BEGLEY and LANDES – J-Integral Estimation Method

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J-Integral estimation method according to BEGLEY and LANDES (BL)

Evaluation method according to Begley and Landes

Basic assumption of the estimation method

J-integral estimation methods are used for the determination of fracture mechanical values according to the J-integral concept.

The proposal for the determination of J_I^BL was made by BEGLEY and LANDES [1] and is based on the neglect of the deformation of the unnotched specimen:

$J_{I}^{BL}={\frac {f({\frac {a}{W}})A_{G}}{B(W-a)}}$

Fig. 1:

Determination of J integral according to BEGLEY and LANDES [1, 2]

Geometry function and determination equations for SENB and CT specimens

The following geometry function f (a/W) applies to the three-point bending test specimen (SENB):

f (a/W) = 2 for a/W > 0.45

This results in the following determination equation for the SENB specimen:

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

In the case of the Compact tension (CT) specimen, the following geometry function is used:

$f({\frac {a}{W}})=2{\frac {1+\alpha }{1+\alpha ^{2}}}$

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

for a/W = 0.5 and f(a/W) = 2.26.

This results in the following determination equation for the CT specimen:

$J_{I}^{BL}={\frac {2.26\ A_{G}}{B(W-a)}}$

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" [3].

See also

• J-integral concept
• J-integral evaluation methods (overview)
• J-integral estimation methods of
  • RICE, PARIS and MERKLE
  • SUMPTER and TURNER
  • MERKLE and CORTEN (MC)
  • KANAZAWA

References

[1]	Landes, J. D., Begley, J. A.: Test Results from J-Integral-Studies: An Attempt to Established a JIC Testing Procedure. ASTM STP 560 (1974) p. 170–186
[2]	Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser, Munich (2022) 3. Edition, p. 258–59 and 267–270, (ISBN 978-1-56990-806-8; e-book 978-1-56990-807-5; see AMK-Library under A 22)
[3]	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