- Email: [email protected]
Initial tensile behaviour of elastomers
ARTICLE IN PRESS
POLYMER TESTING Polymer Testing 25 (2006) 650–655 www.elsevier.com/locate/polytest
Test Method
Initial tensile behaviour of elastomers Jir˘ ı´ Mala´cˇ Department of Polymer Engineering, Faculty of Technology, Tomas Bata University in Zlı´n, 762 72 Zlı´n, Czech Republic Received 18 February 2006; accepted 31 March 2006
Abstract At very small strains the tensile stress–strain relationship of elastomers is often fairly linear and therefore might be used for obtaining initial tensile modulus E. In this work we analysed initial tensile data of unfilled and carbon black filled vulcanised SBR samples to test if this is feasible. Strains from mechanical contact extensometer data have shown that the initial stress–strain dependence is nearly linear, as expected, but does not go through the origin, probably because of random initial time lag between force and extension times at crossing the zero point. Initial strains taken from the crosshead position have lower variation coefficients than initial strains from the mechanical contact extensometer data and, consequently, initial tensile modulus from the crosshead position also has lower variation coefficients than initial tensile modulus from the mechanical contact extensometer data. r 2006 Elsevier Ltd. All rights reserved. Keywords: Elastomers; Initial stress–strain; Initial stress; Initial strain; Initial time lag; Initial tensile modulus
1. Introduction Tensile stress–strain is one of the most commonly performed tests in the rubber industry. These tests are performed on tensile testing instruments where a cured, dumbbell-shaped rubber specimen is pulled apart at a predetermined rate (usually 500 mm/min) while measuring the tensile stress. Generally, ultimate strength, ultimate elongation and tensile stress at different elongations (such as 100% and 300%) are reported. However, many rubber products are not extensionally deformed more than 30%, so tensile stress–strain is not usually of great importance for rubber design [1].
Fax: +420 57 603 1328.
E-mail address: [email protected]. 0142-9418/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.polymertesting.2006.03.015
Recently, the specific tensile deformation energy was chosen as a possible characteristic of elastomers in the lower deformation region, where many rubber goods are working in practice and where influence of rubber-filler interaction might be studied in detail [2]. The Young’s modulus E (i.e. the slope of tensile stress–strain relationship at low deformations) is widely used to characterize the stiffness of hard materials [3]. Unlike metals, elastomer stress–strain curves show a very limited linear portion [1]. A typical result of a tensile test of an elastomer is a stress–strain curve of S-shape [4,5] where the gradient of the curve changes as the elastomer is stretched [6]. Carbon nanotube-reinforced silicon elastomer shows a dramatic enhancement of initial modulus when it is measured by fitting a straight line to the
ARTICLE IN PRESS J. Mala´cˇ / Polymer Testing 25 (2006) 650–655
2. Experimental Styrene–butadiene rubber compounds filled with carbon blacks N220, N330 and N550 were prepared according to ISO 2322-1985. Unfilled compound of similar composition (i.e. without carbon black) was used for comparison. The compounds were compression moulded at 150 1C for t90+5 min to 2 mm sheets and dumbbell specimens cut from these sheets were used for tensile testing. A universal testing machine, Tensometer 2000 (Alpha Technologies), was used and the tensile tests were carried out at a crosshead speed of 500 mm/min in accordance with ISO 37. A mechanical contact extensometer (gauge length 25 mm) measured extension of samples and a 1000 N load cell measured the applied force. Values of time, force, crosshead position and extension were saved each 0.02 s in all tests. Four samples per compound were tested. 3. Results and discussion 3.1. Initial stress– strain Tensile force F and initial cross-section area of sample A0 gives stress s ¼ F =A0 . Extension L and initial gauge length L0 ¼ 25 mm gives strain e ¼ L=L0 . Fig. 1 shows an example of initial tensile stress–strain dependence of elastomers (SBR with carbon black N220). The dependence in Fig. 1 is really fairly linear to about 3% strain and therefore is in agreement with Ref. [6]. However, the regression line determining the Young’s modulus should go through the origin, which is evidently not true.
