True stress

kool

1. True Stress - True Strain Curve: Part One
Abstract:
During stress testing of a material sample, the stress–strain curve is a graphical
representation of the relationship between stress, obtained from measuring the load
applied on the sample, and strain, derived from measuring the deformation of the
sample. The nature of the curve varies from material to material.
A typical stress-strain curve is shown in Figure 1. If we begin from the origin and follow the graph a
number of points are indicated.


Figure 1: A typical stress-strain curve


Point A: At origin, there is no initial stress or strain in the test piece. Up to point A Hooke's Law is
obeyed according to which stress is directly proportional to strain. That's why the point A is also
known as proportional limit. This straight line region is known as elastic region and the material can
regain its original shape after removal of load.

Point B: The portion of the curve between AB is not a straight line and strain increases faster than
stress at all points on the curve beyond point A. Point B is the point after which any continuous
stress results in permanent, or inelastic deformation. Thus, point B is known as the elastic limit or
yield point.

Point C & D: Beyond the point B, the material goes to the plastic stage till the point C is reached. At

2. this point the cross- sectional area of the material starts decreasing and the stress decreases to
point D. At point D the workpiece changes its length with a little or without any increase in stress up
to point E.

Point E: Point E indicates the location of the value of the ultimate stress. The portion DE is called the
yielding of the material at constant stress. From point E onwards, the strength of the material
increases and requires more stress for deformation, until point F is reached.

Point F: A material is considered to have completely failed once it reaches the ultimate stress. The
point of fracture, or the actual tearing of the material, does not occur until point F. The point F is also
called ultimate point or fracture point.

If the instantaneous minimal cross-sectional area can be measured during a test along with P and L
and if the constant-volume deformation assumption is valid while plastic deformation is occurring,
then a true stress-strain diagram can be constructed.

The construction should consist of using the equation ε = log (L/L0) for true strain in the elastic and
initial plastic regions and the equation ε= log (A0/A) once significant plastic deformation has begun.
In practice, however, the equation ε= log (A0/A) is used for the entire strain range since the amount
of error introduced is usually negligible. The equation σ = P/A for true stress is valid throughout the
entire test.

Accurate construction of a true stress-strain diagram becomes exceedingly difficult if the plastic
deformation cannot be assumed to occur at a constant volume.

Finally, it should be mentioned that the neither the true stress-strain diagram nor the engineering
stress-strain diagram accounts for the fact that the state of stress within the necked-down region is
multiaxial. There is no simple way to account for the effect of this multiaxial state of stress on the
material’s response, so it is customarily ignored. A schematic representation of an engineering
stress-strain diagram and the corresponding true stress-strain diagram can be found in Figure 2.

3. Figure 2: Material properties determined from stress-strain diagrams: (a) Engineering stress-
strain diagram; (b) determination σ by the offset method; (c) true stress-strain diagram
True Stress - True Strain Curve: Part Two
Abstract:
Generally, the metal continues to strain-harden all the way up to fracture, so that the
stress required to produce further deformation should also increase. If the true stress,
based on the actual cross-sectional area of the specimen, is used, it is found that the
stress-strain curve increases continuously up to fracture. If the strain measurement is
also based on instantaneous measurements, the curve, which is obtained, is known as
a true-stress-true-strain curve.
The engineering stress-strain curve does not give a true indication of the deformation characteristics
of a metal because it is based entirely on the original dimensions of the specimen, and these

4. dimensions change continuously during the test. Also, ductile metal which is pulled in tension
becomes unstable and necks down during the course of the test.

Because the cross-sectional area of the specimen is decreasing rapidly at this stage in the test, the
load required continuing deformation falls off. The average stress based on original area likewise
decreases, and this produces the fall-off in the stress-strain curve beyond the point of maximum
load. Figure 1 shows the true stress-strain curves in tension at room temperature for various metals.


Figure 1: True stress-strain curves in tension at room temperature for various metals


Actually, the metal continues to strain-harden all the way up to fracture, so that the stress required to
produce further deformation should also increase. If the true stress, based on the actual cross-
sectional area of the specimen, is used, it is found that the stress-strain curve increases
continuously up to fracture. If the strain measurement is also based on instantaneous
measurements, the curve, which is obtained, is known as a true-stress-true-strain curve. This is
also known as a flow curve since it represents the basic plastic-flow characteristics of the material.

Any point on the flow curve can be considered the yield stress for a metal strained in tension by the
amount shown on the curve. Thus, if the load is removed at this point and then reapplied, the
material will behave elastically throughout the entire range of reloading.

5. The true stress  is expressed in terms of engineering stress s by


(1)


The derivation of Eq. (1) assumes both constancy of volume and a homogenous distribution of strain
along the gage length of the tension specimen. Thus, Eq. (1) should only be used until the onset of
necking. Beyond maximum load the true stress should be determined from actual measurements of
load and cross-sectional area.


(2)


The true strain  may be determined from the engineering or conventional strain e by

(3)

Figure 2. Comparison of engineering and true stress-strain curves


This equation is applicable only to the onset of necking for the reasons discussed above. Beyond
maximum load the true strain should be based on actual area or diameter measurements.


(4)


Figure 1 compares the true-stress-true-strain curve with its corresponding engineering stress-strain

6. curve. Note that because of the relatively large plastic strains, the elastic region has been
compressed into the y-axis. In agreement with Eqs. (1) and (3), the true-stress-true-strain curve is
always to the left of the engineering curve until the maximum load is reached. However, beyond
maximum load the high-localized strains in the necked region that are used in Eq. (4) far exceed the
engineering strain calculated from Eq. (1).

Frequently the flow curve is linear from maximum load to fracture, while in other cases its slope
continuously decreases up to fracture. The formation of a necked region or mild notch introduces
triaxial stresses, which make it difficult to determine accurately the longitudinal tensile stress on out
to fracture.
True Stress - True Strain Curve: Part
Three
Abstract:
The parameters that are usually determined from the true stress - true strain curve
include true stress at maximum load, true fracture stress, true fracture strain, true
uniform strain, true local necking strain, strain-hardening exponent and strength
coefficient.
True Stress at Maximum Load

The true stress at maximum load corresponds to the true tensile strength. For most materials
necking begins at maximum load at a value of strain where the true stress equals the slope of the
flow curve. Let u and u denote the true stress and true strain at maximum load when the cross-
sectional area of the specimen is Au. The ultimate tensile strength is given by



Eliminating Pmax yields


(1)

7. True Fracture Stress

The true fracture stress is the load at fracture divided by the cross-sectional area at fracture. This
stress should be corrected for the, triaxial state of stress existing in the tensile specimen at fracture.
Since the data required for this correction are often not available, true-fracture-stress values are
frequently in error.


True Fracture Strain

The true fracture strain f is the true strain based on the original area A0 and the area after fracture Af

(2)

This parameter represents the maximum true strain that the material can withstand before fracture
and is analogous to the total strain to fracture of the engineering stress-strain curve. Since Eq. (3) is
not valid beyond the onset of necking, it is not possible to calculate f from measured values of f.
However, for cylindrical tensile specimens the reduction of area q is related to the true fracture strain
by the relationship

(3)



True Uniform Strain

The true uniform strain u is the true strain based only on the strain up to maximum load. It may be
calculated from either the specimen cross-sectional area Au or the gage length Lu at maximum load.

