ASM Metals HandBook Vol. 8 - Mechanical Testing and Evaluation

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Strain Rate, J. Eng. Mater. Technol. (Trans. ASME), Vol 108 (No. 1), 1986, p 75–80

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During Strip Rolling Using High Strain Rate Torsion Testing, Int. Conf. on Physical Metallurgy of

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Shock Wave Phenomena, Marcel Dekker, 1986, p 633–656

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Behavior of Materials, Vol 1, DGM Informationsgesellschaft mbH, 1988, p 93–110

• D.J. Steinberg, Constitutive Model Used in Computer Simulation of Time-Resolved, Shock-Wave Data,

Hypervelocity Impact, 21–24 Oct 1986 (San Antonio, TX), Int. J. Impact Eng., Vol 5 (No. 1–4), 1987, p

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Data,” Lawrence Livermore National Laboratory, Report DE87008471/GAR, 1987, p 9

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Phys., Vol 58 (No. 2), 1985, p 692–701

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During High Strain-Rate

Deformation, Acta Metall., Vol 33 (No. 12), 1985, p 2143–2153

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High Strain Rate, Hot Torsion, Strength of Metals and Alloys, 12–16 Aug 1985 (Montreal), ICSMA 7,

Vol 2, Pergamon Press Ltd., 1985, p 905–910

• H.S. Yadav and N.K. Gupta, Study of Collapse of a Free Surface Conical Cavity Due to a Plane or

Spherical Shock Wave, Int. J. Impact. Eng., Vol 3 (No. 4), 1985, p 217–232

• S. Yoshimura, K.L. Chen, and S.N. Atluri, A Study of Two Alternate Tangent Modulus Formulations

and Attendant Implicit Algorithms for Creep as Well as High-Strain-Rate Plasticity, Int. J. Plast., Vol 3

(No. 4), 1987, p 391–413

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Dynamic Crack Propagation in a Visco-Plastic Solid, Nucl. Eng. Des., Vol 3 (No. 2), 1989, p 273–289

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Strain Rate, Acta Metall. Sin. (China), Vol 22 (No. 1), 1986, p B31–B39

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Characteristics, Int. Met. Rev., Vol 17, review 161, 1972, p 66–78

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and Lectures, No. 46, Springer-Verlag, 1970

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• H. Kolsky, Stress Waves in Solids, Oxford University Press, London, 1953

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• U.S. Lindholm, Ed., Mechanical Behavior of Materials Under Dynamic Loads, Springer-Verlag, 1968

• U.S. Lindholm and R.L. Bessey, “A Survey of Rate Dependent Strength Properties of Metals,”

Technical Report 69–199, Air Force Materials Laboratory, Wright-Patterson Air Force Base, Dayton,

OH, 1969

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Press, 1981

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Swift, L.B. Greszczuk, and D.R. Curran, Ed., John Wiley & Sons, 1981, p 277–331

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Rates, Plenum Press, 1973

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High Strain Rate Shear Testing

Introduction

SHEAR DEFORMATION is encountered in several types of processing operations, such as punching, grinding,

machining, forming, and events or processes that result in penetration. Using adequate models (like von Mises,

Tresca, Nadai-Tresca, and Nadai-von Mises), one can convert mechanical properties from tension and

compression testing to shear stress and shear strain; however, this conversion seldom extends into a high strain

range. The limit is frequently about 20% strain, which is far less than the strains reached in the aforementioned

applications. At higher plastic strains, the deviation between results can become quite significant, with axial

tests invariably providing higher values on flow stress than shear tests provide (after conversion by either the

von Mises or Tresca flow rule). Therefore, to accurately predict mechanical behavior at high strain (especially

for nonisotropic materials), testing for shear behavior should be performed directly in shear at the appropriate

level of strain, temperature, and strain rate for a given operation. In addition to immediate practical

applications, high strain rate shear data are invaluable for the development of macroscopic constitutive models

and for studies into possible deformation mechanisms for metals. Macroscopic results can be combined with

microscopic observations to make fundamental contributions to the development of constitutive equations

based on the micromechanisms that are dominant during deformation at a particular rate and temperature.

