ASM Metals HandBook Vol. 8 - Mechanical Testing and Evaluation
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being performed as part of a product specification, and the elongation is specified to meet a value of 3% or less,
special techniques, which are described, are to be used to measure the final gage length. These measurements
are discussed in a previous section, “Elongation,” in this article.
Uniaxial Tension Testing
John M. (Tim) Holt, Alpha Consultants and Engineering
Variability of Tensile Properties
Even carefully performed tests will exhibit variability because of the nonhomogenous nature of metallic
materials. Figure 27 (Ref 10) shows the three-sigma distribution of the offset yield strength and tensile strength
values that were obtained from multiple tests on a single aluminum alloy. Distribution curves are presented for
the results from multiple tests of a single sheet and for the results from tests on a number of sheets from a
number of lots of the same alloy. Because these data are plotted with the minus three-sigma value as zero, it
appears there is a difference between the mean values; however, this appearance is due only to the way the data
are presented. Figures 28(a) and (b) show lines of constant offset yield strength and constant tensile strength,
respectively, for a 1 in. thick, quenched and tempered plate of an alloy steel. In this case, rectangular test pieces
1½ in. wide were taken along the transverse direction (T orientation in Fig. 20) every 3 in. along each of the
four test-piece centerlines shown. These data indicate that the yield and tensile strengths vary greatly within this
relatively small sample and that the shape and location of the yield strength contour lines are not the same as
the shape and location of the tensile strength lines.
Fig. 27 Distribution of (a) yield and (b) tensile strengths for multiple tests on single sheet
and on multiple lots of aluminum alloy 7075-T6. Source: Ref 10
Fig. 28 Contour maps of (a) constant yield strength (0.5% elongation under load, ksi) and
(b) constant tensile strength (ksi) for a plate of alloy steel
Effect of Strain Concentrations. During testing, strain concentrations (often called stress concentrations) occur
in the test piece where there is a change in the geometry. In particular, the transition radii between the reduced
section and the grip ends are important, as previously noted in the section on test-piece geometry. Most test
methods specify a minimum value for these radii. However, because there is a change in geometry, there is still
a strain concentration at the point of tangency between the radii and the reduced section. Figure 29(a) (Ref 11)
shows a test piece of rubber with an abrupt change of section, which is a model of a tension test piece in the
transition region. Prior to applying the force at the ends of the model, a rectangular grid was placed on the test
piece. When force is applied, it can be seen that the grid is severely distorted at the point of tangency but to a
much lesser degree at the center of the model. The distortion is a visual measure of strain. The strain
distribution across section n-n is plotted in Fig. 29(b). From the stress-strain curve for the material (Fig. 29c),
the stresses on this section can be determined. It is apparent that the test piece will yield at the point of tangency
prior to general yielding in the reduced section. The ratio between the nominal strain and actual, maximum
strain is often referred to as the strain-concentration factor, or the stress-concentration factor if the actual stress
is less than the elastic limit. This ratio is often abbreviated as k
t
. Studies have shown that k
t
is about 1.25 when
the radii are in., the width (or diameter) of the reduced section is 0.500 in., and the width (or diameter) of the
grip end is in. That is, the actual strain or the actual elastic stress at the transition (if less than the yield of the
material) is 25% greater than would be expected without consideration of the strain or stress concentration. The
value of k
t
decreases as the radii increase such that, for the above example, if the radii are 1.0 in., and k
t
decreases to about 1.15.
Fig. 29 Effect of strain concentrations on section n-n. (a) Strain distribution caused by an
abrupt change in cross section (grid on sheet of rubber) (Ref 11). (b) Schematic of strain
distribution on cross section (Ref 11). (c) Calculation of stresses at abrupt change in cross
section n-n by graphical means
Various techniques have been tried to minimize k
t
, including the use of spirals instead of radii, but there will
always be strain concentration in the transition region. This indicates that the yielding of the test piece will
always initiate at this point of tangency and proceed toward midlength. For these reasons, it is extremely
important that the radii be as large as feasible when testing materials with low ductility.
Strain concentrations can be caused by notches deliberately machined in the test piece, nicks from accidental
causes, or shear burrs, machining marks, or gouges that occur during the preparation of the test piece or from
many other causes.
