Download Effect of carbon black content on the stress relaxation of natural rubber

The 9th International Conference on the Mechanics of Time Dependent Materials
Effect of carbon black content on the stress relaxation of natural rubber
C. Marano a, F. Briatico-Vangosa b, M. Rink c
Dipartimento di Chimica, Materiali e Ingegneria Chimica “Giulio Natta”, Politecnico di Milano, Italy,
a [email protected], b [email protected], c [email protected]
Keywords: Unfilled and Carbon Black filled Natural Rubber, Stress Relaxation, Structural changes
Introduction and objectives
In several applications of rubbers and rubber compounds – such as tires – product performance is
largely determined by material hysteretic behaviour and strength, which are in turn related to
reversible and irreversible phenomena occurring at large strains. Among these phenomena, the
strain‐induced crystallization may be significant.
In order to investigate this phenomenon, stress relaxation tests have been widely adopted on
unfilled rubber both at low [1-3] and room temperature [3-5]. More in general, this kind of test has
been also performed on filled rubber compounds in order to relate the time dependent mechanical
behaviour to the structural modification of the material [6-7]. In this work a systematic study on the
relaxation behaviour of natural rubber compounds differing in carbon black content is performed
and a correlation between the obtained results and changes in rubber microstructure is
investigated.
Materials and Methods
Unfilled (NR0) and N330 carbon black filled (NR25, NR50, NR75 – filler volume fraction 0.12, 0.21
and 0.29) natural rubber compounds, supplied by Bridgestone, were considered. All the considered
materials crystallize at room temperature when stretched above a critical value, λc. [8].
For each compounds different specimens were loaded up to draw ratio levels, λmax, both below and
above the material’s strain induced crystallization onset, λc, through a loading-ramp performed at
constant stretch rate, then stress was let to relax for a time between 104 and 106 s.
The reduced stress, σ*=σn /(λ-λ-2), in which λ=l/l0 with l and l0 respectively the actual and initial
distance between two marks on the sample and σn =P/A0 with P the applied load and A0 the initial
area of the specimen cross section, evolution during time was fitted with a stretched exponential
(KWW) function

  t − tmax  β  

  τ   


σ * (t − tmax ) = σ *max (0) − ∆σ * 1 − exp − 


in which tmax is the time at the end of the loading ramp, when λ=λmax is reached, σ*max(0) is the
reduced stress at tmax, measured directly from experimental data, ∆σ* represents the amount of
relaxation, τ is an average relaxation time while β gives an idea of the breadth of the relaxation
spectrum, being one for a single relaxation time phenomenon. After having determined ∆σ* by least
square fitting of experimental data, the asymptotic value of σ* was calculated as
σ*asymptotic=σ*(∞)=σ*max - ∆σ*.
Results and analysis
In Figure 1 σ*asymptotic and the reduced stress calculated in the loading ramp, σ*, are plotted versus
1/λmax and 1/λ respectively. A similar trend is observed for the “fully relaxed” material (dots) and
the “un-relaxed” one (lines), which is always higher than σ*asymptotic. However, if for NR0 the two
curves depart one from the other when an upturn, due to crystallization, occurs, suggesting that this
phenomenon is the main cause of stress relaxation, in the case of filled rubbers the “fully relaxed”
and “un-relaxed” curves differ in a much wider stretch ratio range, due to the occurrence of several
types of structural changes promoted by the filler. The analysis of the “fully relaxed” reduced stress
allows to highlight and investigate the effects of filler presence and content and of structure changes
after all time dependent phenomena are over.
5
NR0
NR50
NR25
NR75
σtrue/(λ2-1/λ) [MPa]
4
3
2
1
0
0.2
0.4
0.6
0.8
1.0
1/λ [-]
Figure 1: Reduced stress, σ*, and asymptotic reduced stress, σ*asymptotic, for the considered compounds.
References
[1] Gent, N., Trans. Faraday. Soc. 1954, 50, 521-533.
[2] Gent, N.; Zhang, L. Q., Rubber Chemistry and Technology 2002, 5 (75), 923-933.
[3] Toki, S.; Sics, I.; Hsiao, B.S.; Tosaka, M.; Poompradub, S.; Ikeda, Y.; Kohjiy S., Macromolecules 2005, 38,
7064-7073.
[4] Tosaka, M.; Kawakami, D.; Senoo, K.; Kohjiya, S.; Ikeda, Y.; Toki, S.; Hsiao, B.S., ., Macromolecules 2006, 39,
5100-5105.
[5] Rault, J.; Marchal, J.; Judeinstein, P.; Albouy, P.A., Eur. Phys. J .E 2006, 21, (243-261).
[6] Le, HJ.H.; Ilisch, S.; Radush, H.J., Polymer, 2009, 50, (2294-2303).
[7] Tada, T.; Urayama K.; Mabuchi, T.; Muraoka, K.; Takigawa, T., 2010, Journal of Polymer Science: Part B:
Polymer Physics, 48, 1380–1387.
[8] Marano C.; Calabrò R.; Rink M.; 2010, Journal of Polymer Science: Part B: Polymer Physics, 48, 1509–1515.