Shear and torsion testing also have some advantages over uniaxial testing in tension or compression testing. In

particular, with the absence of a Poisson ratio effect, complications caused by radial expansion or contraction

are eliminated during shear and torsion testing. The problems of necking, which occurs in tension tests, and

barreling, which occurs in compression tests, thus, do not occur in shear and torsion testing. Furthermore, due

to the Poisson ratio effect, radial expansion or contraction of stress waves during the initial phase of axial high-

speed tests is opposed by a radial inertia that becomes greater with a shorter pulse and larger amplitude. This

results in a short-pulse radial stress component in the specimen superposed on the axial stress component.

Hence, in axial loading, the state of stress in the specimen is only at constant strain rates. In torsional testing,

however, the inertial and frictional effects from radial expansion or contraction do not occur. The torsional

inertia stresses still remain. Nevertheless, this is one consideration that originally led to the development of the

torsional Kolsky bar, and it has since been shown that the strain rate sensitivities determined by torsion tests on

a variety of materials compare more or less well with those determined by axial tests.

Another advantage of torsion testing at high strain rates is the absence of geometric dispersion. When an axial

stress pulse (tension or compression) travels down a cylindrical bar, the pulse undergoes geometric dispersion;

that is, the different frequency components in an axial pulse have different velocities. In contrast, there is no

geometric dispersion when a torsional pulse travels along an elastic bar in its primary mode; that is, all

frequency components of the torsional pulse have the same velocity. Hence, a torsional pulse initiated either by

explosive detonation or by the release of a stored torque does not change its shape as it propagates toward the

specimen.

On the other hand, with torsion testing, some disadvantages must be considered:

• All tube specimens imply a stress and strain gradient from the inner to the outer wall diameter that can

be diminished by using a relative thin-wall thickness and a large diameter. The limit of “slenderness” is

given by elastic buckling before yielding or plastic buckling while yielding.

• Upper and lower yield stresses, connected with Lüders bands, are flattened out because of the inability

to local compliance.

• Flat products are often unsuited for torsion testing because of nonrotational texture distribution.

This article briefly reviews the dynamic factors and experimental methods for high strain rate shear testing by

the methods listed in Table 1. As for axial loading, a variety of testing machines are available for shear loading.

Selection usually depends on the rate of deformation required. A servo-hydraulic machine provides the most

convenient testing method for rates up to about 10 s

-1

, provided that precautions are observed for wave

propagation effects within the loading column. Wave propagation effects place an upper theoretical limit on the

attainable strain rates. Hence, other methods of testing become necessary. Torsional impact loading has been

widely used to obtain strain rates up to about 10

-1

. Between strain rates of 10

and 10

-1

, the torsional

Kolsky (or split-Hopkinson) bar has proven to be a very convenient method of testing. Other methods of high

strain rate shear testing include double shear and punching, which provide somewhat higher rates than the

torsional Kolsky bar. For rates above 10

up to approximately 10

-1

, plate impact tests are used to subject thin

specimens to combined pressure and shear.

Table 1 Shear tests for high strain rate conditions

Testing technique

Application strain rate, s

-1

Conventional shear

<0.1

Special servo-hydraulic frames

0.1 to 100

Torsional impact

10 to 10

Hopkinson (Kolsky) bar in torsion

to 10

Double-notch shear and punch

to 10

Pressure-shear plate impact 10

to 10

All of the techniques described in this article are capable of producing a complete stress-strain curve for a given

material. Based on a combination of results obtained from tests using the methods already described, a

complete analysis of material behavior in shear over a wide range of dynamic rates (10 to 10

