1.1 This test method covers the determination of fracture toughness (KIc) of metallic materials under predominantly linear-elastic, plane-strain conditions using fatigue precracked specimens having a thickness of 1.6 mm (0.063 in.) or greater2 subjected to slowly, or in special (elective) cases rapidly, increasing crack-displacement force. Details of test apparatus, specimen configuration, and experimental procedure are given in the Annexes.
NOTE 1—Plane-strain fracture toughness tests of thinner materials that are sufficiently brittle (see 7.1) can be made using other types of specimens (1).3 There is no standard test method for such thin materials.
1.2 This test method is divided into two parts. The first part gives general recommendations and requirements for KIc testing. The second part consists of Annexes that give specific information on displacement gage and loading fixture design, special requirements for individual specimen configurations, and detailed procedures for fatigue precracking. Additional annexes are provided that give specific procedures for beryllium and rapid-force testing. 1.3 General information and requirements common to all specimen configurations
3.1 Definitions:Terminology E1823 is applicable to this test method:
3.1.1 stress-intensity factor, K, KI, KII, KIII [FL−3/2]— magnitude of the ideal-crack-tip stress field (a stress-field singularity), for a particular mode of crack displacement, in a homogeneous, linear-elastic body.
220.127.116.11 K is a function of applied force and test specimen size, geometry, and crack size, and has the dimensions of force times length-3/2.
3.1.2 plane-strain fracture toughness, KIc [FL-3/2]—the crack-extension resistance under conditions of crack-tip plane strain in Mode I for slow rates of loading under predominantly linear-elastic conditions and negligible plastic-zone adjustment. The stress intensity factor, KIc, is measured using the operational procedure (and satisfying all of the validity requirements) specified in Test Method E399, that provides for the measurement of crack-extension resistance at the onset (2% or less) of crack extension and provides operational definitions of crack-tip sharpness, onset of crack extension, and crack-tip plane strain.
18.104.22.168 See also definitions of crack-extension resistance, crack-tip plane strain, and mode in Terminology E1823. 3.1.3 crack mouth opening displacement (CMOD), Vm [L]— crack opening displacement resulting from the total deformation (elastic plus plastic), measured under force at the location on a crack surface that has the largest displacement per unit force.
3.1.4 crack plane orientation—identification of the plane and direction of crack extension in relation to the characteristic directions of the product. A hyphenated code defined in Terminology E1823 is used wherein the letter(s) preceding the hyphen represents the direction normal to the crack plane and the letter(s) following the hyphen represents the anticipated direction of crack extension (see Fig. 1).
22.214.171.124 Wrought Products—the fracture toughness of wrought material depends on, among other factors, the orientation and propagation direction of the crack in relation to the material’s anisotropy, which depends, in turn, on the principal directions of mechanical working and grain flow. Orientation of the crack plane shall be identified wherever possible. In addition, product form shall be identified (for example, straight-rolled plate, cross-rolled plate, pancake forging, and so forth) along with material condition (for example, annealed, solution treated plus aged, and so forth). The user shall be referred to product specifications for detailed processing information. 126.96.36.199 For rectangular sections, the reference directions are identified as in Fig. 1(a) and Fig. 1(b), which give examples for rolled plate. The same system is used for sheet, extrusions, and forgings with nonsymmetrical grain flow.
L = direction of principal deformation (maximum grain flow)
T = direction of least deformation
S = third orthogonal direction
188.8.131.52 Using the two-letter code, the first letter designates the direction normal to the crack plane, and the second letter the expected direction of crack propagation. For example, in Fig. 1(a), the T-L specimen fracture plane normal is in the width direction of a plate and the expected direction of crack propagation is coincident with the direction of maximum grain flow (or longitudinal) direction of the plate.
184.108.40.206 For specimens tilted in respect to two of the reference axes as in Fig. 1(b), crack plane orientation is identified by a three-letter code. The designation L-TS, for example, indicates the crack plane to be perpendicular to the principal deformation (L) direction, and the expected fracture direction to be intermediate between T and S. The designation TS-L means that the crack plane is perpendicular to a direction intermediate between T and S, and the expected fracture direction is in the L direction.
220.127.116.11 For cylindrical sections, where grain flow can be in the longitudinal, radial or circumferential direction, specimen location and crack plane orientation shall reference original cylindrical section geometry such that the L direction is always the axial direction for the L-R-C system, as indicated in Fig. 1(c), regardless of the maximum grain flow. Note that this is a geometry based system. As such, the direction of maximum grain flow shall be reported when the direction is known.
NOTE 2—The same system is useful for extruded or forged parts having circular cross section. In most cases the L direction corresponds to the direction of maximum grain flow, but some products such as pancake, disk, or ring forgings can have the R or C directions correspond to the direction of maximum grain flow, depending on the manufacturing method.
L = axial direction
R = radial direction
C = circumferential or tangential direction
18.104.22.168 In the case of complex structural shapes, where the grain flow is not uniform, specimen location and crack plane orientation shall reference host product form geometry and be noted on component drawings.
22.214.171.124 Non-Wrought Products—for non-wrought products, specimen location and crack plane orientation shall be defined on the part drawing. The result of a fracture toughness test from a non-wrought product shall not carry an orientation designation.
126.96.36.199 Discussion—when products are to be compared on the basis of fracture toughness, it is essential that specimen location and orientation with respect to product characteristic
directions be comparable and that the results not be generalized beyond these limits.
3.2 Definitions of Terms Specific to This Standard:
3.2.1 stress-intensity factor rate, K˙ (FL-3/2 t-1)—change in stress-intensity factor, K, per unit time.
