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Created page with "{{Language_sel|LANG=ger|ARTIKEL=Heterogenität}} {{PSM_Infobox}} Heterogeneity of the strain distribution __FORCETOC__ ==Determination of heterogeneity in the tensile test== A prerequisite for determining heterogeneity or strain heterogeneity in the tensile test is the use of a laser extensometer (angle or parallel scanner) to determine the local strain distribution in the..."

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{{Language_sel|LANG=ger|ARTIKEL=Heterogenität}}
{{PSM_Infobox}}
Heterogeneity of the strain distribution
__FORCETOC__

==Determination of heterogeneity in the tensile test==

A prerequisite for determining heterogeneity or strain heterogeneity in the [[Tensile Test | tensile test]] is the use of a [[Laser Extensometry|laser extensometer]] (angle or parallel scanner) to determine the local strain distribution in the plane-parallel part of the [[Multipurpose Test Specimen | multipurpose test specimen]]. The differences determined in the local strain behaviour ('''Fig. 1''') suggest that a heterogeneity value should be defined as a new [[Material Parameter | material parameter]] for [[Polymer Testing | polymer testing]] on the basis of these strain values. '''Figure 1''' shows the maximum (red line) and minimum (black line) local strain, with the integral strain between reflectors 1 to 26. The 2D representation of a polyamide ([[Plastics – Symbols and Abbreviated Terms | abbreviation]]: PA) material with 13 reflectors in '''Fig. 2''', for example, is used to calculate the heterogeneity from the ASCII data.

[[file:heterogenitaet1.jpg]]
{|
|- valign="top"
|width="50px"|'''Fig. 1''':
|width="600px" |Local 3D strain distribution of an ABS material in a [[Tensile Test | tensile test]]
|}

[[file:heterogenitaet2.jpg]]
{|
|- valign="top"
|width="50px"|'''Fig. 2''':
|width="600px" |Local 2D strain distribution of a PA material in the tensile test
|}

If the maximum and minimum strain is determined from '''Fig. 2''' in relation to time or strain, independent of the location of occurrence, and the integral strain is also calculated ('''Fig. 3'''), then the heterogeneity is the difference between the maximum and minimum strain in relation to the integral strain in the test specimen volume. The following equation is used to determine the heterogeneity ''H'':

{|
|-
|width="20px"|
|width="500px" | <math> H=\frac{\epsilon_{l_{max}}-\epsilon_{l_{min}}}{\epsilon_{i}}</math>
|(1)
|}

[[file:heterogenitaet3.jpg]]
{|
|- valign="top"
|width="50px"|'''Fig. 3''':
|width="600px" |Maximum and minimum local and integral strain of a PA material
|}

As the initial range of the heterogeneity function at very small strains results in a de facto division ‘0/0’, similar to the calculation of the [[Poisson's Ratio | Poisson's ratio]], the heterogeneity is related to the registered maximum, resulting in a representation of ''H''rel normalised to 1 as a function of time or integral strain ('''Fig. 4''') ('''Eq. 2'''):

{|
|-
|width="20px"|
|width="500px" | <math> H_{rel} = \frac {H(t)} {H_{max}}</math>
|(2)
|}

[[file:Heterogeneity_4.jpg]]
{|
|- valign="top"
|width="50px"|'''Fig. 4''':
|width="600px" |Heterogeneity function of plastics
|}

In the range of valid heterogeneity values, there is often a critical point at which the heterogeneity increases again after the minimum. This point corresponds to the accumulation of damage and [[Hybrid Methods|hybrid methods]] of [[Polymer Diagnostic|plastic diagnostics]]. When the [[Fracture|fracture]] occurs, the fracture heterogeneity ''H''Brel can then be specified as a [[Material Value|characteristic value]], which allows a simple comparison of different [[Material & Werkstoff|material]] states.

==Application of heterogeneity==

The primary field of application for the [[Material Parameter|material parameter]] heterogeneity is structurally or morphologically heterogeneous materials in which changes in the [[Deformation Mechanisms|deformation or damage mechanism]] are indicated by the heterogeneity function, provided there is sufficient sensitivity. If different PA 6 materials with different glass fibre contents (see also: [[Ashing Method|ashing method]]) are welded together, as is common in the automotive industry, and [[Specimen|test specimens]] are prepared from the plates ('''Fig. 5'''), these can be characterised using [[Laser Extensometry|laser extensometry]] in the [[Tensile Test|tensile test]].

[[file:Heterogeneity_5.jpg]]
{|
|- valign="top"
|width="50px"|'''Fig. 5''':
|width="600px" |Welding of PA 6-GF10 and GF30 sheets and preparation of test specimens
|}

If the base materials PA 6-GF10, PA 6-GF20 and PA 6-GF30 are also analysed using [[Laser Extensometry | laser extensometry]], the heterogeneity functions are obtained as a function of the integral strain as shown in '''Fig. 6'''. The fracture heterogeneity is below 0.2 for all PA 6 modifications and the critical increases occur comparatively late in the non-linear viscoelastic range (see: [[Elasticity | elasticity]]), which is also determined using the [[Hybrid Methods | hybrid methods of plastics diagnostics]].

