Crack Tip Opening Displacement: Using Materials Testing to Control Cracks
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Crack Tip Opening Displacement:
Using Materials Testing to Control Cracks
By Tom Jarvie, Stork Southwestern Laboratories
Introduction
Even the strongest and hardest-working materials on earth—pipes, drills,
munitions, girders—crack. A crack is the beginning of failure, but when and how
dramatically will the failure occur?
The world demands more—greater quantities of energy, taller buildings, longer
pipelines, faster and higher-flying aircraft. Material scientists have responded
with stronger and more durable metals, but every one, given the right set of
circumstances, will crack.
We know more and demand more of materials than ever before. Rather than
reacting to problems as they occur, more and more industries are choosing to be
proactive in failure prevention by testing materials properties beyond the normal
testing requirements. One such test that goes beyond traditional material
property analysis is the CTOD test, which is gaining popularity in the oil and gas
industry.
Crack Tip Opening Displacement (or CTOD) is one of a family of fracture
mechanics tests that measures the resistance of a material to growing a crack.
Similar tests (i.e., da/DN, K1C, KEE, and J1C) can determine fracture resistance
of a material, but CTOD is particularly suited to pipeline and drilling equipment.
The CTOD test is used to determine the fracture mechanics properties of ductile
materials and can be thought of as the simulated opening of a pre-existing
fatigue crack prior to fracture. The data that result from this opening can be used
for critical defect assessment, in which the critical defect size can be determined.
The Test
Please note that the following is a simplified version of the CTOD test process
and does not cover all aspects of the test, such as personalized testing
specifications.
A CTOD test can be broken into 4 main steps:
1) Machining of the test specimen (Sample Machining);
2) Fatiguing of the specimen within specified limits (Pre-Cracking);
3) Breaking of the specimen under controlled conditions (Fracture);
4) Post analysis of the specimen and resultant data to obtain the CTOD
value (Data Analysis).
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Crack Tip Opening Displacement, Tom Jarvie, Stork Southwestern Laboratories, Page 1 of 81) Sample Machining
Unlike other destructive material tests, the CTOD test has multiple factors that
can affect the resultant value. Not only is
the test temperature a variable, but the
specimen size can also affect the results,
as well as the conditions in which the
result can be used. It is important to use
the maximum thickness of specimen
possible when performing the test. As a
general rule, if a material meets the
CTOD test requirements at a given test
size, then the results can be extrapolated
to apply to thinner sections, but not
thicker.
For structural and pipe materials used in the oil and gas industries, the most
commonly used specimens are a rectangular three-point bend or a square three-
point bend. The rectangular three-point bend is preferable, except where there is
limited material or a surface notch needs to be evaluated.
As with other destructive material tests, the CTOD value can vary, depending on
the direction of the test. The various testing specifications have their own
nomenclature to describe the sample and notch direction in respect to the grain
flow or weld direction. This nomenclature is typically the same as that of a charpy
test.
The calculation of the final CTOD value is dependent on the depth of a pre-
fatigue crack from the surface of the specimen. As it is impractical to fatigue a
crack from the actual specimen surface, the specimen is machined to include a
notch, which will act as the initiation point of the fatigue crack and be included in
the overall length of the fatigue crack used for the calculation of the CTOD value.
National standards are used for the actual testing criteria.
2) Pre-Cracking
On completion of machining of the specimen, an actual fatigue crack is induced
at the base of the starter notch. This crack must be of sufficient length to bypass
any area of plastic deformation that may have been occurred during the
machining process. The crack length is typically based on the size of the sample,
the method of notch manufacture, the width of the notch, the shape of the notch,
and practical time restraints. The overall length from the surface of the sample to
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Crack Tip Opening Displacement, Tom Jarvie, Stork Southwestern Laboratories, Page 2 of 8the crack tip must fall within given parameters. Other factors that also must be
considered include the angle of the crack in respect to the specimen and the
difference in length of the crack as seen on the exposed surfaces. The operation
is typically performed in air at room temperature.
Fatiguing the sample requires a minimum and
maximum fatigue load. If the loads selected to
induce the fatigue crack are too low, then the fatigue
time may become restrictive—or, at the extreme, a
crack may not develop. If the loads are too high,
then a plastic zone may result which would affect
the CTOD result—or, again at the extreme, the
sample may fracture prematurely. The national
standards specify criteria to ensure a valid test
sample, including: a minimum to maximum load
ratio of less than 0.1, a change in stress intensity
relating to the modulus of the material, and a
maximum load based on the material tensile
properties, specimen size and span used.