Effect of Strain Rate. Although the mechanical response of different materials varies, the strength properties of
most materials tend to increase at higher strain rates. For example, the variability in yield strength of ASTM A
36 structural steel over a limited range of strain rates is shown in Fig. 30 (Ref 12). A “zero-strain-rate” stress-
strain curve (Fig. 31) is generated by applying forces to a test piece to obtain a small plastic strain and then
maintaining that strain until the force ceases to decrease (Point A). Force is reapplied to the test piece to obtain
another increment of plastic strain, which is maintained until the force ceases to decrease (Point B). This
procedure is continued for several more cycles. The smooth curve fitted through Points A, B, and so on is the
“zero-strain-rate” stress-strain curve, and the yield value is determined from this curve.
Fig. 30 Effect of strain rate on the ratio of dynamic yield-stress and static yield-stress
level of A36 structural steel. Source: Ref 12
Fig. 31 Stress-strain curves for tests conducted at “normal” and “zero” strain rates
The effect of strain rate on strength depends on the material and the test temperature. Figure 32 (Ref 13) shows
graphs of tensile strength and yield strength for a common heat-resistant low-alloy steel (2 Cr-1 Mo) over a
wide range of temperatures and strain rates. In this figure, the strain rates were generally faster than those
prescribed in ASTM E 8.
Fig. 32 Effect of temperature and strain rate on (a) tensile strength and yield strength of
2 Cr-1 Mo Steel. Note: Stain-rate range permitted by ASTM Method E8 when
determining yield strength at room temperature is indicated. Source: Ref 13
Another example of strain effects on strength is shown in Fig. 33 (Ref 14 ). This figure illustrates true yield
stress at various strains for a low-carbon steel at room temperature. Between strain rates of 10
-6
s
-1
and 10
-3
s
-1
(a thousandfold increase), yield stress increases only by 10%. Above 1 s
-1
, however, an equivalent rate increase
doubles the yield stress. For the data in Fig. 33, at every level of strain the yield stress increases with increasing
strain rate. However, a decrease in strain-hardening rate is exhibited at the higher deformation rates. For a low-
carbon steel tested at elevated temperatures, the effects of strain rate on strength can become more complicated
by various metallurgical factors such as dynamic strain aging in the “blue brittleness” region of some mild
steels (Ref 14).
Fig. 33 True stresses at various strains vs. strain rate for a low-carbon steel at room
temperature. The top line in the graph is tensile strength, and the other lines are yield
points for the indicated level of strain. Source: Ref 14
Structural aluminum is less strain-rate sensitive than steels. Figure 34 (Ref 15) shows data obtained for 1060-O
aluminum. Between strain rates of 10
-3
s
-1
and 10
3
s
-1
(a millionfold increase), the stress at 2% plastic strain
increases by less than 20%.
Fig. 34 Uniaxial stress/strain/strain rate data for aluminum 1060-O. Source: Ref 1
