ISO/TR 29381:2008

TECHNICAL ISO/TR
REPORT 29381
First edition
2008-10-15

Metallic materials — Measurement
of mechanical properties by an
instrumented indentation test —
Indentation tensile properties
Matériaux métalliques — Mesure des caractéristiques mécaniques par
un essai de pénétration instrumenté — Caractéristiques de traction par
indentation




Reference number
ISO/TR 29381:2008(E)
©
ISO 2008

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ISO/TR 29381:2008(E)
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ISO/TR 29381:2008(E)
Contents Page
Foreword. iv
Introduction . v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions. 1
4 Symbols and designations . 2
5 Descriptions of the different methods. 3
5.1 Method 1: Representative stress and strain .3
5.2 Method 2: Inverse analysis by FEA. 10
5.3 Method 3: Neural networks. 18
6 Summary. 23
Annex A (informative) Measurement of residual stress by instrumented indentation test. 25
Bibliography . 29

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ISO/TR 29381:2008(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
In exceptional circumstances, when a technical committee has collected data of a different kind from that
which is normally published as an International Standard (“state of the art”, for example), it may decide by a
simple majority vote of its participating members to publish a Technical Report. A Technical Report is entirely
informative in nature and does not have to be reviewed until the data it provides are considered to be no
longer valid or useful.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO/TR 29381 was prepared by Technical Committee ISO/TC 164, Mechanical testing of metals,
Subcommittee SC 3, Hardness testing.

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ISO/TR 29381:2008(E)
Introduction
0.1 General information for tensile properties
For centuries the elastic properties of materials have been described by Hooke’s Law (ca. 1660) and the
practical parameter of Young’s modulus. This simple ratio of stress/strain is a practical, useful measure and,
combined with a value for Poisson’s ratio of a material (a measure of the dimensional change of a material in
directions other than the principal axis in which it is being strained), it is possible to determine the stresses
introduced by loading even quite complex structures. When the applied force is removed from an elastically
deformed structure, it will recover completely. If, however, the stress in a material exceeds its yield point, then
it will deform plastically and will retain a permanent deformation after the applied force is removed. The
simplest description of the mechanical properties of the material is, therefore, a plot of stress vs. strain, from
zero to the strain at which the material fails completely.

