ISO 22889:2007

INTERNATIONAL ISO
STANDARD 22889
First edition
2007-12-15
Metallic materials — Method of test for
the determination of resistance to stable
crack extension using specimens of low
constraint
Matériaux métalliques — Méthode d'essai pour la détermination de la
résistance à la propagation stable de fissures au moyen d'éprouvettes à
faible taux de triaxialité des contraintes

Reference number
©
ISO 2007
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©  ISO 2007
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ii © ISO 2007 – All rights reserved

Contents Page
Foreword. iv
Introduction . v
1 Scope . 1
2 Normative references . 2
3 Terms and definitions. 2
4 Symbols . 3
5 General requirements. 4
5.1 Introduction . 4
5.2 Test specimens . 4
5.3 Pre-test requirements. 6
5.4 Test apparatus . 7
5.5 Test requirements. 8
5.6 Post-test crack measurements. 9
6 Determination of δ − ∆a resistance curve and CTOA . 11
6.1 General. 11
6.2 Test procedure . 11
6.3 R-curve plot . 12
6.4 Critical CTOA determination. 13
7 Test report . 13
7.1 General. 13
7.2 Specimen, material and test environment . 14
7.3 Test data qualification. 14
7.4 Qualification of the δ R-Curve . 16
7.5 Qualification of ψ . 16
c
Annex A (informative) Examples of test reports . 28
Annex B (informative) Apparatus for measurement of crack opening displacement, δ . 33
Annex C (informative) Determination of the crack tip opening angle, ψ . 35
Annex D (informative) Determination of point values of fracture toughness . 45
Bibliography . 48

Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 22889 was prepared by Technical Committee ISO/TC 164, Mechanical testing of metals, Subcommittee
SC 4, Toughness testing — Fracture (F), Pendulum (P), Tear (T).

iv © ISO 2007 – All rights reserved

Introduction
ISO 12135 uses compact and bend specimens to determine specific (point) values of fracture toughness at
the onset of either stable or unstable crack extension, and to quantify resistance to stable crack extension.
These specimen types have near-square remaining ligaments to provide conditions of high constraint. If
certain size requirements are met, then the values of the quantities K , δ and J determined from
Ic 0,2BL 0,2BL
these specimens are considered size insensitive, and regarded as lower-bound fracture toughness values.
Although not explicitly stated, size insensitivity holds also for the crack extension resistance curve (R-curve).
In engineering practice, however, there are cases which are not covered by the method of test in ISO 12135,
for example where
⎯ the component thickness is much less than that required for size-insensitive properties as determined
using ISO 12135,
⎯ the thickness of the available material does not enable fabrication of specimens meeting the criteria for
size insensitivity, and
⎯ the loading conditions in the structural component are characterized by tension rather than bending.
In these cases, constraint in the structural component may be lower than that of the specimens specified by
ISO 12135, thus leading to higher resistance to crack extension and higher load-carrying capability in the
structural component than would have been forecast based on the test in ISO 12135.

INTERNATIONAL STANDARD ISO 22889:2007(E)