References cited in this section
10. W.P. Goepfert, Statistical Aspects of Mechanical Property Assurance, Reproducibility and Accuracy of
Mechanical Tests, STP 626, ASTM, 1977, p 136–144
11. F.B. Seely and J.O. Smith, Resistance of Materials, 4th ed., John Wiley & Sons, p 45
12. N.R.N. Rao et al., “Effect of Strain Rate on the Yield Stress of Structural Steel,” Fritz Engineering
Laboratory Report 249.23, 1964
13. R.L. Klueh and R.E. Oakes, Jr., High Strain-Rate Tensile Properties of 2¼ Cr-1 Mo Steel, J. Eng.
Mater. Technol., Oct 1976, p 361–367
14. M.J. Manjoine, Influence of Rate of Strain and Temperature on Yield Stresses of Mild Steel, J. Appl.
Mech., Vol 2, 1944, p A-211 to A-218
15. A.H. Jones, C.J. Maiden, S.J. Green, and H. Chin, Prediction of Elastic-Plastic Wave Profiles in
Aluminum 1060-O under Uniaxial Strain Loading, Mechanical Behavior of Materials under Dynamic
Loads, U.S. Lindholm, Ed., Springer-Verlag, 1968, p 254–269
16. “Standard Method of Sharp-Notch Tension Testing of High-Strength Sheet Materials,” E 338, ASTM
Uniaxial Tension Testing
John M. (Tim) Holt, Alpha Consultants and Engineering
References
1. D. Lewis, Tensile Testing of Ceramics and Ceramic-Matrix Composites, Tensile Testing, P. Han, Ed.,
ASM International, 1992, p 147–182
2. R.J. Del Vecchio, Tensile Testing of Elastomers, Tensile Testing, P. Han, Ed., ASM International, 1992,
p 135–146
3. N.E. Dowling, Mechanical Behavior of Materials—Engineering Methods for Deformation, Fracture,
and Fatigue, 2nd ed., Prentice Hall, 1999, p 123
4. R.L. Brockenbough and B.G. Johnson, “Steel Design Manual,” United States Steel Corporation,
ADUSS 27 3400 03, 1974, p 2–3
5. P.M. Mumford, Test Methodology and Data Analysis, Tensile Testing, P. Han, Ed., ASM International,
1992, p 55
6. “Standard Test Method for Young's Modulus, Tangent Modulus, and Chord Modulus,” E 111, ASTM
7. Making, Shaping, and Treating of Steel, 10th ed., U.S. Steel, 1985, Fig. 50-12 and 50-13
8. “Standard Test Methods and Definitions for Mechanical Testing of Steel Products,” A 370, Annex 6,
Annual Book of ASTM Standards, ASTM, Vol 1.03
9. “Conversion of Elongation Values, Part 1: Carbon and Low-Alloy Steels,” 2566/1, International
Organization for Standardization, revised 1984
10. W.P. Goepfert, Statistical Aspects of Mechanical Property Assurance, Reproducibility and Accuracy of
Mechanical Tests, STP 626, ASTM, 1977, p 136–144
11. F.B. Seely and J.O. Smith, Resistance of Materials, 4th ed., John Wiley & Sons, p 45
12. N.R.N. Rao et al., “Effect of Strain Rate on the Yield Stress of Structural Steel,” Fritz Engineering
Laboratory Report 249.23, 1964
13. R.L. Klueh and R.E. Oakes, Jr., High Strain-Rate Tensile Properties of 2¼ Cr-1 Mo Steel, J. Eng.
Mater. Technol., Oct 1976, p 361–367
14. M.J. Manjoine, Influence of Rate of Strain and Temperature on Yield Stresses of Mild Steel, J. Appl.
Mech., Vol 2, 1944, p A-211 to A-218
15. A.H. Jones, C.J. Maiden, S.J. Green, and H. Chin, Prediction of Elastic-Plastic Wave Profiles in
Aluminum 1060-O under Uniaxial Strain Loading, Mechanical Behavior of Materials under Dynamic
Loads, U.S. Lindholm, Ed., Springer-Verlag, 1968, p 254–269
Uniaxial Tension Testing
John M. (Tim) Holt, Alpha Consultants and Engineering
Selected References
• “Standard Method of Sharp-Notch Tension Testing of High-Strength Sheet Materials,” E 338, ASTM
• “Standard Method of Sharp-Notch Tension Testing with Cylindrical Specimens,” E 602, ASTM
• “Standard Methods and Definitions for Mechanical Testing of Steel Products,” A 370, ASTM
• “Standard Methods of Tension Testing of Metallic Foil,” E 345, ASTM
• “Standard Test Methods for Poisson's Ratio at Room Temperature,” E 132, ASTM
• “Standard Test Methods for Static Determination of Young's Modulus of Metals at Low and Elevated
Temperatures,” E 231, ASTM
• “Standard Test Methods for Young's Modulus, Tangent Modulus, and Chord Modulus,” E 111, ASTM
• “Standard Methods of Tension Testing of Metallic Materials,” E 8, ASTM
• “Standard Methods of Tension Testing Wrought and Cast Aluminum- and Magnesium-Alloy Products,”
B 557, ASTM
• “Standard Recommended Practice for Elevated Temperature Tension Tests of Metallic Materials,” E 21,
ASTM
• “Standard Recommended Practice for Verification of Specimen Alignment Under Tensile Loading,” E
1012, ASTM
Uniaxial Compression Testing
Howard A. Kuhn, Concurrent Technologies Corporation
Introduction
COMPRESSION LOADS occur in a wide variety of material applications, such as steel building structures and
concrete bridge supports, as well as in material processing, such as during the rolling and forging of a billet.