Equation (3) may be used to convert conventional uniform strain to true uniform strain. The uniform
strain is often useful in estimating the formability of metals from the results of a tension test.

(4)

8. True Local Necking Strain

The local necking strain n is the strain required to deform the specimen from maximum load to
fracture.

(5)
True Stress - True Strain Curve: Part Four
Abstract:
This article describes strain-hardening exponent and strength coefficient, materials
constants which are used in calculations for stress-strain behaviour in work hardening,
and their application in some of the most commonly used formulas, such as Ludwig
equation.
The flow curve of many metals in the region of uniform plastic deformation can be expressed by the
simple power curve relation
(10)
where n is the strain-hardening exponent and K is the strength coefficient. A log-log plot of true
stress and true strain up to maximum load will result in a straight-line if Eq. (10) is satisfied by the
data (Fig. 1).

The linear slope of this line is n and K is the true stress at  = 1.0 (corresponds to q = 0.63). The
strain-hardening exponent may have values from n = 0 (perfectly plastic solid) to n = 1 (elastic solid),
see Fig. 2. For most metals n has values between 0.10 and 0.50, see Table 1.

It is important to note that the rate of strain hardening d /d, is not identical with the strain-
hardening exponent. From the definition of n

or

(11)

9. Figure 2. Log/log plot of true stress-strain curve




Figure 3. Various forms of power curve =K* 
n




Table 1. Values for n and K for metals at room temperature
Metal Condition n K, psi
0,05% C steel Annealed 0,26 77000
SAE 4340 steel Annealed 0,15 93000
0,60% C steel Quenched and tempered 1000
o
F 0,10 228000
0,60% C steel Quenched and tempered 1300
o
F 0,19 178000
Copper Annealed 0,54 46400
70/30 brass Annealed 0,49 130000


There is nothing basic about Eq. (10) and deviations from this relationship frequently are observed,
often at low strains (10
-3
) or high strains (1,0).

One common type of deviation is for a log-log plot of Eq. (10) to result in two straight lines with

10. different slopes. Sometimes data which do not plot according to Eq. (10) will yield a straight line
according to the relationship

(12)

Datsko has shown how 0, can be considered to be the amount of strain hardening that the material
received prior to the tension test.

Another common variation on Eq. (10) is the Ludwig equation

(13)

where 0 is the yield stress and K and n are the same constants as in Eq. (10). This equation may be
more satisfying than Eq. (10) since the latter implies that at zero true strain the stress is zero.

Morrison has shown that 0 can be obtained from the intercept of the strain-hardening point of the
stress-strain curve and the elastic modulus line by


The true-stress-true-strain curve of metals such as austenitic stainless steel, which deviate markedly
from Eq. (10) at low strains, can be expressed by


where e
K
is approximately equal to the proportional limit and n1 is the slope of the deviation of stress
from Eq. (10) plotted against . Still other expressions for the flow curve have been discussed in the
literature.

The true strain term in Eqs.(10) to (13) properly should be the plastic strain
p= total- E= total- /E
Engineering Stress-strain Curve: Part
One
Abstract:
The engineering tension test is widely used to provide basic design information on the
strength of materials and as an acceptance test for the specification of materials. In the
tension test a specimen is subjected to a continually increasing uniaxial tensile force
while simultaneous observations are made of the elongation of the specimen.
The shape and magnitude of the stress-strain curve of a metal will depend on its composition, heat
treatment, prior history of plastic deformation, and the strain rate, temperature, and state of stress

11. imposed during the testing. The parameters, which are used to describe the stress-strain curve of a
metal, are the tensile strength, yield strength or yield point, percent elongation, and reduction
of area. The first two are strength parameters; the last two indicate ductility.

An example of the engineering stress-strain curve for a typical engineering alloy is shown in Figure
1. From it some very important properties can be determined. The elastic modulus, the yield
strength, the ultimate tensile strength, and the fracture strain are all clearly exhibited in an accurately
constructed stress strain curve.

Figure 1: An example of the engineering stress strain curve for a typical engineering alloy

The elastic modulus, E (Young’s modulus) is the slope of the elastic portion of the curve (the steep,
linear region) because E is the proportionality constant relating stress and strain during elastic
deformation: σ = Eε.

The 0.2% offset yield strength is the stress value, σ0.2%YS of the intersection of a line (called the
offset) constructed parallel to the elastic portion of the curve but offset to the right by a strain of
0.002. It represents the onset of plastic deformation.

The ultimate tensile strength is the engineering stress value or σuts, at the maximum of the
engineering stress-strain curve. It represents the maximum load, for that original area, that the
sample can sustain without undergoing the instability of necking, which will lead inexorably to
fracture.

The fracture strain is the engineering strain value at which fracture occurred.

At the outset, though, a clear distinction must be made between a true stress-true strain curve and
an engineering stress-engineering strain curve. The difference is shown in Figure 2, which are
plotted, on the same axes, the stress-strain curve and engineering stress-strain curve for the same
material. The difference is also evident in the definitions of true stress-true strain and engineering

12. stress-engineering strain.


Figure 2: Comparison of engineering and true stress-strain curves

The engineering stress is the load borne by the sample divided by a constant, the original area. The
true stress is the load borne by the sample divided by a variable the instantaneous area. Note that
the true stress always rises in the plastic, whereas the engineering stress rises and then falls after
going through a maximum.

The maximum represents a significant difference between the engineering stress-strain curve and
the true stress-strain curve. In the engineering stress-strain curve, this point indicates the beginning
of necking. The ultimate tensile strength is the maximum load measured in the tension test divided
by the original area.
Engineering Stress-strain Curve: Part Two
Abstract:
The engineering tension test is widely used to provide basic design information on the
strength of materials and as an acceptance test for the specification of materials. The
parameters, which are used to describe the engineering stress-strain curve of a metal,
are the tensile strength, yield strength or yield point, percent elongation,
andreduction of area.
In the tension test a specimen is subjected to a continually increasing uniaxial tensile force while
simultaneous observations are made of the elongation of the specimen. An engineering stress-strain

13. curve is constructed from these measurements, Fig. 1.



Figure 1. The engineering stress-strain curve


It is obtained by dividing the load by the original area of the cross section of the specimen.

(1)

The strain used for the engineering stress-strain curve is the average linear strain, which is obtained
by dividing the elongation of the gage length of the specimen, d, by its original length.

(2)

Since both the stress and the strain are obtained by dividing the load and elongation by constant
factors, the load-elongation curve will have the same shape as the engineering stress-strain curve.
The two curves are frequently used interchangeably.