Metallic materials — Method of test for the determination of
resistance to stable crack extension using specimens of low
constraint
1 Scope
This International Standard specifies methods for determining the resistance to stable crack extension in
terms of crack opening displacement, δ , and critical crack tip opening angle, ψ , for homogeneous metallic
5 c
materials by the quasistatic loading of cracked specimens that exhibit low constraint to plastic deformation.
Compact and middle-cracked tension specimens are notched, precracked by fatigue, and tested under slowly
increasing displacement.
This International Standard describes methods covering tests on specimens not satisfying requirements for
size-insensitive fracture properties; namely, compact specimens and middle-cracked tension specimens in
relatively thin gauges.
Methods are given for determining the crack extension resistance curve (R-curve). Point values of fracture
toughness for compact specimens are determined according to ISO 12135. Methods for determining point
values of fracture toughness for the middle-cracked tension specimen are given in Annex D.
Crack extension resistance is determined using either the multiple-specimen or single-specimen method. The
multiple-specimen method requires that each of several nominally identical specimens be loaded to a
specified level of displacement. The extent of ductile crack extension is marked and the specimens are then
broken open to allow measurement of crack extension. Single-specimen methods based on either unloading
compliance or potential drop techniques can be used to measure crack extension, provided they meet
specified accuracy requirements. Recommendations for single-specimen techniques are described in
ISO 12135. Using either technique, the objective is to determine a sufficient number of data points to
adequately describe the crack extension resistance behaviour of a material.
The measurement of δ is relatively simple and well established. The δ results are expressed in terms of a
5 5
resistance curve, which has been shown to be unique within specified limits of crack extension. Beyond those
limits, δ R-curves for compact specimens show a strong specimen dependency on specimen width, whereas
the δ R-curves for middle-cracked tension specimens show a weak dependency.
CTOA is more difficult to determine experimentally. The critical CTOA is expressed in terms of a constant
value achieved after a certain amount of crack extension. The CTOA concept has been shown to apply to very
large amounts of crack extension and can be applied beyond the current limits of δ applications.
Both measures of crack extension resistance are suitable for structural assessment. The δ concept is well
established and can be applied to structural integrity problems by means of simple crack driving force
formulae from existing assessment procedures.
The CTOA concept is generally more accurate. Its structural application requires numerical methods, i.e. finite
element analysis.
Investigations have shown a very close relation between the concept of constant CTOA and a unique R-curve
for both compact and middle-cracked tension specimens up to maximum load. Further study is required to
establish analytical or numerical relationships between the δ R-curve and the critical CTOA values.
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
ISO 3785, Metallic materials — Designation of test specimen axes in relation to product texture
ISO 7500-1, Metallic materials — Verification of static uniaxial testing machines — Part 1:
Tension/compression testing machines — Verification and calibration of the force-measuring system
ISO 9513, Metallic materials — Calibration of extensometers used in uniaxial testing
ISO 12135:2002, Metallic materials — Unified method of test for the determination of quasistatic fracture
toughness
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
3.1
crack opening displacement
COD
δ
relative displacement of the crack surfaces normal to the original (undeformed) crack plane at the tip of the
fatigue precrack, as measured on the specimen’s side surface over an initial gauge length of 5 mm
3.2
crack tip opening angle
CTOA
ψ
relative angle of the crack surfaces measured (or calculated) at 1 mm from the current crack tip
3.3
stable crack extension
∆a
crack extension that, in displacement control, occurs only when the applied displacement is increased
3.4
crack extension resistance curve
R-curve
variation in δ with stable crack extension ∆a
3.5
critical crack tip opening angle
ψ
c
steady-state value of crack tip opening angle ψ at 1 mm from the current crack tip
NOTE This value is insensitive to the in-plane dimensions specified in this method; however, it may be thickness
dependent.
2 © ISO 2007 – All rights reserved

