Oluschinski: Created page with "{{Language_sel|LANG=ger|ARTIKEL=Erweitertes CTOD-Konzept}} {{PSM_Infobox}} Extended CTOD concept FORCETOC ==Critical crack opening displacement ''δ''== The fracture mechanical parameter crack opening displacement ''δ'' (see: crack opening), determined according to the crack tip opening displacement concept (CTOD), is su..."

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{{Language_sel|LANG=ger|ARTIKEL=Erweitertes CTOD-Konzept}}
{{PSM_Infobox}}
Extended CTOD concept
__FORCETOC__

==Critical crack opening displacement ''δ''==

The fracture mechanical [[Material Parameter|parameter]] crack opening displacement ''δ'' (see: [[Crack Opening|crack opening]]), determined according to the [[Crack Tip Opening Displacement Concept (CTOD)|crack tip opening displacement concept (CTOD)]], is suitable for describing the deformability of [[Material & Werkstoff|materials]]. In the case of a [[SENB-Specimen|three-point bending test specimen]], the determining '''Eq. (1)''' for ''δ'' is:

{|
|-
|width="20px"|
|width="500px" | <math> \delta = \frac{1}{n}(W-a)\frac{4 \ f_{max}}{s}</math>
|(1)
|}

with
{|
|-
|''n''
|width="15px" |
|[[Plastic Hinge Model|rotation factor]]
|-
|''W''
|
|test specimen with
|-
|''a''
|
|notch depth ([[Initial Crack Length|initial crack length]])
|-
|''f''max
|
|maximum deflection
|-
|''s''
|
|support span (see [[Support Distance|support distance]])
|}

Crack opening displacement ''δ'' is always useful when material users or developers are looking for a parameter that clearly describes increasing embrittlement (see:[[Brittle Fracture Promoting Factors|brittle fracture promoting factors]]) and represents a geometry-independent variable (see: [[Geometry Criterion|geometry criterion]]).

==Deflection splitting==

Assuming [1] that the experimentally measured test specimens deflection ''f''max can be calculated from the deflection of the unnotched part ''f''B and the part caused by the [[Deformation|deformation]] in the area of the [[Notch|notch]] ''f''K (notch part) according to '''Eq. (2)'''

{|
|-
|width="20px"|
|width="500px" | <math> f_{max}=f_{K}+f_{B} \!</math>
|(2)
|}

where the bending portion ''f''B is calculated using '''Eq. (3)'''

{|
|-
|width="20px"|
|width="500px" | <math> f_{B}=\frac{F_{max} \ s^3}{4 \ E \ B \ W^3}</math>
|(3)
|}

with ''E'' = [[Elastic Modulus|modulus of elasticity]], the relationship between deflection and the ''a''/''W'' ratio can be interpreted. When using the critical crack opening ''δ'', it is therefore possible to separate the influence of pure [[Bend Test|bending]] in the form of the deflection part and the notch part.

==Application of the extended CTOD concept for polypropylene (PP), polyamide (PA) and chlorinated polyvinyl chloride (PVCC)==

'''Figure 1''' shows that the bending part decreases as the ''a''/''W'' ratio increases, i.e. at ''a''/''W'' = 0.1 it accounts for 40 % of the total deflection and at ''a''/''W'' = 0.7 only 5 %. For high notch depths, the ''f''K part dominates [2].

[[File:erweitertesCTOD1.jpg]]
{|
|- valign="top"
|width="50px"|'''Fig. 1''':
|width="600px" |Deflection parts ''f''max, ''f''K and ''f''B at the beginning of unstable [[Crack Propagation|crack propagation]] for PP [2]
|}

[[File:erweitertesCTOD2.jpg]]
{|
|- valign="top"
|width="50px"|'''Fig. 2''':
|width="600px" |Deflection parts ''f''max, ''f''K and ''f''B at the beginning of unstable [[Crack Propagation|crack propagation]] for polyamide 6 and PVCC [2]
|}

The [[Levels of Knowledge in Fracture Mechanics|fracture mechanics parameters]] ''δ''Id (calculated with ''f''max), ''δ''IdK (calculated with the notch part ''f''K) and ''δ''IdB (calculated with the bending part ''f''B) show a similar qualitative curve progression to the representations selected in '''Fig. 1''' and '''Fig. 2'''.

==See also==

* [[Crack Tip Opening Displacement Concept (CTOD)|Crack tip opening displacement concept (CTOD)]]
* [[Fracture Mechanics|Fracture mechanics]]
* [[Crack Opening|Crack opening]]
* [[Plastic Hinge Model|Plastic hinge model]]
* [[ICIT – Nonlinear Material Behaviour|ICIT – Nonlinear material behaviour]]

==References==

{|
|-valign="top"
|[1]
|Srawley, J. E.: Wide range stress intensity factor expressions for ASTM E 399 standard fracture toughness specimens. International J. of Fracture Mechan. 12 (1976) 475–476 DOI: [https://doi.org/10.1007/BF00032844 https://doi.org/10.1007/BF00032844]
|-valign="top"
|[2]
|[[Grellmann,_Wolfgang|Grellmann, W.]]: Beurteilung der Zähigkeitseigenschaften von Polymerwerkstoffen durch bruchmechanische Kennwerte. Habilitation (1986), [https://de.wikipedia.org/wiki/Technische_Hochschule_Leuna-Merseburg Technische Hochschule Leuna-Merseburg], Wiss. Zeitschrift TH Merseburg 28 (1986) H. 6, S. 787‒788 ([https://www.polymerservice-merseburg.de/fileadmin/inhalte/psm/veroeffentlichungen/Habil_Grellmann_Inhaltsverzeichnis.pdf Inhaltsverzeichnis], [https://www.polymerservice-merseburg.de/fileadmin/inhalte/psm/veroeffentlichungen/Habil_Grellmann_Kurzfassung.pdf Content, Summary])

[[Category:Fracture Mechanics]]
[[Category:Instrumented Impact Test]]

Extended CTOD Concept - Revision history