Characterizing the material response to these loads requires tests that measure the compressive behavior of the
materials. Results of these tests provide accurate input parameters for product-or process-design computations.
Under certain circumstances, compression testing may also have advantages over other testing methods.
Tension testing is by far the most extensively developed and widely used test for material behavior, and it can
be used to determine all aspects of the mechanical behavior of a material under tensile loads, including its
elastic, yield, and plastic deformation and its fracture properties. However, the extent of deformation in tension
testing is limited by necking. To understand the behavior of materials under the large plastic strains during
deformation processing, measurements must be made beyond the tensile necking limit. Compression tests and
torsion tests are alternative approaches that overcome this limitation.
Furthermore, compression-test specimens are simpler in shape, do not require threads or enlarged ends for
gripping, and use less material than tension-test specimens. Therefore, compression tests are often useful for
subscale testing and for component testing where tension-test specimens would be difficult to produce.
Examples of these applications include through-thickness property measurements in plates and forgings (Ref 1),
weld heat-affected zones, and precious metals (Ref 2) where small amounts of material are available.
In addition, characterizing the mechanical behavior of anisotropic materials often requires compression testing.
For isotropic polycrystalline materials, compressive behavior is correctly assumed to be identical to tensile
behavior in terms of elastic and plastic deformation. However, in highly textured materials that deform by
twinning, as opposed to dislocation slip, compressive and tensile deformation characteristics differ widely (Ref
3). Likewise, the failure of unidirectionally reinforced composite materials, particularly along the direction of
reinforcement, is much different in compression than in tension.
In this article, the characteristics of deformation during axial compression testing are described, including the
deformation modes, compressive properties, and compression-test deformation mechanics. Procedures are
described for the use of compression testing for measurement of the deformation properties and fracture
properties of materials.
References cited in this section
1. T. Erturk, W.L. Otto, and H.A. Kuhn, Anisotropy of Ductile Fracture—An Application of the Upset
Test, Metall. Trans., Vol 5, 1974, p 1883
2. W.A. Kawahara, Tensile and Compressive Materials Testing with Sub-Sized Specimens, Exp. Tech.,
Nov/Dec, 1990, p 27–29
3. W.A. Backofen, Deformation Processing, Addison-Wesley, Reading, MA, p 53
Uniaxial Compression Testing
Howard A. Kuhn, Concurrent Technologies Corporation
Deformation Modes in Axial Compression
Compression tests can provide considerable useful information on plastic deformation and failure, but certain
precautions must be taken to assure a valid test of material behavior. Figure 1 illustrates the modes of
deformation that can occur in compression testing. The buckling mode shown in Fig. 1(a) occurs when the
length-to-width ratio of the test specimen is very large, and can be treated by classical analyses of elastic and
plastic buckling (Ref 4). These analyses predict that cylindrical specimens having length-to-diameter ratios,L
/D, less than 5.0 are safe from buckling and can be used for compression testing of brittle and ductile materials.
Practical experience with ductile materials, on the other hand, shows that even L/D ratios as low as 2.5 lead to
unsatisfactory deformation responses. For these geometries, even slightly eccentric loading or nonparallel
compression plates will lead to shear distortion, as shown in Fig. 1(b). Therefore, L/D ratios less than 2.0 are
normally used to avoid buckling and provide accurate measurements of the plastic deformation behavior of
materials in compression.