-1

) can be

obtained. For penetration, punching, machining, etc., a strain rate range of 10

to 10

-1

is of particular interest,

but knowledge of material response over the entire range is very useful. For strain rates up to approximately 10

-1

, the lower yield stress is often found to be proportional to the logarithm of strain rate. At strain rates in

excess of 10

-1

, the lower yield stress is often found to be directly proportional to strain rate, rather than to the

logarithm of strain rate. This implies a new region of mechanical response controlled by a viscous damping

mechanism, in contrast to thermally activated processes at strain rates below 10

-1

High Strain Rate Shear Testing

High Strain Rate Torsion Testing

High strain rate torsion testing involves the use of high-speed hydraulic machines, torsional impact devices, or

the Kolsky (split-Hopkinson) bar.

High Strain Rate Shear Testing

High-Speed Hydraulic Torsional Machines

Hydraulic torsion test machines can be used as an alternative to mechanically driven torsional devices to

provide transient loading. High-speed hydraulic torsion machines are analogous to axial test machines, but a

torsional actuator is used instead of a standard linear hydraulic actuator. A typical high-speed torsional system

without the possibility of compensating axial loads is illustrated schematically in Fig. 1 (Ref 1). As in the

torsional impact device discussed in the next section of this article, a stiff loading system and reaction frame are

required, as well as low inertia in the moving parts. As illustrated in Fig. 1, these requirements are

accomplished by enclosing the system, which features an integral actuator shaft, specimen, and load transducer,

within a rigid housing. The vaned torsional actuator allows a rotation of about 3 rad.

Fig. 1 Dynamic hydraulic torsion test facility. Source: Ref 1

Hydraulic loading of the actuator is maintained by a servovalve and servo-control loop for operating at low

rotational velocities, which provide shear strain rates to about 10 s

-1

. For higher velocities, a solenoid-triggered

quick-release valve conveys pressure from an accumulator directly to the actuator. In this open-loop mode,

strain rates of up to 300 s

-1

have been reported.

In contrast to mechanical impact devices, the rotary actuator shaft, specimen, and load transducer are initially

attached (as in a standard test machine), and no transient mechanical engagement or impact is involved. This

facilitates maintenance of coaxiality and alignment. However, the specimen still undergoes a rapid acceleration

at the higher speeds, and inertial or resonance effects are still experienced by the load transducer.

Figure 2 illustrates a typical record of shear stress, τ, and shaft rotation, θ, as a function of time. The rotation is

obtained from a rotary capacitance transducer that is attached to the bottom of the actuator shaft. The load

transducer is a strain-gage element placed between the specimen and upper housing. Dynamic effects or

“ringing” in the load signal are evident. Finite element analysis of the shaft, specimen, and load transducer

system can be used to ensure that the mean signal from the load transducer is an accurate representation of the

shear stress in the specimen. The computed and measured stresses are compared in Fig. 2. Such dynamic

analysis is often required for proper interpretation or verification of dynamic test procedures. The specimen

geometry is similar to that used with torsional impact devices (thin-walled with a gage length of 3.2 mm, 6.4

mm inner radius θ

max

≈ 2.5 radians).

Fig. 2 Comparison of computed response with experimental results for dynamic torsion test. Source: Ref

Such short specimens of L/D = are preferable for reading high strain at high-strain rates. In order to reach a

stress and strain field as homogeneous as possible, longer gage lengths than the gage radius must be taken. An

L/D ratio of 1 seems to be a minimum (Ref 2). An L/D ratio of 2 is better.

References cited in this section

1. U.S. Lindholm, A. Nagy, G.R. Johnson, and J.M. Hoegfeldt, Large Strain, High Strain Rate Testing of

Copper, J. Eng. Mater. Technol. (Trans. ASME), Vol 102, 1980, p 376–381

2. K. Stiebler, Beitragzum Flieβverhalten der Stähle Ck35 und X2CoNiMnMoNNb211653 unter

zweiachsiger dynamisher Belastung, Ph.D. thesis, RWTH Aachen, Germany, 1989

High Strain Rate Shear Testing

Torsional Impact Testing

Torsional impact loading methods have been used with a number of testing devices that were developed to test

metals at strain rates up to about 10

-1

(Ref 3, 4, 5, 6, 7). Early tests of this type used solid, round specimens.