4. Summary of Test Method
4.1 This test method covers the determination of the planestrain fracture toughness (KIc) of metallic materials by increasing-force tests of fatigue precracked specimens. Force is applied either in tension or three-point bending. Details of the test specimens and experimental procedures are given in the Annexes. Force versus crack-mouth opening displacement (CMOD) is recorded either autographically or digitally. The force at a 5 % secant offset from the initial slope (corresponding to about 2.0 % apparent crack extension) is established by a specified deviation from the linear portion of the record (1).
The value of K Ic is calculated from this force using equations that have been established by elastic stress analysis of the specimen configurations specified in this test method. The validity of the KIc value determined by this test method depends upon the establishment of a sharp-crack condition at
the tip of the fatigue crack in a specimen having a size adequate to ensure predominantly linear-elastic, plane-strain conditions.
To establish the suitable crack-tip condition, the stressintensity factor level at which specimen fatigue precracking is
conducted is limited to a relatively low value.
4.2 The specimen size required for test validity increases as the square of the material’s toughness-to-yield strength ratio.
Therefore a range of proportional specimens is provided.
5. Significance and Use
5.1 The property KIc determined by this test method characterizes the resistance of a material to fracture in a neutral environment in the presence of a sharp crack under essentially
linear-elastic stress and severe tensile constraint, such that (1) the state of stress near the crack front approaches tritensile plane strain, and (2) the crack-tip plastic zone is small
compared to the crack size, specimen thickness, and ligament ahead of the crack.
5.1.1 Variation in the value of KIc can be expected within the allowable range of specimen proportions, a/W and W/B. KIc may also be expected to rise with increasing ligament size.
Notwithstanding these variations, however, KIc is believed to represent a lower limiting value of fracture toughness (for 2 % apparent crack extension) in the environment and at the speed and temperature of the test.
5.1.2 Lower values of KIc can be obtained for materials that
fail by cleavage fracture; for example, ferritic steels in the ductile-to-brittle transition region or below, where the crack front length affects the measurement in a stochastic manner independent of crack front constraint. The present test method does not apply to such materials and the user is referred to Test Method E1921 and E1820. Likewise this test method does not apply to high toughness or high tearing-resistance materials whose failure is accompanied by appreciable amounts of plasticity. Guidance on testing elastic-plastic materials is given in Test Method E1820.
5.1.3 The value of K Ic obtained by this test method may be used to estimate the relation between failure stress and crack size for a material in service wherein the conditions of high constraint described above would be expected. Background information concerning the basis for development of this test method in terms of linear elastic fracture mechanics may be found in Refs (1) and (2).
5.1.4 Cyclic forces can cause crack extension at KI values less than K Ic. Crack extension under cyclic or sustained forces (as by stress corrosion cracking or creep crack growth) can be influenced by temperature and environment. Therefore, when K Ic is applied to the design of service components, differences between laboratory test and field conditions shall be considered.
5.1.5 Plane-strain fracture toughness testing is unusual in that there can be no advance assurance that a valid K Ic will be determined in a particular test. Therefore, compliance with the specified validity criteria of this test method is essential. 5.1.6 Residual stresses can adversely affect the indicated
K Q and KIc values. The effect can be especially significant for specimens removed from as-heat treated or otherwise nonstress relieved stock, from weldments, from complex wrought parts, or from parts with intentionally induced residual stresses. Indications of residual stress include distortion during specimen machining, results that are specimen configuration dependent, and irregular fatigue precrack growth (either excessive crack front curvature or out-of-plane growth). Guide B909 provides supplementary guidelines for plane strain fracture toughness testing of aluminum alloy products for which complete stress relief is not practicable. Guide B909 includes additional guidelines for recognizing when residual stresses may be significantly biasing test results, methods for minimizing the effects of residual stress during testing, and guidelines for correction and interpretation of data.
5.2 This test method can serve the following purposes:
5.2.1 In research and development, to establish in quantitative terms significant to service performance, the effects of metallurgical variables such as composition or heat treatment, or of fabricating operations such as welding or forming, on the fracture toughness of new or existing materials.
5.2.2 In service evaluation, to establish the suitability of a material for a specific application for which the stress conditions are prescribed and for which maximum flaw sizes can be established with confidence.
5.2.3 For specifications of acceptance and manufacturing quality control, but only when there is a sound basis for specifying minimum KIc values, and then only if the dimensions of the product are sufficient to provide specimens of the size required for valid KIc determination. The specification of
K Ic values in relation to a particular application should signify that a fracture control study has been conducted for the component in relation to the expected loading and environment, and in relation to the sensitivity and reliability of the crack detection procedures that are to be applied prior to service and subsequently during the anticipated life.
6.1 Testing Machine and Force Measurement—The calibration of the testing machine shall be verified in accordance with Practices E4. The test machine shall have provisions for autographic recording of the force applied to the specimen; or, alternatively, a computer data acquisition system that may be used to record force and CMOD for subsequent analysis.
6.2 Fatigue Precracking Machine—When possible, the calibration of the fatigue machine and force-indicating device shall be verified statically in accordance with Practices E4. If the machine cannot be calibrated and verified statically, the applied force shall otherwise be known to 62.5 %. Careful alignment of the specimen and fixturing is necessary to encourage straight fatigue cracks. The fixturing shall be such that the stress distribution is uniform across the specimen thickness and symmetrical about the plane of the prospective crack.
6.3 Loading Fixtures—Fixtures suitable for loading the specified specimen configurations are shown in the Annexes. The fixtures are designed to minimize friction contributions to the measured force.
