ASTM E561-08
(Practice)Standard Test Method forK-R Curve Determination
Standard Test Method for<bdit>K-R</bdit> Curve Determination
SIGNIFICANCE AND USE
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.
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). 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 Δae (2).
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.
Conversely, the K-R curve can be shifted left or right in Fig. 1 to bring...
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-R 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 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.
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Designation:E561–08
Standard Test 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. Scope* 2. Referenced Documents
2
1.1 This test method covers the determination of the 2.1 ASTM Standards:
resistance to fracture of metallic materials under Mode I E4 Practices for Force Verification of Testing Machines
loadingatstaticratesusingeitherofthefollowingnotchedand E399 Test Method for Linear-Elastic Plane-Strain Fracture
precrackedspecimens:themiddle-crackedtensionM(T)speci- Toughness K of Metallic Materials
Ic
men or the compact tension C(T) specimen. A K-R curve is a E1823 Terminology Relating to Fatigue and Fracture Test-
continuous record of toughness development (resistance to ing
crackextension)intermsof K plottedagainstcrackextension 2.2 Other Document:
R
3
in the specimen as a crack is driven under an increasing stress AISC Steel Construction Manual
intensity factor, K.
3. Terminology
1.2 Materials that can be tested for K-R curve development
are not limited by strength, thickness, or toughness, so long as 3.1 Definitions—Terminology E1823 is applicable to this
method.
specimensareofsufficientsizetoremainpredominantlyelastic
to the effective crack extension value of interest. 3.2 Definitions of Terms Specific to This Standard:
3.2.1 apparent plane-stress fracture toughness, K —The
1.3 Specimensofstandardproportionsarerequired,butsize
app
is variable, to be adjusted for yield strength and toughness of value of K calculated using the original crack size and the
maximum force achieved during the test. K is an engineer-
the materials.
app
1.4 Only two of the many possible specimen types that ing estimate of toughness that can be used to calculate residual
strength. K depends on the material, specimen size, and
could be used to develop K-R curves are covered in this
app
method. specimen thickness and as such is not a material property.
-2
3.2.2 effective modulus, E (FL )—the value of Young’s
1.5 The test is applicable to conditions where a material
eff
modulusthatproducesanaccuratecorrespondencebetweenthe
exhibits slow, stable crack extension under increasing crack
driving force, which may exist in relatively tough materials experimentally measured compliance at the original crack size
and the analytically developed compliance calculated for the
under plane stress crack tip conditions.
1.6 The values stated in SI units are to be regarded as the same crack size.
3.2.3 plane-stress fracture toughness, K —The value of K
standard. The values given in parentheses are for information
c R
only. at instability in a force-controlled test corresponding to the
maximum force point in the test. K depends on the material,
1.7 This standard does not purport to address all of the
c
safety concerns, if any, associated with its use. It is the specimen size, and specimen thickness and as such is not a
material property.
responsibility of the user of this standard to establish appro-
priate safety and health practices and determine the applica- 3.2.3.1 Discussion—See the discussion of plane-strain frac-
ture toughness in Terminology E1823.
bility of regulatory limitations prior to use.
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, 2008. Published March 2009. Originally the ASTM website.
´1 3
approved in 1974. Last previous edition approved in 2005 as E561–05 . DOI: Available from American Institute of Steel Construction (AISC), One E.
10.1520/E0561-08. 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 ----------------------
E561–08
4. Summary of Test Method
4.1 During slow-stable fracturing, the developing crack
extension resistance K is equal to the applied stress intensity
R
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 values, which are individual data
points that define the K-R
...
This document is not anASTM standard and is intended only to provide the user of anASTM 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.
´1
Designation:E561–05 Designation:E561–08
Standard Test 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
´ NOTE—Equation 6 was editorially corrected in February 2007.
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 anyeither of the following notched and precracked specimens: the middle-cracked tension M(T) specimen, specimen
or the compact tension C(T) specimen, or the crack-line-wedge-loaded C(W) specimen. A K-R curve is a continuous record of
toughness development (resistance to crack extension) in terms of K plotted against crack extension in the specimen as a crack
R
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 threetwo 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.
2. Referenced Documents
2
2.1 ASTM Standards:
E4 Practices for Force Verification of Testing Machines
E399 Test Method for Linear-Elastic Plane-Strain Fracture Toughness K of Metallic Materials
Ic
E1823 Terminology Relating to Fatigue and Fracture Testing
2.2 Other Documents:
AISC Steel Construction ManualOther Document:
3
AISC Steel Construction Manual
3. Terminology
3.1 Definitions—Terminology E1823 is applicable to this method.
3.2 Definitions of Terms Specific to This Standard:
3.2.1 apparent plane-stress fracture toughness, K —Thevalueof Kcalculatedusingtheoriginalcracksizeandthemaximum
app
force achieved during the test. K is an engineering estimate of toughness that can be used to calculate residual strength. K
app app
depends on the material, specimen size, and specimen thickness and as such is not a material property.
-2
3.2.2 effective modulus, E (FL )—the value of Young’s modulus that produces an accurate correspondence between the
eff
experimentally measured compliance at the original crack size and the analytically developed compliance calculated for the same
crack size.
3.2.3 plane-stress fracture toughness, K —The value of K at instability in a force-controlled test corresponding to the
c R
1
This test method is under the jurisdiction ofASTM Committee E08 on Fatigue and Fracture and is the direct responsibility of Subcommittee E08.07 on Linear-Elastic
Fracture.Fracture Mechanics.
Current edition approved JuneNov. 1, 2005.2008. Published September 2005.February 2009. Originally approved in 1974. Last previous edition approved in 19982005
´1
as E561–98.E561–05 .
2
ForreferencedASTMstandards,visittheASTMwebsite,www.astm.org,orcontactASTMCustomerServiceatservice@astm.org.For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
3
Available from American Institute of Steel Construction (AISC), One E. 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 ----------------------
E561–08
maximum force point in the test. K depends on the material, specimen size, and specimen thickness and as such is not a material
c
pro
...
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