ASM Metals HandBook Vol. 8 - Mechanical Testing and Evaluation
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17. Standard Method for Plane-Strain Fracture Toughness of Metallic Materials, E 399-90, Annual Book of
ASTM Standards, Vol 3.01, 1992, ASTM, p 569–596
21. A. Saxena and S.J. Hudak, Review and Extension of Compliance Information for Common Crack
Growth Specimens, Int. J. Fract., Vol 14 (No. 5), 1978, p 453–468
22. J.W. Dally and W.F. Riley, Experimental Stress Analysis, 3rd ed., McGraw-Hill, 1991
23. R.O. Ritchie, G.C. Garrett, and J.F. Knott, Int. J. Fract. Mech., Vol 7, 1971, p 462–467
24. C.Y. Li and R.P. Wei, Mater. Res. Stand., Vol 6, 1966, p 392–445
25. R.O. Ritchie and J.F. Knott, Acta Metall., Vol 21, 1973, p 639–648
26. R.O. Ritchie and K.J. Bathe, Int. J. Fract., Vol 15, 1979, p 47–55
27. G. Clark and J.F. Knott, J. Mech. Phys. Solids, Vol 23, 1975, p 265–276
28. H.H. Johnson, Mater. Res. Stand., Vol 5, 1965, p 442–445
29. G.H. Aronson and R.O. Ritchie, J. Test. Eval., Vol 7, 1979, p 208–215
30. M.A. Ritter and R.O. Ritchie, Fat. Eng. Mater. Struct., Vol 5, 1982, p 91–99
31. G.M. Wilkowski and W.A. Maxey, Fracture Mechanics: 14th Symposium—Vol II: Testing and
Applications, STP 791, J.C. Lewis and G. Sines, Ed., ASTM, 1983, p II-266 to II-294
Fatigue Crack Growth Testing
Ashok Saxena, Georgia Institute of Technology; Christopher L. Muhlstein, University of California, Berkeley
Loading Methods
The goal of a FCGR test is to generate a record of a versus N under specified loading conditions. This
information can be generated by applying cyclic varying loads of specified amplitude and frequency.
The frequency of the test should, when possible, be kept constant; however, it may be necessary to reduce the
frequency of a test in order to make crack-length measurements. Frequency effects are usually not observed in
metals in laboratory air at room temperature over the range of typical testing frequencies (1 to 100 Hz).
Although higher-frequency tests finish more quickly, specimen and loadtrain stiffness, as well as load range,
impose a practical limit on the maximum testing frequency. Steel specimens 50 mm wide can be run on a
typical 90 kN (1 tonf) capacity loadframe at 25 to 50 Hz. If compliance methods are being used to control the
test or monitor crack extensions, the frequency response of the clip gage and recording instruments may limit
the maximum frequency for testing.
The waveform to be used during a test is usually a sine or sawtooth (ramp) shape. Both waveforms will
generate similar data at room temperature in benign environments. However, sine waveforms are easier for
servohydraulic systems to control. Ramp waveforms should be used when elevated-temperature FCGR and
creep-fatigue interaction are of interest (see appendix to this article, “High-Temperature Fatigue Crack Growth
Testing”) or when testing in aqueous environments (Ref 32).
Five types of FCGR tests are used in laboratories today. How the specimen is loaded defines the type of growth
rate test. Different types of tests are often conducted in series to confirm growth rates and to use as much of the
specimen as possible. To avoid load sequence effects, tests conducted in series should adhere to the same
guidelines specified for precracking.
The simplest test type is one in which the load amplitude is kept constant and the applied ΔK increases as the
crack extends. The simplicity of the test is its advantage. However, this test is essentially impractical for crack
growth rates below 1 × 10
-8
m/cycle. In a second type of test, loads are shed manually at increments of 10% or
less. Although cumbersome because they require constant attention, these tests allow the generation of data for
slower crack growth in a more time-efficient manner than the constant-load-amplitude test. The prevalence of
personal computers and modern controls technology in current laboratories has popularized the remaining three
types of so-called “continuous loadshedding” or “K-controlled” experiments.