6.4 Displacement Gage—The displacement gage electrical output represents relative displacement (V) of two precisely located gage positions spanning the crack starter notch mouth. Exact and positive positioning of the gage on the specimen is essential, yet the gage must be released without damage when he specimen breaks. Displacement gage and knife-edge designs shall provide for free rotation of the points of contact between the gage and the specimen. A recommended design for a self-supporting, releasable displacement gage is shown in Fig. 2 and described in Annex A1. The gage’s strain gage
bridge arrangement is also shown in Fig. 2. 6.4.1 The specimen shall be provided with a pair of accurately machined knife edges to support the gage arms and serve as displacement reference points. The knife edges may be machined integral with the specimen as shown in Figs. 2 and 3, or they may be separate pieces affixed to the specimen. A suggested design for attachable knife edges is shown in Fig. 4. This design features a knife edge spacing of 5 mm (0.2 in.). The effective gage length is established by the points of contact between the screw and the hole threads. For the design shown, the major diameter of the screw is used in setting this gage length. A No. 2 screw will permit the use of attachable knife edges for specimens having W > 25 mm (1.0 in.).
6.4.2 Each gage shall be verified for linearity using an extensometer calibrator or other suitable device. The resolution of the calibrator at each displacement interval shall be within 0.00051 mm (0.000020 in.). Readings shall be taken at ten equally spaced intervals over the working range of the gage (see Annex A1). The verification procedure shall be performed three times, removing and reinstalling the gage in the calibration fixture after each run. The required linearity shall correspond to a maximum deviation of 0.003 mm (0.0001 in.) of the individual displacement readings from a least-squares-best-fit straight line through the data. The absolute accuracy, as such, is not important in this application, since the test method is concerned with relative changes in displacement rather than absolute values (see 9.1). Verification of gage calibration shall be performed at the temperature of test 65.6°C (10°F). The gage shall be verified during the time the gage is in use at time intervals defined by established quality assurance practices. Commercial gages are typically verified annually.
6.4.3 It is not the intent of this test method to exclude the use of other types of gages or gage-fixing devices provided the gage used meets the requirements listed above and provided the gage length does not exceed those limits given in the Annex appropriate to the specimen being tested. 7. Specimen Size, Configurations, and Preparation
7.1 Specimen Size:
7.1.1 In order for a result to be considered valid according to this test method (see also 188.8.131.52), the specimen ligament size (W – a) must be not less than 2.5(KIc/σYS)2, where σYS is the 0.2 % offset yield strength of the material in the environment and orientation, and at the temperature and loading rate of the test (1, 3, 4). For testing at rates other than quasi-static see Annex A10, Rapid Force Testing. The specimen must also be of sufficient thickness, B, to satisfy the specimen proportions in 7.2.1 or 184.108.40.206 and meet the P max/PQ requirement in 9.1.3. Meeting the ligament size and Pmax/PQ requirements cannot be assured in advance. Thus, specimen dimensions shall be conservatively selected for the first test in a series. If the form of the material available is such that it is not possible to obtain a test specimen with ligament size equal to or greater than 2.5(KIc/σYS)2, then it is not possible to make a valid KIc measurement according to this test method.
7.1.2 The initial selection of specimen size for a valid KIc measurement is often based on an estimated value of K Ic for the material.
7.1.3 Alternatively, the ratio of yield strength to elastic modulus may be used for selecting a specimen size that will be
adequate for all but the toughest materials When it has been established that 2.5(KIc/σYS)2 is substantially less than the minimum recommended ligament size given
in the preceding table, then a correspondingly smaller specimen can be used.
7.2 Specimen Configurations—Recommended specimen
configurations are shown in Figs. A3.1-A6.1 and Fig. A7.1.
7.2.1 Specimen Proportions—Crack size, a, is nominally
between 0.45 and 0.55 times the width, W. Bend specimens can
have a width to thickness, W/B, ratio of 1 ≤ W/B ≤ 4. Tension
specimen configurations can be 2 ≤ W/B ≤ 4.
220.127.116.11 Recommended Proportions—It is recommended that
the thickness, B, is nominally one-half the specimen width, W
(that is, W/B = 2). Likewise, the crack size, a, should be
nominally equal to one-half the width, W (that is a/W = 1/2).
NOTE 3—Alternative W/B ratios different from the recommended ratio
in 18.104.22.168 but still meeting the requirements in 7.2.1 are sometimes useful,
especially for quality control or lot releases purposes, because they allow
a continuous range of product thicknesses to be tested using a discrete
number of specimen widths while still maintaining specimens of full
product thickness. However, because specimen width influences the
amount of crack extension corresponding to the 95 % slope, KIc obtained
with alternative W/B ratios may not agree with those obtained using the
recommended W/B ratio, particularly in products exhibiting a Type I
force-CMOD record (5). As an example, a specimen with the recommended proportion W/B = 2 would tend to yield a lower KIc than a
specimen with an alternative proportion W/B = 4. Also, because a shorter
ligament length may hinder resistance curve development, an alternative
specimen with W/B < 2 (allowed only for bend specimens) may pass the
max/PQ requirement, while a specimen with the recommended W/B ratio
would fail. Conversely, an alternative specimen with W/B >2 (allowed in
both tension and bend specimens) may fail the Pmax/PQ requirement,
while a specimen with the recommended W/B would pass.
7.2.2 Alternative Specimens—In certain cases it may be
necessary or desirable to use specimens having W/B ratios
other than that specified in 7.2.1. Alternative W/B ratios and side-grooved specimens are allowed as specified in 22.214.171.124 and
126.96.36.199. These alternative specimens shall have the same crack
length-to-specimen width ratio as the standard specimen.
188.8.131.52 Alternative Side-Grooved Specimens—For the compact C(T) and the bend SE(B) specimen configurations sidegrooving is allowed as an alternative to plain-sided specimens.
The total thickness reduction shall not exceed 0.25 B. A total
reduction of 0.20 B has been found to work well (6) for many
materials and is recommended (10% per side). Any included
angle less than 90° is allowed. The root radius shall be 0.5 6
0.2 mm (0.02 6 0.01 in.). Precracking prior to the sidegrooving operation is recommended to produce nearly straight
fatigue precrack fronts. BN is the minimum thickness measured
at the roots of the side grooves. The root of the side groove
shall be located along the specimen centerline. Fig. 6 is a
schematic showing an example cross section of an alternative
side grooved specimen.
