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Created page with "{{Language_sel|LANG=ger|ARTIKEL=Reißmodul}} {{PSM_Infobox}} Tearing modul Formula symbol: ''T''J Unit: [-] The phases of crack propagation in plastics are characterised by the stages of crack blunting, physical crack initiation and crack propagation. To evaluate the material's resistance to crack propagation, an add..."

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{{Language_sel|LANG=ger|ARTIKEL=Reißmodul}}
{{PSM_Infobox}}
Tearing modul

Formula symbol: ''T''J

Unit: [-]

The phases of [[Crack Propagation|crack propagation]] in [[Plastics|plastics]] are characterised by the stages of [[Crack Resistance (R) Curve|crack blunting]], physical [[Crack Initiation|crack initiation]] and crack propagation. To evaluate the material's resistance to crack propagation, an additional [[Material Parameter|material parameter]] is determined from the rise of a crack resistance curve ([[Crack Resistance (R) Curve|crack resistance (R) curve]]), namely the tear modulus or tearing modulus, which quantifies the resistance to stable crack propagation [1–5].

If the R-curve is constructed using the crack field parameter ''J'' (see: [[J-Integral Concept|J-integral concept]]), the material parameter describing the material resistance to stable crack propagation can be derived as a numerical value of the tearing or tear modulus ''T''J (see also: [[JTJ-Concept|JTJ-concept]]).

{|
|-
|width="20px"|
|width="500px" | <math>T_J\,=\,\frac{d J}{d (\Delta a)}\,\cdot\,\frac{E}{{\sigma_F}^2}</math>
|}

with
{|
|-
|∆''a''
|width="15px" |
|stable crack growth, distance between notch and crack fron after stable loading
|-
|''E''
|
|[[Elastic Modulus|modulus of elasticity]]
|-
|''σ''F
|
|yield strength (see: [[Yield Stress|yield stress]])
|}

The [[Elastic Modulus – Examples and Material Values|modulus of elasticity]] is determined under [[Bend Test#The three-point bending test methods|three-point bending stress]] according to the equation

{|
|-
|width="20px"|
|width="500px" | <math>E_{d}=\frac{F_{gy}\ s^3}{4BW^3f_{gy}}</math>.
|}

Analogous to the use of ''J'', the [[Extended CTOD Concept|crack opening displacement]] ''δ'' can also be used to construct an R-curve as a load parameter.

{|
|-
|width="20px"|
|width="500px" | <math>T_\delta\,=\,\frac{\delta}{d (\Delta a)}\,\cdot\,\frac{E}{\sigma_F}</math>
|}

The parameters ''T''J and ''T''δ differ in their significance due to the different evaluation of [[Deformation#Plastic deformation|plastic deformation]].

These parameters are not covered by the currently valid standards [6–8] or draft standards. On the other hand, [9–12] showed that morphological changes in [[Polymer|polymers]] can have a much greater effect on [[Crack Propagation|crack propagation]] behaviour than on [[Crack Initiation|crack initiation behaviour]]. From this perspective, the quantitative inclusion of crack propagation behaviour beyond the limits set by the standards is necessary for the effective application of [[Fracture Mechanics|fracture mechanics]], particularly in the field of [[Material & Werkstoff|materials]] development.

==See also==

* [[JTJ-Concept|JTJ-concept]]
* [[Crack Resistance (R) Curve|Crack resistance (R) curve]]
* [[Crack Resistance Curve – Experimental Methods|Crack resistance (R) curve – Experimental methods]]
* [[Crack Resistance Curve – Elastomers Quasistatic|Crack resistance curve – Elastomers quasistatic]]

==References==

{|
|-valign="top"
|[1]
|[[Grellmann,_Wolfgang|Grellmann, W.]], [[Seidler,_Sabine|Seidler, S.]], (Eds.): Kunststoffprüfung. Carl Hanser, Munich (2022) 3rd Edition, pp. 241–243 (ISBN 978-1-56990-806-89; E-Book: ISBN 978-1-56990-807-5; see [[AMK-Library]] under A 22)
|-valign="top"
|[2]
|Will, P., Michel, B.: Zerbst, U.: JTJ-gesteuertes Risswachstum und die Energiebilanz am duktilen Riss. Technische Mechanik 7 (1986) pp. 58-60
|-valign="top"
|[3]
|Will, P.: Integralkriterien und ihre Anwendung in der Bruchmechanik. Fortschritt-Berichte, VDI-Reihe 18: Mechanik/ Bruchmechanik No. 56, VDI Verlag GmbH, Düsseldorf (1988)
|-valign="top"
|[4]
|Will, P., Michel, B., Schaper, M.: Justification of Nonlinear J-Resistance Curves. Engng. Frac. Mechanics 37 (1990) 275–281
|-valign="top"
|[5]
|Will, P.: R-Curves of Energy Dissipative Materials. J. of Materials Science 29 (1994) 2335–2340
|-valign="top"
|[6]
|Standard Draft ESIS TC 4 (2001): A Testing Protocol for Conduction J-Crack Growth Resistance Curve Tests on Plastics.
|-valign="top"
|[7]
|Standard Draft ESIS TC 4 (1996): A Testing Protocol for Conducting J-Crack Growth Resistance Curve Tests for Plastics under Impact Conditions
|-valign="top"
|[8]
|ASTM D 6068 (2010, reapproved 2018): Standard Test Method for Determining J–R Curves of Plastic Materials
|-valign="top"
|[9]
|Seidler, S., [https://www.researchgate.net/profile/Wolfgang-Grellmann Grellmann, W.]: Zähigkeit von teilchengefüllten und kurzfaserverstärkten Polymerwerkstoffen. Fortschr.-Berichte VDI-Reihe 18: Mechanik/ Bruchmechanik No. 92, VDI Verlag GmbH, Düsseldorf (1991), (ISBN-18-149218-3; siehe [[AMK-Library]] under A 4)
|-valign="top"
|[10]
|[[Seidler,_Sabine|Seidler, S.]]: Anwendung des Risswiderstandskonzeptes zur Ermittlung strukturbezogener bruchmechanischer Werkstoffkenngrößen bei dynamischer Beanspruchung, Habilitation (1997); Martin-Luther-Universität Halle-Wittenberg, VDI Verlag GmbH Düsseldorf, (ISBN 3-18-323118-2; siehe [[AMK-Library]] under B 2-1)
|-valign="top"
|[11]
|[https://de.wikipedia.org/wiki/Wolfgang_Grellmann Grellmann, W.], Seidler, S.: J-Integral of Fibre Reinforced Thermoplastics. Journal of Polymer Engineering 11 (1992) 71–101
|-valign="top"
|[12]
|Seidler, S., Grellmann, W.: Fracture Behaviour and Morphology of PC/ABS Blends. Journal of Materials Science 28 (1993) 4078–4084
|}

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

Tearing Modulus - Revision history