Crack tip opening displacement: Difference between revisions

Revision as of 05:52, 26 December 2020

Revision as of 06:43, 6 July 2022

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== History ==

Examination of fractured test specimens led to the observation that the crack faces had moved apart prior to fracture, due to the blunting of an initially sharp crack by plastic deformation. The degree of crack blunting increased in proportion to the toughness of the material.<ref>{{cite journal |first1=J. C. |last1=Newman Jr.|first2=M. A. |last2=James |first3=U. |last3=Zerbst |title=A review of the CTOA/CTOD fracture criterion |journal=Engineering Fracture Mechanics |volume=30 |issue=3-43–4 |pages=371–385 |publisher=Elsevier |date=2003|doi=10.1016/S0013-7944(02)00125-X }}</ref> This observation led to considering the opening at the crack tip as a measure of fracture toughness. The COD was originally independently proposed by [[Alan Cottrell]] and A. A. Wells.<ref>A. A. Wells, ''Crack Propagation Symposium'', Cranfield, (1961) 210</ref><ref>{{Cite book|last=Soboyejo|first=W. O.|url=http://worldcat.org/oclc/300921090|title=Mechanical properties of engineered materials|date=2003|publisher=Marcel Dekker|isbn=0-8247-8900-8|chapter=11.7.1 Crack Opening Displacement|oclc=300921090}}</ref> This parameter became known as CTOD. [[George Rankine Irwin|G. R. Irwin]] later postulated that crack-tip plasticity makes the crack behave as if it were slightly longer. Thus, estimation of CTOD can be done by solving for the displacement at the physical crack tip.

== Use as a design parameter ==

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== Relation with other crack tip parameters ==

=== K and CTOD ===

CTOD can be expressed in terms of stress intensity factor <math>K</math> as: <ref>{{cite book |first=T. L. |last=Anderson |title=Fracture Mechanics: Fundamentals and Applications |edition=Third |url={{google books |plainurl=y |id=MxrtsC-ZooQC}}|date=24 June 2005|publisher=CRC Press|isbn=978-0-8493-1656-2 |pppages=104–105}}</ref>

:<math>\delta_\text{t} = \frac{4}{\pi}\frac{K^2}{m\sigma_\text{y} E} </math>

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=== J-integral and CTOD ===

The relationship between the CTOD and J is given by: <ref name="suresh04"/><ref>{{Cite book|last=Zehnder|first=Alan T.|url=https://www.worldcat.org/oclc/773034407|title=Fracture mechanics|date=3 January 2012 |isbn=978-94-007-2595-9|___location=Dordrecht|pages=172|oclc=773034407}}</ref>

:<math>\delta_\text{t} = d_n \frac{J}{\sigma_\text{y}}</math>