Crack Resistance (R) Curve

Sprachauswahl/Language selection

Dieser Artikel ist auch auf Deutsch verfügbar Risswiderstandskurve

A service provided by
Polymer Service GmbH Merseburg
Tel.: +49 3461 30889-50 E-Mail: info@psm-merseburg.de Web: https://www.psm-merseburg.de
Our further education offers: https://www.psm-merseburg.de/weiterbildung
PSM on Wikipedia: https://de.wikipedia.org/wiki/Polymer Service Merseburg

Crack resistance (R) curve concept

Construction of an R curve

When applying the J-integral concept, it should be noted that, in most cases, fracture is initiated by stable crack propagation. The assessment of crack toughness is based on crack resistance (R) curves. To construct the R curve, the J-value is selected as the loading parameter and plotted as a function of the stable crack growth Δa (Fig. 1).

Fig. 1:

Crack resistance curve of the elastic-plastic fracture mechanics

Phases of crack propagation

The J-Δa curve, also known as the JR-curve, consists of two regions that describe the phases of crack blunting and crack propagation. The blunting line marks the region where blunting occurs at the crack tip in the form of a bulge in the crack front (see: crack opening) and the stretch zone forms before stable crack growth begins. The following equation applies to the blunting line

$J\,=\,q\cdot \sigma _{F}\cdot \Delta a,$

(1)

where the yield strength (see: yield stress) is determined on the basis of the applied load. The factor q depends on the material’s hardening behaviour and is generally given as q = 2.

The crack propagation behaviour is described by a power law of the form,

$J\,=\,c_{1}\,\Delta a^{c_{2}}$

(2)

where

c1, c2

...

represent material constants.

Physical crack initiation

The crack initiation phase is quantified by the actual physical crack initiation value and, approximately, by technical crack initiation values. The physical crack initiation value is determined at the site of the original crack termination by measuring the width of the stretch zone (Fig. 1). This procedure requires SEM images of the fracture surface.

Technical crack initiation values J_0.2 are determined at a crack extension Δa = 0.2 mm onset or from the intersection of the crack propagation curve (Eq. 2) and the blunting line shifted parallel by 0.2 mm (Fig. 1).

For plastics, in contrast to metallic materials, the determination of J_0.2 at Δa = 0.2 mm onset in accordance with ESIS TC 4 has become the established practice. When determining crack initiation values, it must be taken into account that the evaluation may only be carried out within specific validity ranges.

The tearing modulus is derived from the rise of the J-Δa curve as an additional material parameter,

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

(3)

which quantifies the resistance to stable crack propagation.

The J_TJ-concept by WILL and MICHEL

WILL and MICHEL propose a model according to which stable crack growth occurs when the energy dissipated in the plastic zone, which varies depending on the material, compensates for the excess available energy caused by the crack propagation. According to this model, stable crack growth should be understood as JTJ -controlled crack growth.

In the same way as the crack field parameter J, the crack opening displacement δ can be used to construct the R-curve. From the δ-Δa curves, the physical crack initiation value δ_i, the technical crack initiation value δ_0.2 and the parameter δT_δ can be derived. The parameters based on the CTOD concept differ in their informative value from those determined from J-Δa curves, due to the evaluation being based on plastic deformation.

See also

• Crack resistance curve – Experimental method
• Crack resistance curve – Examples
• Crack resistance curve – Elastomers quasistatic
• ICIT – Stop block method
• ICIT – Extended stop-block method
• Stretch zone
• J-integral concept
• JTJ-concept

References

• Will, P., Michel, B., Zerbst, U.: JTJ-gesteuertes Risswachstum und die Energiebilanz am duktilen Riss. Technische Mechanik 7 (1986) 58–60; https://journals.ub.ovgu.de/index.php/techmech/article/view/1640 (Access: 17.04.2026)
• Grellmann, W., Seidler, S. (Eds.): Kunststoffprüfung. Carl Hanser, Munich (2025) 4th Edition, pp. 250/251 (ISBN 978-3-446-44718-9; E-Book: ISBN 978-3-446-48105-3; see AMK-Library under A 23)
• ESIS TC 4 (2001): A Testing Protocol for Conducting J-Crack Resistance Curve Test on Plastics
• PD ISO/TS 28660 (2023-03): Plastics – Determination of J-R-Curves – Fracture Toughness
• ASTM D 6068 (2010; reapproved 2018): Standard Test Method for Determining J-R Curves of Plastic Materials