NOTE 4— Side-grooves increase the level of constraint with respect to
the recommended specimen. The increased constraint promotes a more
uniform stress state along the crack front and inhibits shear lip development. As a result, the KIc value from a side-grooved specimen is expected
to be lower than the K
Ic obtained from the recommended specimen,
particularly for thin products or products exhibiting Type I behavior. The
value of K
Ic from a side-grooved specimen may better represent the
fracture toughness of the material in structural situations where plasticity
is more highly constrained by the crack front geometry such as may be the
case for a surface or corner crack, or by structural details such as keyways,
radii, notches, etc. The value of KIc from the recommended specimen may
better represent the fracture toughness of the material in structural
situations where surface plasticity and shear lip development is not
constrained such as a through crack in a region of uniform thickness.
Side-grooving increases the likelihood of meeting the Pmax/PQ
requirement, enabling a valid KIc to be obtained in products for which it
would not be possible using the recommended specimen. Side grooving
after precracking beneficially removes a portion of the non-linear crack
front at the ends of the crack front, thus increasing the likelihood of
meeting crack front straightness requirements. However, side grooving
may also remove material that influences service performance. This is
often true for cast parts and those for which thermo-mechanical working
is part of the heat treating cycle. The increased constraint also can lead to
increased likelihood of material delamination, for instance, in the plane of
the specimen, which could lead to test results different from those
obtained from plane-sided specimens.
NOTE 5—No interlaboratory ‘round robin’ test program has yet been
conducted to compare the performance of plain-sided and side-grooved
specimens. However, the results of several studies (6) indicate that KIc
from side-grooved specimens is zero to 10 % less than that of plain-sided
specimens, the difference increasing with increasing material toughness.
The within-laboratory repeatability was determined according to the
conditions in Terminology E456 and the results are presented in 11.3.
184.108.40.206 For lot acceptance testing, side-grooved specimens
shall not be used unless specifically allowed by the product
specification or by agreement between producer and user.
7.3 Specimen Preparation—All specimens shall be tested in
the finally heat-treated, mechanically-worked, and
environmentally-conditioned state. Specimens shall normally
be machined in this final state. However, for material that
cannot be machined in the final condition, the final treatment
may be carried out after machining provided that the required
dimensions and tolerances on specimen size, shape, and overall
finish are met (see specimen drawings of Figs. A3.1-A6.1 and
Fig. A7.1), and that full account is taken of the effects of
specimen size on metallurgical condition induced by certain
heat treatment procedures; for example, water quenching of
7.3.1 Fatigue Crack Starter Notch—Three fatigue crack
starter notch configurations are shown in Fig. 5. To facilitate
fatigue precracking at low stress intensity levels, the suggested
root radius for a straight-through slot terminating in a V-notch
is 0.08 mm (0.003 in.) or less. For the chevron form of notch,
the suggested root radius is 0.25 mm (0.010 in.) or less. For the
slot ending in a drilled hole, it is necessary to provide a sharp
stress raiser at the end of the hole. Care shall be taken to ensure
that this stress raiser is so located that the crack plane
orientation requirements of 8.2.4 can be met.
7.3.2 Fatigue Precracking—Fatigue precracking procedures
are described in Annex A8. Fatigue cycling is continued until
a crack is produced that satisfies the requirements of 220.127.116.11
and 18.104.22.168 that follow.
22.214.171.124 Crack size (total size of crack starter plus fatigue
crack) shall be between 0.45W and 0.55W.
126.96.36.199 The size of the fatigue crack on each face of the
specimen shall not be less than the larger of 0.025W or 1.3 mm
(0.050 in.) for the straight-through crack starter configuration,
not less than the larger of 0.5D or 1.3 mm (0.050 in.) for the
slot ending in a hole (of diameter D < W/10), and need only
emerge from the chevron starter configuration.
8. General Procedure
8.1 Number of Tests—It is recommended that triplicate tests,
minimum, be made for each material condition.
8.2 Specimen Measurement—Specimen dimensions shall
conform to the drawings of Figs. A3.1-A6.1 and Fig. A7.1.
Measurements essential to the calculation of K
Ic are specimen thickness, B (and in the case of side-grooved alternative
specimens, BN), crack size, a, and width, W.
8.2.1 Specimen thickness, B (and in the case of sidegrooved alternative specimens, BN), shall be measured before
testing to the nearest 0.03 mm (0.001 in.) or to 0.1 %,
whichever is larger. For plain-sided specimens, B shall be
measured adjacent the notch. For side-grooved specimens, BN
shall be measured at the root of the notch and B adjacent the
NOTE 6—For plane-sided specimens the value of BN is equal to the
8.2.2 Specimen width, W, shall be measured, in conformance with the procedure of the annex appropriate to the
specimen configuration, to the nearest 0.03 mm (0.001 in.) or
0.1 %, whichever is larger, at not less than three positions near
the notch location, and the average value recorded.
8.2.3 Specimen crack size, a, shall be measured after
fracture to the nearest 0.5 % at mid-thickness and the two
quarter-thickness points (based on B for plain-sided specimens
N for side-grooved specimens). The average of these three
measurements shall be taken as the crack size, a. The difference between any two of the three crack size measurements
shall not exceed 10 % of the average. The crack size shall be
measured also at each surface. For the straight-through notch
starter configuration, no part of the crack front shall be closer
to the machined starter notch than 0.025W or 1.3 mm (0.050
in.), whichever is larger; furthermore, neither surface crack size
measurement shall differ from the average crack size by more
than 15 % and their difference shall not exceed 10 % of the
average crack size. For the chevron notch starter configuration,
the fatigue crack shall emerge from the chevron on both
surfaces; furthermore, neither surface crack size measurement
shall differ from the average crack size by more than 15 %, and
their difference shall not exceed 10 % of the average crack size.