0.50 0.45 0.40 0.35 stress (MPa]
stress–strain data below 10% strain [7]. (The stress–strain plot of such systems is nearly linear to the ‘‘pseudo-yield’’ value.) In the very small strain region, the tensile stress–strain curve of other elastomers is also very often fairly linear and therefore might qualify as Young’s modulus (which follows Hooke’s law) [6]. Initial tensile behaviour could characterize the properties of filled elastomers with original structure of the filler network in the practically important region. Therefore, we tried to analyse the initial tensile data of unfilled and carbon black filled elastomers to test if this characterization is feasible.
651
0.30 0.25 0.20 0.15 0.10 0.05 0.00 0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 strain
Fig. 1. Initial stress–strain for SBR with carbon black N220.
On the basis of Fig. 1 we can lay down two questions: (1) Why does the regression line of initial stress– strain dependence not go through origin? (2) Is it really possible to obtain initial tensile modulus E of elastomers from normal tensile testing? To answer these questions a detail analysis of initial tensile behaviour of elastomers was done in this work. 3.2. Initial stress The initial force–time dependence in Fig. 2 has two parts. The first is negative and roughly constant while the second linearly increases with time. For the first 15 positive and increasing force points of force–time dependence in Fig. 2 we obtained parameters kF and qF of the linear regression equation F ¼ kF t þ qF (where F is force and t is time). Parameter kF characterizes here initial rate of force increase (i.e. dF/dt). Division of kF by the initial cross-section area of the sample A0 gives initial rate of stress s increase (as kF =A0 ¼ _ Arithmetic means of the so obtained ds=dt ¼ s). initial ds/dt values for the tested SBR samples are shown in Fig. 3. As expected, the mean value of initial ds/dt for unfilled sample in Fig. 3 is much lower than values for carbon black filled SBR. The mean values of initial ds/dt for carbon black filled samples increase
ARTICLE IN PRESS J. Mala´cˇ / Polymer Testing 25 (2006) 650–655
652
4.0 0.8
3.5 extension (mm)
3.0 force (N)
2.5 2.0 1.5 1.0
0.6 0.4 0.2
0.5 0.0
0.0 -0.5 66.8
66.9
67.0
67.1 67.2 time (s)
67.3
67.4
Fig. 2. Initial force–time for SBR with carbon black N220.
66.8
67.0 67.2 time (s)
67.4
67.6
Fig. 4. Initial extension–time for SBR with carbon black N220.
initial gauge length L0 ¼ 25 mm gives the initial rate of strain e increase (as kL =L0 ¼ de=dt ¼ e_). The problem is that the first 15 positive and increasing values of extension–time and force–time dependencies do not correspond to the same times and, therefore, the first times for force and the first times for extension are shifted. This fact apparently requires some explanation.
1.2 1.0 d (sigma)/dt (MPa/s)
-0.2 66.6
0.8 0.6 0.4
3.4. Initial time lag
0.2 0.0 N220
N330 N550 carbon blacks
no
Fig. 3. Mean values for initial rate of stress increase ds/dt: carbon black filled and unfilled SBR.
with increasing reinforcing effect of the carbon blacks. 3.3. Initial strain from extensometer data The initial extension–time dependence in Fig. 4 also has two parts. The first is negative while the second linearly increases with time. For the first 15 positive and increasing extension values of extension–time dependence in Fig. 4 we obtained parameters kL and qL of the linear regression equation L ¼ kL t þ qL (where L is extension and t is time). Parameter kL characterizes here initial rate of extension increase (i.e. dL/dt). Division of kL by the
If we compare Figs. 2 and 4 (data are from the same tensile test) we see that the force–time dependence crosses the zero level before the extension–time does. Therefore, there is an initial time lag between force–time and extension–time data at the time of crossing zero level, and this initial time lag can simply explain why the stress– strain regression line in Fig. 1 does not go through the origin. Exact values of zero level crossing times were obtained from the parameters of the respective regression equations. For force–time zero level crossing time tF ¼ qF =kF , for extension–time zero level crossing time tL ¼ qL =kL , and initial time lag is Dt ¼ tL 2tF . Arithmetic means of initial time lag Dt values for tested SBR samples are shown in Fig. 5 and the variation coefficients of initial time lag are in Table 1. Because of the initial time lag variations shown in Fig. 5 and Table 1, we are not able to unambiguously assign force–extension and stress–strain data to each other and to directly get precise E values. Hence, random values of initial time lag seem to be
ARTICLE IN PRESS J. Mala´cˇ / Polymer Testing 25 (2006) 650–655
145.5
0.16 crosshead position (mm)
0.14 0.12 time lag (s)
653
0.10 0.08 0.06 0.04 0.02 N330 N550 carbon blacks
no
Fig. 5. Mean values for initial time lag: carbon black filled and unfilled SBR.