Continuous loadshedding tests are those in which loads are shed at steps of 2% or less for a predetermined
increment of crack extension. During these tests, the crack length is continuously monitored by electric
potential, compliance, or another suitable technique. Loads are shed or increased according to the following
relation proposed by Saxena et al. (Ref 33):
ΔK = ΔK
0
exp[c(a - a
0
)]
(Eq 14)
where ΔK is the applied range of ΔK, ΔK
0
is the initial range of ΔK, c is the normalized K-gradient, a is the
current crack length, and a
0
is the initial crack length. The normalized K-gradient is defined as:
(Eq 15)
The use of Eq 14 for changing fatigue loads is ideally suited for personal computers, and it allows testing under
K-controlled conditions. If the normalized K-gradient is less than zero, the applied ΔK will be decreased as the
crack extends. These tests are termed K-decreasing tests. Conversely, c ≥ 0 will lead to increasing ΔK as the
crack extends.
The appropriate value of c for a decreasing ΔK test is that which avoids the anomalous growth rates caused by
shedding loads too quickly. Investigators have determined that c = 0.08 mm
-1
(-2 in.
-1
) is an appropriate value
for decreasing ΔK tests on most metals (Ref 34). This value of c was derived to eliminate load-interaction
effects caused by crack-tip plasticity in metals. The same value of c for a K-decreasing test in intermetallics and
ceramics is recommended. This value ensures that sufficient data can be obtained over the narrow range of
stable crack growth, even though plastic zones are considerably smaller or nonexistent in these materials (Ref
35, 36).
Increasing ΔK tests (i.e., c > 0) are usually conducted to confirm the growth rates measured during the previous
K-decreasing portion of the test. Increasing ΔK tests may, if necessary, be conducted with larger normalized K-
gradients. It is important to note that during an increasing ΔK test, loads may have to be decreased as the crack
extends, which could lead to difficulties with control. Hence, it is preferable to use the simple constant-
amplitude test instead of a controlled increasing ΔK test.
The first type of continuous loadshedding test is where the load ratio (R) is held constant. Constant-R tests
generate the same type of information as constant-amplitude tests. Low- and high-R (R = 0.1 and 0.5,
respectively) tests are usually conducted for comparison purposes.
Another type of K-controlled test is a constant-K
max
test, which is essentially a variable-R test. When K
max
is
held constant as the crack extends, R will vary as shown schematically in Fig. 18. Once again, the value of ΔK
to be applied to the specimens is dictated by Eq 14. The advantage of this test is that it quickly establishes the
role of R on crack growth rate. For decreasing ΔK in constant-K
max
tests with negative c, the lower crack growth
rates are at very high values of R. The behavior of threshold cracks under these conditions has been used as a
measure of “closure free” fatigue crack growth, reflecting the “intrinsic resistance” of the material to fatigue
(Ref 37).
Fig. 18 Constant K
max
test load ratio
The last type of continuous loadshedding fatigue test is a constant-K
mean
test. Much like the constant-K
max
test, a
constant-K
mean
test can be used as a comparison with constant K
max
to help establish the role of K
mean
versus
K
max
on fatigue crack growth rates. Constant-K
max
and -K
mean
tests have been popular in the testing of brittle
materials where definitive mechanisms for crack advance have yet to be established.
Once testing is complete, the final crack in the specimen should be measured optically on both sides of the
specimen. This measurement will be compared to the terminal crack length predicted by other measurement
techniques in the analysis of the investigation.
Electromechanical Fatigue Testing Systems. The primary function of electromechanical fatigue testers is to
apply millions of cycles to a test piece at oscillating loads up to 220 kN (2.5 tonf) to investigate fatigue life, or
the number of cycles to failure under controlled cyclic loading conditions. Variables associated with fatigue-life
tests are frequency of loading and unloading, amplitude of loading (maximum and minimum loads), and control
capabilities. The fundamental data output requirement is the number of cycles to failure, as defined by the
application.
