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ASTM E561-10e2

(Test Method)

Standard Test Method for K-R Curve Determination

Standard Test Method for <emph type="bdit">K-R</emph> Curve Determination

SIGNIFICANCE AND USE
5.1 The K-R curve characterizes the resistance to fracture of materials during slow, stable crack extension and results from the growth of the plastic zone ahead of the crack as it extends from a fatigue precrack or sharp notch. It provides a record of the toughness development as a crack is driven stably under increasing applied stress intensity factor K. For a given material, K-R curves are dependent upon specimen thickness, temperature, and strain rate. The amount of valid K-R data generated in the test depends on the specimen type, size, method of loading, and, to a lesser extent, testing machine characteristics.  
5.2 For an untested geometry, the K-R curve can be matched with the crack driving (applied K) curves to estimate the degree of stable crack extension and the conditions necessary to cause unstable crack propagation (1).4 In making this estimate, K-R  curves are regarded as being independent of original crack size ao and the specimen configuration in which they are developed. For a given material, material thickness, and test temperature, K-R curves appear to be a function of only the effective crack extension Δa e (2).  
5.2.1 To predict crack behavior and instability in a component, a family of crack driving curves is generated by calculating  K as a function of crack size for the component using a series of force, displacement, or combined loading conditions. The K-R curve may be superimposed on the family of crack driving curves as shown in Fig. 1, with the origin of the K-R curve coinciding with the assumed original crack size ao. The intersection of the crack driving curves with the K-R curve shows the expected effective stable crack extension for each loading condition. The crack driving curve that develops tangency with the K-R curve defines the critical loading condition that will cause the onset of unstable fracture under the loading conditions used to develop the crack driving curves.
FIG. 1 Schematic Representation of K-R curve and Appl...
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1.1 This test method covers the determination of the resistance to fracture of metallic materials under Mode I loading at static rates using either of the following notched and precracked specimens: the middle-cracked tension M(T) specimen or the compact tension C(T) specimen. A K-R curve is a continuous record of toughness development (resistance to crack extension) in terms of K R plotted against crack extension in the specimen as a crack is driven under an increasing stress intensity factor, K.  
1.2 Materials that can be tested for K-R curve development are not limited by strength, thickness, or toughness, so long as specimens are of sufficient size to remain predominantly elastic to the effective crack extension value of interest.  
1.3 Specimens of standard proportions are required, but size is variable, to be adjusted for yield strength and toughness of the materials.  
1.4 Only two of the many possible specimen types that could be used to develop K-R curves are covered in this method.  
1.5 The test is applicable to conditions where a material exhibits slow, stable crack extension under increasing crack driving force, which may exist in relatively tough materials under plane stress crack tip conditions.  
1.6 The values stated in SI units are to be regarded as the standard. The values given in parentheses are for information only.  
1.7 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.

General Information

Status
Historical
Publication Date
31-Oct-2010
ICS
77.040.10 - Mechanical testing of metals
Technical Committee
E08 - Fatigue and Fracture
Drafting Committee
E08.07 - Fracture Mechanics
Current Stage
Ref Project

Relations

Replaces
ASTM E561-10e1 - Standard Test Method for <span class="bdit">K-R</span> Curve Determination
Effective Date
01-Nov-2010
Replaced By
ASTM E561-15 - Standard Test Method for <emph type="bdit">K<inf>R</inf></emph> Curve Determination
Effective Date
15-Oct-2015
Referred By
ASTM E647-23a - Standard Test Method for Measurement of Fatigue Crack Growth Rates
Effective Date
01-Nov-2010
Referred By
ASTM B909-21a - Standard Guide for Plane Strain Fracture Toughness Testing of Non-Stress Relieved Aluminum Products
Effective Date
01-Nov-2010
Referred By
ASTM B645-21 - Standard Practice for Linear-Elastic Plane-Strain Fracture Toughness Testing of Aluminum Alloys
Effective Date
01-Nov-2010
Referred By
ASTM E740/E740M-03(2016) - Standard Practice for Fracture Testing with Surface-Crack Tension Specimens
Effective Date
01-Nov-2010
Referred By
ASTM B646-19 - Standard Practice for Fracture Toughness Testing of Aluminum Alloys
Effective Date
01-Nov-2010
Referred By
ASTM E1823-23 - Standard Terminology Relating to Fatigue and Fracture Testing
Effective Date
01-Nov-2010
Referred By
ASTM D7779-20 - Standard Test Method for Determination of Fracture Toughness of Graphite at Ambient Temperature
Effective Date
01-Nov-2010
Referred By
ASTM E2472-12(2018)e2 - Standard Test Method for Determination of Resistance to Stable Crack Extension under Low-Constraint Conditions
Effective Date
01-Nov-2010