[[file:heterogenitaet6.jpg]]
{|
|- valign="top"
|width="50px"|'''Fig. 6''':
|width="600px" |Heterogeneity function and fracture heterogeneity of the base materials
|}

If identical materials are welded together, the conventional weld factor can be used as a quotient between the [[Strength | strength]] of the weld seam and the base material. In the case of dissimilar welding partners, this weld seam parameter cannot be used, as there are two base materials with different [[Strength | strengths]]. In this case, it is advisable to use the heterogeneity as a basis for comparing the welds. As can be seen in '''Fig. 7''', the functions are at a significantly higher level and the fracture heterogeneities reach values between 0.5 and 0.8 depending on the combination of welding partners. The critical point of the increase in the heterogeneity function, i.e. the onset of damage (see also: [[Micro-Damage Limit | micro-damage limit]]), is shifted to smaller strains, which was validated by simultaneous measurement of the [[Acoustic Emission | acoustic emission]].

[[file:heterogenitaet7.jpg]]
{|
|- valign="top"
|width="50px"|'''Fig. 7''':
|width="600px" |Heterogeneity function of the welded PA 6 materials
|}

==See also==

* [[Hybrid Methods | Hybrid methods]] of plastic diagnostics
* [[Polymer Diagnostic | Polymer diagnostics]]
* [[Laser Extensometry | Laser extensometry]]
* [[Laser Heterogeneity of Strain Distribution | Laser heterogeneity of strain distribution]]

'''References'''

* [[Bierögel,_Christian|Bierögel, C.]]: Hybrid Methods of Polymer Diagnostics. In: [[Grellmann, Wolfgang|Grellmann, W.]], [[Seidler, Sabine|Seidler, S.]] (Eds.): Polymer Testing. Carl Hanser, Munich (2022) 3rd Edition, pp. 497–514 (ISBN 978-1-56990-806-8; E-Book: ISBN 978-1-56990-807-5; see [[AMK-Büchersammlung | AMK-Library]] under A 22)
* Bierögel, C., [https://www.researchgate.net/profile/Wolfgang-Grellmann Grellmann, W.]: Determination of Local Deformation Behaviour of Polymers by Means of Laser Extensometry. In: Grellmann, W., Seidler, S. (Eds.): Deformation and Fracture Behaviour of Polymers. Springer, Berlin (2001) 365–384 (ISBN 3-540-41247-6)
* [https://de.wikipedia.org/wiki/Wolfgang_Grellmann Grellmann, W.], Bierögel, C.: Laserextensometrie anwenden. Einsatzmöglichkeiten und Beispiele aus der Kunststoffprüfung. Materialprüfung 40 (1998) 452–459
* Bierögel, C., Fahnert, T., Grellmann, W.: Deformation Behaviour of Reinforced Polyamide Materials Evaluated by Laser Extensometry and Acoustic Emission Analysis. Strain Measurement in the 21st Century, Lancaster (UK) 5.–6. September 2001, Proceedings (2001) 56–59 [https://www.polymerservice-merseburg.de/fileadmin/inhalte/psm/veroeffentlichungen/Deformation_Behaviour_of_Reinforced_Polyamide_Materials_2001.pdf Download als pdf]
* Grellmann, W., Langer, B.: Methods for Polymer Diagnostics for the Automotive Industry. Materialprüfung 55 (2013) 17–22 [https://www.polymerservice-merseburg.de/fileadmin/inhalte/psm/veroeffentlichungen/Methods_for_Polymer_Diagnostics_for_the_Automotive_Industry__Grellmann_Langer_2013_.pdf Download as pdf]
* Bierögel, C., Grellmann, W.: Ermittlung des lokalen Deformationsverhaltens von Kunststoffen mittels Laserextensometrie. In: Grellmann, W., Seidler, S. (Eds.): Deformation und Bruchverhalten von Kunststoffen. Springer, Berlin (1998) 331–344 (ISBN 3-540-63671-4; e-Book (2014): ISBN 978-3-642-58766-5; see [[AMK-Büchersammlung | AMK-Library]] under A 6)
* Grellmann, W., Bierögel, C., König, S.: Evaluation of Deformation Behaviour of Polyamide Using Laserextensometry. Polymer Testing 16 (1997) 225–240
* Bierögel, C., Fahnert, T., Lach, R., Grellmann, W.: Bewertung von Kunststoffschweißnähten mittels laseroptischer Dehnmesstechniken. In: Frenz, H., Wehrstedt, A. (Eds.): Kennwertermittlung für die Praxis. Tagungsband Werkstoffprüfung 2002, Wiley VCH, Weinheim (2003) 334–339 [https://www.polymerservice-merseburg.de/fileadmin/inhalte/psm/veroeffentlichungen/Bewertung_von_Kunststoffschweissnaehten_WP2002.pdf Download als pdf]
* Bierögel, C., Grellmann, W., Fahnert, T., [https://researchgate.net/profile/Ralf-Lach Lach, R.]: Material Parameters for Evaluation of Polymer Welds Using Laser Extensometry. Polym. Test. 25 (2006) 1024–1037; https://doi.org/10.1016/j.polymertesting.2006.07.001

[[category: Laser Extensometry | Laser extensometry]]

Heterogeneity - Revision history