The general shape of the engineering stress-strain curve (Fig. 1) requires further explanation. In the
elastic region stress is linearly proportional to strain. When the load exceeds a value corresponding
to the yield strength, the specimen undergoes gross plastic deformation. It is permanently deformed
if the load is released to zero. The stress to produce continued plastic deformation increases with
increasing plastic strain, i.e., the metal strain-hardens. The volume of the specimen remains
constant during plastic deformation, A·L = A0·L0 and as the specimen elongates, it decreases
uniformly along the gage length in cross-sectional area.

14. Initially the strain hardening more than compensates for this decrease in area and the engineering
stress (proportional to load P) continues to rise with increasing strain. Eventually a point is reached
where the decrease in specimen cross-sectional area is greater than the increase in deformation
load arising from strain hardening. This condition will be reached first at some point in the specimen
that is slightly weaker than the rest. All further plastic deformation is concentrated in this region, and
the specimen begins to neck or thin down locally.

Because the cross-sectional area now is decreasing far more rapidly than strain hardening increases
the deformation load, the actual load required to deform the specimen falls off and the engineering
stress likewise continues to decrease until fracture occurs.


Tensile Strength
The tensile strength, or ultimate tensile strength (UTS), is the maximum load divided by the original
cross-sectional area of the specimen.

(3)

The tensile strength is the value most often quoted from the results of a tension test; yet in reality it
is a value of little fundamental significance with regard to the strength of a metal. For ductile metals
the tensile strength should be regarded as a measure of the maximum load, which a metal can
withstand under the very restrictive conditions of uniaxial loading. It will be shown that this value
bears little relation to the useful strength of the metal under the more complex conditions of stress,
which are usually encountered.

For many years it was customary to base the strength of members on the tensile strength, suitably
reduced by a factor of safety. The current trend is to the more rational approach of basing the static
design of ductile metals on the yield strength.

However, because of the long practice of using the tensile strength to determine the strength of
materials, it has become a very familiar property, and as such it is a very useful identification of a
material in the same sense that the chemical composition serves to identify a metal or alloy.

Further, because the tensile strength is easy to determine and is a quite reproducible property, it is
useful for the purposes of specifications and for quality control of a product. Extensive empirical
correlations between tensile strength and properties such as hardness and fatigue strength are often
quite useful. For brittle materials, the tensile strength is a valid criterion for design.

15. Engineering Stress-strain Curve: Part
Three
Abstract:
The engineering tension test is widely used to provide basic design information on the
strength of materials and as an acceptance test for the specification of materials. In the
tension test a specimen is subjected to a continually increasing uniaxial tensile force
while simultaneous observations are made of the elongation of the specimen. The
parameters, which are used to describe the stress-strain curve of a metal, are
the tensile strength, yield strength or yield point, percent elongation, and
reduction of area. The first two are strength parameters; the last two indicate ductility.
Measures of Yielding
The stress at which plastic deformation or yielding is observed to begin depends on the sensitivity of
the strain measurements. With most materials there is a gradual transition from elastic to plastic
behavior, and the point at which plastic deformation begins is hard to define with precision. Various
criteria for the initiation of yielding are used depending on the sensitivity of the strain measurements
and the intended use of the data.
1. True elastic limit based on micro strain measurements at strains on order of 2 x 10
-6
in | in. This
elastic limit is a very low value and is related to the motion of a few hundred dislocations.
2. Proportional limit is the highest stress at which stress is directly proportional to strain. It is
obtained by observing the deviation from the straight-line portion of the stress-strain curve.
3. Elastic limit is the greatest stress the material can withstand without any measurable
permanent strain remaining on the complete release of load. With increasing sensitivity of strain
measurement, the value of the elastic limit is decreased until at the limit it equals the true elastic
limit determined from micro strain measurements. With the sensitivity of strain usually employed
in engineering studies (10
-4
in | in), the elastic limit is greater than the proportional limit.
Determination of the elastic limit requires a tedious incremental loading-unloading test
procedure.
4. The yield strength is the stress required to produce a small-specified amount of plastic
deformation. The usual definition of this property is theoffset yield strength determined by the
stress corresponding to the intersection of the stress-strain curve and a line parallel to the elastic
part of the curve offset by a specified strain. In the United States the offset is usually specified as
a strain of 0.2 or 0.1 percent (e = 0.002 or 0.001).

(4)

16. A good way of looking at offset yield strength is that after a specimen has been loaded to its 0.2
percent offset yield strength and then unloaded it will be 0.2 percent longer than before the test. The
offset yield strength is often referred to in Great Britain as the proof stress, where offset values are
either 0.1 or 0.5 percent. The yield strength obtained by an offset method is commonly used for
design and specification purposes because it avoids the practical difficulties of measuring the elastic
limit or proportional limit.

Some materials have essentially no linear portion to their stress-strain curve, for example, soft
copper or gray cast iron. For these materials the offset method cannot be used and the usual
practice is to define the yield strength as the stress to produce some total strain, for example, e =
0.005.


Measures of Ductility
At our present degree of understanding, ductility is a qualitative, subjective property of a material. In
general, measurements of ductility are of interest in three ways:
1. To indicate the extent to which a metal can be deformed without fracture in metalworking
operations such as rolling and extrusion.
2. To indicate to the designer, in a general way, the ability of the metal to flow plastically before
fracture. A high ductility indicates that the material is "forgiving" and likely to deform locally
without fracture should the designer err in the stress calculation or the prediction of severe
loads.
3. To serve as an indicator of changes in impurity level or processing conditions. Ductility
measurements may be specified to assess material quality even though no direct relationship
exists between the ductility measurement and performance in service.
The conventional measures of ductility that are obtained from the tension test are the engineering
strain at fracture ef (usually called the elongation) and the reduction of area at fracture q. Both of
these properties are obtained after fracture by putting the specimen back together and taking
measurements of Lf and Af .

(5)

(6)
Because an appreciable fraction of the plastic deformation will be concentrated in the necked region
of the tension specimen, the value of efwill depend on the gage length L0 over which the
measurement was taken. The smaller the gage length the greater will be the contribution to the
overall elongation from the necked region and the higher will be the value of ef. Therefore, when
reporting values of percentage elongation, the gage length L0 always should be given.

17. The reduction of area does not suffer from this difficulty. Reduction of area values can be converted
into an equivalent zero-gage-length elongation e0. From the constancy of volume relationship for
plastic deformation A*L = A0*L0, we obtain

(7)
This represents the elongation based on a very short gage length near the fracture.

