ASTM E561-23
(Test Method)Standard Test Method for KR Curve Determination
Standard Test Method for <emph type="bdit">K<inf>R</inf></emph> 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...
SCOPE
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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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.
Designation: E561 − 23
Standard Test Method for
1
K Curve Determination
R
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. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope* Development of International Standards, Guides and Recom-
mendations issued by the World Trade Organization Technical
1.1 This test method covers the determination of the
Barriers to Trade (TBT) Committee.
resistance to fracture of metallic materials under Mode I
loading at static rates using either of the following notched and
2. Referenced Documents
precracked specimens: the middle-cracked tension M(T) speci-
3
2.1 ASTM Standards:
men or the compact tension C(T) specimen. A K curve is a
R
E4 Practices for Force Calibration and Verification of Test-
continuous record of toughness development (resistance to
ing Machines
crack extension) in terms of K plotted against crack extension
R
E111 Test Method for Young’s Modulus, Tangent Modulus,
in the specimen as a crack is driven under an increasing stress
2
and Chord Modulus
intensity factor, K. (1)
E399 Test Method for Linear-Elastic Plane-Strain Fracture
1.2 Materials that can be tested for K curve development
R
Toughness of Metallic Materials
are not limited by strength, thickness, or toughness, so long as
E1823 Terminology Relating to Fatigue and Fracture Testing
specimens are of sufficient size to remain predominantly elastic
E3076 Practice for Determination of the Slope in the Linear
to the effective crack extension value of interest.
Region of a Test Record
1.3 Specimens of standard proportions are required, but size
2.2 Other Document:
4
is variable, to be adjusted for yield strength and toughness of
AISC Steel Construction Manual
the materials.
3. Terminology
1.4 Only two of the many possible specimen types that
could be used to develop K curves are covered in this method. 3.1 Definitions:
R
3.1.1 Terminology E1823 is applicable to this method.
1.5 The test is applicable to conditions where a material
-2
3.1.2 effective modulus, E [FL ]—an elastic modulus that
eff
exhibits slow, stable crack extension under increasing crack
allows a theoretical (modulus normalized) compliance to
driving force, which may exist in relatively tough materials
match an experimentally measured compliance for an actual
under plane stress crack tip conditions.
initial crack size a .
o
1.6 The values stated in SI units are to be regarded as
3.2 Definitions of Terms Specific to This Standard:
standard. The values given in parentheses after SI units are
3.2.1 apparent fracture toughness, K
app
provided for information only and are not considered standard.
–3/2
[FL ]—The stress intensity factor, K, (under non-plane
1.7 This standard does not purport to address all of the
strain conditions of crack-tip stress) calculated using the initial
safety concerns, if any, associated with its use. It is the
crack size and the maximum force achieved during the test.
responsibility of the user of this standard to establish appro-
3.2.1.1 Discussion—K is an engineering estimate of
app
priate safety, health, and environmental practices and deter-
toughness that can be used to calculate residual strength. K
app
mine the applicability of regulatory limitations prior to use.
not only depends on the material, but also specimen type, size,
1.8 This international standard was developed in accor-
and thickness and as such is not a material property
dance with internationally recognized principles on standard-
3.2.1.2 Discussion—K has been historically referred to as
app
ization established in the Decision on Principles for the
apparent plane-stress fracture toughness, however in practice it
is used to describe apparent fracture toughness under non-plane
1
This test method is under the jurisdiction of ASTM Committee E08 on Fatigue
and Fracture and is the direct responsibility of Subcommittee E08.07 on Fracture
3
Mechanics. For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Current edition approved May 1, 2023. Published May 2023. Originally contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
approved in 1974. Last previous edition approved in 2022 as E561 – 22. DOI: Standards volume information, refer to the standard’s Document Summary page on
10.1520/E0561-23. the ASTM website.
2 4
The boldface numbers in parentheses refer to the list of references at the end of Available from American Institute of Steel Constructi
...
This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: E561 − 22 E561 − 23
Standard Test Method for
1
K Curve Determination
R
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. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope*
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 curve is a continuous record of toughness development (resistance to crack extension) in terms of
R
2
K plotted against crack extension in the specimen as a crack is driven under an increasing stress intensity factor, K.(1)
R
1.2 Materials that can be tested for K curve development are not limited by strength, thickness, or toughness, so long as
R
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 curves are covered in this method.
R
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 Recommendations issued
by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
2. Referenced Documents
3
2.1 ASTM Standards:
E4 Practices for Force Calibration and Verification of Testing Machines
1
This test method is under the jurisdiction of ASTM Committee E08 on Fatigue and Fracture and is the direct responsibility of Subcommittee E08.07 on Fracture
Mechanics.
Current edition approved May 1, 2022May 1, 2023. Published June 2022May 2023. Originally approved in 1974. Last previous edition approved in 20212022 as
E561 – 21.E561 – 22. DOI: 10.1520/E0561-22.10.1520/E0561-23.
2
The boldface numbers in parentheses refer to the list of references at the end of this standard.
3
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
*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
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E561 − 23
E111 Test Method for Young’s Modulus, Tangent Modulus, and Chord Modulus
E399 Test Method for Linear-Elastic Plane-Strain Fracture Toughness of Metallic Materials
E1823 Terminology Relating to Fatigue and Fracture Testing
E3076 Practice for Determination of the Slope in the Linear Region of a Test Record
2.2 Other Document:
4
AISC Steel Construction Manual
3. Terminology
3.1 Definitions:
3.1.1 Terminology E1823 is applicable to this method.
-2
3.1.2 effective modulus, E [FL ]—an elastic modulus that allows a theoretical (modulus normalized) compliance to match an
eff
experimentally measured compliance for an actual initial crack size a .
o
3.2 Definitions of Terms Specific to This Standard:
3.2.1 apparent fracture toughness, K
app
–3/2
[FL ]—The stress intensity factor, K, (under non-plane strain conditions of crack-tip stress) calculated using the initial crack
size and the maximum force achieved during the test.
3.2.1.1 Discussion—
K is an engineering estimate
...
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