More recently, short, thin-walled tubular specimens in which nearly homogeneous stress and strain states can

be achieved have been used.

The devices generally consist of a stationary supported specimen, initially uncoupled from the drive

mechanism. The energy to deform the specimen is stored in a rotating flywheel and/or a drive shaft. The

rotating system is brought to the desired angular velocity, and a release and engagement mechanism quickly

couples the torsional load to the specimen.

Torsional impact systems require the following conditions:

• Alignment and concentricity of the specimen with the drive and engagement system

• Low inertia and high stiffness of the load train to minimize inertial effects and resonances during impact

• Adequate frequency response in the load-measuring and strain-measuring devices

• Sufficient energy in the drive system to maintain nearly constant strain rate in the test specimen during

deformation

A typical torsional impact system is illustrated in Fig. 3. In this device, a commercial lathe bed and drive

mechanism are utilized; however, the arrangement is typical of all torsional impact systems. The specimen is

rotated in the chuck of the lathe, which has speeds from 500 to 2000 rpm. Other devices attach either the drive

unit or the specimen to a flywheel, which is driven by a variable-speed motor. In either case, the drive unit is

brought up to constant rotational speed before engagement of the specimen.

Fig. 3 Cross section of torsional impact machine. Source: Ref 4

When the rotational speed is established, a release mechanism (the trigger rod in Fig. 3) allows a compressed

drive spring to engage the drive unit with the specimen by means of mated, tapered engagement beads. In the

mechanical design of this type of device, alignment, coaxiality, and details of the engagement mechanism are

important. An alternative to the arrangement in Fig. 3 consists of a stationary specimen and load cell and a

rotating drive unit. Such an arrangement is described in Ref 4.

Torsional load is measured with a strain-gage elastic tubular element in the load train. The stiffness of this gage

section should be as high as possible so that torsional resonances of the system induced by the impact on

engagement do not produce excessive “ringing” in the load signal. These resonant frequencies are also

governed by the total length of the load train between the rigid supports.

The mean shear strain rate,

, in the specimen is related to the angular velocity of the two ends of the

specimen by:

where

(Eq 1)

and where R

and R

are the outer and inner radii, respectively, and L is the length of the specimen gage section.

Typical gage section dimensions are on the order of 3.2 mm (0.125 in.) in length, 6.4 mm (0.250 in.) in radius,

and 0.76 mm (0.030 in.) in wall thickness. Thus, the shear strain rate is approximately twice the rotational

speed of the drive mechanism.

Depending on the total angle of twist (θ) allowed, very large strains can be achieved, often in the range of γ = 1

to 5. Because such large strains generally are involved, the rotational velocity (either initial or transient) is used

to determine strain rate (Eq 1) or strain. If the energy stored in the drive mechanism is large compared with the

strain energy to deform the specimen, a nearly constant strain rate can be assumed to be proportional to the

initial θ. Generally, direct strain measurements on the specimen are seldom made. Only Stiebler (Ref 2 and 3)

has used strain gages; Meyer and Hahn have used stream gages as high-speed electro-optical devices. A

photographic technique employing a drum camera to record the transient strain distribution in the specimen

during deformation is described in Ref 4.

A significant aspect of dynamic torsion testing is the occurrence of plastic instabilities due to thermal feedback

when the test conditions approach adiabatic deformation (Ref 2, 7, 8). For fully adiabatic conditions, the

temperature rise, ΔT

, in the specimen is given by:

(Eq 2)

where τ and γ are the shear stress and strain, respectively; k is a proportionality constant (ratio of plastic work

converted to thermal energy); ρ is density; and C is specific heat. Instability occurs when the thermal softening

due to the adiabatic temperature rise overcomes the intrinsic strain-hardening capacity of the test material.