N220 N330 N550 No
23.51 24.77 88.09 46.51
143.5 143.0
Fig. 6. Initial crosshead position–time for SBR with carbon black N220.
0.14 0.12 d (epsilon)/dt (1/s)
Variation coefficient of initial time lag (%)
144.0
time (s)
Table 1 Variation coefficients of initial time lag: carbon black filled and unfilled SBR Carbon blacks
144.5
142.5 66.6 66.7 66.8 66.9 67.0 67.1 67.2 67.3 67.4
0.00 N220
145.0
0.10 0.08 0.06 0.04 0.02
a main source of error in E values obtained on the basis of initial strains from extension data. Random initial time lags in Fig. 5 and Table 1 indicate that a mechanical contact extensometer, which is very useful for higher deformations, is probably not sensitive enough to obtain exact data in the region of initial tensile deformations. Therefore, for more reliable initial E values we have to use deformation data from another source. 3.5. Initial strain from crosshead position It would be possible to use a laser extensometer instead of a mechanical contact extensometer but laser extensometers are not that common in contemporary rubber tensile testing. Another possibility is derivation of deformation data from initial crosshead positions. Crosshead position–time dependence in Fig. 6 also has two parts. The first is horizontal and the second linearly increases with time. For the first 15 increasing values of crosshead position–time dependence in Fig. 6 we obtained
0.00 N220
N330 N550 carbon blacks
no
Fig. 7. Mean values for initial rate of strain increase de/dt: carbon black filled and unfilled SBR.
parameters kH and qH of the linear regression equation H ¼ kH t þ qH (where H is crosshead position and t is time). The main advantage is that the first 15 increasing crosshead position values are measured at identical times as the first 15 positive and increasing values of force, and so force–position and stress–strain relations are here unambiguously assigned. Parameter kH of the linear regression equation characterizes initial crosshead rate (i.e. dH/dt). Division of kH by the initial gap between the crosshead and fixed member H 0 ¼ 60 mm gives the initial rate of strain e increase (as kH =H 0 ¼ de=dt ¼ e_). Arithmetic means of initial de/dt values so obtained for tested SBR samples are shown in Fig. 7.
ARTICLE IN PRESS J. Mala´cˇ / Polymer Testing 25 (2006) 650–655
654
The horizontal line in Fig. 7 holds for strain rate obtained from the predetermined crosshead speed of 500 mm/min (which is 8.333 mm/s) by dividing it by initial gap between crosshead and fixed member, 60 mm. The result is 0.1389 s1. In Fig. 7 we expected the mean rates de/dt for all samples to be roughly equal to the strain rate for the predetermined crosshead speed. In reality the mean rates de/dt in Fig. 7 are rather lower than the strain rate from the predetermined crosshead speed and increase slightly with decreasing initial modulus of the tested samples. 3.6. Initial E modulus Arithmetic mean values of initial E modulus obtained from initial rate of stress and initial rate of _ e) for the strain increase (from relation E ¼ s=_ carbon black filled and unfilled SBR compounds are given in Fig. 8. As expected, the mean value of initial E modulus for the unfilled sample in Fig. 8 is much lower than values for carbon black filled SBR. The mean values 10
E modulus (MPa)
8 6 4 2
of carbon black filled samples increase with increasing reinforcing effect of carbon blacks. Variation coefficients of initial E modulus in Table 2 are reasonably low. Values of initial E modulus from crossheadposition strains seem to be exact enough to be used also for evaluation of different theoretical models of filler reinforcement. 3.7. Initial ED modulus As we saw in Fig. 1, the initial tensile stress–strain dependence of elastomers is fairly linear but the regression line does not go through origin. Nevertheless, the slope of the regression line for the first 15 positive stress–strain values can be used to obtain directly initial ED modulus. As we have already shown the values of initial ED modulus are influenced by the initial time lag and therefore are not equal to the initial E modulus obtained in paragraph 3.6. Arithmetic mean values of initial modulus ED are given in Fig. 9. If we compare the mean values of E modulus in Fig. 8 with mean values of ED modulus in Fig. 9 we can see that the ED modulus is rather less sensitive to the reinforcing effect of carbon blacks. Because of the initial time lag effect in case of ED the variation coefficients of ED in Table 3 should be higher than variation coefficients of E in Table 2. As expected, some values of variation coefficient in Table 3 are significantly higher and the explanation of the higher variation coefficients is probably random initial time lag causing errors in the ED modulus.
