View source for BEGLEY and LANDES – J-Integral Estimation Method

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<span style="font-size:1.2em;font-weight:bold;"> ''J''-Integral estimation method according to BEGLEY and LANDES (BL)</span>
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'''Evaluation method according to Begley and Landes'''

==Basic assumption of the estimation method==

[[J-Integral Evaluation Method (Overview) |''J''-integral estimation methods]] are used for the determination of fracture mechanical [[Material Value | values]] according to the [[J-Integral Concept | ''J''-integral concept]].

The proposal for the determination of ''J<sub>I</sub><sup>BL</sup>'' was made by BEGLEY and LANDES [1] and is based on the neglect of the deformation of the unnotched [[Specimen | specimen]]:
{|
|-
|width="20px"|
|width="500px" | <math> J_{I}^{BL}=\frac{f(\frac{a}{W})A_{G}}{B(W-a)}</math>
|}

[[file:J int BL-1.jpg]]
{| 
|- valign="top"
|width="50px"|'''Fig. 1''': 
|width="600px" |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 [[SENB-Specimen | 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:

{|
|-
|width="20px"|
|width="500px" | <math> J_{I}^{BL}=\frac{2\ A_{G}}{B(W-a)}</math>
|}

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

{|
|-
|width="20px"|
|width="500px" | <math> f(\frac{a}{W})=2\frac{1+\alpha}{1+\alpha^2}</math>
|}
 
{|
|-
|width="20px"|
|width="500px" | with <math> \alpha=\sqrt{(\frac{2a}{W-a})^2+2(\frac{2a}{W-a})+2-(\frac{2a}{W-a}+1)}</math>
|}

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

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

{|
|-
|width="20px"|
|width="500px" | <math> J_{I}^{BL}=\frac{2.26\ A_{G}}{B(W-a)}</math>
|}

==Evaluation procedure==

The experimental procedure for determining geometry-independent fracture-mechanical characteristic values with the aid of the [[Instrumented Charpy Impact Test | instrumented Charpy impact test]] (ICIT) under dynamic loading is explained in detail in the validated procedure of the testing laboratory "Mechanical Testing of Plastics": [http://wiki.polymerservice-merseburg.de/index.php/MPK-Prozedur_MPK-IKBV_englisch  MPK procedure "MPK-ICIT"] [3].

==See also==

*[[J-Integral Concept|J-integral concept]]
*[[J-Integral Evaluation Methods (Overview)|J-integral evaluation methods (overview)]]
*J-integral estimation methods of
**[[RICE, PARIS and MERKLE – J-Integral Estimation Method | RICE, PARIS and MERKLE]]
**[[SUMPTER and TURNER – J-Integral Estimation Method | SUMPTER and TURNER]]
**[[MERKLE and CORTEN – J-Integral Estimation Method | MERKLE and CORTEN (MC)]]
**[[KANAZAWA – J-Integral Estimation Method | KANAZAWA ]]

'''References'''
{|
|-valign="top"
|[1]
|Landes, J. D., Begley, J. A.: Test Results from J-Integral-Studies: An Attempt to Established a J<sub>IC</sub> Testing Procedure. ASTM STP 560 (1974) p. 170–186
|-valign="top"
|[2]
|[[Grellmann, Wolfgang|Grellmann, W.]], [[Seidler, Sabine|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-Büchersammlung | AMK-Library]] under A 22)
|-valign="top"
|[3]
|[http://wiki.polymerservice-merseburg.de/index.php/MPK-Prozedur_MPK-IKBV_englisch 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

[[Category:Fracture Mechanics]]
[[Category:Instrumented Impact Test]]