4 Symbols
For the purposes of this International Standard, the following symbols and units apply. For all parameters, the
temperature is assumed to be the test temperature unless otherwise noted.
Symbol Unit Designation
a mm crack length
a mm final crack length (a + ∆a )
f 0 f
a mm length of machined crack starter notch
m
a mm initial crack length
mm stable crack extension
∆a
∆a mm crack extension beyond which ψ is nearly constant
min c
mm
∆a crack extension limit for δ or ψ controlled crack extension
max 5 c
mm final stable crack extension
∆a
f
B mm specimen thickness
E
MPa Young’s modulus of elasticity
F kN applied force
F kN maximum fatigue precracking force
f
R MPa 0,2 % offset yield strength perpendicular to crack plane at the test temperature
p0,2
R
MPa tensile strength perpendicular to crack plane at the test temperature
m
α degrees crack path deviation
W mm width of compact specimen, half width of middle-cracked tension specimen
mm uncracked ligament length
W − a
W − a mm initial uncracked ligament length
mm final uncracked ligament length
W − a
f
degrees crack tip opening angle (CTOA)
ψ
degrees critical crack tip opening angle (critical CTOA)
ψ
c
Poisson’s ratio
ν
mm crack opening displacement over a 5 mm gauge length at tip of fatigue precrack
δ
NOTE This is not a complete list of parameters. Only the main parameters are given here; other parameters are
referred to and defined in the text.
5 General requirements
5.1 Introduction
The resistance to stable crack extension of metallic materials can be characterized in terms of either specific
(single point) values (see Annex D) or a continuous curve relating fracture resistance to crack extension over
a limited range of crack extension (see Clause 6). Any one of the fatigue-cracked test specimen configurations
specified in this method may be used to measure or calculate any of these fracture resistance parameters.
Tests are performed by applying slowly increasing displacement to the test specimen and measuring the
resulting force and corresponding crack opening displacement and angle. The measured forces,
displacements and angles are then used in conjunction with certain pre-test and post-test specimen
measurements to determine the material’s resistance to crack extension. Details of test specimens and
general information relevant to the determination of all fracture parameters are given in this method. A flow-
chart illustrating the way this International Standard can be used is presented in Figure 1.
Fracture resistance symbols identified for use in this International Standard method of test are given in
Table 1:
Table 1 — Fracture resistance symbols
Size-sensitive quantities
Size-insensitive
Parameter Qualifying limits
(specific to thickness B
quantities
tested)
See Annex D Not applicable
δ , point value of fracture
toughness
Not applicable a , (W − a ) W 4B ∆a < ∆a = 0,25(W − a )
δ R-curve
0 0 max 0
for compact specimens;
∆a < ∆a = W − a − 4B
max 0
for middle-cracked
tensile specimens
Not applicable a , (W − a ) W 4B ∆a > ∆a = 50/(5 + B)
ψ
0 0 min
c
∆a < ∆a = W − a − 4B
max 0
(see Figure 11)
NOTE The qualifying limit for ψ , ∆a > ∆a = 50/(5 + B) was established using surface measurements of crack extension for
c min
aluminium alloys and steels in sheet thicknesses ranging from 1 mm to 25 mm.

5.2 Test specimens
5.2.1 Specimen configuration and size
Specimen dimensions and tolerances shall conform to those shown in Figures 2 and 3.
The choice of specimen design shall take into consideration the likely outcome of the test (see Figure 1),
which fracture resistance value (δ or ψ) is to be determined, the crack plane orientation of interest, and the
amount and condition of test material available.
NOTE Both specimen configurations (Figures 2 and 3) are suitable for determination of δ and ψ values.
5 c
For both specimen configurations, the conditions [a , (W − a )] W 4B shall be satisfied.
0 0
4 © ISO 2007 – All rights reserved