8.2.4 The plane of the fatigue precrack and subsequent 2 %
crack extension (in the central flat fracture area; that is,
excluding surface shear lips) shall be parallel to the plane of the
starter notch to 610°. For side-grooved specimens, the plane
of the fatigue precrack and subsequent 2% crack extension
shall be within the root of the side-groove.
8.2.5 There shall be no evidence of multiple cracking (that
is, more than one crack) (7).
8.3 Loading Rate—For conventional (quasi-static) tests, the
specimen shall be loaded such that the rate of increase of
stress-intensity factor is between 0.55 and 2.75 MPa√m/s (30
and 150 ksi√in./min) during the initial elastic displacement.
Loading rates corresponding to these stress-intensity factor
rates are given in the Annex appropriate to the specimen being
tested. For rapid-force tests, loading rates are to be as specified
in Annex A10.
8.4 Test Record—A record shall be made of the output of the
force-sensing transducer versus the output of the displacement
gage. The data acquisition system shall be set such that not less
than 50 % of full range is used for the test record. If an
autographic recorder is used, it shall be adjusted such that the
slope of the initial portion of the force-CMOD record is
between 0.7 and 1.5. Alternatively, if a computer data acquisition system is used, it shall be programmed to capture enough
data to permit the calculations of Section 9.
8.4.1 The test shall be continued until the specimen can
sustain no further increase in applied force. The maximum
force (Pmax) shall be noted and recorded.
9. Calculation and Interpretation of Results
9.1 Interpretation of Test Record and Calculation of KIc—In
order to substantiate the validity of a KIc determination, it is
first necessary to calculate a conditional result, KQ, which
involves a construction on the test record, and then to determine whether this result is consistent with the size and yield
strength of the specimen according to 7.1. The procedure is as
9.1.1 When an autographic recorder is used, the conditional
Q is determined by drawing the secant line OP5, (see
Fig. 7) through the origin (point O) of the test record with slope
(P/V)5 equal to 0.95(P/V)o, where (P/V)o is the slope of the
tangent OA to the initial linear portion of the record (Note 7).
In practice the origin (point O) is not necessarily at the
intersection of the displacement- and force-axes. The point O
lies on the best fit line through the initial linear portion of the
record and at the intersection of the best fit line with the
displacement-axis. Thus, in calculating the secant line OP5, the
rotation point of the slope adjustment should be at the
intersection of the line OA with the displacement-axis. The
Q is then defined as follows: if the force at every point
on the record which precedes P5 is lower than P5 (Fig. 7, Type
I), then P5 is PQ; if, however, there is a maximum force
preceding P5 which exceeds it (Fig. 7, Types II and III), then
this maximum force is P
NOTE 7—Slight initial nonlinearity of the test record is frequently
observed, and is to be ignored. However, it is important to establish the
initial slope of the record with high precision. Therefore it is advisable to
minimize this nonlinearity by preliminarily loading the specimen to a
maximum force corresponding to a stress-intensity factor level not
exceeding that used in the final stage of fatigue cracking, then unloading.
NOTE 8—Residual stresses can adversely affect the indicated KQ and KIc
values. The applied loading is superimposed on the residual stresses,
resulting in a total crack tip stress-intensity different from that based solely
on the externally applied forces. In addition, residual stresses will likely
redistribute during machining when the specimen is extracted from the
host material. Hence, the magnitude of their influence on KQ and KIc in
the test specimen may be quite different from that in the original or finish
machined product (see also 5.1.6.)
9.1.2 When a computer data acquisition system is used, the
data reduction program shall determine the same forces (PQ
max) as above. The algorithms for doing this are discretionary.
9.1.3 The ratio P
max/PQ, where Pmax is the maximum force
the specimen was able to sustain (see 8.4.1), shall be calculated. If this ratio does not exceed 1.10, proceed to calculate KQ
as described in the Annex appropriate to the specimen configuration. If P
max/PQ does exceed 1.10, then the test is not a valid
Ic test and the user is referred to Test Method E1820 on
elastic-plastic fracture toughness.
9.1.4 The value 2.5(KQ/σYS)2, where σYS is the 0.2 % offset
yield strength in tension (see Test Methods E8/E8M), shall be
calculated. If this quantity is less than the specimen ligament
size, W–a then KQ is equal to KIc. Otherwise, the test is not a valid K
Ic test. Expressions for calculating KQ are given in the
Annexes for each specified specimen configuration.
9.1.5 If the test result fails to meet the requirements of 9.1.3
or 9.1.4, or both, it will be necessary to use a larger specimen
to determine K
10.1 The specimen configuration code shown on the specimen drawing (in the appropriate Annex) shall be reported. This
code shall be followed with the loading code (T for tension, B
for bending) and the code for crack plane orientation (see
3.1.4). The latter two codes shall appear in separate parentheses. As an example, a test result obtained using the compact
specimen (see Annex A4) might be designated as follows:
C(T)(S-T). The first letter (C) indicates the specimen to be a
compact configuration. The second letter (T) denotes the
loading as tension. The first of the two letters in the last bracket
(S) indicates the normal to the crack plane to be normal to the
direction of principal deformation. The second of these letters
(T) indicates the intended direction of crack extension to be
parallel with the direction of least deformation. For cylindrical
sections, where grain flow can be in the longitudinal, radial or
circumferential direction, the direction of maximum grain flow
shall be reported when the direction is known (see 3.1.4).
10.2 The following information shall be additionally reported for each specimen tested:
10.2.1 Characterization of the material (alloy code or chemistry and metallurgical condition) and product form (sheet,
plate, bar, forging, casting, and so forth) tested.