A variety of electromechanical fatigue testers have been developed for different applications. Forced-
displacement, forced-vibration, rotational-bending, resonance, and servomechanical systems are discussed in
this article and are compared in Table 2. Other specialized electromechanical systems are available to perform
specific tasks.
Table 2 Comparison of electromechanical fatigue systems
Parameter Forced
displacement
Forced
vibration
Rotational
bending
Resonance
Servomechanical
Tension Yes Yes No Yes
Yes
Compression Yes Yes No Yes
Yes
Reverse stress Yes Yes Yes Yes
Yes
Bending Yes Yes Yes Yes
Yes
Frequency
range
Fixed Fixed, 1800
rpm
0–10,000 rpm 40–300 Hz
0–1 Hz
Load range Typically <450 N
(<100 lbf)
Up to 220
kN (50,000
lbf)
… Up to 180 kN
(40,000 lbf)
Up to 90 kN
(20,000 lbf)
Type
Control
Open-loop Open-loop Open-loop Closed-loop
Closed-loop
Mode Displacement Load Rotation/bending Load
Load,
displacement,
strain
Maximum … 25.4 mm … 1.0 mm (0.040
100 mm (4 in.)
deflection (1.00 in.) in.)
Advantages Simple,
straightforward
Versatile,
efficient,
durable
Efficient, durable,
simple
Fully closed-
loop, extremely
efficient
Fully closed-
loop, high
precision
Disadvantages No load control,
very limited
applications
(soft samples)
Fixed
frequency,
limited
control
(open-loop)
Rotational
bending only,
limited
applications
Operating
frequency
directly
proportional to
sample
stiffness
Low frequency
only
Servohydraulic testing machines are particularly well suited to provide the control capabilities required for
fatigue testing. Extreme demands for sensitivity, resolution, stability, and reliability are imposed by fatigue
evaluations. Displacements may have to be controlled (often for many days) to within a few microns, and
forces can range from 100 kN (1 tonf) to just a few newtons. This wide range of performance can be obtained
with servomechanisms in general and, in particular, with the modular concept of servohydraulic systems.
Usually, the problem of selecting the appropriate system is simply a matter of optimizing the various
components to form a system best suited to the given testing application. With any type of control system, the
objective is to obtain an output that relates as closely as possible to the programmed input. In a fatigue testing
system, it may be desired to vary the force on a specimen in a sinusoidal manner, at a frequency of 1 Hz over a
force range of 0 to 100 kN (0 to 1 tonf). The only practical means of precision accomplishment is through the
use of a negative-feedback closed-loop system.
References cited in this section
32. R.J. Selines and R.M. Pelloux, Effect of Cyclic Stress Waveform on Corrosion Fatigue Crack
Propagation in Al-Zn-Mn Alloys, Metall. Trans., Vol 13, 1972, p 2525–2531
33. A. Saxena, S.J. Hudak, Jr., J.K. Donald, and D.W. Schmidt, J. Test. Eval., Vol 6 (No. 3), May 1978, p
167–174
34. R.J. Bucci, Development of a Proposed ASTM Standard Test Method for Near-Threshold Fatigue Crack
Growth Rate Measurement, Fatigue Crack Growth Measurement and Data Analysis, S.J. Hudak, Jr. and
R.J. Bucci, Ed., STP 738, ASTM, 1981, p 5–28
35. K.T. Venkateswara Rao, Y.W. Kim, C.L. Muhlstein, and R.O. Ritchie, Mater. Sci. Eng. A, Vol 192/193,
1995, p 474–487
36. R.J. Dauskardt, W. Yu, and R.O. Ritchie, J. Am. Ceram. Soc., Vol 70 (No. 10), Oct 1987, p C248–C252
37. R.W. Hertzberg, W.A. Herman, and R.O. Ritchie, Scr. Metall., Vol 21, 1987, p 1541
Fatigue Crack Growth Testing
Ashok Saxena, Georgia Institute of Technology; Christopher L. Muhlstein, University of California, Berkeley
Analysis of Crack Growth Data
The two major aspects of FCGR test analysis are to ensure suitability of the test data and to calculate growth
rates from the data. In addition to growth rate calculations, analysis also may require the calculation of fatigue
crack closure levels and the characterization of fracture surface and metallographic features, as discussed in this
section. Combining the results from all of these areas is necessary to develop an understanding of the FCGR
behavior of the material. Finally, the reliability of “real time” analysis by personal computers must be verified,
and the sophisticated tests performed in modern laboratories must undergo some degree of analysis. Hence, it is
essential that computer-controlled tests generate records of a versus N as well as FCGR.
