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{{Language_sel|LANG=ger|ARTIKEL=Risswiderstandskurve – Elastomere quasistatisch}}
{{PSM_Infobox}}
Crack resistance curve – Elastomers quasistatic
__FORCETOC__

==Registration of R curves using quasi-static fracture mechanics tests==

To characterise the [[Crack Toughness|crack behaviour]] of [[Elastomers|elastomeric materials]]—i.e. their resistance to stable [[Crack Initiation|crack initiation]] and [[Crack Propagation|propagation]]—[[Quasi-static Test Methods|quasi-static]] [[Fracture Mechanical Testing|fracture mechanics tests]] are frequently carried out using a [[Material Testing Machine|universal testing machine]]. In this experiment, the use of a single test specimen (single-specimen method) or several identical [[Specimen|test specimens]] (multi-specimen method) enables the recording of a crack resistance curve (R-curve) through the simultaneous recording of the load-extension diagram and the notch opening ''l''R.

Experience in recent years [1‒4] has shown that the use of a single-specimen method (SSM) can make a significant contribution to understanding stable [[Crack Initiation|crack initiation]] and [[Crack Propagation|crack propagation]] behaviour. The advantage of this method compared to the multi-specimen method (MSM) lies in the reduced material consumption and the resulting cost savings, which enable the characterisation of [[Toughness|toughness]] under [[Quasi-static Test Methods|quasi-static test]] conditions as early as the initial stages of material development.

Single-notched tensile specimens ([[SENT-Specimen|SENT-specimens]]) can be used to carry out experiments (see '''Fig. 1'''). To ensure a [[Plane Stress and Strain State|plane strain]] condition during [[Stress|loading]] and thus determine [[Material Value|material values]] that are [[Geometry Criterion|independent of geometry]], specimens with a thickness ''B'' = 6 mm are typically used. The length ''L'' of the [[Specimen|specimens]] is 100 mm and the width ''W'' = 25 mm. For [[Specimen|standard specimens]], the notch depth ''a'' is selected such that an ''a''/''W'' ratio of 0.2 is achieved. The [[Notch|notches]] are cut using a metal blade (see: [[Notching|notching]]).

[[File:R_Kurve_Elastomere-1.JPG|450px]]
{|
|- valign="top"
|width="50px"|'''Fig. 1''':
|width="600px"|Schematic diagram of a [[SENT-Specimen|SENT-specimen]]
|}

The [[Specimen|test specimens]] should be [[Testing|tested]] at room temperature at a [[Crosshead Speed|crosshead speed]] of 10 or 50 mm/min, depending on the [[Material & Werkstoff|material]], ensuring that the speed is not too high. The clamping length is 40 mm (see also: [[Specimen Clamping|specimen clamping]]).

==Identification of physical crack initiation==

By observing the prepared notch base (see: [[Notch Geometry|notch geometry]]), the point at which [[Crack Initiation|cracking initiates]] is determined, thereby enabling the calculation of physical crack initiation values ''J''i. Following crack initiation, the [[Elastomers|elastomer]] test specimen undergoes increasingly [[Deformation#Elastic deformation|elastic deformation]] as the test progresses, whilst the [[Crack Opening|crack opening]] also increases. This process is illustrated schematically in '''Fig. 2'''.

[[File:Crack R Curve Elastomers Fig-2.jpg|450px]]
{|
|- valign="top"
|width="50px"|'''Fig. 2''':
|width="600px"|Schematic representation of the increasing [[Deformation|deformation]] and [[Crack Opening|crack opening]] (blue) in a [[SENT-Specimen|SENT-specimen]] due to external [[Tensile Test|tensile stress]] during a [[Quasi-static Test Methods|quasi-static]] [[Fracture Mechanical Testing|fracture mechanics test]]
|}

When working with dark or black [[Material & Werkstoff|materials]], the notch base is prepared using a white TiO₂ powder, which adheres strongly to the surface and thus makes the formation of a new [[Fracture Surface|fracture surface]] clearly visible (see '''Fig. 3''').

