herbert, and Y.F. Gao: Annu. Rev. Mater. Res. Vol. 40 (2010), p.271.
[6] X.J. Ren, R.M. Hooper, C. Griffiths, J.L. Henshall: Philosophical Mag. A. Vol. 10 (2002), p.2113.
[7] H. Li, A. Ghoshs, Y.H. Han and R.C. Bradt: Journal of Materials Research Vol. 8 (1993), p.1028.
[8] W.D. Nix and H. Gao: J Mech Phys Solids Vol.46(1998), p.411.
Advances in Materials and Materials Processing
10.4028/www.scientific.net/AMR.652-654
Analysis of Indentation Size Effect of Vickers Hardness Tests of Steels
10.4028/www.scientific.net/AMR.652-654.1307
Analysis of Indentation Size
Effect of Vickers Hardness
Tests of Steels
by I Nyoman Budiarsa
FILE
T IME SUBMIT T ED
SUBMISSION ID
1-AMR.652-654.1307.PDF (266.6K)
06-JUN-2015 02:11PM
548514909
WORD COUNT
1771
CHARACT ER COUNT 9222
Analysis of Indentation Size Effect of Vickers Hardness
Tests of Steels
18
ORIGINALITY REPORT
%
SIMILARIT Y INDEX
9%
INT ERNET SOURCES
18%
PUBLICAT IONS
3%
ST UDENT PAPERS
PRIMARY SOURCES
1
N. K. Mukhopadhyay. "Micro- and
nanoindentation techniques for mechanical
characterisation of materials", International
Materials Reviews, 08/01/2006
Publicat ion
2
3
st.sdhykx.cn
Int ernet Source
Sangwal, K.. "Analysis of the indentation size
effect in the microhardness measurement of
some cobalt-based alloys", Materials
Chemistry & Physics, 20030115
Publicat ion
4
5
www.crystalresearch.com
Int ernet Source
Gong, J.. "Analysis of the indentation size
effect on the apparent hardness for
ceramics", Materials Letters, 199902
Publicat ion
6
M. Majić. "Load dependence of the apparent
Knoop hardness of SiC ceramics in a wide
range of loads", Materialwissenschaft und
5%
3%
2%
2%
1%
1%
Werkstofftechnik, 03/2011
Publicat ion
7
Riscob, B., Mohd Shakir, N. Vijayan, K. K.
Maurya, M. A. Wahab, and G.
Bhagavannarayana. "Unidirectional crystal
growth and crystalline perfection of Larginine phosphate monohydrate", Journal of
Applied Crystallography, 2012.
Publicat ion
8
A. Abu El-Fadl. "Influence of x-irradiation on
indentation size effect and formation of
cracks for [Ky(NH4)1-y]2ZnCl4 mixed
crystals", Crystal Research and Technology,
04/2007
Publicat ion
9
Ryou, H.. "Nanoscopic dynamic mechanical
properties of intertubular and peritubular
dentin", Journal of the Mechanical Behavior
of Biomedical Materials, 201203
Publicat ion
10
11
www.eng.livjm.ac.uk
Int ernet Source
P. Sayan. "Effect of Various Impurities on the
Hardness of NaCl Crystals", Crystal Research
and Technology, 11/2001
Publicat ion
12
Maier, Verena, Christopher Schunk, Mathias
Göken, and Karsten Durst. "Microstructuredependent deformation behaviour of bcc-
1%
1%
1%
1%
Online available since 2013/Jan/25 at www.scientific.net
© (2013) Trans Tech Publications, Switzerland
doi:10.4028/www.scientific.net/AMR.652-654.1307
Analysis of Indentation Size Effect of Vickers Hardness Tests of Steels
Nyoman Budiarsa, Andrew Norbury, Xiaoxiang Su, Gareth Bradley
and Xuejun Ren
School of Engineering, Liverpool John Moores University, L3 3AF, UK
Keywords: Vickers hardness, indentation size effect, H/E.