Another way to avoid the complication from necking is to base the percentage elongation on the
uniform strain out to the point at which necking begins. The uniform elongation eu correlates well with
stretch-forming operations. Since the engineering stress-strain curve often is quite flat in the vicinity
of necking, it may be difficult to establish the strain at maximum load without ambiguity. In this case
the method suggested by Nelson and Winlock is useful.
Steel properties at low and high
temperatures
Abstract:
Aircraft and chemical processing equipment are now required to work at subzero
temperatures and the behavior of metals at temperatures down to -150°C needs
consideration, especially from the point of view of welded design where changes in
section and undercutting at welds may occur.
Steel Properties at Low Temperatures
Aircraft and chemical processing equipment are now required to work at subzero temperatures and
the behavior of metals at temperatures down to -150°C needs consideration, especially from the
point of view of welded design where changes in section and undercutting at welds may occur.
An increase in tensile and yield strength at low temperature is characteristic of metals and alloys in
general. Copper, nickel, aluminium and austenitic alloys retain much or all of their tensile ductility
and resistance to shock at low temperatures in spite of the increase in strength.
In the case of unnotched mild steel, the elongation and reduction of area is satisfactory down to -
130°C and then falls off seriously. It is found almost exclusively in ferritic steels, however, that a
sharp drop in Izo-d value occurs at temperatures around 0°C (see Figs. 1 and 2).
The transition temperature at which brittle fracture occurs is lowered by:
 a decrease in carbon content, less than 0,15% is desirable
 a decrease in velocity of deformation
 a decrease in depth of `notch`
 an increase in radius of `notch`, e.g. 6 mm minimum
 an increase in nickel content, e.g. 9%

18.  a decrease in grain size; it is desirable, therefore, to use steel deoxidized with aluminium
normalized to give fine pearlitic structure and to avoid the presence of bainite even if tempered
subsequently
 an increase in manganese content; Mn/C ratio should be greater than 21, preferably 8.

Figure 1. (a) Yield and cohesive stress curves
(b) Slow notch bend test

(c) Effect of temperature on the Izod value of mild
steel

Figure 2. Effect of low temperatures on the mechanical
properties of steel in plain and notched conditions
Surface grinding with grit coarser than 180 and shot-blasting causes embrittlement at -100°C due to
surface work-hardening, which, however, is corrected by annealing at 650-700°C for 1 h. This heat-
treatment also provides a safeguard against the initiation of brittle fracture of welded structures by
removing residual stresses.

19. Where temperatures lower than -100°C or where notch-impact stresses are involved in equipment
operating below zero, it is preferable to use an 18/8 austenitic or a non-ferrous metal.
The 9% Ni steel provides an attractive combination of properties at a moderate price. Its excellent
toughness is due to a fine-grained structure of tough nickel-ferrite devoid of embrittling carbide
networks, which are taken into solution during tempering at 570°C to form stable austenite islands.
This tempering is particularly important because of the low ferrite-austenite transformation
temperatures.
A 4% Mn Ni (rest iron) is suitable for castings for use down to -196°C. Care should be taken to select
plates without surface defects and to ensure freedom from notches in design and fabrication. Fig. 3
shows tensile and impact strengths for various alloys.

Figure 3. Tensile and impact strengths of various alloys at subzero temperatures
Steel Properties at High Temperatures
Creep is the slow plastic deformation of metals under a constant stress, which becomes important
in:
1. The soft metals used at about room temperature, such as lead pipes and white metal bearings.
2. Steam and chemical plant operating at 450-550°C.
3. Gas turbines working at high temperatures.
Creep can take place and lead to fracture at static stresses much smaller than those which will break
the specimen when loaded quickly in the temperature range 0,5-0,7 of the melting point Tm.

20. The Variation with time of the extension of a metal under different stresses is shown in Fig. 4a.
Three conditions can be recognized:
 The primary stage, when relatively rapid extension takes place but at a decreasing rate. This is
of interest to a designer since it forms part of the total extension reached in a given time, and
may affect clearances.
 The secondary period during which creep occurs at a more or less constant rate, sometimes
referred to as the minimum creep rate. This is the important part of the curve for most
applications.
 The tertiary creep stage when the rate of extension accelerates and finally leads to rupture. The
use of alloys in this stage should be avoided; but the change from the secondary to the tertiary
stage is not always easy to determine from creep curves for some materials.


Figure 4. a) Family of creep curves at stresses increasing from
A to C

21. b) Stress-time curves at different creep strain and
repture
The limited nature of the information available from the creep curve is clearer when a family of
curves is considered covering a range of operating stresses.
As the applied stress decreases the primary stage decreases and the secondary stage is extended
and the extension during the tertiary stage tends to decrease. Modifying the temperature of the test
has a somewhat similar effect on the shape of the curves.
Design data are usually given as series of curves for constant creep strain (0,01-0,03%, etc.),
relating stress and time for a given temperature. It is important to know whether the data used are
for the secondary stage only or whether it also includes the primary stage (Fig. 4b).
In designing plants that work at temperatures well above atmospheric temperatures, the designer
must consider carefully what possible maximum strains he can allow and what the final life of the
plant is likely to be. The permissible amounts of creep depend largely on the article and service
conditions. Examples for steel are:
Rate of Creep mm/min Time, h
Maximum
Permissible Strain,
mm
Turbine rotor wheels, shrunk on shafts 10
-11
100000 0,0025
Steam piping, welded joints, boiler
tubes
10
-9
100000 0,075
Superheated tubes 10
-8
20000 0,5
In designing missiles data are needed at higher temperatures and stresses and shorter time (5-60
min) than are determined for creep tests. This data is often plotted as isochronous stress-strain
curves.
Creep tests
For long-time applications it is necessary to carry out lengthy tests to get the design data. It is
dangerous to extrapolate from short time tests, which may not produce all the structural changes,
e.g. spheroidation of carbide. For alloy development and production control short time tests are
used.
Long time creep tests
A uniaxial tensile stress is applied by the means of a lever system to a specimen (similar to that
used in tensile testing) situated in a tubular furnace and the temperature is very accurately
controlled. A very sensitive mirror extensometer (of Martens type) is used to measure creep rate of
1×10
-8
strain/h. From a series of tests at a single temperature, a limiting creep stress is estimated for
a certain arbitrary small rate of creep, and a factor of safety is used in design.
Short time tests
The rupture test is used to determine time-to-rupture under specified conditions of temperature and
stress with only approximate measurement of strain by dial gauge during the course of the
experiments because total strain may be around 50%. It is a useful test for sorting out new alloys

22. and has direct application to design where creep deformation can be tolerated but fracture must be
prevented.
Tensile Testing Of Metallic Materials
Abstract:
Tensile testing of metallic materials is specified according to European EN 10002
standard. In this article the terms, definitions and designation for tensile test made at
ambient temperature is described. The test involves straining a test piece in tension,
generally to fracture, for the purpose of determining mechanical properties.
Tensile testing of metallic materials is specified according to European EN 10002 standard. This
standards consists of five parts:
 EN 10002-1 - Method of testing at ambient temperature
 EN 10002-2 - Verification of the force measuring system of the tensile testing machine
 EN 10002-3- Calibration of force proving instruments used for the verification of uniaxial testing machines
 EN 10002-4 - Verification of extensometers used in uniaxial testing
 EN 10002-5 - Method of testing at elevated temperatures
In this article the terms, definitions and designation for tensile test made at ambient temperature is
described. The test involves straining a test piece in tension, generally to fracture, for the purpose of
determining mechanical properties.
Terms and definitions
For the purpose of this European Standard, the following terms and definitions apply:
 gauge length (L) - length of the cylindrical or prismatic portion of the test piece on which elongation is measured. In
particular, a distinction is made between:
o original gauge length (Lo) - gauge length before application of force
o final gauge length (Lu) - gauge length after rupture of the test piece
o parallel length (Lc) - parallel portion of the reduced section of the test piece
 elongation - increase in the original gauge length (Lo) at any moment during the test
 percentage elongation - elongation expressed as a percentage of the original gauge length (Lo)
 percentage permanent elongation - increase in the original gauge length of a test piece after removal of a specified
stress, expressed as a percentage of the original gauge length (Lo)
 percentage elongation after fracture (A) - permanent elongation of the gauge length after fracture (Lu - Lo),
expressed as a percentage of the original gauge length (Lo). In the case of proportional test pieces, where original
gauge length is other than 5.65√So, the symbol A should be supplemented by an index indicating the coefficient of
proportionality used (A11,3 for Lo=11.3√ So) or by an index indicating the original gauge length (A80 mm for Lo=80 mm)
 percentage elongation at maximum force - increase in the gauge length of the test piece at maximum force,
expressed as a percentage of the original gauge length (Lo)
 extensometer gauge length (Le) - length of the parallel portion of the test piece used for the measurement of
extension by means of an extensometer