Validity of the Test Data. The first step is to ensure the validity of the test data and make corrections to the
crack length, if necessary. Crack measurement intervals are recommended in ASTM E 647 according to
specimen type. For CT specimens:
For MT specimens:
At the end of the test, the final crack length is measured on both sides of the specimen. A comparison should be
made between optical measurements and the final predicted crack length by any nonoptical techniques used.
Differences between the measured crack lengths should be corrected using a linear relationship. In other words,
the error between the final measured and predicted crack size is linearly distributed over the crack extension
range. If periodic optical measurements were made during the test, other more appropriate correction
procedures can be used.
Thicker specimens should be fractured after testing to determine the degree of crack front curvature. Cooling
the specimen to liquid nitrogen temperatures allows the brittle fracture of most metallic materials and reveals a
clear demarcation between the fatigued and fractured portions of the specimen. Five evenly spaced
measurements of crack length should be made across the crack front. The average length should then be used as
the final crack length, and the corrections should be applied using this value instead of the surface
measurements.
Crack Growth Rate Calculation. A number of different numerical techniques have been used to calculate crack
growth rates from the set of (a
i
, N
i
) data points of a given crack growth rate test (Table 3). The secant and
incremental polynomial methods are the most widely used. When the data are processed to a final smoothed
da/dN = f(ΔK) format, these methods provide approximately equivalent results. However, the scatter of
individual da/dN values about the average depends greatly on the data reduction method.
Table 3 Methods for calculating crack growth rates
Incremental polynomial method:
A least-squares, second-order polynomial is obtained for successive sets of (2k + 1) data points:
where C
1
= (N
i + k
+ N
i - k
)/2 and C
2
= (N
i + k
- N
i - k
)/2 are centering and scaling constants, respectively, that
are introduced to prevent numerical problems in obtaining the least squares fit. The crack growth rate at
a
i
, the predicted central crack length at N
i
, is given by the derivative:
Typical values of k are 1, 2, or 3, resulting in the second-order polynomial being estimated on the basis of
3, 5, or 7 successive data points. The estimated crack growth rate function loses k data points at each end.
Less apparent scatter is obtained for larger k values.
Secant method:
In the secant method for differentiating the a versus N data, the average crack extension per cycle is
calculated for each pair of data points, and ΔK is calculated at the midpoint of the crack lengths:
This method is simple but exhibits the most scatter in da/dN values.
Modified difference methods:
These methods are finite difference techniques for estimating the derivative at the midpoint of a data set.
These methods use numerical derivatives. The formula for estimating the derivative at the midpoint a
i
of
three successive data points is given by:
The secant method fits a line between adjacent data points. The slope of the line is the crack growth rate, da/dN.
The load at the average crack length of the interval is used to calculate the corresponding ΔK. It is not
uncommon to collect data points more closely spaced than the 0.25 mm (0.010 in.) minimum crack extension
for growth rate calculations. When more data are available, a straight line through the multiple data points can
be fitted by regression analysis to calculate crack growth rates. A 50% overlap between data sets used for
calculating successive crack growth rates can considerably reduce scatter in the processed data. This method is
termed the modified secant method.
The polynomial method uses the derivative of a second-order polynomial fitted to a fixed number of data points
(often five or seven). The growth rate and ΔK level are calculated for the average value of crack length in the
interval. This method tends to provide data with less scatter than the secant method. In practice, there are no
systematic differences in the da/dN versus ΔK trends if the same data are processed by these different
techniques (Ref 38). In fact, little difference is observed between the data processed by the modified secant
method and the polynomial method.