[[File:Crack_R_Curve_Elastomers_Fig-3.jpg|550px]]
{|
|- valign="top"
|width="50px"|'''Fig. 3''':
|width="600px"|A sequence of photographs illustrating the progressive opening of the crack during a quasi-static fracture mechanics test on a carbon-black-reinforced specimen (black), together with a schematic diagram defining the crack opening ''l''R, which becomes increasingly visible in the white-prepared notch base
|}

Alternatively, light-coloured test specimens can be coated with a dark, fine-grained powder, such as carbon black, as shown in '''Fig. 4'''. Following the approach of Gerber and Struve [5], the distance between the two notch tips was measured in [1] and the value was defined as the damage parameter ''l''R (crack opening).

[[File:R_Kurve_Elastomere-4.JPG|250px]]
{|
|- valign="top"
|width="50px"|'''Fig. 4''':
|width="600px"|Determination of the crack opening on a light-coloured specimen whose notch base has been treated with carbon black
|}

To determine pairs of ''J''- ''l''R values, at least 10 images of the test specimen were analysed to establish the current [[Crack Opening|crack opening]] value. Furthermore, the deformation energy ''A'' at the respective time point was determined from the recorded load–traverse path diagram. Using this data, the deformation energy values were extracted at the corresponding time points, which were used to calculate the ''J''-values (see: [[J-Integral Concept|J-integral concept]]).

==Multi-specimen technique==

Another method for recording [[Crack Resistance (R) Curve|crack resistance (R) curves]] involves the use of the [[Quasi-static Test Methods|quasi-static]] [[Fracture Mechanical Testing|fracture mechanics test]] and the multi-specimen method, which was also employed in the studies reported in [6–9]. In each case, up to 10 identical [[SENT-Specimen|SENT-specimens]] with the same geometry as in the single-specimen tests were used. The [[Stress|load]] was also applied at a [[Crosshead Speed|crosshead speed]] of 10 to 50 mm/min. For each [[Specimen|specimen]], the time of [[Crack Initiation|crack initiation]] was again determined by observing the notch base.

Following [[Crack Initiation|crack initiation]], the test specimens were subjected to loading until the [[Crack Opening|crack opening]] reached various sizes. The test was then stopped in each case before complete failure occurred. From the corresponding load–displacement diagrams, which were recorded using the [[Material Testing Machine|universal testing machine]] both during loading and unloading, the two energies ''A''diss and ''A''tot were determined as shown in '''Fig. 5'''; these were used as load parameters for the [[Crack Resistance (R) Curve|crack resistance curve]] to calculate the [[J-Integral Concept|J-values]] according to '''Eq. (1)''' and '''Eq. (2)''' respectively.

{|
|-
|width="20px"|
|width="500px"|<math>J_{diss}=\eta \cdot\frac{A_{diss}}{B(W-a_{0})}</math>
|(1)
|}

{|
|-
|width="20px"|
|width="500px"|<math>J_{ges}=\eta \cdot\frac{A_{tot}}{B(W-a_{0})}</math>
|(2)
|}

where Atot = Adiss + Ael

[[File:Crack_R_Curve_Elastomers_Fig-5.jpg|500px]]
{|
|- valign="top"
|width="50px"|'''Fig. 5''':
|width="600px"|Schematic representation of a load–traverse path diagram from a quasi-static fracture mechanics test (multi-specimen method) showing the loading and unloading curves
|}

After unloading in the actual experiment, the specimens are slightly deformed once again and, in this state, cut apart in the plane of crack propagation using a metal blade. '''Figure 6''' shows an example of a [[Fracture Surface|fracture surface]] produced in this way on a 6 mm wide [[SENT-Specimen|SENT-specimen]].

[[File:Crack_R_Curve_Elastomers_Fig-6.jpg|300px]]
{|
|- valign="top"
|width="50px"|'''Fig. 6''':
|width="600px"|Photograph of a fracture/cut surface of a [[SENT-Specimen|SENT-specimen]] from the quasi-static fracture mechanics test (multi-specimen method), illustrating the measurement of the stable crack growth Δ''a''
|}

The various regions – the metal blade notch, the region of stable crack growth Δa and the cross-section immediately following the region of stable crack growth – are clearly visible. The value of Δ''a'' can therefore be determined using optical microscopy. Δ''a'' can be measured, for example, using a VHX 500 F 3D stereo microscope from Keyence. '''Figure 6''' illustrates how individual measures are taken at a minimum of 8 points distributed across the overall width of the test specimen, and the mean value is subsequently determined.