23.  extension - increase in the extensometer gauge length (Le) at a given moment of the test
 percentage permanent extension - increase in the extensometer gauge length, after removal from the test piece of
a specified stress, expressed as a percentage of the extensometer gauge length (Le)
 percentage yield point extension (Ae) - in discontinuous yielding materials, the extension between the start of
yielding and the start of uniform work hardening
 percentage reduction of area (Z) - maximum change in cross-sectional area which has occurred during the test
(So - Su) expressed as a percentage of the original cross-sectional area (So)
 maximum force (Fm) - the greatest force which the test piece withstands during the test once the yield point has
been passed. For materials, without yield point, it is the maximum value during the test
 stress - force at any moment during the test divided by the original cross-sectional area (So) of the test piece
 tensile strength (Rm) - stress corresponding to the maximum force (Fm)
 yield strength - when the metallic material exhibits a yield phenomenon, stress corresponding to the point reached
during the test at which plastic deformation occurs without any increase in the force. A distinction is made between:
o upper yield strength (ReH) - value of stress at the moment when the first decrease in force is observed
o lower yield strength (ReL) - lowest value of stress during plastic yielding, ignoring any initial transient effects
 proof strength, non-proportional extension (Rp) - stress at which a non-proportional extension is equal to a
specified percentage of the extensometer gauge length (Le). The symbol used is followed by the suffix giving the
prescribed percentage, such as Rp0,2
 proof strength, total extension (Rt) - stress at which total extension (elastic extension plus plastic extension) is
equal to a specified percentage of the extensometer gauge length (Le). The symbol used is followed by the suffix
giving the prescribed percentage, such as Rt0,5
 permanent set strength (Rr) - stress at which, after removal of force, a specified permanent elongation or extension
expressed respectively as a percentage of the original gauge length (Lo) or extensometer gauge length (Le) has not
been exceeded
 fracture - phenomena which is deemed to occur when total separation of the test piece occurs or force decreases to
become nominally zero
Symbols and designations
Symbols and corresponding designations of the test piece are given in table 1.
The shape and dimensions of the test pieces depend on the shape and dimensions of the metallic
product from which the test pieces are taken (Figure1). Their cross-section may be circular, square,
rectangular, annular or, in special cases, of some other shape. The test piece is usually obtained by
machining a sample from the product or a pressed blank or casting. However, products of constant
cross-section and as cast test pieces may be tested without being machined.
Table 1. Symbols and designations of the test piece.
Reference
(Figure1)
Symbol Unit Designation
1. a mm
Thickness of a flat test piece or wall thickness of a
tube
2. b mm
Width of the parallel length of a flat test piece or
average width of the longitudinal strip taken from a

24. tube or width of flat wire
3. d mm
Diameter of the parallel length of a circular test
piece, or diameter of round wire or internal diameter
of a tube
4. D mm External diameter of a tube
5. Lo mm Original gauge length
- L`o mm Initial gauge length for determination of Ag
6. Lc mm Parallel length
- Le mm Extensometer gauge length
7. Lt mm Total length of test piece
8. Lu mm Final gauge length after fracture
- L`u mm
Final gauge length after fracture for determination of
Ag
9. So mm
2
Original cross-sectional area of the parallel length
10. Su mm
2
Minimum cross-sectional area after fracture
- k - Coefficient of proportionality
11. Z % Percentage reduction of area: (So - Su) / So x 100
12. - - Gripped ends

Figure 1. Typical standard test piece
The test piece shall be held by suitable means such as wedges, screwed grips, parallel jaw faces,
shouldered holders, etc. Every endeavour should be made to ensure that pieces are held in such a
way that the tension is applied as axially as possible in order to minimize bending. This is very
important for testing brittle materials or when determining proof or yield strength.
For determination of percentage elongation, the two broken test pieces are carefully fitted back
together so that their axis lie in a straight line. Elongation after fracture shall be determined to the
nearest 0.25 mm with a measuring device with a sufficient resolution and the value of percentage
elongation after fracture shall be rounded to the nearest 0.5% (Table 2). On the Figure 2 schematic
definitions of elongation are given.

25. Table 2. Different types of elongation
Reference
(Figure 2)
Symbol Unit Elongation
13. - mm Elongation after fracture: Lu - Lo
14. A %
Percentage elongation after fracture: (Lu - Lo) / Lo x
100
15. Ae % Percentage yield point extension
- Lm mm Extension at maximum force
16. Ag %
Percentage non-proportional elongation at maximum
force (Fm)
17. Agt % Percentage total elongation at maximum force (Fm)
18. At % Percentage total elongation at fracture
19. - % Specified percentage non-proportional extension
20. - % Percentage total extension
21. - %
Specified percentage permanent set extension or
elongation

Figure 2. Definitions of elongation
The designations and related curves for yield, proof and tensile strength are given in the Table 3 and
on the Figure 3.
Table 3. Symbols and designations for different types of strength

26. Reference
(Figure 3)
Symbol Unit Force and strength
22. Fm N Maximum force
- - - Yield strength -Proof strength -Tensile strength
23. ReH MPa Upper yield strength
24. ReL MPa Lower yield strength
25. Rm MPa Tensile strength
26. Rp MPa Proof strength, non-proportional extension
27. Rr MPa Permanent set strength
28. Rt MPa Proof strength, total extension
- E MPa Modulus of elasticity

Figure 3. Definitions of upper and lower yield strengths for different types of curves
The test report shall contain reference to the standard, identification of the test piece, specified
material, type of the test piece, location and direction of sampling test pieces and test results. In the
absence of sufficient data on all types of metallic materials it is not possible, at present, to fix values
of uncertainty for the different properties measured by tensile test.