0 N550 N330 carbon blacks
8
no
Fig. 8. Mean values of initial E modulus: carbon black filled and unfilled SBR.
Table 2 Variation coefficients of initial E modulus: carbon black filled and unfilled SBR Carbon blacks
Variation coefficient of initial E modulus (%)
N220 N330 N550 No
5.92 5.62 2.54 6.67
7 ED modulus (MPa)
N220
6 5 4 3 2 1 0 N220
N330 N550 carbon blacks
no
Fig. 9. Mean values for initial ED modulus: carbon black filled and unfilled SBR.
ARTICLE IN PRESS J. Mala´cˇ / Polymer Testing 25 (2006) 650–655 Table 3 Variation coefficients of initial ED modulus: carbon black filled and unfilled SBR Carbon blacks
Variation coefficient of initial ED modulus (%)
N220 N330 N550 No
1.68 14.94 12.04 5.85
655
Initial tensile modulus from crosshead position has lower variation coefficients than initial tensile modulus from mechanical contact extensometer data. Values of initial tensile modulus from crosshead position seem to be exact enough to be used also for testing the initial structure of particle network in samples and for evaluation of different theoretical models.
4. Conclusions
References
Initial stress–strain dependencies were linear in tensile tests on unfilled and carbon black filled vulcanised SBR samples. The initial stress–strain dependencies do not go through origin, probably because of initial time lag between force and extension times at crossing the zero point. Random values of initial time lag at zero crossing influence the variation coefficients of initial strains from mechanical contact extensometer data. Initial strain values from the crosshead position have lower variation coefficients than strains from mechanical contact extensometer data.
[1] J.S. Dick (Ed.), Rubber Technology, Compounding and Testing for Performance, Hanser, 2001. [2] J. Malac, Elastomers: characterization of tensile behaviour at lower deformations, Polym. Test. 24 (2005) 790. [3] P.C. Powell, Engineering with Polymers, Chapman and Hall, London, 1983. [4] W. Hoffmann. Handbuch der Kautschuk-Technologie, Heinz Gupta, 2001. [5] J.C. Samuells, C.A. Stevens, K.J. Wilson, Dumbbell Testing: Measurement of Rubber or Machine? Meeting of the Rubber Division, ACS, Pittsburgh, 1994 (paper no. 46). [6] A. Ciesielski, An Introduction to Rubber Technology, RAPRA Technology, 2000. [7] M.D. Frogley, D. Ravich, H.D. Wagner, Mechanical properties of carbon nanoparticle-reinforced elastomers, Compos. Sci. Technol. 63 (2003) 1647.