n
⎧ ε < ε ⎫
Eε y
⎛⎞
E
⎪ ⎪
σε=+⎜⎟1
⎨ ⎬
p
⎜⎟
σ
y
⎪ ⎪
σ⎝⎠ εε>
yy
⎩⎭



Key
E is Young's modulus
σ , ε are the yield point coordinates
y y
ε is the nonlinear part of the total accumulated strain beyond ε
p y
ε is the elasto-plastic strain induced by σ , the stress above the yield point
r r
Figure 1 — Schematic of a typical true stress-strain curve for a work-hardening metal
Figure 1 shows just such a curve. From this curve, the key tensile properties of the material can be obtained.
⎯ Young’s modulus E is the gradient of the initial portion of the curve. It is also the gradient of the straight
line along which elastic recovery occurs from any point along the curve.
⎯ The deviation of the curve from a straight line marks the yield point, often described as the yield stress. A
straight-line recovery, of gradient E, from any point at higher stress or strain than this point would no
longer pass through the origin, i.e. plastic deformation will have occurred.
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ISO/TR 29381:2008(E)
⎯ The gradient of the curve after yielding is a measure of the work hardening of the material, i.e. elastic
recovery occurs along a straight line, gradient E, and re-stressing the material also follows the same line
such that further plastic deformation only begins once the previous maximum stress has been exceeded.
⎯ The point at which the material fails completely marks two parameters of interest, one being the ultimate
tensile stress (UTS); the other being the strain at failure.
These parameters form the key material specifications for any structural or functional design. It can be seen
that the stress-strain curve is an essential “fingerprint” of the type of material. An elastic then perfectly plastic
material will deform elastically up to the yield stress, and then it will continue to strain at constant stress until
failure occurs at the strain-to-failure point. The yield stress is therefore also the UTS. A perfectly elastic, brittle
material does not have a yield point, but exhibits a straight line (gradient of the Young’s modulus) until it fails
by fracture. A work-hardening material yields but is able to support increasing stresses as it strains to its UTS
and maximum strain at failure point. The toughness of the material is often related to the area under the curve
up to the failure point. This is a measure of the energy absorbed by the material before it fails. The tougher a
material is, the more energy it absorbs before failure.
Beyond extraction of the key tensile properties described above, the whole stress-strain curve is highly
desirable input for the design of structures and components, to ensure that they do not yield or fail in service.
Computing power has become more available and so the use of software such as Finite Element Analysis
(FEA) programs, which determine the stress and strain throughout structures by considering them as an array
of connected small volumes of material, is increasingly common. For a purely elastic calculation, the input
parameters of Young’s modulus and Poisson’s ratio are exactly the same as for an analytical stress analysis.
However, if plasticity is to be considered, then a yield stress is required plus a description of the amount of
plastic deformation that will occur at each stress above the yield point. This in effect requires input of the
entire stress-strain curve.
Measurement of the tensile properties of a material is most commonly performed using a uniaxial tensile
testing machine. A sample of material is clamped in the machine and the strain is induced by the application
of an ever-increasing stress (stress and strain being measured by suitable means). The exact method has
improved and evolved over time, but the general principle has remained the same for centuries. It is possible
[1]
to obtain the Young’s modulus of a material by other means, e.g. by using acoustic wave propagation , and
[2]
materials property reference sources often quote elasticity values obtained by just this method , but tensile
testing is the traditional method of choice for obtaining the yield stress and the plasticity part of the stress-
strain curve.
The uniaxial tensile test has the benefit of making a measurement that is very similar to the final application in
an easily understood way. However, it has a number of significant drawbacks.
⎯ It has proved surprisingly difficult to reduce the test uncertainty below the 10 % level, although recent
European projects have improved the identification and control of key uncertainties (EU project
TENSTAND). Alignment in the instrument and the methods used to measure strain are key sources of
uncertainty, as is the wide variety of algorithms used to obtain the tensile properties from the measured
data.
⎯ The material must be available in volumes large enough to be tested. Small-scale testing and micro-
tensile testing are becoming possible but have additional uncertainties.
⎯ It must be possible to machine the materials to a controlled geometry without damaging them or changing
their properties (in particular their work-hardened state).
⎯ The test is destructive and averaging includes uncertainties due to sample-to-sample inhomogeneity.
0.2 General information for indentation and tensile properties
The widespread use of FEA to simulate indentation force vs. displacement curves is ample evidence that
there is a direct forward link from a stress-strain curve to the indentation response of a material. However, the
increasing use of modelling and the attendant requirement to obtain the stress-strain curve as input to the
models raises the question of whether it is possible to solve the inverse problem, i.e. obtain a stress-strain
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ISO/TR 29381:2008(E)
curve from the indentation response of a material. If this were possible, it would remove many of the
drawbacks of tensile testing and revolutionize the availability of tensile property information. Nano-indentation
is able to measure microscopic volumes of material, thus the tensile properties of materials that exist only as
small particles or as surface treatments or coatings would become obtainable. Indentation testing can be
made portable and thus non-destructive, in situ, on-site testing would become available, with relatively little (or
no) sample preparation. Lifetime monitoring of real structures would become cheaper and easier without the
need for witness specimens.
[3]
In 1951, Tabor demonstrated empirically that there was clearly a relationship of some form between the
hardness response and the relative strain imposed by indentation, since plots of mean indentation pressure vs.
relative indentation size (the ratio of indent radius to indenter radius, a/R, see Figure 2) appeared to map onto
stress-strain curves for many metals.