10.2.2 Specimen thickness, B, for plain-sided configurations. For side-grooved specimens, B, BN and (B· BN)1/2.
10.2.3 Specimen width (depth), W.
10.2.3.1 Loading hole offset, X, for the arc-shaped tension
10.2.3.2 Outer and inner radii, r2 and r1, for arc-shaped
10.2.4 Fatigue precracking conditions, specifically the
maximum stress-intensity factor, Kmax, stress-intensity factor
range, ∆KI, and number of cycles for the final 2.5 % of the
overall crack size, a (size of notch plus fatigue crack extension).
10.2.5 Crack size measurements, after fracture, at midthickness and the two quarter-thickness positions on the crack
front, as well as at the intersection of the crack front with the
10.2.6 Test temperature.
10.2.7 Relative humidity as determined by Test Method
10.2.8 Loading rate in terms of K˙ I (change in stressintensity factor per unit time) (2).
10.2.9 Force-versus-crack mouth opening displacement
(CMOD) record and associated calculations.
10.2.10 Yield strength as determined by Test Methods
Ic (or, KQ followed by the parenthetical statement
“invalid according to Sections(s) _____ of Test Method
10.3 Fig. 8 is a convenient format for tabulating the information required in 10.1 and 10.2.
11. Precision and Bias
11.1 The precision of KIc measurements has been examined
in several interlaboratory round-robin studies. Selected aluminum alloys and high-strength steels were tested using standard
bend SE(B) (8), compact C(T) (9), and arc-shaped tension A(T)
(10) specimen configurations. The results are summarized in
11.3 (Precision) and 11.5 (Bias) that follow. Not all of the
results reported satisfied all of the validity requirements of this
test method. Statistical analysis (9, 10, 11) was used to exclude
data that were likely influenced by deviations from the validity
requirements. No round-robin program has been conducted for the disk-shaped compact DC(T) specimen configuration, but
limited data for that specimen configuration are compared with
data for other specimen configurations in Annex A5. Roundrobin studies specific to the quasi-static testing of beryllium
and the dynamic testing of a strain-rate sensitive steel, and
which involved special testing procedures, are presented in
Annex A9 and Annex A10.
11.2 It should be emphasized that the measures of precision
given in Table 1, Table 2, and Table 3 apply to alloys that
essentially exhibited no transitional fracture behavior with
temperature or strain rate under the specific test conditions of
the interlaboratory studies.
11.3 Precision—The precision of KIc determination is affected by errors in the measurement of test force and specimen
dimensions, especially the crack size. This test method specifies a precision for each measured quantity and, based on these
specifications and the round-robin results, a theoretical precision is rendered (12). Analysis of the method’s specifications
suggests that precision decreases with increasing relative crack
size, more for the bend than for the compact configuration. In
practice, the precision of KIc measurement may depend to an
unknown extent on the characteristics of the test record and
analysis skills of the laboratory personnel. It is possible to
derive useful information concerning the precision of KIc measurement from three round-robin programs (9, 10, 11) as
described below. Results for bend, compact, and arc-shaped
specimen configurations were obtained for several aluminum
alloys and high strength steels. The materials were chosen for
their reproducible, uniform composition and microstructure.
Thereby the contribution of material variability to the measurement of K
Ic was minimized.
11.3.1 An interlaboratory study (8) for the measurement of
plane strain fracture toughness, KIc on metallic materials, using
SE(B) specimens, was conducted among nine laboratories
using four metallic materials (one aluminum alloy and three
high-strength steels). 180 specimens were tested (5 per laboratory and material). Analyses were undertaken in accordance
with Practice E691, see ASTM Research Report No. E08-
10045 and Table 1.
11.3.2 A second interlaboratory study (9) for the measurement of plane strain fracture toughness, KIc on metallic
materials, using C(T) specimens, was conducted among nine
laboratories using the same four metallic materials (one aluminum alloy and three high-strength steels). 216 specimens
were tested (6 per laboratory and material). Analyses were
undertaken in accordance with Practice E691, see ASTM
Research Report No. E08-10056 and Table 2.
11.3.3 A third interlaboratory study (10) for the measurement of plane strain fracture toughness, KIc, using arc-shaped
A(T) specimens, with two different loading hole configurations
(X/W = 0 and X/W = 0.5), was conducted among eight
laboratories using one high strength steel (Ni-Cr-Mo-V
vacuum-degassed steel, yield strength σYS = 1324 MPa). 48
specimens were tested (from 3 to 5 per laboratory). Analyses
were undertaken in accordance with Practice E691, see ASTM
Research Report No.E08-10067 and Table 3.
11.3.4 The terms repeatability limit and reproducibility limit
are used as specified in Practice E177.
11.3.5 The results presented in Table 1, Table 2, and Table
3 shall not be transferred to materials or K
Ic levels other than
those relevant to the specific interlaboratory studies(8, 9, 10).
11.4 Alternative side-grooved specimens were tested to
determine within-laboratory limit and repeatability according
to the conditions in Terminology E456. The testing was
performed on aluminum alloy 7055–T7951 using C(T) specimens having a nominal dimensions W=50.8 (2.0 in), B =25.4
mm (1.0 in.) BN = 20.3 mm (0.80 in.) notch root angle = 45°
and notch root radius = 0.5mm (0.02 in.). The results are given
in Table 4 along with results obtained from plain-sided
specimens from manufactured the same lot of material, tested
at the same time, and under the same test conditions The
repeatability standard deviation for this test series 0.22 MP√m
(0.20 ksi√in.) for side-grooved specimens and 0.33 MPa√m
(0.30 ksi√in.) for the plane-sided specimens.
