View source for JTJ-Concept

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<span style="font-size:1.2em;font-weight:bold;">JT<sub>J</sub> -concept </span>
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==Fundamentals of stable crack growth==

In many cases, the [[Fracture|fracture]] of [[Plastics|plastics]] is initiated by stable crack growth (see: [[Crack Propagation|crack propagation]]). In this case, the [[Crack Toughness|crack toughness]] is evaluated on the basis of crack resistance (R) curves (see: [[Crack Resistance (R) Curve|crack resistance (R) curve]]). To construct an R curve, the ''J'' or ''δ'' value is selected as the stress parameter, which is determined using suitable approximate equations and plotted as a function of the measured crack growth ∆''a''.

The R curve, also known as the ''J''<sub>R</sub> curve, consists of two areas that describe the stages of crack blunting (see: [[Crack Resistance (R) Curve|crack resistance (R) curve]]) and [[Crack Propagation|crack propagation]]. The characteristic values determined for crack blunting are the physical crack initiation value ''J''<sub>i</sub> or ''δ''<sub>i</sub> and, as an approximation, a technical crack initiation value (see also: [[Crack Initiation|crack initiation]]). The [[Tearing Modulus|tearing modulus]] is determined as the material resistance to crack propagation (see also: [[Levels of Knowledge in Fracture Mechanics|levels of knowledge in fracture mechanics]]).

==The JT<sub>J</sub> -concept by Will and Michel==

In 1986, Will and Michel proposed an approach that is also suitable for plastics, which is referred to in the literature as the JT<sub>J</sub> -concept. According to this concept, stable crack growth occurs when the energy dissipated in the [[Plastic Zone|plastic zone]] specific to the material compensates for the excess available energy caused by the crack growth. According to this concept, stable crack growth can be understood as JT<sub>J</sub>-controlled crack growth. The JT<sub>J</sub> value is a sensitive indicator for quantitatively evaluating the increased energy absorption capacity of plastics as a function of load parameters and structural parameters (see: [[Microscopic Structure|microscopic structure]]). The crack propagation behaviour is described by a power law of the form

{|
|-
|width="20px"|
|width="500px" | <math>J\,=\,C_1\cdot\Delta a^{\frac{1}{2}}</math>
|}

with
{|
|-
|''C''<sub>1</sub>
|width="15px" |
|material constant.
|}

A large number of [[Plastics|plastics]] can be evaluated using the JT<sub>J</sub> -concept.

==See also==

* [[Fracture Mechanics|Fracture mechanics]]
* [[J-Integral Concept|J-integral concept]]
* [[Levels of Knowledge in Fracture Mechanics|Levels of knowledge in fracture mechanics]]
* [[Crack Resistance (R) Curve|Crack resistance (R) curve]]
* [[Crack Resistance Curve – Experimental Methods|Crack resistance curve – Experimental methods]]
* [[Tearing Modulus|Tearing modulus]]

==References==

* Will, P., Michel, B., Zerbst, U.: JTJ-gesteuertes Risswachstum und die Energiebilanz am duktilen Riss. Technische Mechanik 7 (1986) pp. 58–60
*[[Grellmann,_Wolfgang|Grellmann, W.]], [[Seidler,_Sabine|Seidler, S.]] (Eds.): Polymer Testing. Carl Hanser, Munich (2022) 3rd Edition, pp. 241–243 (ISBN 978-1-56990-806-8; E-Book ISBN: 878-1-56990-807-5; see [[AMK-Library]] under A 22)
* [https://de.wikipedia.org/wiki/Wolfgang_Grellmann Grellmann, W.], Seidler, S., (Eds): Kunststoffprüfung. Carl Hanser, Munich (2025) 4th Edtion, p. 251 (ISBN 978-3-446-44718-9; E-Book: ISBN 978-3-446-48105-3; see [[AMK-Library]] under A 23)
* [https://www.researchgate.net/profile/Wolfgang-Grellmann Grellmann, W.], [[michler,_Goerg_Hannes|Michler, G. H.]], Schierjott, U., Haudel, G.: Bruchverhalten und Morphologie von TPU/ABS-Kombinationen – Anwendung des Risswiderstandskonzeptes zur Bestimmung des JTJ-gesteuerten Risswachstums. Plaste und Kautschuk 36 (1989), No. 2, pp. 63–67 ([https://www.polymerservice-merseburg.de/fileadmin/inhalte/psm/veroeffentlichungen/Publ_47_Plaste_und_Kautschuk_36_1989__H_2_S_63-67.pdf Download as pdf)
* Grellmann, W., Michler, G., Schierjott, U.: Anwendung des R-Kurven-Konzeptes zur Bestimmung des JTJ-gesteuerten Risswachstums von TPU/ABS-Kombinationen. Institut für Mechanik, Karl-Marx-Stadt, Report Nr. 24 (1989), Part 2, pp. 238–244
* Grellmann, W., Seidler, S.: Chracterization of Crack Resistance Behaviour of Polymers with JTJ-Concept. ECF 9, European Conference on Fracture, Varna 21–25 September 1992, Proceedings Vol. 1 (1992) 202–207
* Seidler, S., Grellmann, W.: Charakterisierung des Risswiderstandsverhaltens von Kunststoffen mit dem JTJ-Konzept. Tagung Werkstoffprüfung 1992, 3 and 4 December 1992, Bad Nauheim, Proceedings, pp. 387–393 (Download as pdf)

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