27. Charpy Impact Test for Metallic Materials
Abstract:
Charpy impact test method for metallic materials is specified by European EN 10045
standard. This specification defines terms, dimension and tolerances of test pieces, type
of the notch (U or V), test force, verification of impact testing machines etc.
The test consists of breaking by one blow from a swinging pendulum, under conditions
defined by standard, a test piece notched in the middle and supported at each end. The
energy absorbed is determined in joules. This absorbed energy is a measure of the
impact strength of the material.
Charpy impact test method for metallic materials is specified by European EN 10045 standard. This
specification defines terms, dimension and tolerances of test pieces, type of the notch (U or V), test
force, verification of impact testing machines etc.
For certain particular metallic materials and applications, Charpy impact test may be the subject of
specific standards and particular requirements. The test consists of breaking by one blow from a
swinging pendulum, under conditions defined by standard, a test piece notched in the middle and
supported at each end. The energy absorbed is determined in joules. This absorbed energy is a
measure of the impact strength of the material.
The designations applicable to this standard are as indicated in the Table 1 and on the Figure1.
Table 1. Characteristics of test piece and testing machine
Reference
(Figure 1)
Designation Unit
1 Length of test piece mm
2 Height of test piece mm
3 Width of test piece mm
4 Height below notch mm
5 Angle of notch Degree
6 Radius of curvature of base of notch mm
7 Distance between anvils mm
8 Radius of anvils mm
9 Angle of taper of each anvil Degree
10 Angle of taper of striker Degree
11 Radius of curvature of striker mm
12 Width of striker mm
- Energy absorbed by breakage KU or KV Joule

28. Figure 1. Charpy impact test
Test pieces
The standard test piece shall be 55 mm long and of square section with 10 mm sides. In the centre
of the length, there shall be a notch. Two types of notch are specified:
a. V notch of 45°, 2 mm deep with a 0,25 mm radius of curve at the base of notch. If standard test
piece cannot be obtained from the material, a reduced section with a width of 7,5 mm or 5 mm
shall be used, the notch being cut in one of the narrow faces.

29. b. U notch or keyhole notch, 5 mm deep, with 1 mm radius of curve at the base of notch. The test
pieces shall be machined all over, except in the case of precision cast foundry test pieces in
which the two faces parallel to the plane of symmetry of the notch can be unmachined.
The plane of symmetry of the notch shall be perpendicular to the longitudinal axis of the test piece.
The tolerances of the specified dimensions of the test piece are given by standard as well. For the
standard test piece, machining tolerance in length is 0.6 mm for both type of tests, and tolerances in
height are 0.11 mm for U and 0.06 mm for V notch test piece. Tolerances for angle between plane of
symmetry of the notch and longitudinal axis of test piece as well as for angle between adjacent
longitudinal faces of test piece are ± 2° only.
Comparison of results is only of significance when made between test pieces of the same form and
dimensions. Machining shall be carried out in such a way that any alternation of the test piece, for
example due to cold working or heating, is minimized. The notch shall be carefully prepared so that
no grooves, parallel to the base of the notch, are visible to the naked eye. The test piece may be
marked on any face not in contact with the supports or anvils and at a point at least 5 mm from the
notch to avoid the effects of cold working due to marking.
Testing machine
The testing machine shall be constructed and installed rigidly and shall be in accordance with
European Standard 10 045 part 2.
Standard test condition shall correspond to nominal machine energy of 300±10J at the use of a test
piece of standard dimensions. The reported absorbed energy under these conditions shall be
designated by the following symbols:
 KU for a U notch test piece
 KV for a V notch test piece
Testing machines with different striking energies are permitted, in which case the symbol KU or KV
shall be supplemented by an index denoting the energy of the testing machine.
For example KV 150 denotes available energy of 150 J, and KU 100 denotes available energy of
100 J. KU 100 = 65 J means that:
 nominal energy is100 J
 standard U notch test piece is used
 energy absorbed during fracture is 65 J.
For tests on a subsidiary V notch test piece, the KV symbol shall be supplemented by indices
denoting first the available energy of the testing machine and second the width of the test piece,
e.g.:
 KV 300 / 7,5: available energy 300 J, width of test piece 7.5 mm
 KV 150 / 5: available energy 150 J, width of test piece 5 mm
 KV 150 / 7,5 = 83 J denotes:
o nominal energy 150 J
o reduced section test piece of width 7,5 mm
o energy absorbed during fracture: 83 J.

30. The test piece shall lie against the anvils in such a way that the plane of symmetry of the notch shall
be no more than 0.5 mm from the plane of symmetry of the anvils. If the test temperature is not
specified in the product standard, it shall be about 23°C.
National standards corresponding to EN 10045-2 are DIN 51306 (1983), NFA 03-508 (1985), BS
131 Part 4 (1972) and international ISO 442 (1965).
Hardenability testing
Abstract:
The rate at which austenite decomposes to form ferrite, pearlite and bainite is
dependent on the composition of the steel, as well as on other factors such as the
austenite grain size, and the degree of homogeneity in the distribution of the alloying
elements. It is extremely difficult to predict hardenability entirely on basic principles, and
reliance is placed on one of several practical tests, which allow the hardenability of any
steel to be readily determined.
The rate at which austenite decomposes to form ferrite, pearlite and bainite is dependent on the
composition of the steel, as well as on other factors such as the austenite grain size, and the degree
of homogeneity in the distribution of the alloying elements. It is extremely difficult to predict
hardenability entirely on basic principles, and reliance is placed on one of several practical tests,
which allow the hardenability of any steel to be readily determined.
The Grossman test
Much of the earlier systematic work on hardenability was done by Grossman and coworkers who
developed a test involving the quenching, in a particular cooling medium, of several cylindrical bars
of different diameter of the steel under consideration. Transverse sections of the different bars on
which hardness measurements have been made will show directly the effect of hardenability. In Fig
1, which plots this hardness data for an SAE 3140 steel (1.1-1.4% Ni, 0.55-0.75% Cr, 0.40% C) oil-
quenched from 815‹C, it is shown that the full martensitic hardness is only obtained in the smaller
sections, while for larger diameter bars the hardness drops off markedly towards the center of the
bar. The softer and harder regions of the section can also be clearly resolved by etching.
In the Grossman test, the transverse sections are metallographically examined to determine the
particular bar, which has 50% martensite at its center. The diameter of this bar is then designated
the critical diameter D0. However, this dimension is of no absolute value in expressing the
hardenability as it will obviously vary if the quenching medium is changed, e.g. from water to oil. It is
therefore necessary to assess quantitatively the effectiveness of the different quenching media. This
is done by determining coefficients for the severity of the quench usually referred to as H-
coefficients. The value for quenching in still water is set at 1, as a standard against which to
compare other modes of quenching.
Using the H-coefficients, it is possible to determine in place of D0, an ideal critical diameter Di which
has 50% martensite at the center of the bar when the surface is cooled at an infinitely rapid rate, i.e.

31. when H = ‡. Obviously, in these circumstances D0 = Di, thus providing the upper reference line in a
series of graphs for different values of H. In practice, H varies between about 0.2 and 5.0, so that if a
quenching experiment is carried out at an H-value of, say, 0.4, and D0 is measured, then the graph
can be used to determine Di. This value will be a measure of the hardenability of given steel, which
is independent of the quenching medium used.