NOTE For a sphere, the strain induced by the indenter is proportional to a/R and is therefore a function of depth.
Figure 2 — Spherical indentation
The availability of instrumented indentation has made the collection of such information a simple matter.
Indeed, there is a common instrumented indentation testing cycle, often called the ‘partial unloading’
[4]
method , which applies a progressively increasing force but stops at a series of steps where the force is
partially removed to obtain the top part of the force-removal curve necessary to obtain the contact stiffness
and contact depth (hence the contact radius, a) at that force. Progressively increasing and partially removing
the force on an indenter in this way allows a wide range of indentation sizes to be applied in the same place.
This makes it possible to make a truly local measurement of material response over a wide range of strains,
which might then be repeated with relative ease to form a map of the mechanical properties of a material.
This Technical Report is intended to be a summary of the state of the art in deriving tensile properties from the
indentation response of a material. Three approaches are described, and the key requirements, advantages
and drawbacks are summarized in table form. The three methods are:
a) representative stress and strain,
b) inverse FEA methods, and
c) neural networks.
All three methods have been shown to “work”, in that they are able to obtain from indentation data a stress vs.
strain relation that can be validated against tensile testing. However, more extensive intercomparison and
sensitivity analyses are necessary to establish the robustness of each method’s ability to identify the unique,
best solution to the problem.
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The three methods described all start from the assumption that input of the correct stress-strain curve into a
suitable FEA package will enable exact simulation of the observed indentation response. Therefore, in
principle, the inverse method is a brute force simulation, using all possible combinations of input parameters
until the best fit to the measured indentation response is found. Such an inverse method is the benchmark
method, as it can unambiguously identify the globally best solution and, if convergence is not possible, can
identify that fact and demonstrate where the lack of convergence lies. Surprisingly, the increasing availability
of distributed computing networks makes this less unlikely than it might at first seem. It is clear, however, that
any method that can economise on this amount of effort and obtain equivalent results (perhaps validated
against selected distributed computing solutions) would be preferable. All of the methods described here are,
in effect, different strategies for reducing the computing required by the user.
The representative stress vs. strain approach uses FEA to generate a one-off set of simulations, and uses
empirical fitting to this set of results to derive general results. These relationships then place only a very low
computational load on the user because no further FEA is required to obtain specific results. The best results
are obtained by grouping materials with similar stress vs. strain relationships and generating a set of
representative relationships for each group. Each group can be classified according to material hardening
behaviour, e.g. as power-law hardening material or linear hardening material. For blind testing, these
classifications can be made before testing by considering material factors such as magnetism and σ /E. The
y
key user requirement is therefore to ensure that the correct sets of empirical relationships are used for the
material being tested. This method is well suited to users of a small range of materials, or a range of similar
materials, who wish to check or track the material properties over time.
The class of inverse methods in this Technical Report are distinguished by retaining the need for the user to
perform some form of FEA simulation for each stress-strain curve obtained. A number of strategies for
reducing the computational load by using other information obtainable from the indentation experiments are
described. This method is the most flexible, in that it can obtain a result from an unknown material. It is
therefore well suited to users who have FEA ability and need to be able to test any material without prior
knowledge of what that material might be. This method typifies an approach wherein the objective is to find
values for material parameters that minimize the variation between the experimental indentation data and the
functional output by simulation. The values obtained by this method include uncertainties, and a proper
calculation of these uncertainties must be considered.
In the final category, the method is a trained neural network. This can be thought of as a sophisticated method
of encapsulating a large number of pre-generated FEA-derived solutions. The network is trained using a
particular material response model until it has developed a function that enables it to predict a result for
situations that fall between the exact solutions it has “learned”. This method therefore sits between the first
two methods. The computational load to run a neural network is much lower than FEA, and is in many ways a
“black box” to the user. It is able to deal with a wide range of unknown materials. However, it does have a limit
to its abilities, which is defined by the size and quality of the input data and the extent and validity of the
training process.
The objective of the methods described in this Technical Report is to derive a true stress-strain curve from
indentation data measured experimentally and to obtain tensile properties such as yield strength, tensile
strength and work-hardening exponent from the derived curve.
When using these methods to obtain tensile properties from indentation, it should be taken into account that
indentation is, by comparison with bulk uniaxial tensile testing, predominantly a local property measurement.
The mechanical response measured is from a very small volume of material close to the indentation site. This
has the benefit of high spatial resolution testing and enables property mapping. For instance, its localized
nature allows testing of the heat-affected zones of weldments, which cannot be tested destructively because
of their irregular shape and small volume.
It has also the drawback that a local measurement is not always representative of the bulk-averaged response.
Empirical observation indicates that indentation into metals creates a plastic deformation zone under the
indenter that typically extends below the surface to about ten times the indentation depth. This is a practical
limit to the region of validity of the information obtained, as beyond this depth the material is deformed only
elastically. For example, if a case-hardened material, where the surface properties differ significantly from
those of the bulk, were tested, the results would reflect the properties of the surface and not the bulk.
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ISO/TR 29381:2008(E)
The methods in this Technical Report allow the derivation of a true stress-strain curve for the material tested
by the application of particular models. Tensile properties, such as yield stress and ultimate tensile strength,
are then inferred from these curves, but are not directly measured. Thus, the tensile properties obtained by
the methods in this report are not intended to replace the requirement for destructive uniaxial tensile testing in
the laboratory, where conditions make this possible. One of the greatest advantages of the instrumented
indentation test (IIT) lies in non-destructive testing of in-service components in field applications where tensile
testing is not available. Table 1 summarizes the characteristics of the indentation method and tensile testing.
Table 1 — Comparison of the main features of the tensile test
and the instrumented indentation test (IIT)
Tensile test IIT