Abstract. In this work, the indentation size effect (ISE) in Vickers hardness tests of steel with
selected heat treatments (annealed or tempered) has been investigated and analysed. Systematical
hardness tests were performed within a commonly used micro-load range. The experimental data was
analysed according to the Meyer power-law and the proportional specimen resistance (PSR) models
and the link between ISE and material properties was discussed. The results showed that the
experimental data fitted well with the Mayers power-law (P = A.dn) and the PSR (P/d = al + a2d)
models. The ISE index (n) showed a good correlation with the hardness-elastic modulus ratio (H/E),
which potentially could be used to predict the relative contributions of the elastic and plastic
deformation contact area under indentation load and to normalize the hardness values for inverse
material properties .
Introduction
Vickers microhardness testing is widely used in testing different types of materials. It requires only a
small amount of material and is convenient to use. In some cases, the property distributions over a
wide area can be mapped, which is particularly useful for situations such as welded joints, surface
integrities of machined surfaces or gradient materials. Recent developments in inverse FE modelling
could potentially extend the use of hardness tests to a new area of predicting the constitutive plastic
properties (e.g. yield strength and work hardening coefficients). This is particular appealing to
situations such as heat treatments of steels where hardness tests are routinely used for process
developments and/or quality control. However, the results of a hardness test can be influenced by
many factors, among which ISE, i.e. observation of the phenomena that the hardness is dependent on
the applied load [1], is the most significant issue. ISE could directly influence the analysis of hardness
results, in particular when comparing data from different sources. This has to be investigated to be
able to accurately predict/compare the material properties from hardness tests.
ISE has been studied extensively for indenters of various shapes including both sharp (conical or
pyramidal) and spherical indenters over different material groups [2-5]. The source of ISE is still a
subject of study, which has been attributed to a number of phenomena and mechanisms, including:
elastic recovery, work hardening during indentation and strain gradients associated with dislocations
[5-8]. The scale of ISE has been correlated to different material properties such as elastic modules,
dislocation density, etc. [2, 5-7]. Previous work by Ren et al [3] on Knoop hardness tests of single
crystal ceramics showed the ISE coefficients exhibited a good correlation with the hardness to
modulus ratio (H/E) of the materials. It is of interest to extend the work to steels with different teat
treatments due to their widespread applications.
In this work, the ISE of steels with selected heat treatments (annealed or tempered) has been
investigated and analysed. Systematical hardness tests were performed within a commonly used
micro-load range. The experimental data was analysed according to the Meyer power-law and the
PSR models and the link between ISE to material properties is explored.
All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP,
www.ttp.net. (ID: 180.254.211.210, Liverpool John Moores University, United Kingdom-12/08/13,01:53:57)
1308
Advances in Materials and Materials Processing
Materials and Experimental
The sample material used was a medium carbon steel with 0.54 % C (0.54 C; 0.9 Mn, 0.055 P, 0.014
S, 0.19 Si, 0.014Ni) in the form of steel rods (5 mm in diameter). The hardnesses of samples under
annealed or quenched and tempered (200°C, 400°C and 600°C) conditions were compared to
establish the ISE over a load range commonly used in testing heat-treated components. The samples
were sectioned, mounted in resin before being polished with diamond paste. The hardness tests were
undertaken carried out on a Duramin Vickers microhardness tester and the experimental data
analysed utilising the power law and PSR models.
Results and Discussions
Fig. 1 shows the variation in the Vickers hardness of the materials with respect to applied load. Each
data point represents the mean value of six measurements. As shown in the figure, there is a clear
variation in the ISE of the Vickers hardness on steel with different heat-treatment conditions. The
hardness of the annealed sample is much lower than the other tempered samples, with the hardness
value decreasing with increasing tempering temperature. In all the cases, within the testing load used,
the data clearly showed that increasing the applied load resulted in decreased hardness values. As the
tempering temperature increased, the variations of hardness with respect to load became less
significant.
