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{{Language_sel|LANG=ger|ARTIKEL=Auswertemethode nach Sumpter und Turner}}
{{PSM_Infobox}}
''J''-integral estimation method according to SUMPTER and TURNER (ST)
__FORCETOC__

==Basic assumption==

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

Sumpter and Turner [1] proposed to determine ''J''IST values by splitting the total energy ''A''G introduced by the external force into two parts, i.e., an elastic ''A''el and a plastic ''A''pl part with:

''A''G = ''A''el + ''A''pl

[[file:EvaluationMethod_ST1.jpg]]
{|
|- valign="top"
|width="50px"|'''Fig. 1''':
|width="600px" |Determination of ''J''-integral according to Sumpter and Turner [1, 2]
|}

==Determination equation for SENB and CT specimen==

The determination of ''J''IST values is then given by the following equation:

{|
|-
|width="20px"|
|width="500px" | <math> J_{I}^{ST}=\eta_{el}\frac{A_{el}}{B(W-a)}+\eta_{pl}\frac{A_{pl}}{B(W-a)}\cdot (\frac{W-a_{eff}}{W-a})</math>
|}

valid for 0 < ''a''/''W'' < 1

''f''(''a''/''W'') = 2 für ''a''/''w'' > 0.45

with:
{|
|-
|''A''el
|width="15px" |
|elastic part of the deformation energy 
|-
|''A''pl
|
|plastic part of the deformation energy 
|-
|''η''el
|
|elastic factor 
|-
|''η''pl
|
|plastic factor and 
|-
|''η''el, ''η''pl
|
|= ''f''(''a''/''W'') 
|}

''η''el can be determined from the elastic part of the load–load point displacement curve

''η''pl is for [[SENB-Specimen | three-point bending test specimens]] for ''a''/''W'' > 0.2 ''η''pl = 2

''η''pl is for [[Compact Tension (CT) Specimen | compact tension specimens]] for ''a''/''W'' > 0,6 ''η''pl = 2 (see ASTM STP 700)

For [[SENB-Specimen | SENB test specimens]], the following relationship applies for ''η''el:

{|
|-
|width="20px"|
|width="500px" | <math> \eta_{el}=\frac{2F_{Gy}s^2(W-a)}{f_{Gy}EBW^3}f^2\left( \frac{a}{W}\right )(1-\nu^2)</math>
|}

with: ''f'' (''a''/''W'') as correction function

In the literature, Schwalbe [3] and Blumenauer [4] give the following correlation (table):

'''Table''': Values for ''η''el for different test specimens and ''a''/''W'' ratios
{| border="1px" style="border-collapse:collapse"
!! style="width:30px; background:#DCDCDC" | ''η''el
!! style="width:80px; background:#DCDCDC" | ''a''/''W''
!! style="width:30px; background:#DCDCDC" | 0.2
!! style="width:30px; background:#DCDCDC" | 0.3
!! style="width:30px; background:#DCDCDC" | 0.4
!! style="width:30px; background:#DCDCDC" | 0.5
!! style="width:30px; background:#DCDCDC" | 0.6
!! style="width:30px; background:#DCDCDC" | 0.7
|-
|SENB
|style="text-align:center" | ''s''/''W'' = 4.0
|style="text-align:center" | 1.4
|style="text-align:center" | 1.7
|style="text-align:center" | 1.9
|style="text-align:center" | 2.0
|style="text-align:center" | 2.0
|style="text-align:center" | 1.9
|-
|CT
|style="text-align:center" | ''H''/''W'' = 1.2
|style="text-align:center" | 3.7
|style="text-align:center" | 2.7
|style="text-align:center" | 2.4
|style="text-align:center" | 2.3
|style="text-align:center" | 2.2
|style="text-align:center" | 2.2
|}

[[file:EvaluationMethod_ST2.jpg]]
{|
|- valign="top"
|width="50px"|'''Fig. 2''':
|width="600px" |Correlation between elastic factor and ''a''/''W''-ratio [5, 6]
|}

''η''el is defined for the [[SENB-Specimen | SENB test specimen]] as follows:

''η''el = 5 (''a''/''W'')2 + 5.5 (''a''/''W'') + 0.5

''J''pl can also be determined using the COD test technique, but then requires knowledge of the rotation factor ''n'':

{|
|-
|width="20px"|
|width="500px" | <math> \eta_{pl}=2-\frac{\left(1-\frac{a}{W}\right)(0.892)-4.476\frac{a}{W}}{1.125+0.892\frac{a}{W}-2.238\left( \frac{a}{W}\right )^2}</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"] [7].

==See also==

*[[J-Integral Concept | J-integral concept]]
*[[J-Integral Evaluation Method (Overview) | J-Integral evaluation method (overview)]]
*J-integral estimation methods of

::- [[RICE, PARIS and MERKLE – J-Integral Estimation Method | RICE, PARIS and MERKLE]]
::- [[MERKLE and CORTEN – J-Integral Estimation Method | MERKLE and CORTEN (MC)]]
::- [[BEGLEY and LANDES – J-Integral Estimation Method | BEGLEY and LANDES]]
::- [[KANAZAWA – J-Integral Estimation Method | KANAZAWA ]]

'''References'''

{|
|-valign="top"
|[1]
|Sumpter, J. D. G., Turner, C. E.: ASTM STP 601 (1976): Cracks and Fracture. Method for Laboratory Determination of Jc. p. 3–18
|-valign="top"
|[2]
|[[Grellmann,_Wolfgang|Grellmann, W.]], [[Seidler,_Sabine|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)
|-valign="top"
|[3]
|Schwalbe, K.-H.: Bruchmechanik metallischer Werkstoffe. Carl Hanser Verlag, München Wien (1980), (ISBN 3-446-12983-9; siehe [[AMK-Büchersammlung | AMK-Library]] under E 15)
|-valign="top"
|[4]
|[[Blumenauer, Horst|Blumenauer, H.]], Pusch, G.: Technische Bruchmechanik. Deutscher Verlag für Grundstoffindustrie, Leipzig Stuttgart (2003) 3rd Edition (see [[AMK-Büchersammlung | AMK-Library]] under E 29-3)
|-valign="top"
|[5]
|Sumpter, J. D. G.: Elastic-Plastic Fracture Analysis and Design Using the Finite Element Method. Ph.D thesis University of London (1974)
|-valign="top"
|[6]
|Chipperfield, C. G.: A Summary and Comparison of J Estimation Procedure. Journal of Testing and Evaluation (JTEVA), Vol. 6 No. 4 July (1978) 253–259 (https://doi.org/10.1520/JTE10951J)
|-valign="top"
|[7]
|[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]]

SUMPTER and TURNER – J-Integral Estimation Method - Revision history