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ASTM E561-10e2 - Standard Test Method for <emph type="bdit">K-R</emph> Curve DeterminationASTM E561-10e2 - Standard Test Method for <emph type="bdit">K-R</emph> Curve Determination
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ASTM E561-10e2 - Standard Test Method for <emph type="bdit">K-R</emph> Curve Determination
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NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Contact ASTM International (www.astm.org) for the latest information
´2
Designation: E561 − 10
StandardTest Method for
1
K-R Curve Determination
This standard is issued under the fixed designation E561; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1
ε NOTE—3.2.2 was editorially updated in December 2011.
2
ε NOTE—3.2.2 was editorially updated in March 2013.
1. Scope* 2. Referenced Documents
2
2.1 ASTM Standards:
1.1 This test method covers the determination of the
resistance to fracture of metallic materials under Mode I E4Practices for Force Verification of Testing Machines
E399Test Method for Linear-Elastic Plane-Strain Fracture
loadingatstaticratesusingeitherofthefollowingnotchedand
precrackedspecimens:themiddle-crackedtensionM(T)speci- Toughness K of Metallic Materials
Ic
E1823TerminologyRelatingtoFatigueandFractureTesting
men or the compact tension C(T) specimen. A K-R curve is a
continuous record of toughness development (resistance to 2.2 Other Document:
3
crackextension)intermsof K plottedagainstcrackextension
AISCSteel Construction Manual
R
in the specimen as a crack is driven under an increasing stress
3. Terminology
intensity factor, K.
3.1 Definitions—Terminology E1823 is applicable to this
1.2 Materials that can be tested for K-R curve development
method.
are not limited by strength, thickness, or toughness, so long as
specimensareofsufficientsizetoremainpredominantlyelastic
3.2 Definitions of Terms Specific to This Standard:
to the effective crack extension value of interest. 3.2.1 apparent plane-stress fracture toughness, K —The
app
value of K calculated using the original crack size and the
1.3 Specimensofstandardproportionsarerequired,butsize
maximum force achieved during the test. K is an engineer-
app
is variable, to be adjusted for yield strength and toughness of
ing estimate of toughness that can be used to calculate residual
the materials.
strength. K depends on the material, specimen size, and
app
1.4 Only two of the many possible specimen types that
specimen thickness and as such is not a material property.
could be used to develop K-R curves are covered in this
-2
3.2.2 effective modulus, E [FL ]—an elastic modulus that
eff
method.
allows a theoretical (modulus normalized) compliance to
1.5 The test is applicable to conditions where a material
match an experimentally measured compliance for an actual
exhibits slow, stable crack extension under increasing crack
initial crack size a .
o
driving force, which may exist in relatively tough materials
3.2.3 plane-stress fracture toughness, K —The value of K
c R
under plane stress crack tip conditions.
at instability in a force-controlled test corresponding to the
1.6 The values stated in SI units are to be regarded as the
maximum force point in the test. K depends on the material,
c
standard. The values given in parentheses are for information
specimen size, and specimen thickness and as such is not a
only.
material property.
3.2.3.1 Discussion—See the discussion of plane-strain frac-
1.7 This standard does not purport to address all of the
ture toughness in Terminology E1823.
safety concerns, if any, associated with its use. It is the
responsibility of the user of this standard to establish appro-
4. Summary of Test Method
priate safety and health practices and determine the applica-
4.1 During slow-stable fracturing, the developing crack
bility of regulatory limitations prior to use.
extension resistance K is equal to the applied stress intensity
R
1 2
This test method is under the jurisdiction ofASTM Committee E08 on Fatigue For referenced ASTM standards, visit the ASTM website, www.astm.org, or
and Fracture and is the direct responsibility of Subcommittee E08.07 on Fracture contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
Mechanics. Standards volume information, refer to the standard’s Document Summary page on
Current edition approved Nov. 1, 2010. Published November 2010. Originally the ASTM website.
ε1 3
approved in 1974. Last previous edition approved in 2008 as E561–08 . DOI: Available from American Institute of Steel Construction (AISC), One E.
10.1520/E0561-10E02. Wacker Dr., Suite 3100, Chicago, IL 60601-2001.
*A Summary of Changes section appears at the end of this standard
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
1

