RICE, PARIS and MERKLE – J-Integral Estimation Method

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J-integral estimation method according to RICE, PARIS and MERKLE (RPM)

Basic assumption of the estimation method

J-integral estimation methods are used to determine fracture-mechanical characteristic values according to the J-integral concept.

The proposal for the determination of J^RPM values according to RICE, PARIS and MERKLE [1] is based on the consideration of the deformation of the unnotched specimen and represents a one-sample approximation method which is applicable for deeply notched specimens with a/W > 0.6.

Fig. 1:

Determination of load–loadpoint displacement diagrams for the calculation of JIRPM (JIcRPM, JIdRPM) [1, 2]

Determination equation for SENB an CT specimen

The equation of determination is as follows:

$J_{I}^{RPM}={\frac {\lambda _{1}}{B(W-a)}}\int _{f_{0}}^{f_{max}}Fdf_{max}={\frac {\lambda _{1}(A_{G}-A_{0})}{B(W-a)}}$

For the three-point bending test specimen (SENB), the following specification applies to λ₁:

λ₁ = 2 für a/W > 0.6

In the case of the Compact Tension (CT) Specimen, the following relationship is used:

$\lambda _{1}=f(a|W){\frac {1+\alpha }{1+\alpha ^{2}}}\ mit\ \alpha =\left[\left[({\frac {2a}{W-a}})^{2}+2({\frac {2}{W-a}})+2\right]^{\frac {1}{2}}-({\frac {2a}{W-a}})\right]$

A₀ can be determined experimentally from the deformation of the unnotched test specimen or also calculated (see [3]).

Evaluation procedure

The experimental procedure for determining geometry-independent fracture-mechanical characteristic values with the aid of the instrumented Charpy impact test (ICIT) under dynamic loading is explained in detail in the validated procedure of the testing laboratory "Mechanical Testing of Plastics": MPK procedure "MPK-ICIT" [4].

See also

• J-integral concept
• J-Integral evaluation method (overview)
• J-integral estimation methods of

- BEGLEY and LANDES

- SUMPTER and TURNER

- MERKLE and CORTEN (MC)

- KANAZAWA

References

[1]	Rice, J. R., Paris, J. G., Merkle, J. G.: Some Further Results of J-Integral Analysis and Estimates. In: Progress in Flaw Growth and Fracture Toughness Testing. ASTM STP 536 (1973) 231–245 (https://doi.org/10.1520/STP49643S)
[2]	Blumenauer, H., Pusch, G.: Technische Bruchmechanik. Deutscher Verlag für Grundstoffindustrie, Leipzig Stuttgart (1993) 3. Edition (ISBN 3-342-00659-5; see AMK-Library under E 29-3)
[3]	Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser, Munich (2022) 3. Edition, p. 246 and 251–253, (ISBN 978-1-56990-806-8; e-book 978-1-56990-807-5; see AMK-Library under A 22))
[4]	MPK procedure "MPK-ICIT" (2016-03): Testing of Plastics – Instrumented Charpy Impact Test (ICIT): Procedure for Determining the Crack Resistance Behaviour Using the Instrumented Impact Test; Part I: Determination of Characteristic Fracture Mechanics Parameters for Resistance Against Unstable Crack Propagation; Part II: Determination of Characteristic Fracture Mechanics Parameters for Resistance Against Stable Crack Propagation