Fig. 1 Variation of the Vickers microhardness
data for steel (0.54%C) under different heattreatment conditions.
Fig. 2 Indentation data for steel plotted
according to the Meyer power
law in logarithmic form.
The ISE has traditionally been described in terms of the Meyer power law and the proportional
specimen resistance model [6-7]. The power law described relationships between the applied load
(P), and the resulting indentation size (d):
P = A d
(1)
Log P = log A + n log d
(2)
where P is the applied load, d is the diagonal length and, A and n are constants. The exponent n, is a
measure of the ISE behaviour, which has been experimentally observed between 1.5 and 2.0 [5-6].
When n > 2, there is reverse ISE behaviour, whilst when n=2, the hardness is independent of the
applied test load, and is given by Kick’s law:
Advanced Materials Research Vols. 652-654
P = A d
Where A0 is geometric conversion factor for the indenter used.
1309
(3)
Fig. 2 plots the indentation data according to the Meyer power law in logarithmic form. It is evident
from the figure, that this equation describes the data well for all samples. The slope, which represents
the ISE index n, was higher for the tempered condition than the annealed condition and exhibited an
increasing trend with increasing tempering temperature indicating less significant ISE over the load
range used. This suggested that ISE increased with increasing nominal hardness values.
Proportional specimen resistance (PSR) approaches resulted in a relationship between the applied
load (P) and the resulting indentation size d (µm) with which, the normal ISE behaviour could be
described by the relation [6]:
P = a d + a d
= a + a d
(4)
(5)
Where the parameter a1 characterises the load dependence of hardness and a2 is a load-independent
constant. a1 represents the energy consumed in creating new surface and a2 represents the work of
permanent deformation or the volume energy of deformation. Equation (5) could be used to describe
the measured data as depicted in Fig. 3. The correlation coefficients were again greater than 0.99 in all
cases. There was a clear difference between the slope of data for the annealed condition and the
tempered conditions, which increased as the hardness of the samples increased.
Fig. 3 Indentation data for steel plotted
according to the PSR model.
Fig. 4 Power-law index n and PSR a1 vs. the
hardness-to-modulus ratio H/E.
The hardness test results showed that in all the cases, there was a clear ISE in the heat-treated steel
samples tested. Both power law and PSR model could accurately depict the ISE observed. Previous
work has linked the ISE to the Young’s modulus, but it is commonly accepted that the Young’s
modulus of steels does not vary significantly with heat treatments, so elastic resistance could not be
the main cause of ISE observed over the load range employed. Fig. 4 depicts the power-law index n
against the hardness-to-modulus ratio H/E. It is clearly shown that the ISE parameters exhibited a
reasonable agreement with the H/E values. This suggests, similar to the Knoop hardness in single
crystals of ceramics [6], that the ISE could be linked to the hardness-Elastic modulus. This potentially
could provide a method to normalise ISE in order to inversely predict the plastic material parameters
of metals with different heat treatment conditions. Further work is required to study this trend with a
more comprehensive set of data.
1310
Advances in Materials and Materials Processing
Summary
In this work, the indentation size effect (ISE) in hardness tests of steel with selected heat treatments
(annealed or tempered) was investigated and analysed. Systematical hardness tests were performed
within a commonly used micro-load range. The experimental data was analysed according to the
Meyer power-law and the proportional specimen resistance (PSR) models and the link between ISE
to material properties was also discussed. The results showed that the experimental data fitted well
with the Mayers power-law (P = A.dn) and the PSR (P/d = al + a2d) models. The Mayers index (n)
showed a good correlation with hardness-elastic modulus ratio (H/E), which potentially could be used
to predict the relative contributions of elastic and plastic deformation contact area under indentation
load. Further work, with a more comprehensive set of data, is required to study this trend and
establish a procedure to normalize the data in order to predict the constitutive materials properties
inversely from hardness tests.