---------------------- Page: 1 ----------------------
´2
E561 − 10
factor K. The crack is driven forward by continuously or
incrementally increasing force or displacement. Measurements
are made periodically for determination of the effective crack
size and for calculation of K
...

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6.1 Creep crack growth rate expressed as a function of the steady state C* or K characterizes the resistance of a material to crack growth under conditions of extensive creep deformation or under brittle creep conditions. Background information on the rationale for employing the fracture mechanics approach in the analyses of creep crack growth data is given in (11, 13, 30-35).  
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6.2.1 Expressing CCI time, t0.2 and CCG rate, da/dt as a function of an appropriate fracture mechanics related parameter generally provides results that are independent of specimen size and planar geometry for the same stress state at the crack tip for the range of geometries and sizes presented in this document (see Annex A1). Thus, the appropriate correlation will enable exchange and comparison of data obtained from a variety of specimen configurations and loading conditions. Moreover, this feature enables creep crack growth data to be utilized in the design and evaluation of engineering structures operated at elevated temperatures where creep deformation is a concern. The concept of similitude is assumed, implying that cracks of differing sizes subjected to the same nominal C*(t), Ct, or K will advance by equal increments of crack extension per unit time, provided the conditions for the validity for the specific crack growth rate relating parameter are met. See 11.7 for details.  
6.2.2 The effects of crack tip constraint arising from variations in specimen size, geometry and material ductility can influence t0.2 and da/dt. For example, crack growth rates at the same value of C*(t), Ct in creep-ductile materials generally increases with increasing thickness. It is therefore necessary to keep the component dimensions in mind when selecti...
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1.1 This test method covers the determination of creep crack initiation (CCI) and creep crack growth (CCG) in metals at elevated temperatures using pre-cracked specimens subjected to static or quasi-static loading conditions. The solutions presented in this test method are validated for base material (that is, homogenous properties) and mixed base/weld material with inhomogeneous microstructures and creep properties. The CCI time, t0.2, which is the time required to reach an initial crack extension of δai = 0.2 mm to occur from the onset of first applied force, and CCG rate, a˙  or da/dt are expressed in terms of the magnitude of creep crack growth correlated by fracture mechanics parameters, C* or K, with C* defined as the steady state determination of the crack tip stresses derived in principal from C*(t) and Ct   (1-17).2 The crack growth derived in this manner is identified as a material property which can be used in modeling and life assessment methods (17-28).  
1.1.1 The choice of the crack growth correlating parameter C*, C*(t), Ct, or K depends on the material creep properties, geometry and size of the specimen. Two types of material behavior are generally observed during creep crack growth tests; creep-ductile (1-17) and creep-brittle (29-44). In creep ductile materials, where creep strains dominate and creep crack growth is accompanied by substantial time-dependent creep strains at the crack tip, the crack growth rate is correlated by the steady state definitions of Ct or C*(t) , defined as C* (see 1.1.4). In creep-brittle materials, creep crack growth occurs at low creep ductility. Consequently, the time-dependent creep strains are comparable to or dominated by accompanying elastic strains local to the crack tip. Under such steady state creep-brittle conditions, Ct or K could be chosen as the correlating parameter (8-14).  
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ASTM E740/E740M-23(Practice)
Standard Practice for Fracture Testing with Surface-Crack Tension Specimens