Initiation and propagation of a fatigue crack is
dependent on the configuration of the sample, the crack length and the loading
conditions. This relationship determines the stress intensity factor (K) at the
fatigue crack tip, and can be determined for a three-point bend by the following
formula:
a 0.5 a a a 2 .7 a 2
3( ) (1.99 − ( )(1 − )(2.15 − 3.93 + 2.7 ))
FS W W W W W2
K= x (1)
B (W )1.5 2a a
2(1 + )(1 − )1.5
W W
[Where K is the stress intensity factor, F is the load, S the span, B the specimen
thickness, W the specimen width and a the crack length].
During the fatigue operation, W, B and
S remain constant. The equation
demonstrates a definitive relationship
between the crack length, load and
stress intensity.
To initiate and grow a fatigue crack for
a CTOD test, various methods can be
used.
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Crack Tip Opening Displacement, Tom Jarvie, Stork Southwestern Laboratories, Page 3 of 8a) Constant Load. A constant load amplitude ( load ) is the most
common situation. However, for the purposes of growing a fatigue crack
for a CTOD test, it is not the most practical. In order to meet the validity
requirements imposed by the specifications, the load ratio selected would
have to be determined based on the final crack length. As a result, the
crack growth rate would increase as the length increased; however, it
would be slow in the initial stages of crack length. This method can result
in an extended time to grow the crack of the required length.
b) Decreasing Load. By calculating the load restrictions for a given crack
length, it is possible to start the fatigue operation with a high load and
decrease it to the limits required as the crack grows. Done carefully, this
can save time in obtaining valid fatigue crack front, but it should be noted
that reducing the load by too great an amount can result in the crack
propagation slowing or even stopping. In this case, a given number of
fatigue cycles would be needed to initiate the crack again.
c) Constant K. During the fatiguing of a CTOD sample, S, W and B will
remain constant. As such, the relationship between the crack length, load
and stress intensity can be utilized in the growth of a fatigue crack. From
the equation it can be seen that by keeping the change in stress intensity
constant, the load will drop proportionally as the crack length increases.
This method will result in an even load drop as the crack grows and will
prevent the crack arrest that can occur when method b is used.
It is possible to combine aspects of the three methods to further increase to
efficiencies of the crack propagation. By starting with a high K and reducing it
as the crack extends, one can reduce the time necessary to grow a crack while
keeping within the specification requirements.
50.00
16 26
45.00
14 24
40.00
12 22
Crack Length (m
35.00
10 20
Load
30.00
Load (kN
8 18
25.00
6 16
20.00
4 14
15.00
Delta-P N
2 12
10.00 Crack Length mm
5.00
0 10
0 10,000 20,000 30,000 40,000 50,000
0.00
0.300 0.350 0.400 0.450 0.500 0.550 0.600 Cycles
a/W 6.4.5 a) 6.4.5 b) E1290 Estimate
Tracking the actual crack length can be done in a number of ways, such as:
a) Visual measurement can be made on the sample. Using this method, only
the crack length at the outer surface can be determined. To enhance the
crack, nondestructive testing techniques such as dye penetrant or
magnetic permeability work well.
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Crack Tip Opening Displacement, Tom Jarvie, Stork Southwestern Laboratories, Page 4 of 8b) The compliance technique depends on a 5th order polynomial in which
the coefficients are based on the specimen geometry and material
properties. Typically, a clip gage is attached to the sample at the
machined opening and electronically records the opening that is then
related to the crack length. The recorded length can then be used to
automatically adjust the load, based on the method decided for the crack
growth, resulting in a smooth load drop.
c) The potential drop across the crack depends on ohm’s law: as a crack
grows the potential will increase. As with the compliance technique, this
method can be directly associated with the load control and hence give a
smooth load transition.
While performing the fatigue operation, it is important to remember that only the
outer surface can be measured and confirmed. The fatigue is propagating across
a plane inside the sample, and as such the length cannot be visually confirmed
until the test is complete and the sample fractured open. The compliance and
potential drop techniques can provide information about the internal situation of
the fatigue crack.
Variance in length across the fatigue crack front increases in materials in which
an even stress distribution is not present, i.e. in a weldment. In these cases,
various operations may be necessary to produce a linear crack front. Pre-
compression of the sides of the sample and reverse bending are two of the most
common techniques employed.
On completion of the fatigue operation, the visible crack front must be visually
examined to ensure compliance to the specification, e.g. within length tolerances
from the surface and between sides, straightness and the absence of any
obvious surface bifurcations.
