ISO/TR 29381:2008
(Main)Metallic materials — Measurement of mechanical properties by an instrumented indentation test — Indentation tensile properties
Metallic materials — Measurement of mechanical properties by an instrumented indentation test — Indentation tensile properties
ISO/TR 29381:2008 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 14577-1:2002, but the range of force recommended is from 2 N to 3 kN. ISO/TR 29381:2008 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. 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.
Matériaux métalliques — Mesure des caractéristiques mécaniques par un essai de pénétration instrumenté — Caractéristiques de traction par indentation
General Information
Standards Content (Sample)
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 2008
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ii © ISO 2008 – All rights reserved
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
Foreword
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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.
iv © ISO 2008 – All rights reserved
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.
⎯ 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
vi © ISO 2008 – All rights reserved
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 measurem
...
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