==Significance of single- and multi-specimen techniques for determining mechanical values==

The main differences between the single-specimen and multi-specimen methods therefore lie in the fact that the actual value of the stable crack growth Δ''a'' is determined instead of the crack opening ''l''R, and that recording the loading and unloading curves makes it possible to split the total deformation energy ''A''tot into the elastic deformation energy ''A''el and the dissipated energy ''A''diss [7, 10].

This is significant in that, depending on the deformability of the material under investigation, elastic deformation can occur even far from the [[Crack|crack]] tip. Furthermore, in addition to the energy required to create the new crack surface ''A''Crack, a significant proportion of the external energy is converted into energy dissipation within the deformed volume of [[Elastomers|elastomeric materials]]. This energy dissipation involves the generation of heat due to internal friction, but for [[Particle-filled Thermoplastics|filler-reinforced materials]] it also includes the proportion of energy that must be expended to break filler‒filler and filler‒polymer bonds.

The quantity ''A''diss , which can be determined experimentally, thus comprises three components: the energy required to create a new surface, thermal energy, and the energy required to break the bonds. Based on current knowledge, it is assumed that the majority of dissipation processes occur within a limited region around the [[Crack|crack]] tip, as this is where the highest local stresses and strains exist during loading, as has already been demonstrated on numerous occasions for [[Elastomers|elastomers]] [11‒14].

The ''J''–''l''R and ''J''–Δ''a'' values, obtained using either single-specimen or multi-specimen methods, were plotted graphically for further quantitative analysis, and curve-fitting was performed using suitable software to fit a mathematical function. As the final stage of the analysis, crack propagation values ''T''J* were thus determined for each material (see also: [[Tearing Modulus|tearing modul]]).

If the crack opening ''l''R is also determined whilst using the multi-specimen method, it is possible to verify whether there is a functional relationship between the two damage parameters ''l''R and Δ''a''. This is important, particularly in view of the sometimes extremely large elastic [[Deformation|deformation]] of the whole test specimen, with regard to the informative value of the parameter ''l''R and thus the applicability of the single-specimen method.

==See also==

* [[Crack Resistance (R) Curve|Crack resistance (R) curve]]
* [[Crack Resistance Curve – Experimental Methods|Crack resistance curve – Experimental methods]]
* [[Crack Resistance Curve – Examples|Crack resistance curve – Examples]]
* [[Fracture Mechanics|Fracture mechanics]]
* [[Tearing Modulus|Tearing modulus]]
* [[J-Integral Concept|J-Integral concept]]