Fig.1: Steel Ni-0.75Cr-0.4C. Hardness data from transverse sections through water-quenched bars
of increasing diameter
The Jominy and quench test
While the Grossman approach to hardenability is very reliable, other less elaborate tests have been
devised to provide hardenability data. Foremost amongst these is the Jominy test, in which a
standardized round bar (25.4 mm diameter, 102 mm long) is heated to the austenitizing temperature,
then placed on a rig in which one end of the rod is quenched by a standard jet of water (Fig.2).

32. Fig.2: The Jominy test: A - specimen size; B - quenching rig
This results in a progressive decrease in the rate of cooling along the bar from the quenched end,
the effects of which are determined by hardness measurements on flats ground 4 mm deep and
parallel to the bar axis (Fig. 3). A typical hardness plot for a En 19B steel containing 1% Cr,
0.25% Mo and 0.4% C, where the upper curve represents the hardness obtained with the upper limit
of composition for the steel, while the lower curve is that for the composition at the lower limit. The
area between the lines is referred to as a hardenability or Jominy band.
Additional data, which is useful in conjunction with these results, is the hardness of quenched steels
as a function both of carbon content and of the proportion of martensite in the structure. Therefore,
the hardness for 50% martensite can be easily determined for a particular carbon content and, by
inspection of the Jominy test results, the depth at which 50 % martensite is achieved can be
determined.

33. Fig.3: The Jominy and quench test
The Jominy test is now widely used to determine hardenabilities in the range Di = 1-6; beyond this
range the test is of limited use.
The results can be readily converted to determine the largest diameter round bar which can be fully
hardened. Fig. 4 plots bar diameter against the Jominy positions at which the same cooling rates as
those in the centers of the bars are obtained for a series of different quenches. Taking the ideal
quench (H = ‡) the highest curve, it can be seen that 12.5 mm along the Jominy bar gives a
cooling rate equivalent to that at the center of a 75 mm diameter bar. This diameter reduces to just
over 50 mm for a quench in still water (H = 1). With, for example, a steel which gives 50 %
martensite at 19 mm from the quenched end after still oil quenching (H = 0.3), the critical diameter
D0 for a round rod will be 51 mm.
The diagram in Fig. 4 can also be used to determine the hardness at the center of a round bar of a
particular steel, provided a Jominy end quench test has been carried out.

34. Fig.4: Equivalent Jominy positions and bar diameter, where the cooling rate for the bar center is the
same as that for the point in the Jominy specimen.
For example, if the hardness at the center of a 5 cm diameter bar, quenched in still water, is
required, Fig. 3 shows that this hardness will be achieved at about 12 mm along the Jominy test
specimen from the quenched end. Reference to the Jominy hardness distance plot, then gives the
required hardness value. If hardness values are required for other points in round bars, e.g. surface
or at half radius, suitable diagrams are available for use.
Hardness Testing
Abstract:
The hardness of a material is a poorly defined term which has many meanings
depending upon the experience of the person involved. In general, hardness usually
implies a resistance to deformation, and for metals the property is a measure of their
resistance to permanent or plastic deformation.
There are three general types of hardness measurements depending on the manner in
which the test is conducted. These are:
 scratch hardness
 indentation hardness, and
 rebound, or dynamic, hardness.
The hardness of a material is a poorly defined term which has many meanings depending upon the
experience of the person involved. In general, hardness usually implies a resistance to deformation,
and for metals the property is a measure of their resistance to permanent or plastic deformation. To

35. a person concerned with the mechanics of materials testing, hardness is most likely to mean the
resistance to indentation, and to the design engineer it often means an easily measured and
specified quantity which indicates something about the strength and heat treatment of the metal.
There are three general types of hardness measurements depending on the manner in which the
test is conducted. These are:
 scratch hardness
 indentation hardness, and
 rebound, or dynamic, hardness.
Only indentation hardness is of major engineering interest for metals.
Scratch hardness is of primary interest to mineralogists. With this measure of hardness, various
minerals and other materials are rated on their ability to scratch one another. Scratch hardness is
measured according to the Mohs’ scale. This consists of 10 standard minerals arranged in the order
of their ability lo be scratched. The softest mineral in this scale is talc (scratch hardness 1), while
diamond has a hardness of 10. The Mohs’ scale is not well suited for metals since the intervals are
not widely spaced in the high-hardness range. Most hard metals fall in the Mohs’ hardness range of
4 to 8.
In dynamic-hardness measurements the indenter is usually dropped onto the metal surface, and the
hardness is expressed as the energy of impact. The Shore seleroscope, which is the commonest
example of a dynamic-hardness tester, measures the hardness in terms of the height of rebound of
the indenter.
Brinell Hardness
The first widely accepted and standardized indentation-hardness test was proposed by J. A. Brinell
in 1900. The Brinell hardness test consists in indenting the metal surface with a 10-mm-diameter
steel ball at a load of 3,000 kg mass (∼29400 N). For soft metals the load is reduced to 500 kg to
avoid too deep an impression, and for very hard metals a tungsten carbide ball is used to minimize
distortion of the indenter. The load is applied for a standard time, usually 30 s, and the diameter of
the indentation is measured with a low-power microscope after removal of the load. The average of
two readings of the diameter of the impression at right angles should be made.
The Brinell hardness number (BHN) is expressed as the load P divided by the surface area of the
indentation. This is expressed by the formula:

where
P - applied load, N
D - diameter of ball mm
d - diameter of indentation, mm
t - depth of the impression, mm

36. It will be noticed that the units of the BHN are MPa.
Unless precautions are taken to maintain P/D2 constant, which may be experimentally inconvenient,
the BHN generally will vary with load. Over a range of loads the BHN reaches a maximum at some
intermediate load. Therefore, it is not possible to cover with a single load the entire range of
hardnesses encountered in commercial metals.
The relatively large size of the Brinell impression may be an advantage in averaging out local
heterogeneities. Moreover, the Brinell test is less influenced by surface scratches and roughness
than other hardness tests. On the other hand, the large size of the Brinell impression may preclude
the use of this test with small objects or in critically stressed parts where the indentation could be a
potential site of failure.
Meyer Hardness
Meyer suggested that a more rational definition of hardness than that proposed by Brinell would be
one based on the projected area of the impression rather than the surface area. The mean pressure
between the surface of the indenter and the indentation is equal to the load divided by the projected
area of the indentation. Meyer proposed that this mean pressure should be taken as the measure of
hardness. It is referred to as the Meyer hardness.
Like the Brinell hardness, Meyer hardness has units of MPa. The Meyer hardness is less sensitive to
the applied load than the Brinell hardness. For a cold-worked material the Meyer hardness is
essentially constant and independent of load, while the Brinell hardness decreases as the load
increases. For an annealed metal the Meyer hardness increases continuously with the load because
of strain hardening produced by the indentation. The Brinell hardness, however, first increases with
load and then decreases for still higher loads. The Meyer hardness is a more fundamental measure
of indentation hardness; yet it is rarely used for practical hardness measurements.
Meyer proposed an empirical relation between the load and the size of the indentation. This
relationship is usually called Meyer’s law.
P = kd
n’