5.2.2 Specimen preparation
5.2.2.1 Material condition
Specimens shall be machined from stock in the final heat-treated and mechanically worked conditions.
In exceptional circumstances where material cannot be machined in the final condition, final heat treatment
may be carried out after machining, provided that the required dimensions and tolerances for the specimen, its
shape, and its surface finish are met. Where dimensions of the machined specimen are substantially different
from the pre-machined stock, a size effect on the heat-treated microstructure and mechanical properties shall
be taken into account in the service application.
5.2.2.2 Crack plane orientation
Orientation of the crack plane shall be decided before machining, identified in accordance with ISO 3785, and
recorded in accordance with Table A.1.
NOTE Crack extension resistance depends on the orientation and direction of crack extension in relation to the
principal directions of mechanical working, grain flow and other forms of anisotropy.
5.2.2.3 Machining
The specimen notch profile shall not exceed the envelope shown in Figure 4. The root radius of a milled notch
shall be not greater than 0,10 mm. Sawn, disk ground, or spark-eroded notches shall not have a width greater
than 0,15 mm.
5.2.2.4 Fatigue precracking
5.2.2.4.1 General
Fatigue precracking shall be performed with the material in the final heat-treated, mechanically worked or
environmentally conditioned state. Intermediate treatments between fatigue precracking and testing are
acceptable only when such treatments are necessary to simulate the conditions of a specific structural
application; such departure from recommended practice shall be (explicitly) reported.
Maximum fatigue precracking force during any stage of the fatigue precracking process shall be accurate to
±2,5 %.
Measured values of specimen thickness, B, and width, W, determined in accordance with 5.3.1, shall be
recorded and used to determine the maximum fatigue precracking force F in accordance with 5.2.2.4.3 and
f
5.2.2.4.4.
The ratio of minimum-to-maximum force in the fatigue cycle shall be in the range 0 to 0,1 except that, in order
to expedite crack initiation, one or more cycles of −1,0 may be applied first.
5.2.2.4.2 Equipment and fixtures
Fixtures for fatigue precracking shall be carefully aligned and arranged so that loading is uniform through the
specimen thickness B and symmetrical about the plane of the prospective crack.
5.2.2.4.3 Compact specimens
For compact specimens, the maximum fatigue precracking force during the final 1,3 mm or 50 % of precrack
extension, whichever is less, shall be the lowest value of
⎡⎤
BW
F = ξΕ (1)
⎢⎥
f
ga(/W)
⎢⎥
⎣⎦
−40,5
where ξ=×1, 6 10 m , and
−1,5 2 3 4
⎡⎤
aa a a a a
⎡ ⎤ ⎡ ⎤ ⎛⎞ ⎛⎞ ⎛⎞
00 0 0 0 0
⎢⎥
ga( /W )= 1− 2+ 0,886+ 4,64−+−13,32 14,72 5,6 (2)
10 ⎢⎥ ⎢ ⎥ ⎜⎟ ⎜⎟ ⎜⎟
WW W W W W
⎢⎥
⎣ ⎦ ⎣ ⎦ ⎝⎠ ⎝⎠ ⎝⎠
⎣⎦
5.2.2.4.4 Middle-cracked tension specimens
For middle-cracked tension specimens, the maximum fatigue precracking force during the final 1,3 mm or
50 % of precrack extension, whichever is less, shall be the lowest value of
−0,5
⎡⎤πa
FE=πξB2sW aec (3)
f
⎢⎥
2W
⎣⎦
−40,5
where ξ=×1, 6 10 m
5.3 Pre-test requirements
5.3.1 Pre-test measurements
The dimensions of specimens shall conform to those shown in Figures 2 and 3. Measurement of the thickness
B and width W shall be within 0,02 mm or to ±0,2 %, whichever is the larger.
Specimen thickness B shall be measured, before testing, at a minimum of three equally spaced positions
along the intended crack extension path. The average of these measurements shall be taken as the thickness
B.
Specimen width W of the middle-cracked tension specimen shall be measured at a minimum of three equally
spaced positions within ±0,1 W of the crack plane. The average of these measurements shall be taken as the
width W.
The compact specimen width W shall be measured with reference to the loading-hole centreline. Customarily,
the loading-hole centreline is established first, and then the dimension W is measured to the specimen edge
ahead of the crack tip in the plane of the crack. This measurement shall be made at a minimum of three
equally spaced positions across the specimen thickness. The dimension 1,25 W (between the specimen
edges ahead and behind the crack tip) shall be measured in addition, at the same equally spaced positions
across the thickness in a plane as close as possible to the plane of the crack.
5.3.2 Crack front shape and length requirements
A fatigue crack shall be developed from the root of the machined notch of the specimen as follows:
⎯ for compact specimens (see Figure 2), the ratio a /W shall be in the range 0,45 to 0,65;
⎯ for middle-cracked tension specimens, the ratio a /W shall be in the range 0,25 to 0,50.
6 © ISO 2007 – All rights reserved