SIGNIFICANCE AND USE
4.1 The surface-crack tension (SCT) test is used to estimate the load-carrying capacity of simple sheet- or plate-like structural components having a type of flaw likely to occur in service. The test is also used for research purposes to investigate failure mechanisms of cracks under service conditions.  
4.2 The residual strength of an SCT specimen is a function of the crack depth and length and the specimen thickness as well as the characteristics of the material. This relationship is extremely complex and cannot be completely described or characterized at present.  
4.2.1 The results of the SCT test are suitable for direct application to design only when the service conditions exactly parallel the test conditions. Some methods for further analysis are suggested in Appendix X1.  
4.3 In order that SCT test data can be comparable and reproducible and can be correlated among laboratories, it is essential that uniform SCT testing practices be established.  
4.4 The specimen configuration, preparation, and instrumentation described in this practice are generally suitable for cyclic- or sustained-force testing as well. However, certain constraints are peculiar to each of these tests. These are beyond the scope of this practice but are discussed in Ref. (1).
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1.1 This practice covers the design, preparation, and testing of surface-crack tension (SCT) specimens. It relates specifically to testing under continuously increasing force and excludes cyclic and sustained loadings. The quantity determined is the residual strength of a specimen having a semielliptical or circular-segment fatigue crack in one surface. This value depends on the crack dimensions and the specimen thickness as well as the characteristics of the material.  
1.2 Metallic materials that can be tested are not limited by strength, thickness, or toughness. However, tests of thick specimens of tough materials may require a tension test machine of extremely high capacity. The applicability of this practice to nonmetallic materials has not been determined.  
1.3 This practice is limited to specimens having a uniform rectangular cross section in the test section. The test section width and length must be large with respect to the crack length. Crack depth and length should be chosen to suit the ultimate purpose of the test.  
1.4 Residual strength may depend strongly upon temperature within a certain range depending upon the characteristics of the material. This practice is suitable for tests at any appropriate temperature.  
1.5 Residual strength is believed to be relatively insensitive to loading rate within the range normally used in conventional tension tests. When very low or very high rates of loading are expected in service, the effect of loading rate should be investigated using special procedures that are beyond the scope of this practice.  
Note 1: Further information on background and need for this type of test is given in the report of ASTM Task Group E24.01.05 on Part-Through-Crack Testing (1).2  
1.6 The values stated in either SI units or inch-pound units are to be regarded separately as standard. The values stated in each system may not be exact equivalents; therefore, each system shall be used independently of the other. Combining values from the two systems may result in non-conformance with the standard.  
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Standard Test Method for Determining Plane-Strain Crack-Arrest Fracture Toughness, KIa, of Ferritic Steels

SIGNIFICANCE AND USE
5.1 In structures containing gradients in either toughness or stress, a crack may initiate in a region of either low toughness or high stress, or both, and arrest in another region of either higher toughness or lower stress, or both. The value of the stress intensity factor during the short time interval in which a fast-running crack arrests is a measure of the ability of the material to arrest such a crack. Values of the stress intensity factor of this kind, which are determined using dynamic methods of analysis, provide a value for the crack-arrest fracture toughness which will be termed KA  in this discussion. Static methods of analysis, which are much less complex, can often be used to determine K at a short time (1 to 2 ms) after crack arrest. The estimate of the crack-arrest fracture toughness obtained in this fashion is termed K a. When macroscopic dynamic effects are relatively small, the difference between KA  and Ka  is also small (1-4). For cracks propagating under conditions of crack-front plane-strain, in situations where the dynamic effects are also known to be small, KIa  determinations using laboratory-sized specimens have been used successfully to estimate whether, and at what point, a crack will arrest in a structure (5, 6). Depending upon component design, loading compliance, and the crack jump length, a dynamic analysis of a fast-running crack propagation event may be necessary in order to predict whether crack arrest will occur and the arrest position. In such cases, values of K Ia  determined by this test method can be used to identify those values of K below which the crack speed is zero. More details on the use of dynamic analyses can be found in Ref (4).  
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5.1 Assuming the presence of a preexisting, sharp, fatigue crack, the material fracture toughness values identified by this test method characterize its resistance to: (1)  fracture of a stationary crack, (2) fracture after some stable tearing, (3) stable tearing onset, and (4) sustained stable tearing. This test method is particularly useful when the material response cannot be anticipated before the test. Application of procedures in Test Method E1921 is recommended for testing ferritic steels that undergo cleavage fracture in the ductile-to-brittle transition.  
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5.2.3 The values of δc, δu, Jc, and Ju  may be affected by specimen dimensions.
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Note 1: Until this version, KIc could be evaluated using this test method as well as by using Test Method E399. To avoid duplication, the evaluation of KIc has been removed from this test method and the user is referred to Test Method E399.  
1.2 The recommended specimens are single-edge bend, [SE(B)], compact, [C(T)], and disk-shaped compact, [DC(T)]. All specimens contain notches that are sharpened with fatigue cracks.  
1.2.1 Specimen dimensional (size) requirements vary according to the fracture toughness analysis applied. The guidelines are established through consideration of material toughness, material flow strength, and the individual qualification requirements of the toughness value per values sought.  
Note 2: Other standard methods for the determination of fracture toughness using the parameters K, J, and CTOD are contained in Test Methods E399, E1290, and E1921. This test method was developed to provide a common method for determining all applicable toughness parameters from a single test.  
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SIGNIFICANCE AND USE
5.1 Fatigue crack growth rate expressed as a function of crack-tip stress-intensity factor range, da/dN versus ΔK, characterizes a material's resistance to stable crack extension under cyclic loading. Background information on the ration-ale for employing linear elastic fracture mechanics to analyze fatigue crack growth rate data is given in Refs (3) and (4).  
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1.1 This test method2 covers the determination of fatigue crack growth rates from near-threshold (see region I in Fig. 1) to Kmax  controlled instability (see region III in Fig. 1.) Results are expressed in terms of the crack-tip stress-intensity factor range (ΔK), defined by the theory of linear elasticity.  
1.9 Special requirements for the various specimen configurations appear in the following order:
The Compact Specimen  
Annex A1  
The Middle Tension Specimen  
Annex A2  
The Eccentrically-Loaded Single Edge Crack Tension Specimen  
Annex A3  
1.10 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.11 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