Observation of adiabatic shear instabilities in torsion test specimens are reported in Ref 2, 4, and 8. Depending

on material properties and specimen geometry, such instabilities occur in the strain rate range from 10 to 10

-1

When instability occurs, sharp temperature and strain gradients may arise in the specimen. Transient

measurement of these profiles is difficult, but post-test examination of the test specimen may reveal the

existence of localized straining in the form of either deformation bands or, in some cases (e.g., steels),

transformation bands (Ref 7, 8).

References cited in this section

2. K. Stiebler, Beitragzum Flieβverhalten der Stähle Ck35 und X2CoNiMnMoNNb211653 unter

zweiachsiger dynamisher Belastung, Ph.D. thesis, RWTH Aachen, Germany, 1989

3. K. Stiebler, H.-D. Kunze, and E. El-Magd, Description of the Flow Behaviour of a High Strength

Austenitic Steel under Biaxial Loading by a Constitutive Equation, Nuclear Engineering and Design,

Vol 127, 1991

4. R.S. Culver, Torsional-Impact Apparatus, Exp. Mech., Vol 12, 1972, p 398–405

5. C.E. Work and T.J. Dolan, The Influence of Strain Rate and Temperature on the Strength and Ductility

of Mild Steel in Torsion, Proc. ASTM, Vol 53, 1953, p 611–626

6. N.G. Calvert, Impact Torsion Experiments, Inst. Mech. Eng., Vol 169 (No. 44), 1955, p 897

7. R.S. Culver, Thermal Instability Strain in Dynamic Plastic Deformation, Metallurgical Effects at High

Strain Rates, R.W. Rohde, B.M. Butcher, J.R. Holland, and C.H. Karnes, Ed., Plenum Press, 1973, p

519–530

8. U.S. Lindholm and G.R. Johnson, Strain-Rate Effects in Metals at Large Shear Strains, Material

Behavior under High Stress and Ultrahigh Loading Rates, J. Mescall and V. Weiss, Ed., Plenum Press,

1983, p 61–79

High Strain Rate Shear Testing

Torsional Kolsky (Split-Hopkinson) Bar

The torsional Kolsky bar is a reliable apparatus for testing materials in the 10

to 10

-1

strain rate regime (Ref

9). In general, the torsional Kolsky bar is well suited for conducting quasi-static and incremental strain rate

tests, as well as dynamic strain rate tests. Thus, strain rate and strain rate history studies can be conducted using

the same apparatus, thereby eliminating differences in test apparatus as a source of error in determining these

effects. In the torsional Kolsky bar, a dynamic strain rate can be superposed on the quasi-static strain rate so

that unloading does not occur, and the stress and strain rate increments can be measured directly for greater

accuracy (Ref 10).

As previously noted, testing materials in torsion has some advantages over axial loading due to the absence of

Poisson's ratio effects and geometric dispersion. When a torsional pulse travels along an elastic bar in its

primary mode, all its frequency components have the same velocity. Hence, a torsional pulse initiated either by

explosive detonation or by the release of a stored torque does not change its shape as it propagates toward the

specimen. In Kolsky bar experiments, the absence of geometric dispersion in torsion means that a pulse

initiated with a short rise time will maintain this rise time until it reaches the specimen, independent of the

length of the Kolsky bar. Also, the torsional strain gage stations can be located as near or as far from the

specimen as desired and still reveal the correct-shaped pulse incident on or reflected from the specimen. In an

axial Kolsky bar, however, a gage placed too close to the specimen is subject to errors due to three-dimensional

end effects, while a gage placed too far from the specimen produces unsatisfactory results because of geometric

dispersion.