The minimum fatigue crack extension shall be the larger of 1,3 mm or 2,5 % of the specimen width W. The
notch plus fatigue crack shall be within the limiting envelope shown in Figure 4.
5.4 Test apparatus
5.4.1 Calibration
Calibration of all measuring apparatus shall be traceable either directly or indirectly via a hierarchical chain to
an accredited calibration laboratory.
5.4.2 Force application
The combined force sensing and recording device shall conform to ISO 7500-1.
The test machine shall operate at a constant displacement rate.
A force measuring system of nominal capacity exceeding 1,2 F shall be used, where
L
⎯ for compact specimens
BW()−a
F = R (4)
Lm
(2Wa+ )
⎯ or for middle-cracked tension specimens
F=−2(BW a )R (5)
L0m
5.4.3 Displacement measurement
The displacement gauge used for the determination of δ shall have an electrical output that accurately
represents the displacement between two precisely located gauge positions 5 mm apart, spanning the crack
at the fatigue crack tip. The design of the displacement gauge (or transducer where appropriate) and
specimen shall allow free rotation of the points of contact between the gauge and specimen.
NOTE 1 Guidance for determining δ is given in Annex B.
NOTE 2 The crack mouth opening displacement is not needed for the δ and ψ determinations, but a force crack
5 c
mouth opening displacement record may be suitable for evaluating the methods from finite element analyses and other
fracture analysis methods. Examples of proven displacement gauge designs are given in References [1] and [2] (see
Bibliography), and similar gauges are commercially available.
Gauges for crack mouth opening displacement measurement shall be calibrated in accordance with ISO 9513,
as interpreted in relation with this International Standard, and shall be at least of Class 1. Calibration shall be
performed at least each week when the gauges are in use.
NOTE Calibration may be carried out more frequently depending on use and agreement between contractual parties.
Verification of the displacement gauge shall be performed at the test temperature ±5 °C. The response of the
gauge shall be true to ±0,003 mm for displacements up to 0,3 mm and to ±1 % of the actual reading thereafter.
5.4.4 Test fixtures
Compact specimens shall be loaded using a clevis and pin arrangement designed to minimize friction. The
arrangement shall ensure load train alignment as the specimen is loaded under tension. Clevises for R-curve
measurements shall have flat-bottomed holes (see Figure 5) so that the loading pins are free to roll throughout
the test. Round-bottomed holes (see Figure 6) shall not be allowed for single-specimen (unloading
compliance) tests. Fixture-bearing surfaces shall have a hardness greater than 40 HRC (400 HV) or a yield
strength of at least 1 000 MPa. Middle-cracked tension specimens shall be loaded using hydraulically clamped
or bolted grips designed to carry the applied load by friction. Bolt bearing should be avoided in order to
minimize non-uniform loading. The arrangement shall ensure alignment of the specimen with minimal in-plane
and out-of-plane bending. All specimens shall be tested with anti-buckling guide plates, as shown in Figure 7.
The anti-buckling guide plates shall cover a large portion of the specimen. Support only along the crack plane
has been shown to be insufficient to prevent buckling between the grip lines and the crack plane for thin-sheet
materials. Flat plates are sufficient for small middle-cracked tension specimens (W < 600 mm); but flat plates
and I-beams, as illustrated in Figure 7a), are required for middle-cracked tension specimens with widths larger
than about 600 mm. A suitable design for compact specimens is shown in Figure 7b).
5.5 Test requirements
It is recommended that anti-buckling plates be attached to both sides of the tension specimen covering the
expected path of the crack for a distance four times the initial total crack length perpendicular to the crack.
Frictional forces between the specimen and anti-buckling plates shall be minimized by the use of an inert
lubricant such as Teflon® applied to the mating surfaces. An access hole is required in one of the plates for
mounting the δ gauge on the specimen or, if the potential method is used, for the attachment of cables.
5.5.1 Compact specimen testing
5.5.1.1 Specimen and fixture alignment
The loading clevises shall be aligned to within 0,25 mm, and the specimen shall be centred on the loading
pins within 0,75 mm with respect to the clevis opening.
5.5.1.2 Crack opening displacement δ
A method of measuring the crack opening displacement δ is described in Annex B.
5.5.1.3 Crack tip opening angle ψ
The crack tip opening angle ψ may be measured or calculated as described in Annex C.
5.5.2 Middle-cracked tension specimen testing
5.5.2.1 Specimen and fixture alignment
The fixture shall be designed to distribute the load uniformly over the cross-section of the specimen. The
fixture may be rigidly connected to the machine if uniform loading of the specimen in the machine can be
assured at all loads. Otherwise, pinloading via detachable grips is recommended.
5.5.2.2 Crack opening displacement δ
A method of measuring the crack opening displacement δ is given in Annex B.
5.5.2.3 Crack tip opening angle ψ
The crack tip opening angle ψ may be measured or calculated as described in Annex C.
5.5.3 Specimen test temperature
Specimen test temperature shall be controlled and recorded to an accuracy of ±2 °C. For this purpose, a
thermocouple or platinum resistance thermometer shall be placed in contact with the surface of the specimen
in a region not further than 5 mm from the fatigue crack tip. When substantial amounts of crack extension are
anticipated, additional sensors (thermocouples or thermometers) shall be placed in proximity to the anticipated
8 © ISO 2007 – All rights reserved

