MERKLE and CORTEN – J-Integral Estimation Method

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J-integral estimation method according to Merkle and Corten (MC)

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_I^MC was made by MERKLE and CORTEN [1, 2] and is based on the consideration of the deformation of the unnotched test specimen:

$J_{I}^{MC}=G+{\frac {2}{B(W-a)}}\left[D_{1}A_{G}+D_{2}A_{K}-(D_{1}+D_{2})A_{el}\right]$

for 0 < a/W < 1

with $D_{1}={\frac {1+\gamma }{1+\gamma ^{2}}}\ and\ D_{2}={\frac {\gamma (1-2\gamma -\gamma ^{2})}{(1+\gamma ^{2})^{2}}}$

Fig. 1:

Determination of J integral according to MERKLE and CORTEN [1, 2, 4]

Determination equation for SENB and CT specimen

For the Compact Tension (CT) specimen in the plane strain condition (EDZ), the following equation applies to γ:

$\gamma ={\frac {{\sqrt {2(1+(a/W)^{2})}}-(1+a/W)}{1-a/W}}$

The following applies to the SENB test specimen:

$\gamma ={\frac {1.456(W-a)}{s}}$

In the case of longer crack lengths, the following proposal was made in 1977 by ASTM Working Group E24.01.09 (Elastic-Plastic-Fracture)

$J_{I}^{MC77}={\frac {2}{B(W-a)}}\left[D_{1}A_{G}+D_{2}A_{K}\right]$

which was modified again in 1979 by the same Working Group [3]:

$J_{I}^{MC79}={\frac {2}{B(W-a)}}D_{1}A_{G}$

For the geometry functions D₁, D₂ and γ the following graphical dependence on the a/W ratio results:

Fig. 2:

Dependence of geometry factors on a/W ratio

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" [5].

See also

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

- RICE, PARIS and MERKLE

- SUMPTER and TURNER

- BEGLEY and LANDES

- KANAZAWA

Literaturhinweise

[1]	Merkle, J. G., Corten, H. T.: J. of Pressure Vessel Technology, Vol. 96 (1974) 4 p. 286 https://doi.org/10.1115/1.3454183
[2]	Merkle, J. G., Corten, H. T.: A J-integral Analysis for the Compact Specimen Considering Axial Forces as well as Bending Effects. Pressure Vessels and Piping Materials Nuclear Conf. Miami Beach, Florida (1974)
[3]	Clarke, G. A., Andrews, W. R., Begley, J. A., Donald, J. K. Embley, G.T., Landes, J. D., McCabe, D. E. Underwood, J. H.: A Procedure for the Determination of Ductile Fracture Toughness Values Using J Integral Techniques. Journal of Testing and Evaluation 7 (1979) 1 p. 49–56; https://doi.org/10.1520/JTE11201J
[4]	Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser, Munich (2022) 3. Edition, 251–253, (ISBN 978-1-56990-806-8; e-book 978-1-56990-807-5; see AMK-Library under A 22)
[5]	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 http://wiki.polymerservice-merseburg.de/index.php/MPK-Prozedur_MPK-IKBV_englisch