There is, however, a disadvantage in a non-dispersive pulse. If a torsional pulse is noisy when initiated (i.e., if

some high-frequency components are superposed on the main pulse), this characteristic will be maintained,

regardless of the length of the Kolsky bar. As a result, the strain rate imposed on the specimen will not be

constant. In an axial Kolsky bar, such high-frequency components gradually disappear. Hence, an axial pulse

tends to become flat—that is, tends to smooth out—as it travels along an elastic bar. A noisy torsional pulse

such as that associated with explosive initiation of the pulse (Ref 11) will retain this characteristic; it will never

become flat and, hence, will not provide deformation at a constant strain rate. As a result, for explosive

initiation of a torsional pulse, a mechanical filter or pulse smoother is required to eliminate the high-frequency

components. This type of device usually is not required when the torsional pulse is initiated by the stored-

torque technique, because the amplitude is constant.

Torsional split-Hopkinson bar testing is described in more detail in the article “Torsional Kolsky Bar Testing”

in this Volume. As in the case of pressure bar testing, values of torsional stress and strain in the specimen can

be inferred from the measured records of the torsional strain in the incident and transmitter bars. These

relations, which were first derived by Kolsky for the axial bar, can be transposed to shear values. In accordance

with the analysis of Kolsky, the reflected pulse in a torsion bar provides a measure of the shear strain rate in the

specimen (t) and, through a single integration, provides the shear strain in the specimen, γ

(t). The shear strain

in the specimen is given by the difference in rotation between its two ends divided by its length:

(Eq 3)

where φ

and φ

are the angles of twist in the incident and transmitter bars, respectively; D

is the mean

diameter of the thin-walled specimen; and L

is its length. The value of φ

can be determined from the shear

strain measured at the surface of the transmitter bar through:

where D is the diameter of the Kolsky bar, and c = is the torsional velocity in the Kolsky bar. As a

result:

(Eq 4)

Similarly, φ

can be determined from the difference in strains due to the incident and reflected pulses:

(Eq 5)

where the negative sign is necessary because the reflected pulse travels in the -x direction. If Eq 3is

differentiated and Eq 4and 5 are utilized:

(Eq 6)

where the strains are all functions of time. For a homogenous state of strain in the specimen, the transmitted

pulse is the difference between the incident and reflected pulses, so that γ

= γ

- (-γ

) and hence:

(Eq 7)

Because γ

is determined from the output of the strain gages on the incident bar during passage of the reflected

pulse and because all other quantities in Eq 7 are known, it provides a measure of the strain rate in the specimen

as a function of time. The signal is integrated electronically to yield γ

(t), which is the strain in the specimen.

Kolsky also showed that the transmitted pulse provides a direct measure of the average shear stress in the

specimen, γ

(t). For a thin-walled tube in torsion, the stress is given by:

(Eq 8)

where t

is the wall thickness, and T

is the average torque. The average torque in the specimen is also given by

the average of the torques at each of its ends:

(Eq 9)

where T

is the torque at the interface with the incident bar, and T

is the torque at the interface with the

transmitter bar. The former is given in terms of the strain at the surface of the bar—that is, by the strain in the

incident and reflected pulses—by T

= G(γ

+ γ

)πD

/16. For the homogeneous state of stress in the specimen,

+ γ

≈ γ

so that:

(Eq 10)

Thus, Eq 7 and 10 provide stress and strain in the specimen as functions of time. Eliminating time yields the

stress-strain curve for the material at the strain rate provided through Eq 7.

References cited in this section

9. K.A. Hartley, J. Duffy, and R.H. Hawley, The Torsional Kolsky (Split-Hopkinson) Bar, Mechanical

Testing, Vol 8, Metals Handbook, 9th ed., American Society for Metals, 1985, p 218–230

10. R.A. Frantz and J. Duffy, The Dynamic Stress-Strain Behavior in Torsion of 1100-O Aluminum

Subjected to a Sharp Increase in Strain Rate, J. Appl. Mech., Vol 39, 1972, p 939–945