Variability. Although the apparently variability in the resulting da/dN value depends on the calculation method,
none of the methods introduces a significant bias to an overall mean trend curve. Figure 19(b) plots da/dN
versus ΔK, as calculated from the data of Fig. 19(a), using the secant, incremental polynomial, and five-point
modified difference methods. Because methods of analyzing and interpreting the scatter in da/dN are not
currently available, the simpler techniques—the secant and incremental polynomial methods—are often chosen.
Fig. 19 Comparison of da/dN calculation methods. (a) Crack length test data. (b) Plot of calculated da/dN
rates from the data in (a)
Crack Closure Analysis. The determination of the fatigue crack closure load is a subject of vigorous debate.
Visual inspection of compliance curves can be used to estimate closure levels. However, the method is
subjective and not well suited for large amounts of data. ASTM task groups have explored the use of the
compliance offset and correlation method for closure analysis (Ref 39). In the compliance offset method, crack
closure levels are determined by finding the point that deviates from the linear portion (i.e., is offset) by a set
amount (usually 1, 2, 4, or 8%). The correlation method determines the closure level by mathematically
representing the “strength” of the linear relationship between load and displacement/strain along the curve. To
confirm that the methods are applied correctly, algorithms should be tested with hypothetical, bilinear
compliance curves, for which both methods should yield identical results.
The compliance offset method is generally applied using a computer, because the calculations do not lend
themselves to the use of spreadsheets. The procedure is as follows:
1. Collect digitized strain/displacement and load data for a complete load cycle. The data sampling rate
should be high enough to ensure that at least one data pair (displacement and load) is taken in every 2%
interval of the cyclic load range.
2. Starting with the first data sample below maximum load on the unloading curve, fit a least-squares
straight line to a segment of the curve spanning approximately the uppermost 25% of the cyclic load
range. The slope of this line is the compliance value that corresponds to the fully open crack
configuration.
3. Starting with the first data sample below maximum load on the loading curve, fit least-squares straight
lines to segments of the curve that span approximately 10% of the cyclic load range and that overlap
each other by approximately 5% of the range. Store the compliance (slope) and the corresponding mean
load for each segment in a vertical array with the highest load location at the top.
4. Replace the compliance stored in each location in the array with the corresponding compliance offset,
which is computed as a percentage of the “open crack” compliance and is given by:
(Eq 16)
5. Identify the highest load location in the array that has a compliance offset greater than the selected
offset criterion, and for which all array locations below have compliance offsets greater than the offset
criterion.
6. Starting at the array location identified in step 5, identify the nearest, higher load location that has a
compliance offset less than the selected offset criterion, and for which all array locations above it have
compliance offsets less than the offset criterion.
7. Determine the opening load corresponding to the selected offset criterion by linear interpolation
between the two (compliance offset, load) points identified in steps 5 and 6 (Ref 39).
An alternative to the offset method is the correlation coefficient method. The correlation coefficient, r, is
defined as (Ref 39):
(Eq 17)
where n is the number of data pairs, Σ denotes the summation from i = 1 to n, x
i
are individual load data
samples, and y
i
are individual displacement data samples. The closure level is defined as the load at which the
correlation coefficient has the highest value. In contrast to the offset method, in which different levels of offset
can be selected, there is only one criterion in this method. Both methods generate similar closure levels for the
same data. However, issues of data quality are currently the biggest problem for consistent experimental closure
analysis. Methods to characterize data quality are presently being explored.
Fracture Surface Characterizations. Cracked specimens are also useful for establishing modes of crack advance
and other interactions of the crack with the microstructure. Scanning electron microscopy is used to
characterize the fracture surface. Care should be taken to establish the level of ΔK associated with the image of
the fracture surface. This relationship is especially important when working with brittle materials where
inspection of the surface does not reveal an obvious difference in fracture surface morphology between the
fatigued material and posttest fracture.
Portions are often removed from the interior of the specimen and mounted for metallographic preparation.