crack path so that the specified specimen temperature can be assured for the material being tested. Tests
shall be made in situ in suitable low- or high- temperature media. Before testing in a liquid medium, the
specimen shall be retained in the liquid for at least 30 s/mm of thickness B after the specimen surface has
reached the test temperature. When using a gaseous medium, a soaking time of at least 60 s/mm of thickness
shall be employed. Minimum soaking time at the test temperature shall be 15 min. The temperature of the test
specimen shall remain within ±2 °C of the nominal test temperature throughout the test and shall be recorded
as required in Clause 7.
5.5.4 Recording
The force and corresponding displacement outputs shall be recorded.
NOTE Corresponding displacements are either crack opening displacement δ (for determining the δ R-curve) or the
5 5
crack mouth opening displacement CMOD (not required here, but useful for supplementary evaluations).
5.5.5 Testing rates
Tests shall be conducted under crack mouth opening, load-line, or crosshead-displacement control. The load-
line displacement rate shall be such that, within the linear elastic region, the stress intensification rate is within
0,5 −1 0,5 −1
the range 0,2 MPa·m ·s to 3 MPa·m ·s . For each series of tests, all specimens shall be loaded at the
same nominal rate.
5.5.6 Test analyses
Analyses for point determinations of fracture toughness for compact specimens are given in Annex D, and for
δ resistance-curve determinations in Clause 6 (see Figure 1).
5.6 Post-test crack measurements
The specimen shall be broken open after testing and its fracture surface examined to determine the original
crack length a , and the final stable crack extension ∆a .
0 f
For some tests, it may be necessary to mark the extent of stable crack extension before breaking open the
specimen. Marking of stable crack extension may be done by either heat tinting or post-test fatiguing. Care
shall be taken to minimize post-test deformation of the specimen. Cooling ferritic steels to ensure brittle
behaviour may be helpful.
5.6.1 Initial crack length a
5.6.1.1 Compact specimens
The initial crack length a shall be measured from the centreline of the pinhole to the tip of the fatigue crack
with an instrument accurate to ±0,1 % or ±0,025 mm, whichever is the greater. Measurements shall be made
at five positions through the specimen thickness. The value of a is obtained by first averaging the two surface
measurements made at positions 0,01B inward from the surface (see Figure 8) and then averaging these
values with those at the three equispaced inner measurement points:
j=4
⎡⎤
1⎛⎞aa+
01 05
⎢⎥
aa=+ (6)
00⎜⎟ j
∑
42⎢⎥
⎝⎠
j=2
⎣⎦
5.6.1.2 Middle-cracked tension specimens
The initial crack length a shall be measured as one-half of the total crack length to the tips of both fatigue
cracks with an instrument accurate to ±0,1 % or 0,025 mm, whichever is the greater. Measurements are made
using a 5-point average. The value of a is obtained by first averaging the two surface measurements made at
positions 0,01B inward from the surface (see Figure 9), averaging these values with those at the three
equispaced inner measurement points, and then dividing the resulting value by 2:
j=4
⎡⎤
1⎛⎞22aa+
01 05
⎢⎥
aa=+ 2 (7)
⎜⎟
00∑ j
82⎢⎥
⎝⎠
j=2
⎣⎦
NOTE For both compact and middle-cracked tension specimens of thickness B < 5 mm, a 3-point average is
sufficient. The value of a is obtained by first averaging the two surface measurements a and a , and then averaging
0 0,1 0,5
that with the measurement made at mid-plane of the specimen, a :
0,3
⎡⎤
aa=+0,5 a / 2+a
()
0,1 0,5 0,3
⎣⎦
5.6.1.3 Requirements
The initial crack length a shall satisfy the following.
a) The ratio a /W shall be within the range 0,45 to 0,65 for compact specimens, and within the range 0,25 to
0,50 for middle-cracked tension specimens.
b) If a five-point average for determining a has been used, then the difference between any one of the
central three points and the five-point average shall not exceed 0,1 a .
c) If a three-point average for determining a has been used, then the difference between the central point
and the three-point average shall not exceed 0,1 a .
d) No part of the fatigue precrack front shall be closer to the crack starter notch than 1,3 mm or 0,025W,
whichever is the larger.
e) The fatigue precrack shall be within the envelope shown in Figure 4.
If the above requirements are not satisfied, the test result is not qualified according to this method of test.
5.6.2 Stable crack extension, ∆a
The total final crack extension (including any crack tip blunting) ∆a between the initial and final crack fronts
f
shall be measured with an instrument accurate to ±0,025 mm using the averaging procedure of 5.6.1. For
middle-cracked tension specimens, the crack extension ∆a is given by the average of the crack extension
f
values measured at both crack fronts. Any irregularities in crack extension, such as spikes and isolated
‘islands’ of crack extension, shall be reported in accordance with Clause 7.
NOTE 1 It may only be practical to estimate the length of irregular cracks by ignoring the spikes or subjectively
averaging the crack extension region. Care should be exercised when the results derived from highly irregular crack fronts
are used in analysis. It is useful to provide an additional sketch or photograph of such irregular cracks in reporting results.
All individual pre-test and post-test measurements are to be recorded and used for calculations in accordance with
Clause 6.
NOTE 2 For specimens with thickness B < 5 mm, a three-point average as in 5.6.1.2 is suggested.
10 © ISO 2007 – All rights reserved