==References==

{|
|-valign="top"
|[1]
|[[Reincke, Katrin|Reincke, K.]]: Elastomere Werkstoffe – Zusammenhang zwischen Mischungsrezeptur, Struktur und mechanischen Eigenschaften sowie dem Deformations- und Bruchverhalten, Habilitation, Martin-Luther-Universität Halle-Wittenberg, Shaker Publishing House (2016) (ISBN 978-3-8440-4637-3; see [[AMK-Library]] under B 2-2)
|-valign="top"
|[2]
|[[Grellmann, Wolfgang|Grellmann, W.]], Reincke, K.: Technical material diagnostics – Fracture mechanics of filled elastomer blends. In: [https://www.researchgate.net/profile/Wolfgang-Grellmann Grellmann, W.], [https://de.wikipedia.org/wiki/Gert_Heinrich Heinrich, G.], Kaliske, M., Klüppel, M., Schneider, K., [https://de.wikipedia.org/wiki/Thomas_A._Vilgis Vilgis, T.] (Eds.): Fracture Mechanics and Statistical Mechanics of Reinforced Elastomeric Blends. Springer, Berlin Heidelberg (2013), pp. 227–268, (ISBN 978-3-642-37909-3; see [[AMK-Library]] under A 14)
|-valign="top"
|[3]
|Reincke, K., Oßwald, K., [https://de.wikipedia.org/wiki/Wolfgang_Grellmann Grellmann, W.]: Experimental investigations for characterization of crack toughness of filler-reinforced SBR vulcanizates. 11th Tagung "Problemseminar: Deformation und Bruchverhalten von Kunststoffen", June 20–22, 2007, Merseburg, Proceedings CD-ROM (ISBN 978-3-86010-918-2), pp. 131–141
|-valign="top"
|[4]
|Reincke, K., Grellmann, W., Heinrich, G.: Engineering Fracture Mechanics for Crack Toughness Characterisation of Elastomers. In: Proceedings of the European Conference of Fracture (ECF 16), Alexandroupolis, Greece, July 3–7 (2006) pp. 507–508 and Full Paper CD: 2T18, (2006) 1–6
|-valign="top"
|[5]
|Gerber, G., Struve, J.: Einfluss der Mischungszusammensetzung und Belastungsart auf das Versagensverhalten von Elastomeren. Kautschuk Gummi Kunststoffe 52 (1999) 400–405
|-valign="top"
|[6]
|Reincke, K.: Bruchmechanische Bewertung von ungefüllten und gefüllten Elastomerwerkstoffen. PhD thesis, Mensch & Buch Publishing House, Berlin, (2005), (ISBN 978-3-89820-779-9; see [[AMK-Library]] under B 1-13)
|-valign="top"
|[7]
|Reincke, K., Grellmann, W., Heinrich, G.: Fracture mechanical investigations of filler-reinforced elastomers. In: Boukamel, A., Laiarinandrasana, L., Méo, S., Verron, E. (Eds.): Constitutive Models for Rubber V, Taylor & Francis Group London (2008) 221–227
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|[8]
|März, J.: Untersuchungen zur Weiterentwicklung bruchmechanischer Methoden zur quantitativen Beschreibung des Deformations- und Bruchverhaltens von Elastomerwerkstoffen. Master's thesis, Martin-Luther-Universität Halle-Wittenberg (2011); see [[AMK-Library]] under B 3-172
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|[9]
|Reincke, K., Grellmann, W.: Mechanical and fracture mechanics properties of rubber compositions with reinforcing components. In: Galimberti, M. (Ed.): Rubber-Clay Nanocomposites: Science, Technology and Applications. John Wiley & Sons, 1st Edition (2011) 305–342, (ISBN 978-0-470-56210-9; see [[AMK-Library]] under K 5)
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|[10]
|Netzker, C., Horst, T., Reincke, K., Behnke, R., Kaliske, M., Heinrich, G., Grellmann, W.: Analysis of stable crack propagation in filled rubber based on a global energy balance. Int. J. Fracture 181 (2013) 12–23, DOI: https://doi.org/10.1007/s10704-013-9816-5
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|Stommel, M.: Beschreibung der viskoelastischen mechanischen Eigenschaften, der Betriebsfestigkeit und des Bruchverhaltens von Elastomerbauteilen mit der Finite‐Elemente‐Methode. IKV – Berichte aus der Kunststoffverarbeitung, Volume 92, Publishing House Mainz, Wissenschaftsverlag Aachen (1999)
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|[12]
|Horst, T.: Spezifische Ansätze zur bruchmechanischen Charakterisierung von Elastomeren, PhD thesis, Technische Universität Dresden (2011) TUDpress 2011; (ISBN 978-3-942710-33-6; see [[AMK-Library]] under K 11)
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|[13]
|Stoček, R.: [https://www.researchgate.net/publication/279845036_Dynamische_Rissausbreitung_in_Elastomerwerkstoffen Dynamische Rissausbreitung in Elastomerwerkstoffen]. PhD thesis, Technische Universität Chemnitz (2012); [https://www.researchgate.net/publication/279845036_Dynamische_Rissausbreitung_in_Elastomerwerkstoffen Download as PDF]
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|[14]
|Stange, J.: Bruchmechanische Untersuchungen von Elastomeren zur Bewertung des Versagensverhaltens unter besonderer Berücksichtigung der Prüfkörpergeometrie. Master's thesis, Martin‐Luther‐Universität Halle‐Wittenberg (2001); see [[AMK-Library]] under B 3-97
|}

[[Category:Elastomers]]
[[Category:Hybrid Methods]]

Crack Resistance Curve – Elastomers Quasistatic - Revision history