“Crack profiles” can be useful for demonstrating the interaction of the crack with the microstructure. There can
be marked differences in how cracks interact with microstructures, especially in instances where crack closure
and distributed damage are important.
References cited in this section
38. W.G. Clark and S.J. Hudak, The Analysis of Fatigue Crack Rate Data, Application of Fracture
Mechanics to Design, J.J. Burke and V. Weiss, Ed., Vol 22, Plenum, 1979, p 67–81
39. E.P. Phillips, “Results of the Second Round Robin on Opening Load Measurement Conducted by
ASTM Task Group E24.04.04 on Crack Closure Measurement and Analysis,” Technical Memorandum
109032, National Aeronautics and Space Administration, Nov 1993
Fatigue Crack Growth Testing
Ashok Saxena, Georgia Institute of Technology; Christopher L. Muhlstein, University of California, Berkeley
Appendix: High-Temperature Fatigue Crack
Growth Testing
David C. Maxwell, University of Dayton; Theodore Nicholas, Wright-Patterson Air Force Base
Introduction
The concepts and procedures for fatigue crack growth testing at room or ambient temperature described in this
article are generally applicable to elevated-temperature conditions. In this appendix, some of the features
unique to testing and measurement at high temperatures are reviewed. In particular, methods for heating and
controlling temperature are discussed briefly. Other aspects related to instrumentation, measurement, and test
techniques are also highlighted. While there are no well-established standards for elevated-temperature crack
growth testing, one standard testing procedure has been recommended recently based on a cooperative study
using 304 stainless steel (Ref 40). While documentation on methods employed in elevated-temperature crack
growth testing are scattered widely in the open literature, conferences devoted to this particular subject include
many papers that provide details of individual investigations (e.g., Ref 41).
Specimen Design. In general, the specimens used in room-temperature testing are equally applicable for high-
temperature testing. In fact, in making comparisons of crack growth rates as a function of temperature, it is
considered good practice to retain the same test specimen geometry at all temperatures tested.
An exception to this practice is the specialized instance of testing under thermomechanical fatigue (TMF) crack
growth conditions. Here, the temperature as well as the load is cycled. In order to control the cyclic temperature
on the specimen, effective means of both heating and cooling the specimen must be employed. This procedure
usually requires either a thin planar specimen or a thin-walled tube, both of which minimize the thermal mass
and allow for more rapid heating or cooling and better control of temperature gradients. Information on some of
the techniques that have been employed for TMF can be found in conference proceedings, such as those of
ASTM (Ref 42, 43), American Society of Mechanical Engineers (ASME) (Ref 44), or the International
Conferences on Fatigue and Fatigue Thresholds (Ref 45, 46).
Another aspect of TMF crack growth almost unique to this type of test is the use of strain control as the mode
of load application, similar to that used in low-cycle fatigue. A brief discussion of the problems and limitations
of the use of strain control in elevated-temperature or TMF crack growth testing can be found in Ref 47.
The final consideration in TMF crack growth testing is the ability to heat and cool the specimen, or the access
of heat and cooling air to the specimen. For example, clevises used on CT specimens tend to shield the
specimen from the heating or cooling source and make it difficult to control the temperature cycle. Therefore,
other geometries, such as MT geometries, are generally used for this type of test.
Specimen Gripping. There are two main considerations in gripping specimens at high temperature. The first
consideration is the possible introduction of friction at any type of pin joint. Whereas friction can be minimized
at room temperature through lubrication or careful surface finishing, these methods are less effective at elevated
temperatures. Special high-temperature lubricants or oxidation-resistant materials for pins and clevises are
methods for minimizing the development of friction in pin joints. Rigid fixtures and grips, on the other hand, do
not require such considerations.
The second aspect of gripping at high temperatures is the possible loss of friction due to mismatches in the
coefficient of thermal expansion of grips and specimens. Calculations or experimental evaluations should be
made to ensure that the load-carrying capacity of the gripping system does not degrade due to differential
thermal expansions so that slippage might occur.