5.6.3 Crack path
The crack plane may deviate during stable crack extension from the original fatigue precrack plane (which is a
flat surface perpendicular to the applied force). Typically, the transition is to shear planes at the specimen
surfaces. When such shear planes are sloped similarly with respect to the original fatigue precrack plane, then
crack extension is said to be in a single-shear mode. When they are sloped differently, such as to resemble a
roof in cross-section (the mating fracture surface then resembles a V-groove), crack extension occurs in a
double-shear mode. Shear fracture surfaces are typically sloped 30° to 45°.
NOTE Depending on the material and specimen thickness, the fracture surface in the central part of the specimen
thickness may still be perpendicular to the applied force. This is a mixed mode of crack extension.
5.6.3.1 Crack extension resistance
For fractures that deviate from planarity, the crack extension resistance of those exhibiting double shear is
customarily higher than for those exhibiting single shear. Test results for such double-shear fractures are
considered to be not qualified to characterize the material.
5.6.3.2 Crack path deviation
When the angle α between the original flat precrack plane and the plane of the deviated crack surface
exceeds 10°, the test result is no longer considered qualified according to this method of test.
6 Determination of δ − ∆a resistance curve and CTOA
6.1 General
Fracture behaviour is characterized by this method in terms of the variation of either δ (COD) or ψ (CTOA)
with the crack extension ∆a. It is important to note, however, that ψ versus ∆a is not treated here as a crack
extension resistance curve.
6.2 Test procedure
Load specimens and evaluate the resulting amount of crack extension in accordance with 5.5 and 5.6.
6.2.1 Multiple-specimen procedure
A series of nominally identical specimens shall be loaded to selected displacement levels and the
corresponding amounts of crack extension determined. Each specimen tested provides one point on the
δ − ∆a crack resistance curve (hereafter referred to generically as the R-curve).
NOTE Six or more favourably positioned points are required to generate an R-curve. Loading the first specimen to a
point just past maximum load and measuring the resulting stable crack extension helps to determine the displacement
levels needed to position data points favourably in additional tests.
6.2.2 Single-specimen procedure
The single-specimen procedure makes use of electric potential, elastic compliance or another technique to
obtain multiple points on the resistance curve from the test of a single specimen. Single-specimen testing
procedures are described in ISO 12135.
Using a direct method (e.g. elastic compliance), the estimated final crack extension ∆a shall be within 15 % of
f
the measured crack extension or 0,15 mm, whichever is the greater, for ∆a u 0,2(W − a ), and within
f 0
0,03(W − a ) for ∆a > 0,2(W − a ). For techniques that require an a priori estimate of the initial crack length a
0 f 0 0
for subsequent determination of crack extension, such as the unloading-compliance technique, the estimated
a shall be within 2 % of the (post-test) measured a value.
0 0
For indirect techniques (e.g. electrical potential), the first specimen tested shall be used to establish a
correlation between experimental output and measured crack extension to beyond the ∆a defined in 6.4. At
max
least one additional test shall be conducted to estimate crack extension using the results from the first test.
Agreement between the estimated and actual crack extension ∆a shall be within 15 % or 0,15 mm, whichever
is the greater; otherwise the procedure shall not be accepted.
6.2.3 Final crack front straightness
The final crack length shall be determined as the sum of the initial crack length and the final stable crack
extension measured using the averaging methods of 5.6.1 and 5.6.2. If the five-point averaging method is
used, none of the three interior final crack length measurements shall differ from the five-point average value
by more than 0,1a ; if the three-point averaging method is used, the central final crack length measurement
shall not differ from the three-point average by more than 0,1a ; otherwise the result is not qualified.
6.3 R-curve plot
The points of crack opening displacement, δ , versus stable crack extension, ∆a, form the fracture resistance
R-curve (see Figure 10). The data may be used in tabular form or as a plotted graph. An equation may be
fitted to the graph for analysis, or the plot itself may be used for analysis.
6.3.1 Plot construction
Construct a plot of the crack opening displacement, δ , versus the stable crack extension, ∆a, from the data
obtained in 5.5.1.2, 5.5.2.2 and 5.6.2 (see Figure 10).
For each compact specimen tested, calculate ∆a from
max
∆=aW0,25 −a (8)
()
max 0
For each middle-cracked tension specimen tested, calculate ∆a from
max
∆=aW−a− 4B (9)
()
max 0
Plot δ versus ∆a as shown in Figure 10.
Tests terminating in unstable fracture shall be reported as such and, if the amount of stable crack extension to
fracture can be measured on the fracture surface, include that datum point in the R-curve plot. Unstable
fracture data points shall be clearly marked on the R-curve plot and appropriately noted in the test report (see
Annex A).
NOTE The point of unstable failure can depend on the specimen size and geometry.
6.3.2 Data spacing and curve fitting
A minimum of six data points shall be used to define the R-curve.
When an equation is to be fitted to the R-curve, at least one data point shall reside within each of the four
equal crack extension regions shown in Figure 10. The curve shall be best-fitted through the data points lying
between the 0 and ∆a exclusion lines (see Figure 10) using the power-law Equation (10):
max
γ
δα=+β∆a (10)
where α and β W 0, and 0 u γ u 1.
12 © ISO 2007 – All rights reserved

