Tearing Modulus

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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 additional material parameter is determined from the rise of a crack resistance 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), 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).

$T_{J}\,=\,{\frac {dJ}{d(\Delta a)}}\,\cdot \,{\frac {E}{{\sigma _{F}}^{2}}}$

with

∆a		stable crack growth, distance between notch and crack fron after stable loading
E		modulus of elasticity
σF		yield strength (see: yield stress)

The modulus of elasticity is determined under three-point bending stress according to the equation

$E_{d}={\frac {F_{gy}\ s^{3}}{4BW^{3}f_{gy}}}$.

Analogous to the use of J, the crack opening displacement δ can also be used to construct an R-curve as a load parameter.

$T_{\delta }\,=\,{\frac {\delta }{d(\Delta a)}}\,\cdot \,{\frac {E}{\sigma _{F}}}$

The parameters T_J and T_δ differ in their significance due to the different evaluation of 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 polymers can have a much greater effect on crack propagation behaviour than on 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, particularly in the field of materials development.

See also

• JTJ-concept
• Crack resistance (R) curve
• Crack resistance (R) curve – Experimental methods
• Crack resistance curve – Elastomers quasistatic

References

[1]	Grellmann, W., 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)
[2]	Will, P., Michel, B.: Zerbst, U.: JTJ-gesteuertes Risswachstum und die Energiebilanz am duktilen Riss. Technische Mechanik 7 (1986) pp. 58-60
[3]	Will, P.: Integralkriterien und ihre Anwendung in der Bruchmechanik. Fortschritt-Berichte, VDI-Reihe 18: Mechanik/ Bruchmechanik No. 56, VDI Verlag GmbH, Düsseldorf (1988)
[4]	Will, P., Michel, B., Schaper, M.: Justification of Nonlinear J-Resistance Curves. Engng. Frac. Mechanics 37 (1990) 275–281
[5]	Will, P.: R-Curves of Energy Dissipative Materials. J. of Materials Science 29 (1994) 2335–2340
[6]	Standard Draft ESIS TC 4 (2001): A Testing Protocol for Conduction J-Crack Growth Resistance Curve Tests on Plastics.
[7]	Standard Draft ESIS TC 4 (1996): A Testing Protocol for Conducting J-Crack Growth Resistance Curve Tests for Plastics under Impact Conditions
[8]	ASTM D 6068 (2010, reapproved 2018): Standard Test Method for Determining J–R Curves of Plastic Materials
[9]	Seidler, S., 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)
[10]	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)
[11]	Grellmann, W., Seidler, S.: J-Integral of Fibre Reinforced Thermoplastics. Journal of Polymer Engineering 11 (1992) 71–101
[12]	Seidler, S., Grellmann, W.: Fracture Behaviour and Morphology of PC/ABS Blends. Journal of Materials Science 28 (1993) 4078–4084