The parameter n’ is the slope of the straight line obtained when log P is plotted against log d,
and k is the value of P at d = 1. Fully annealed metals have a value of n’ of about 2.5, while n’ is
approximately 2 for fully strain-hardened metals. This parameter is roughly related to the strain-
hardening coefficient in the exponential equation for the true-stress-true-strain curve. The exponent
in Meyer’s law is approximately equal to the strain-hardening coefficient plus 2.
Vickers Hardness
The Vickers hardness test uses a square-base diamond pyramid as the indenter. The included angle
between opposite faces of the pyramid is 136°. This angle was chosen because it approximates the
most desirable ratio of indentation diameter to ball diameter in the Brinell hardness test.
Because of the shape of the indenter, this is frequently called the diamond-pyramid hardness test.
The diamond-pyramid hardness number (DPH), or Vickers hardness number (VHN, or VPH), is

37. defined as the load divided by the surface area of the indentation. In practice, this area is calculated
from microscopic measurements of the lengths of the diagonals of the impression. The DPH may be
determined from the following equation:

where
P - applied load, kg
L - average length of diagonals, mm
θ - angle between opposite faces of diamond = 136°
The Vickers hardness test has received fairly wide acceptance for research work because it provides
a continuous scale of hardness, for a given load, from very soft metals with a DPH of 5 to extremely
hard materials with a DPH of 1,500. The Vickers hardness test is described in ASTM Standard E92-
72.
Rockwell Hardness Test
The most widely used hardness test is the Rockwell hardness test. Its general acceptance is due to
its speed, freedom from personal error, ability to distinguish small hardness differences in hardened
steel, and the small size of the indentation, so that finished heat-treated parts can be tested without
damage.
This test utilizes the depth of indentation, under constant load, as a measure of hardness. A minor
load of 10 kg is first applied to seat the specimen. This minimizes the amount of surface preparation
needed and reduces the tendency for ridging or sinking in by the indenter. The major load is then
applied, and the depth of indentation is automatically recorded on a dial gage in terms of arbitrary
hardness numbers.
The dial contains 100 divisions, each division representing a penetration of 0.00008 in (0.002 mm).
The dial is reversed so that a high hardness, which corresponds to a small penetration, results in a
high hardness number. This is in agreement with the other hardness numbers described previously,
but unlike the Brinell and Vickers hardness designations, which have units of MPa, the Rockwell
hardness numbers are purely arbitrary.
Major loads of 60, 100, and 150 kg are used. Since the Rockwell hardness is dependent on the load
and indenter, it is necessary to specify the combination which is used. This is done by prefixing the
hardness, number with a letter indicating the particular combination of load and indenter for the
hardness scale employed. A Rockwell hardness number without the letter prefix is meaningless.
Hardened steel is tested on the C scale with the diamond indenter and a 150-kg major load. The
useful range for this scale is from about RC 20 to RC 70. Softer materials are usually tested on the B
scale with a 1/16-in-diameter steel ball and a 100-kg major load. The range of this scale is from RB 0
to RB 100. The A scale (diamond penetrator, 60-kg major load) provides the most extended

38. Rockwell hardness scale, which is usable for materials from annealed brass to cemented carbides.
Many other scales are available for special purposes.
The Rockwell hardness test is a very useful and reproducible one provided that a number of simple
precautions are observed. Most of the points filled below apply equally well to the other hardness
tests:
 The indenter and anvil should be clean and well seated.
 The surface to be tested should be clean and dry, smooth, and free from oxide. A rough-ground surface is usually
adequate for the Rockwell test.
 The surface should be flat and perpendicular to the indenter.
 Tests on cylindrical surfaces will give low readings, the error depending on the curvature, load, indenter, and
hardness of the material. Theoretical and empirical corrections for this effect have been published.
 The thickness of the specimen should be such that a mark or bulge is not produced on the reverse side of the piece.
It is recommended that the thickness be at least 10 times the depth of the indentation. The spacing between
indentations should be three to five times the diameter of the indentation.
 The speed of application of the load should be standardized. This is done by adjusting the dashpot on the Rockwell
tester. Variations in hardness can be appreciable in very soft materials unless the rate of load application is carefully
controlled.
Microhardness Tests
Many metallurgical problems require the determination of hardness over very small areas. The
measurement of the hardness gradient at a carburized surface, the determination of the hardness of
individual constituents of a microstructure, or the checking of the hardness of a delicate watch gear
might be typical problems. The use of a scratch-hardness test for these purposes was mentioned
earlier, but an indentation-hardness test has been found to be more useful. The development of the
Knoop indenter by the National Bureau of Standards and the introduction of the Tukon tester for the
controlled application of loads down to 25 g have made micro hardness testing a routine laboratory
procedure.
The Knoop indenter is a diamond ground to a pyramidal form that produces a diamond-shaped
indentation with the long and short diagonals in the approximate ratio of 7:1 resulting in a state of
plane strain in the deformed region. The Knoop hardness number (KHN) is the applied load divided
by the unrecovered projected area of the indentation.
The special shape of the Knoop indenter makes it possible to place indentations much closer
together than with a square Vickers indentation, e.g., to measure a steep hardness gradient. The
other advantage is that for a given long diagonal length the depth and area of the Knoop indentation
are only about 15 percent of what they would be for a Vickers indentation with the same diagonal
length. This is particularly useful when measuring the hardness of a thin layer (such as an
electroplated layer), or when testing brittle materials where the tendency for fracture is proportional
to the volume of stressed material.
Hardness at Elevated Temperatures

39. Interest in measuring the hardness of metals at elevated temperatures has been accelerated by the
great effort which has gone into developing alloys with improved high-temperature strength. Hot
hardness gives a good indication of the potential usefulness of an alloy for high-temperature strength
applications.
In an extensive review of hardness data at different temperatures, Westbrook showed that the
temperature dependence of hardness could be expressed by
H = Ae
-BT

where
H = hardness, kg/mm
2

T = test temperature, K
A,B constants
Plots of log H versus temperature for pure metals generally yield two straight lines of different slope.
The change in slope occurs at a temperature which is about one-half the melting point of the metal
being tested. Similar behavior is found in plots of the logarithm of the tensile strength against
temperature. Above mentioned figure shows this behavior for copper. It is likely that this change in
slope is due to a change in the deformation mechanism at higher temperature.
The constant A derived from the low-temperature branch of the curve can be considered to be the
intrinsic hardness of the metal, that is, H at 0 K. Westbrook correlated values of A for different
metals with the heat content of the liquid metal at the melting point and with the melting point. This
correlation was sensitive to crystal structure.
The constant B, derived from the slope of the curve, is the temperature coefficient of hardness. This
constant was related in a rather complex way to the rate of change of heat content with increasing
temperature. With these correlations it is possible to calculate fairly well the hardness of a pure
metal as a function of temperature up to about one-half its melting point.