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ASTM E399-23(Test Method)
Standard Test Method for Linear-Elastic Plane-Strain Fracture Toughness of Metallic Materials

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 and more highly variable values of fracture toughness can be obtained from specimens that fail by cleavage fracture; for example, specimens of ferritic steels tested at temperatures in the ductile-to-brittle transition region or below. Specimens failing by cleavage are also more likely to exhibit warm prestressing effects, where precracking at a temperature higher than the test temperature can artificially increase the fracture toughness measured (2). The present test method is not intended for cleavage fracture. Instead, the user is referred to Test Method E1921 and E1820 which are applicable to cleavage fracture and contain safeguards against warm prestressing. Likewise this test method should not be used when specimen failure is accompanied by appreciable plastic deformation even after the specimen size has been maximized within product dimensional constraints. Guidance on testing elastic-plastic materials is given in Test Method E1820.  
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1.1 This test method covers the determination of fracture toughness (KIc and optionally KIsi) 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. Two procedures are outlined for using the experimental data to calculate fracture toughness values:  
1.1.1 The KIc test procedure is described in the main body of this test standard and is a mandatory part of the testing and results reporting procedure for this test method. The KIc test procedure is based on crack growth of up to 2 % percent of the specimen width. This can lead to a specimen size dependent rising fracture toughness resistance curve, with larger specimens producing higher fracture toughness results.  
1.1.2 The KIsi test procedure is described in Appendix X1 and is an optional part of this test method. The KIsi test procedure is based on a fixed amount of crack extension of 0.5 mm, and as a result, KIsi is less sensitive to specimen size than KIc. This less size-sensitive fracture toughness, KIsi, is called size-insensitive throughout this test method. Appendix X1 contains an optional procedure for reinterpreting the force-displacement test record recorded as part of this test method to calculate the additional fracture toughness value, KIsi.
Note 1: Plane-strain fracture toughness tests of materials thinner than 1.6 mm (0.063 in.) 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 testing and includes specific requirements for the KI...