A method for evaluating the constants α, β and γ is given in ISO 12135:2002, Annex H. If α or β is less than
zero from the linearized regression, then the result is unacceptable and the fitted equation is not
representative of the R-curve. In such cases, additional tests or the use of a single-specimen test procedure
are suggested.
The R-curve thus obtained characterizes the material for the thickness and specimen geometry tested, and is
independent of the in-plane dimensions of either compact specimens or middle-cracked tension specimens.
6.4 Critical CTOA determination
A steady-state (average) value of ψ, ψ , is established after a minimum amount of crack extension.
c
Construct a plot of the crack tip opening angle (CTOA), ψ, versus the crack extension, ∆a, from the data
obtained in 5.5.1.3, 5.5.2.3 and 5.6.2 (see Figure 11).
For each specimen tested, calculate the maximum amount of crack extension, ∆a , from
max
∆=aW−a− 4B (11)
()
max 0
The minimum amount of crack extension, ∆a , is that value of ∆a where ψ in Figure 11 attains a constant
min
value. These two values of ∆a serve as the upper and lower bounds for the crack extension over which the
critical CTOA, ψ , is evaluated.
c
NOTE 1 Due to the developing nature of the CTOA method, the ∆a limits are based on limited experience.
Four methods (optical microscope, digital image correlation, microtopography analysis and finite element
analysis) may be used to determine the CTOA. Details are given in Annex C.
Measurements of CTOA may be made at any amount of crack extension, in particular between the crack
extension limits. CTOA values measured outside the crack extension limits are for informational purposes only.
Plot ψ against ∆a as shown in Figure 11. Determine ψ from the ψ − ∆a plot between the limiting crack
c
extension limits, ∆a and ∆a .
min max
NOTE 2 Crack tip opening angles measured on the surface of a specimen in the initial phase of crack extension are
generally large due to crack tip blunting and crack tunnelling. But in the interior region, which is under high local constraint,
the ψ values are generally lower than the surface values (see Figure 11).
For CTOA testing, evaluate the critical value o
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