Crack Resistance Curve – Elastomers Quasistatic

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Crack resistance curve – Elastomers quasistatic

Registration of R curves using quasi-static fracture mechanics tests

To characterise the crack behaviour of elastomeric materials—i.e. their resistance to stable crack initiation and propagation—quasi-static fracture mechanics tests are frequently carried out using a universal testing machine. In this experiment, the use of a single test specimen (single-specimen method) or several identical 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 and 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 under quasi-static test conditions as early as the initial stages of material development.

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

Fig. 1:

Schematic diagram of a SENT-specimen

The test specimens should be tested at room temperature at a crosshead speed of 10 or 50 mm/min, depending on the material, ensuring that the speed is not too high. The clamping length is 40 mm (see also: specimen clamping).

Identification of physical crack initiation

By observing the prepared notch base (see: notch geometry), the point at which cracking initiates is determined, thereby enabling the calculation of physical crack initiation values J_i. Following crack initiation, the elastomer test specimen undergoes increasingly elastic deformation as the test progresses, whilst the crack opening also increases. This process is illustrated schematically in Fig. 2.

Fig. 2:

Schematic representation of the increasing deformation and crack opening (blue) in a SENT-specimen due to external tensile stress during a quasi-static fracture mechanics test

When working with dark or black 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 clearly visible (see Fig. 3).

Fig. 3:

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 lR, 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).

Fig. 4:

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 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).

Multi-specimen technique

Another method for recording crack resistance (R) curves involves the use of the quasi-static 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-specimens with the same geometry as in the single-specimen tests were used. The load was also applied at a crosshead speed of 10 to 50 mm/min. For each specimen, the time of crack initiation was again determined by observing the notch base.

Following crack initiation, the test specimens were subjected to loading until the 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 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 curve to calculate the J-values according to Eq. (1) and Eq. (2) respectively.

$J_{diss}=\eta \cdot {\frac {A_{diss}}{B(W-a_{0})}}$

(1)

$J_{ges}=\eta \cdot {\frac {A_{tot}}{B(W-a_{0})}}$

(2)

where A_tot = A_diss + A_el

Fig. 5:

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 produced in this way on a 6 mm wide SENT-specimen.

Fig. 6:

Photograph of a fracture/cut surface of a SENT-specimen from the quasi-static fracture mechanics test (multi-specimen method), illustrating the measurement of the stable crack growth Δa

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 Δa can therefore be determined using optical microscopy. Δa 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 Δa 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 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 elastomeric materials. This energy dissipation involves the generation of heat due to internal friction, but for 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 tip, as this is where the highest local stresses and strains exist during loading, as has already been demonstrated on numerous occasions for elastomers [11‒14].

The J–l_R and J–Δa 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 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 Δa. This is important, particularly in view of the sometimes extremely large elastic 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 curve – Experimental methods
• Crack resistance curve – Examples
• Fracture mechanics
• Tearing modulus
• J-Integral concept

References

[1]	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)
[2]	Grellmann, W., Reincke, K.: Technical material diagnostics – Fracture mechanics of filled elastomer blends. In: Grellmann, W., Heinrich, G., Kaliske, M., Klüppel, M., Schneider, K., 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)
[3]	Reincke, K., Oßwald, K., 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
[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
[5]	Gerber, G., Struve, J.: Einfluss der Mischungszusammensetzung und Belastungsart auf das Versagensverhalten von Elastomeren. Kautschuk Gummi Kunststoffe 52 (1999) 400–405
[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)
[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
[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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[11]	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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