References
[1] X. Kong, Q. Yang , B. Li , G. Rothwell, R. English and X.J. Ren: Materials & Design Vol 29(8)
(2008), p.1554.
[2] M. Atkinson: Journal Mech. Sci. Vol. 33 (1991), p.843.
[3] X.J. Ren, R.M. Hooper, C. Griffiths, J.L. Henshall: J Materials science Vol. 22 (2003), p.1105.
[4] Y.V. Milman, A.A. Golubenko, S.N. Dub: Acta Materialia Vol.59 (2011), p.7480.
[5] G.M. Pharr, E.G. Herbert, and Y.F. Gao: Annu. Rev. Mater. Res. Vol. 40 (2010), p.271.
[6] X.J. Ren, R.M. Hooper, C. Griffiths, J.L. Henshall: Philosophical Mag. A. Vol. 10 (2002), p.2113.
[7] H. Li, A. Ghoshs, Y.H. Han and R.C. Bradt: Journal of Materials Research Vol. 8 (1993), p.1028.
[8] W.D. Nix and H. Gao: J Mech Phys Solids Vol.46(1998), p.411.
Advances in Materials and Materials Processing
10.4028/www.scientific.net/AMR.652-654
Analysis of Indentation Size Effect of Vickers Hardness Tests of Steels
10.4028/www.scientific.net/AMR.652-654.1307
Analysis of Indentation Size
Effect of Vickers Hardness
Tests of Steels
by I Nyoman Budiarsa
FILE
T IME SUBMIT T ED
SUBMISSION ID
1-AMR.652-654.1307.PDF (266.6K)
06-JUN-2015 02:11PM
548514909
WORD COUNT
1771
CHARACT ER COUNT 9222
Analysis of Indentation Size Effect of Vickers Hardness
Tests of Steels
18
ORIGINALITY REPORT
%
SIMILARIT Y INDEX
9%
INT ERNET SOURCES
18%
PUBLICAT IONS
3%
ST UDENT PAPERS
PRIMARY SOURCES
1
N. K. Mukhopadhyay. "Micro- and
nanoindentation techniques for mechanical
characterisation of materials", International
Materials Reviews, 08/01/2006
Publicat ion
2
3
st.sdhykx.cn
Int ernet Source
Sangwal, K.. "Analysis of the indentation size
effect in the microhardness measurement of
some cobalt-based alloys", Materials
Chemistry & Physics, 20030115
Publicat ion
4
5
www.crystalresearch.com
Int ernet Source
Gong, J.. "Analysis of the indentation size
effect on the apparent hardness for
ceramics", Materials Letters, 199902
Publicat ion
6
M. Majić. "Load dependence of the apparent
Knoop hardness of SiC ceramics in a wide
range of loads", Materialwissenschaft und
5%
3%
2%
2%
1%
1%
Werkstofftechnik, 03/2011
Publicat ion
7
Riscob, B., Mohd Shakir, N. Vijayan, K. K.
Maurya, M. A. Wahab, and G.
Bhagavannarayana. "Unidirectional crystal
growth and crystalline perfection of Larginine phosphate monohydrate", Journal of
Applied Crystallography, 2012.
Publicat ion
8
A. Abu El-Fadl. "Influence of x-irradiation on
indentation size effect and formation of
cracks for [Ky(NH4)1-y]2ZnCl4 mixed
crystals", Crystal Research and Technology,
04/2007
Publicat ion
9
Ryou, H.. "Nanoscopic dynamic mechanical
properties of intertubular and peritubular
dentin", Journal of the Mechanical Behavior
of Biomedical Materials, 201203
Publicat ion
10
11
www.eng.livjm.ac.uk
Int ernet Source
P. Sayan. "Effect of Various Impurities on the
Hardness of NaCl Crystals", Crystal Research
and Technology, 11/2001
Publicat ion
12
Maier, Verena, Christopher Schunk, Mathias
Göken, and Karsten Durst. "Microstructuredependent deformation behaviour of bcc-
1%
1%
1%
1%