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ASTM
ASTM E468/E468M-23(Practice)
Standard Practice for Presentation of Constant Amplitude Fatigue Test Results for Metallic Materials

SIGNIFICANCE AND USE
4.1 Fatigue test results may be significantly influenced by the properties and history of the parent material, the operations performed during the preparation of the fatigue specimens, and the testing machine and test procedures used during the generation of the data. The presentation of fatigue test results should include citation of basic information on the material, specimens, and testing to increase the utility of the results and to reduce to a minimum the possibility of misinterpretation or improper application of those results.
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1.1 This practice covers the desirable and minimum information to be communicated between the originator and the user of data derived from constant-force amplitude axial, bending, or torsion fatigue tests of metallic materials tested in air and at room temperature.  
Note 1: Practice E466, although not directly referenced in the text, is considered important enough to be listed in this standard.  
1.2 The values stated in either SI units or inch-pound units are to be regarded separately as standard. The values stated in each system are not necessarily exact equivalents; therefore, to ensure conformance with the standard, each system shall be used independently of the other, and values from the two systems shall not be combined.  
1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.4 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

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ASTM
ASTM E561-23(Test Method)
Standard Test Method for KR Curve Determination

SIGNIFICANCE AND USE
5.1 The KR curve characterizes the resistance to fracture of materials during slow, stable crack extension and results from the growth of the plastic zone ahead of the crack as it extends from a fatigue precrack or sharp notch. It provides a record of the toughness development as a crack is driven stably under increasing applied stress intensity factor K. For a given material, KR curves are dependent upon specimen thickness, temperature, and strain rate. The amount of valid KR data generated in the test depends on the specimen type, size, method of loading, and, to a lesser extent, testing machine characteristics.  
5.2 For an untested geometry, the KR curve can be matched with the applied-K curves (crack driving curves) to estimate the degree of stable crack extension and the conditions necessary to cause unstable crack propagation (2). In making this estimate, KR curves are regarded as being independent of initial crack size ao and the specimen configuration in which they are developed. For a given material, material thickness, and test temperature, KR curves appear to be a function of only the effective crack extension Δae (3).  
5.2.1 To predict crack behavior and instability in a component, a family of applied-K curves is generated by calculating  K as a function of crack size for the component using a series of force, displacement, or combined loading conditions. The KR curve may be superimposed on the family of applied-K curves as shown in Fig. 1, with the origin of the KR curve coinciding with the assumed initial crack size ao. The intersection of the applied-K curves with the KR curve shows the expected effective stable crack extension for each loading condition. The applied-K curve that develops tangency with the KR curve defines the critical loading condition that will cause the onset of unstable fracture under the loading conditions used to develop the applied-K curves.
FIG. 1 Schematic Representation of KR curve and Applied K Curves to Predict Insta...
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1.1 This test method covers the determination of the resistance to fracture of metallic materials under Mode I loading at static rates using either of the following notched and precracked specimens: the middle-cracked tension M(T) specimen or the compact tension C(T) specimen. A KR curve is a continuous record of toughness development (resistance to crack extension) in terms of KR plotted against crack extension in the specimen as a crack is driven under an increasing stress intensity factor, K. (1)2  
1.2 Materials that can be tested for KR curve development are not limited by strength, thickness, or toughness, so long as specimens are of sufficient size to remain predominantly elastic to the effective crack extension value of interest.  
1.3 Specimens of standard proportions are required, but size is variable, to be adjusted for yield strength and toughness of the materials.  
1.4 Only two of the many possible specimen types that could be used to develop KR curves are covered in this method.  
1.5 The test is applicable to conditions where a material exhibits slow, stable crack extension under increasing crack driving force, which may exist in relatively tough materials under plane stress crack tip conditions.  
1.6 The values stated in SI units are to be regarded as standard. The values given in parentheses after SI units are provided for information only and are not considered standard.  
1.7 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.8 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Reco...

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ASTM E2789-10(2021)(Guide)
Standard Guide for Fretting Fatigue Testing

