JTJ-Concept

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JT_J -concept

Fundamentals of stable crack growth

In many cases, the fracture of plastics is initiated by stable crack growth (see: crack propagation). In this case, the crack toughness is evaluated on the basis of crack resistance (R) curves (see: 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_R curve, consists of two areas that describe the stages of crack blunting (see: crack resistance (R) curve) and crack propagation. The characteristic values determined for crack blunting are the physical crack initiation value J_i or δ_i and, as an approximation, a technical crack initiation value (see also: crack initiation). The tearing modulus is determined as the material resistance to crack propagation (see also: levels of knowledge in fracture mechanics).

The JT_J -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_J -concept. According to this concept, stable crack growth occurs when the energy dissipated in the 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_J-controlled crack growth. The JT_J 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). The crack propagation behaviour is described by a power law of the form

$J\,=\,C_{1}\cdot \Delta a^{\frac {1}{2}}$

with

C1

material constant.

A large number of plastics can be evaluated using the JT_J -concept.

See also

• Fracture mechanics
• J-integral concept
• Levels of knowledge in fracture mechanics
• Crack resistance (R) curve
• Crack resistance curve – Experimental methods
• 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, W., 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)
• 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)
• Grellmann, W., 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)