Properties characterized
Bulk (average) Local (surface)
Testing nature
Destructive Non-destructive
Sample preparation Machining Surface polishing
Laboratory (conventional) In-field
Potential examples
Large volume Small volume


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TECHNICAL REPORT ISO/TR 29381:2008(E)

Metallic materials — Measurement of mechanical properties
by an instrumented indentation test — Indentation tensile
properties
1 Scope
This Technical Report describes methods for evaluating tensile properties of metallic materials (true stress-
strain curve and derived parameters) using an instrumented indentation test.
The ranges of application of instrumented indentation tests are in line with the classification of ISO 14577-1,
but the range of force recommended is from 2 N to 3 kN.
This Technical Report includes the following three methods, all of which are sound in principle, are capable of
practical use and are appropriate for the specified materials.
⎯ Method 1: representative stress and strain;
⎯ Method 2: inverse analysis by FEA;
⎯ Method 3: neural networks.
In every method, tensile curves are derived from the experimentally measured indentation force-depth curve,
from which indentation tensile properties are evaluated. The three methods described all need different user
strategies and abilities to obtain the indentation tensile properties. The information required differs for each
method and is described in detail in Clause 5.
The main assumption in the three methods is the absence of residual stress within the test piece. Existing
residual stress can affect the estimation of indentation tensile properties. A procedure for evaluating residual
stress using an instrumented indentation test is given for reference in Annex A.
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
ISO 14577-1:2002, Metallic materials — Instrumented indentation test for hardness and materials
parameters — Part 1: Test method
ISO 14577-2:2002, Metallic materials — Instrumented indentation test for hardness and materials
parameters — Part 2: Verification and calibration of testing machines
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
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ISO/TR 29381:2008(E)
3.1
instrumented indentation test
IIT
test to appraise mechanical properties of a material by measuring test force and indentation depth when a test
piece is indented with an indenter
NOTE See ISO 14577-1.
3.2
indentation tensile properties
mechanical properties of materials such as indentation yield strength, indentation tensile strength and
indentation work-hardening exponent, obtained by analysing a true stress-strain curve determined by
instrumented indentation testing
4 Symbols and designations
For the purposes of this Technical Report, the symbols and designations in Table 2 are used.
Table 2 — Symbols and designations in common
Symbol Designation Unit
F Test force N
F Maximum test force N
max
h Indentation depth mm
h Maximum indentation depth at F mm
max max
h Depth of contact of the indenter with the test piece at F mm
c max
h Permanent indentation depth after removal of test piece at F mm
p max
R Radius of spherical indenter mm
2
A (h ) Projected area of the contact of the indenter at distance h from the tip mm
p c c
2
H Indentation hardness N/mm
IT
2
E Indentation modulus (Young’s modulus) N/mm
IT
2
σ Indentation yield strength N/mm
y,IT
2
σ Indentation tensile strength N/mm
u,IT
n Indentation work-hardening exponent —
IT
α Angle, specific to the shape of the sharp indenter °
2
σ True stress N/mm
T
ε True strain —
T
S Stiffness (the slope of tangent to unloading curve at F) N/mm
max
NOTE 1 To avoid very long numbers, the use of multiples or sub-multiples of the units is permitted.
2
NOTE 2 1 N/mm = 1 MPa.
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5 Descriptions of the different methods
5.1 Method 1: Representative stress and strain
5.1.1 Principle (see Figure 3)
True stress-strain points on the tensile curve are obtained by defining the stress and strain states in a material
at various indentation depths formed by a spherical indenter as representative stress-strain points. Indentation
tensile properties can be evaluated by fitting the constitutive equation to the true stress-strain points.