11.5 Bias—There is no accepted standard value for the
plane-strain fracture toughness of any material. In the absence
of such a true value, any statement concerning bias is not
DOUBLE-CANTILEVER DISPLACEMENT GAGE
A1.1 The displacement gage consists of two cantilever
beams and a spacer block clamped together with a single bolt
and nut (Fig. 2). Electrical-resistance strain gages are adhesively bonded to the tension and compression surfaces of each
beam, and are connected as a Wheatstone bridge incorporating
a suitable balancing resistor. The beams are made of material
with a high ratio of yield strength-to-elastic modulus. One such
material is solution treated Ti-13V-11Cr-3Al titanium alloy.
For material of different modulus, the spring constant of the
assembly is correspondingly different, but other characteristics
are unaffected. Detailed dimensions for the beams and spacer
block are given in Figs. A1.1 and A1.2. Those particular values
provide a linear (working) range from 3.8 to 7.6 mm (0.15 to
0.30 in.) and a gage length of 5.1 to 6.4 mm (0.20 to 0.25 in.).
The gage length can be adjusted by substituting a differently
sized spacer block. The gage’s required precision is stated as a
maximum deviation of 60.003 mm (0.0001 in.) from a
least-squares-best-fit straight line through its displacement
calibration data (see 6.4.2). Additional details concerning
design, construction and use of the gage are given in (13).
A2.1 Bend Specimen Loading Fixture
A2.1.1 The bend test is performed using fixtures designed to
minimize friction effects by allowing the support rollers to
rotate and translate slightly as the specimen is loaded, thereby
achieving rolling contact. A design suitable for testing standard
bend (SE(B)) and arc-shaped bend (A(B)) specimens is shown
in Fig. A2.1. While free to roll and translate during test, the
rollers are initially positioned against stops that set the span
length and are held in place by low-tension springs (such as
A2.1.2 The bend fixture is aligned such that the line of
action of the applied force passes midway between the support
rollers to 61.0 % of the span, S, and is perpendicular to the
roller axes to 62° (14). The span is to be measured to 60.5 %.
A2.2 Compact Specimen Loading Clevis
A2.2.1 A loading clevis suitable for testing standard compact (C(T)), arc-shaped tension (A(T)), and disk-shaped compact (DC(T) specimens is shown in Fig. A2.2. Both ends of the
specimen are held in the clevis and loaded through pins in
order to allow rotation of the specimen during testing. The
clevis holes are provided with small flats on the loading
surfaces to provide rolling contact, thereby minimizing friction
A2.2.2 The size, proportions, and tolerances for the clevis
shown in Fig. A2.2 are all scaled to specimens with W/B = 2 for
B ≥ 13 mm (0.5 in.), and W/B = 4 for B ≤ 13 mm (0.5 in.).
Clevis and pins made from 1930 MPa (280 ksi) yield strength
maraging steel are suitable for testing specimens of the sizes
ys/E ratios of 7.1.3. For lower-strength clevis material or
substantially larger specimens at a given σys/E ratio, larger
clevises are required. As indicated in Fig. A2.2, the clevis
corners may be trimmed sufficiently to accommodate seating of
the displacement gage in specimens less than 9.53 mm (0.375
A2.2.3 To minimize eccentricity in the load train, the
loading rods shall be aligned to 60.8 mm (0.03 in.) and the
specimen centered in the clevis slot to 60.8 mm (0.03 in.).
A3.1.1 The standard bend specimen configuration is a
single- edge-notched and fatigue precracked beam loaded in
three-point bending. The support span, S, is nominally equal to
four times the specimen width, W. The general proportions of
the standard configuration are shown in Fig. A3.1.
A3.1.2 Alternative configurations may have 1 ≤ W/B ≤ 4;
however, these specimens shall also have a nominal support
span equal to 4W.
A3.2 Specimen Preparation
A3.2.1 Generally applicable specifications regarding specimen size, configuration and preparation are given in Section 7.
A3.2.2 In the interest of K-calibration accuracy, it is desirable to fatigue precrack bend specimens using the same loading
fixture to be used in subsequent testing.
A3.2.3 Bend specimens are occasionally precracked in cantilever bending, especially for reversed force cycling (see
A188.8.131.52). If the three-point bending K-calibration is used for
cantilever bending, the cantilever bending moment for a given
K value will be underestimated (7). The crack tip stress field in
cantilever bending can be distorted by excessive clamping
forces, thereby affecting fatigue crack planarity.
A3.3.1 Bend Test Fixture—The loading fixture for bend
testing is illustrated in Fig. A2.1 and discussed in A2.1. The fixture is designed to minimize friction effects by allowing the
rollers to rotate and translate slightly as the specimen is loaded,
thus providing rolling contact.
A3.3.2 Displacement Gage—Details regarding displacement gage design, calibration, and use are given in 6.4. For the
bend specimen, displacements are essentially independent of
gage length up to W/2.
A3.4.1 Measurement—Specimen width (depth), W, is measured from the notched edge of the specimen to the opposite
edge. Crack size a, is measured from the notched edge to the
A184.108.40.206 General requirements concerning specimen measurement are given in 8.2.
A3.4.2 Bend Specimen Testing—General principles concerning the loading fixture and its setup appear in A2.1.
A220.127.116.11 Locate the specimen with the crack tip midway
between the rolls to within 1 % of the span, and square to the
roll axes within 2°. The displacement gage is seated on the
knife edges such as to maintain registry between knife edges
and gage grooves. In the case of attachable knife edges, the
gage is seated before the knife edge positioning screws are
A18.104.22.168 The specified rate of increase of the stressintensity factor (see 8.3) ranges from 0.55 and 2.75 MPa√m/s
(30 and 150 ksi√in./min) and corresponds to a loading rate for
a standard (W/B = 2) 25.4 mm (1 in.) thick specimen between
0.30 to 1.5 kN/s (4.0 and 20 klbf/min).
A22.214.171.124 Details concerning recording of the test record are
given in 8.4.
A3.5.1 Interpretation of Test Record—General requirements
and procedures for interpreting the test record are given in 9.1.