Further, it should be demonstrated that excessive clamping stresses do not develop such that the specimen is
crushed or the grips fail. This aspect of high-temperature testing is only applicable to instances where “hot”
grips are used, such as when the grips and specimens are both contained within a furnace. Cold grips, on the
other hand, produce high-temperature gradients along the length of the specimen and make it more difficult to
maintain a constant temperature over the gage length or the crack growth region of the specimen.
Heating Methods. There are several methods available for heating specimens and maintaining a constant and
uniform temperature during elevated-temperature crack growth testing. One of the more common methods is to
use a commercially available or homemade furnace and power controllers that produce one or more zones of
uniform, controlled temperature. Temperature control is achieved from thermocouple feedback, either from
within the chamber, where the air temperature is being controlled, or from thermocouples directly attached to
the specimen at one or more locations. In either situation, temperature control with commercial units is
generally accurate and reliable and can be considered a mature, state-of-the-art technology.
A second method of heating specimens is through the use of induction heaters, where the specimen is heated by
alternating currents produced by an EMF generated by the inductance coil surrounding the test specimen.
Shielding of the specimen by grips may cause nonuniform temperature distribution. Therefore, single-edge-
tension specimen geometries are generally preferred. The number and spacing of the coils, though calculated
from formulas provided with such apparatus, is determined most often from trial and error and usually requires
a certain amount of experience for optimal performance. Feedback is provided from one or more thermocouples
attached to the specimen, and uniformity of temperature must be checked with some type of temperature
mapping system, such as multiple thermocouples on a dummy specimen.
Another method of heating used in several laboratories is the use of radiant energy from quartz lamps mounted
in reflective and cooled housings. Each lamp focuses energy over a limited portion of the test specimen, so
multiple lamps, multiple thermocouples, and good thermal conductivity across the specimen all lead to more
uniform temperature fields. A description of the technique of quartz lamp heating can be found in Ref 48.
The last common method of specimen heating is direct resistance heating. Here, a current is passed directly
through the specimen from one end to another. The test apparatus must be electrically insulated from the input
and output leads. Uniform gage length specimens are better adapted to this method of heating than highly
nonuniform ones; therefore, a MT specimen would be a much better candidate than a CT specimen. Because
the high current passes through the specimen, no conducting leads can be attached to the specimen that would
provide an alternative path for the current. Thus, temperature measurement from thermocouples attached
directly to the specimen and electric potential crack growth measurements cannot be made with this type of
heating. Similarly, extensometry that attaches directly to the specimen must use nonconducting elements.
Temperature Measurement. The science of the measurement of temperature, known as pyrometry, dates back
before World War II. Books on the subject of pyrometry in general (Ref 49), or optical pyrometry in particular
(Ref 50), were published in 1941 and provide detailed descriptions of the theory and the methods used in that
era. The basic principles have not changed. The most common method for temperature measurement is through
the use of thermocouples, or thermoelectric pyrometer, directly attached to the specimen. A thermocouple is
made by welding two dissimilar wires together at one end. A change in temperature will generate an EMF that
can be recorded on an instrument attached to the other end of the wires. These readings provide a real-time,
continuous record of temperatures at a given point on a specimen, and they are commonly used for temperature
control feedback as well as direct temperature measurement.
Another commonly used method of measuring temperature is through the use of commercially available
infrared detectors, which sense the radiation emitted from a sample and convert the frequency of the radiation
to temperature after appropriate calibration. The theory and methods of optical pyrometry are documented in
numerous places (e.g., Ref 51, 52). The emissivity of the test material whose temperature is being measured is
the quantity used as the basis of the measurement. Emissivity is the ratio between total radiant energy per
square centimeter per second between the specimen being measured and a black body at the same temperature.
Thus, as the emissivity of a material decreases from 1, the apparent temperature as measured by an optical
pyrometer will deviate from the actual temperature by a greater amount.
The emissivity of a heated specimen will always be less than 1, and the apparent temperature will, therefore, be
less than the desired test temperature. Emissivity can be influenced by surface roughness, the spectral
transmission of any windows between the test specimen and the measuring instrument, and the chemical
changes of the specimen surface due to oxidation or other environmental degradation. All these issues should