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...
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 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.
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Designation: E561 − 10
StandardTest Method for
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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.
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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
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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
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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
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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
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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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