A3.5.2 Validity Requirements—Validity requirements in
terms of limitation on P
max/PQ and mandatory specimen size
are given in 9.1.3 through 9.1.4.
A3.5.3 Calculation of KQ—Bend specimen KQ is calculated
in SI or inch-pound units of Pa√m (psi√in.) as follows (see
=BBN W3/2·ƒS Wa D (A3.1)
3ŒWa · 1.99 2
2.15 2 3.93
Q = force as determined in 9.1.1, N (lbf),
B = specimen thickness as determined in 8.2.1, m (in.),
N = specimen thickness between the roots of the side
grooves, as determined in 8.2.1, m (in.),
S = span as determined in A3.4.2 (see also A2.1), m (in.),
W = specimen width (depth) as determined in A3.4.1, m
a = crack size as determined in 8.2.3, m (in.).
NOTE A3.1—Example: for a/W = 0.500, ƒ(a/W) = 2.66.
NOTE A3.2—This expression for a/W is considered to be accurate
within 1 % over the range 0.2 ≤ a/W ≤ 1 for S/W = 4 (16).
A3.5.4 Calculation of Crack Mouth Opening Compliance
Using Crack Size Measurements—Bend specimen crack mouth
opening compliance, Vm/P, is calculated in units of m/N (in./lb)
as follows (see Note A3.4):
eW·qS WaD (A3.3)
qS WaD 5 (A3.4)
6S WaD F 0.76 2 2.28Wa 13.87S WaD 2 2 2.04S WaD 310.66/S 1 2 WaD 2G
E’ = elastic constraint modulus (E for plane stress;
E/(1 − ν2) for plane strain), Pa (psi),
ν = Poisson’s Ratio,
e = B – (B– BN)2/B, and
S, B, BN, W, and a are defined in A3.5.3.
NOTE A3.3—Example: for a/W = 0.500, q(a/W) = 8.92.
NOTE A3.4—This expression is considered to be accurate within 1.0 %
over the entire range 0 ≤ a/W ≤ 1 for S/W = 4 (17). It is valid only for crack
mouth opening displacement measured at the location of the integral knife
edges shown in Fig. 3. Attachable knife edges must be reversed or inset to
effect the same measurement points.
A3.5.5 Calculation of Crack Size Using Crack Mouth
Opening Compliance Measurements—Bend specimen normalized crack size is calculated as follows (see Note A3.5):
1.000 2 3.950·U12.982·U2 2 3.214·U3151.516·U4 2 113.031·U5
11ŒS E’ BPeVmD S 4SWD (A3.6)
= crack mouth opening displacement, m (in.),
P = applied force, N (lbf), and
e = B – (B– BN)2/B, and
E’ is defined in A3.5.4 and S, B, BN, W and a are defined in
NOTE A3.5—This expression fits the equation in A3.5.4 within 0.05 %
of W in the range 0.3 ≤ a/W ≤ 0.9 for S/W = 4 (18). It is valid only for crack
mouth opening displacement measured at the location of the integral knife
edges shown in Fig. 3. Attachable knife edges must be reversed or inset to
effect the same measurement points.
A4. SPECIAL REQUIREMENTS FOR TESTING COMPACT SPECIMENS
A4.1.1 The standard compact specimen configuration is a
single-edge-notched and fatigue precracked plate loaded in
tension. The general proportions of the standard configuration
are shown in Fig. A4.1.
A4.1.2 Alternative configurations may have 2 ≤ W/B ≤ 4,
but with other proportions unchanged.
A4.2 Specimen Preparation
A4.2.1 Generally applicable specifications regarding specimen size, configuration and preparation are given in Section 7.
A4.3.1 Tension Testing Clevis—A loading clevis suitable for
testing compact specimens is shown in Fig. A2.2 and discussed
in A2.2. The clevis is designed to minimize friction effects by
providing for rolling contact of the loading pins and rotation of
the specimen during specimen loading.
A4.3.2 Displacement Gage—Details regarding displacement gage design, calibration, and use are given in 6.4. For the
compact specimen, displacements are essentially independent
of gage length up to 1.2W.
A4.4.1 Measurement—Specimen width, W, and crack size,
a, are measured from the plane of the centerline of the loading
holes. The notched edge may be used as a convenient reference
line, taking into account (that is, subtracting) the distance from
the centerline of the holes to the notched edge to arrive at W
A126.96.36.199 General requirements concerning specimen measurement are given in 8.2.
A4.4.2 Compact Specimen Testing—General principles concerning the loading clevis and its setup appear in A2.2. When
assembling the loading train (clevises and their attachments to
the tensile machine), care shall be taken to minimize eccentricity of loading due to misalignments external to the clevises.
A188.8.131.52 The displacement gage is seated on the knife edges
such as to maintain registry between knife edges and gage
grooves. In the case of attachable knife edges, the gage is
seated before the knife edge positioning screws are tightened.
A184.108.40.206 The specified rate of increase of the stressintensity factor is within the range 0.55 and 2.75 MPa√m/s (30
and 150 ksi√in./min) corresponding to a loading rate for a
standard (W/B = 2) 25 mm (1.0 in.) thick specimen between
0.33 and 1.67 kN/s (4.5 to 22.5 klbf/min).
A220.127.116.11 Details concerning recording of the test record are
given in 8.4.
A4.5.1 General requirements and procedures for interpreting the test record are given in 9.1.
A4.5.2 Validity Requirements—Validity requirements in
terms of limitation on P
max/PQ and mandatory specimen size
are given in 9.1.3 through 9.1.4.
A4.5.3 Calculation of KQ—Compact specimen KQ is calculated in SI or inch-pound units of Pa√m (psi√in.)
تلخيص النصوص العربية والإنجليزية اليا باستخدام الخوارزميات الإحصائية وترتيب وأهمية الجمل في النص
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