Key
a, b, c correlated constants
n strain hardening exponent
Figure 3 — Principle of Method 1
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ISO/TR 29381:2008(E)
5.1.2 Symbols and designations for Method 1
See Table 3.
Table 3 — Symbols and designations for Method 1
Symbol Designation Unit
*
h Height of plastic pile-up mm
pile
*
h Elastic contact depth mm
c
Projected area of the contact of the indenter at distance h correlated
2
c
A mm
* *
c
to h and h from the tip
pile c
Ψ Plastic constraint factor —
ξ Proportional constant of true strain and tanθ —
θ Half of contact angle °
K Strength coefficient —
ε True uniform strain —
u
NOTE For power-law hardening materials, Ψ = 3 and ξ = 0,14 are useful values.

5.1.3 Testing machine
The testing machine should be
⎯ capable of measuring and reporting applied force, indentation depth and time throughout the testing
cycle;
⎯ capable of applying predetermined test forces within the required scope of the test;
⎯ capable of applying test forces of multiple unloading;
⎯ protected from shock and vibration, air movements and variations in temperature that can significantly
influence the test result.
The indenter used should be a spherical indenter made of polished tungsten carbide or a material having
greater stiffness than that of the test piece. The user is referred to ISO 14577-2 for further specifications.
Further information on machine compliance, utilizing the appropriate indenter area function, indenter shapes
and temperature calibration, are found in Clause 5 of ISO 14577-1:2002;
5.1.4 Test piece
See Clause 6 of ISO 14577-1:2002 for a description of the test piece.
5.1.5 Procedure for obtaining force-depth curve
The user is referred to specifications in Clause 7 of ISO 14577-1:2002.
In order to avoid significant increase in testing machine compliance, firm support or fixing of the test piece is
recommended.
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The indentations should be positioned at least three times their indentation diameter from interfaces or free
surfaces; the distance between indentations should be at least five times the largest indentation diameter.
Partial repetition of the force-removal procedure and acquisition of indentation parameters such as F , h
max max
and S from each partial unloading is carried out to obtain the data necessary to generate the force-depth curve.
The testing cycle should be either indentation depth-controlled or force-controlled, with a full description of all
parts of the testing cycle given in the test report, including:
a) the nature of the control (i.e. force or displ
...