SIGNIFICANCE AND USE
4.1 Fretting fatigue tests are used to determine the effects of several fretting parameters on the fatigue lives of metallic materials. Some of these parameters include differing materials, relative displacement amplitudes, normal force at the fretting contact, alternating tangential force, the contact geometry, surface integrity parameters such as finish, and the environment. Comparative tests are used to determine the effectiveness of palliatives on the fatigue life of specimens with well-controlled boundary conditions so that the mechanics of the fretting fatigue test can be modeled. Generally, it is useful to compare the fretting fatigue response to plain fatigue to obtain knockdown or reduction factors from fretting fatigue. The results may be used as a guide in selecting material combinations, design stress levels, lubricants, and coatings to alleviate or eliminate fretting fatigue concerns in new or existing designs. However, due to the synergisms of fatigue, wear, and corrosion on the fretting fatigue parameters, extreme care should be exercised in the judgment to determine if the test conditions meet the design or system conditions.  
4.2 For data to be comparable, reproducible, and correlated amongst laboratories and relevant to mimic fretting in an application, all parameters critical to the fretting fatigue life of the material in question will need to be replicated. Because alterations in environment, metallurgical properties, fretting loading (controlled forces and displacements), compliance of the test system, etc. can affect the response, no general guidelines exist to quantitatively ascertain what the effect will be on the specimen fretting fatigue life if a single parameter is varied. To assure test results can be correlated and reproduced, all material variables, testing information, physical procedures, and analytical procedures should be reported in a manner that is consistent with good current test practices.  
4.3 Because of the wear phenome...
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1.1 This guide defines terminology and covers general requirements for conducting fretting fatigue tests and reporting the results. It describes the general types of fretting fatigue tests and provides some suggestions on developing and conducting fretting fatigue test programs.  
1.2 Fretting fatigue tests are designed to determine the effects of mechanical and environmental parameters on the fretting fatigue behavior of metallic materials. This guide is not intended to establish preference of one apparatus or specimen design over others, but will establish guidelines for adherence in the design, calibration, and use of fretting fatigue apparatus and recommend the means to collect, record, and reporting of the data.  
1.3 The number of cycles to form a fretting fatigue crack is dependent on both the material of the fatigue specimen and fretting pad, the geometry of contact between the two, and the method by which the loading and displacement are imposed. Similar to wear behavior of materials, it is important to consider fretting fatigue as a system response, instead of a material response. Because of this dependency on the configuration of the system, quantifiable comparisons of various material combinations should be based on tests using similar fretting fatigue configurations and material couples.  
1.4 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.  
1.5 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

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ASTM
ASTM E466-21(Practice)
Standard Practice for Conducting Force Controlled Constant Amplitude Axial Fatigue Tests of Metallic Materials

SIGNIFICANCE AND USE
4.1 The axial force fatigue test is used to determine the effect of variations in material, geometry, surface condition, stress, and so forth, on the fatigue resistance of metallic materials subjected to direct stress for relatively large numbers of cycles. The results may also be used as a guide for the selection of metallic materials for service under conditions of repeated direct stress.  
4.2 In order to verify that such basic fatigue data generated using this practice is comparable, reproducible, and correlated among laboratories, it may be advantageous to conduct a round-robin-type test program from a statistician's point of view. To do so would require the control or balance of what are often deemed nuisance variables; for example, hardness, cleanliness, grain size, composition, directionality, surface residual stress, surface finish, and so forth. Thus, when embarking on a program of this nature it is essential to define and maintain consistency a priori, as many variables as reasonably possible, with as much economy as prudent. All material variables, testing information, and procedures used should be reported so that correlation and reproducibility of results may be attempted in a fashion that is considered reasonably good current test practice.  
4.3 The results of the axial force fatigue test are suitable for application to design only when the specimen test conditions realistically simulate service conditions or some methodology of accounting for service conditions is available and clearly defined.
SCOPE
1.1 This practice covers the procedure for the performance of axial force controlled fatigue tests to obtain the fatigue strength of metallic materials in the fatigue regime where the strains are predominately elastic, both upon initial loading and throughout the test. This practice is limited to the fatigue testing of axial unnotched and notched specimens subjected to a constant amplitude, periodic forcing function in air at room temperature.  
1.2 The use of this test method is limited to specimens and does not cover testing of full-scale components, structures, or consumer products.  
1.3 The values stated in inch-pound units are to be regarded as standard. The values given in parentheses are mathematical conversions to SI units that are provided for information only and are not considered standard.  
1.4 The text of this standard references notes and footnotes that provide explanatory material. These notes and footnotes (excluding those in tables and figures) shall not be considered as requirements of the standard.
Note 1: The following documents, although not directly referenced in the text, are considered important enough to be listed in this practice:
E739 Practice for Statistical Analysis of Linear or Linearized Stress-Life (S-N) and Strain-Life (ε-N) Fatigue Data
STP 566 Handbook of Fatigue Testing2
STP 588 Manual on Statistical Planning and Analysis for Fatigue Experiments3
STP 731 Tables for Estimating Median Fatigue Limits4  
1.5 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

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