3) Fracture
The actual breaking of the specimen is performed under monotonic conditions,
which means that the sample is under increasing load until fracture, and at a
static temperature.
Fractures can be affected by
temperature, therefore it is important
to control the temperature throughout
the test. Testing in a liquid alcohol
bath with CO2 as a cooling medium is
one of the most common methods to
achieve this.
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Crack Tip Opening Displacement, Tom Jarvie, Stork Southwestern Laboratories, Page 5 of 8The rate of testing is determined by the change in the stress intensity factor
during the initial application of load. As was seen in the equation, the stress
intensity is dependent on the load and crack length. Since the crack length is not
measurable until the sample is fractured, it is not possible to confirm the actual
testing rate until completion of the test. An
estimated crack length must be used to determine
the testing rate—with the actual test rate confirmed
to be with in the validation limits.
During the application of the load, a clip gage is
used to measure the opening at the mouth of the
fatigue crack. This opening is plotted against the
load applied.
5) Data Analysis
After the sample has been fractured, scientists perform various operations to
determine the CTOD type and value.
The fracture face must be examined in conjunction with
the plot of the load vs. the crack mouth opening. From
this, the type of fracture can be determined.
Three main categories of fracture exist:
a) m – in which the fracture face exhibits tearing and
the final fracture occurs under decreasing load
b) u – in which the fracture face exhibits tearing and
the final fracture occurs under increasing load
c) c – in which the fracture face does not exhibit
tearing and the final fracture occurs under
increasing load
A 4th type of failure can occur which is known as a pop-in.
In this situation, either a load drop, a displacement
increase, or both is observed, and the load then recovers
to exceed the initial condition. When a pop-in occurs, the
material has partially fractured; however, the remaining
ligand is sufficient to withstand the increase in load. It is
often possible to see the cause of the pop-in on the
fracture face. The validity of the pop-in is evaluated based
on the changes in load and/or displacement. If deemed
valid, the final calculation of the CTOD value is based on the load and
displacement at the pop-in occurrence.
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Crack Tip Opening Displacement, Tom Jarvie, Stork Southwestern Laboratories, Page 6 of 8The length of the fatigue fracture and any tearing (in the case of a u type fracture
only) should be measured. The fatigue crack length is used in the CTOD
calculation.
c u
50 50
45 45
40 40
35 35
30 30
Load
Load
25
25
20
20
15
15
10
10
5
5
0
0 0.0 0.5 1.0 1.5 2.0 2
0.0 0.5 1.0 1.5 2
Opening
Opening
m pop-in
45 50
40 45
40
35
35
30
30
25
Load
Load
25
20
20
15
15
10
10
5
5
0 0
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
Opening Opening
From the plot, the maximum load and the plastic component (Vp) of the crack
opening is determined for use in the CTOD calculation.
The CTOD value is calculated from the following formula:
2
⎡ a 0 .5 a a a 2.7 a 2 ⎤
⎢ FS − − − +
W 2 ⎥⎥ x ⎡ (1 − v ) ⎤ + ⎡ 0.4(W − a )Vp ⎤ (2)
3( ) (1. 99 ( )(1 )( 2. 15 3. 93 2 . 7 )) 2
δ =⎢ x W W W W
⎢ ⎥ ⎢ ⎥
⎥ ⎣ 2σ YS E ⎦ ⎣ 0.4W + 0.6a + z ⎦
1.5
⎢ BW 2a a
2(1 + )(1 − )1.5
⎣⎢ W W ⎦⎥
where δ is the CTOD, F is the load, S the span, B the specimen thickness, W the
specimen width, a the crack length, v the poison’s ratio, Vp the plastic
component corresponding to the load at the critical event, z is the clip gage
height and σYS is the yield at test temperature.
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Crack Tip Opening Displacement, Tom Jarvie, Stork Southwestern Laboratories, Page 7 of 86) The Final Result
When the graphical data has been analyzed, the sample measured and
examined, and the CTOD value calculated, the validity of the result must also be
evaluated.
As discussed above, some of the validity requirements of the CTOD test cannot
be determined until the test is completed. A value may be obtained, there may be
a minimum value of CTOD and/or type of fracture restrained, but, the test must
also be valid. It is possible to have a result with a sufficient value to meet the
specification requirement, but still have an invalid test. Similarly, your result may
be lower than required with an invalid test. In these cases, the result obtained
should not be used and the test should be repeated.
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