Fig. 1 Modes of deformation in compression. (a) Buckling, when L/D > 5. (b) Shearing,
whenL/D > 2.5. (c) Double barreling, whenL/D > 2.0 and friction is present at the contact
surfaces. (d) Barreling, when L/D < 2.0 and friction is present at the contact surfaces. (e)
Homogenous compression, when L/D < 2.0 and no friction is present at the contact
surfaces. (f) Compressive instability due to work-softening material
Friction is another source of anomalous deformation in compression testing of ductile materials. Friction
between the ends of the test specimen and the compression platens constrains lateral flow at the contact
surfaces, which leads to barreling or bulging of the cylindrical surface. Under these circumstances, for L/D
ratios on the order of 2.0, a double barrel forms, as shown in Fig. 1(c), smaller L/D ratios lead to a single barrel,
as in Fig. 1(d). Barreling indicates that the deformation is nonuniform (i.e., the stress and strain vary throughout
the test specimen), and such tests are not valid for measurement of the bulk elastic and plastic properties of a
material. Barreling, however, can be beneficial for the measurement of the localized fracture properties of a
material, as described in the section “Instability in Compression” of this article.
If the compression test can be carried out without friction between the specimen and compression platens,
barreling does not occur, as shown in Fig. 1(e), and the deformation is uniform (homogenous). For
measurement of the bulk deformation properties of materials in compression, this configuration must be
achieved.
A final form of irregular deformation in axial compression is an instability that is the antithesis of necking in
tension. In this case, the instability occurs due to work softening of the material and takes the form of rapid,
localized expansion, as shown in Fig. 1(f).
Reference cited in this section
4. J.H. Faupel and F.E. Fisher, Engineering Design, John Wiley & Sons, 1981, p 566–592
Uniaxial Compression Testing
Howard A. Kuhn, Concurrent Technologies Corporation
Compressive Properties
The bulk elastic and plastic deformation characteristics of polycrystalline materials are generally the same in
compression and tension. As a result, the elastic-modulus, yield-strength, and work-hardening curves will be
the same in compression and tension tests. Fracture strength, ultimate strength, and ductility, on the other hand,
depend on localized mechanisms of deformation and fracture, and are generally different in tension and
compression testing. Anisotropic materials, such as composite materials and highly textured polycrystalline
materials, also exhibit considerable differences between tensile and compressive behaviors beyond initial
elastic response.
Measurements of bulk elastic modulus and yield strength require accurate measurements of the axial strain of
the material under compression testing. This is accomplished by attaching to the specimen an extensometer,
which uses a differential transformer or strain gages to provide an electronic signal that is proportional to the
displacement of gage marks on the specimen. Extensometers are most easily used in tension testing because
tension test specimens are long and provide ample space for attachment of the extensometer clips. Due to the
limitations noted in the previous section (Fig. 1a and b), compression-test specimens are considerably smaller
in length and make attachment of the extensometer clips difficult. Alternatively, a differential transformer can
be used to measure the displacement between the compression platen surfaces. Because the measurement is not
made directly on the specimen, however, elastic distortion and slight rotations of the platens during testing will
give false displacement readings.
Measurement of the work-hardening, or plastic-flow, curve of a material is best carried out by compression
testing, particularly if the application, such as bulk metalworking, requires knowledge of the flow behavior at
large plastic strains beyond the necking limit in tension testing. In this case, the strains are many orders of
magnitude larger than the elastic strains, and indirect measurement of the axial strain by monitoring the motion
of the compression platens is sufficiently accurate. Any systematic errors caused by elastic deformation of the
platens or test equipment are insignificant compared to the large plastic displacements of the compression
specimen.
The fracture strength of a material is much different in tension and compression. In tension, the fracture
strength of a ductile material is determined by its necking behavior, which concentrates the plastic deformation
in a small region, generates a triaxial stress state in the neck region, and propagates ductile fracture from voids
that initiate at the center of the neck region. The fracture strength of a brittle material in tension, on the other
hand, is limited by its cleavage stress.
In compression of a ductile material, necking does not occur, so the void generation and growth mechanism that
leads to complete separation in the tension test does not terminate the compression test. Ductile fractures can
form, however, on the barreled surface of a compression specimen with friction. These fractures generally grow
slowly and do not lead to complete separation of the specimen, so the load-carrying capacity of the material is
not limited. As a result, there is no definition of fracture strength in compression of ductile materials. Surface
cracks that may form on the barreled surface of compression tests with friction depend not only on the material,