POLYMER TESTING Polymer Testing 25 (2006) 650–655 www.elsevier.com/locate/polytest
Test Method
Initial tensile behaviour of elastomers Jir˘ ı´ Mala´cˇ Department of Polymer Engineering, Faculty of Technology, Tomas Bata University in Zlı´n, 762 72 Zlı´n, Czech Republic Received 18 February 2006; accepted 31 March 2006
Abstract At very small strains the tensile stress–strain relationship of elastomers is often fairly linear and therefore might be used for obtaining initial tensile modulus E. In this work we analysed initial tensile data of unfilled and carbon black filled vulcanised SBR samples to test if this is feasible. Strains from mechanical contact extensometer data have shown that the initial stress–strain dependence is nearly linear, as expected, but does not go through the origin, probably because of random initial time lag between force and extension times at crossing the zero point. Initial strains taken from the crosshead position have lower variation coefficients than initial strains from the mechanical contact extensometer data and, consequently, initial tensile modulus from the crosshead position also has lower variation coefficients than initial tensile modulus from the mechanical contact extensometer data. r 2006 Elsevier Ltd. All rights reserved. Keywords: Elastomers; Initial stress–strain; Initial stress; Initial strain; Initial time lag; Initial tensile modulus
1. Introduction Tensile stress–strain is one of the most commonly performed tests in the rubber industry. These tests are performed on tensile testing instruments where a cured, dumbbell-shaped rubber specimen is pulled apart at a predetermined rate (usually 500 mm/min) while measuring the tensile stress. Generally, ultimate strength, ultimate elongation and tensile stress at different elongations (such as 100% and 300%) are reported. However, many rubber products are not extensionally deformed more than 30%, so tensile stress–strain is not usually of great importance for rubber design [1].
Fax: +420 57 603 1328.
E-mail address: [email protected]. 0142-9418/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.polymertesting.2006.03.015
Recently, the specific tensile deformation energy was chosen as a possible characteristic of elastomers in the lower deformation region, where many rubber goods are working in practice and where influence of rubber-filler interaction might be studied in detail [2]. The Young’s modulus E (i.e. the slope of tensile stress–strain relationship at low deformations) is widely used to characterize the stiffness of hard materials [3]. Unlike metals, elastomer stress–strain curves show a very limited linear portion [1]. A typical result of a tensile test of an elastomer is a stress–strain curve of S-shape [4,5] where the gradient of the curve changes as the elastomer is stretched [6]. Carbon nanotube-reinforced silicon elastomer shows a dramatic enhancement of initial modulus when it is measured by fitting a straight line to the
ARTICLE IN PRESS J. Mala´cˇ / Polymer Testing 25 (2006) 650–655
2. Experimental Styrene–butadiene rubber compounds filled with carbon blacks N220, N330 and N550 were prepared according to ISO 2322-1985. Unfilled compound of similar composition (i.e. without carbon black) was used for comparison. The compounds were compression moulded at 150 1C for t90+5 min to 2 mm sheets and dumbbell specimens cut from these sheets were used for tensile testing. A universal testing machine, Tensometer 2000 (Alpha Technologies), was used and the tensile tests were carried out at a crosshead speed of 500 mm/min in accordance with ISO 37. A mechanical contact extensometer (gauge length 25 mm) measured extension of samples and a 1000 N load cell measured the applied force. Values of time, force, crosshead position and extension were saved each 0.02 s in all tests. Four samples per compound were tested. 3. Results and discussion 3.1. Initial stress– strain Tensile force F and initial cross-section area of sample A0 gives stress s ¼ F =A0 . Extension L and initial gauge length L0 ¼ 25 mm gives strain e ¼ L=L0 . Fig. 1 shows an example of initial tensile stress–strain dependence of elastomers (SBR with carbon black N220). The dependence in Fig. 1 is really fairly linear to about 3% strain and therefore is in agreement with Ref. [6]. However, the regression line determining the Young’s modulus should go through the origin, which is evidently not true.
0.50 0.45 0.40 0.35 stress (MPa]
stress–strain data below 10% strain [7]. (The stress–strain plot of such systems is nearly linear to the ‘‘pseudo-yield’’ value.) In the very small strain region, the tensile stress–strain curve of other elastomers is also very often fairly linear and therefore might qualify as Young’s modulus (which follows Hooke’s law) [6]. Initial tensile behaviour could characterize the properties of filled elastomers with original structure of the filler network in the practically important region. Therefore, we tried to analyse the initial tensile data of unfilled and carbon black filled elastomers to test if this characterization is feasible.
651
0.30 0.25 0.20 0.15 0.10 0.05 0.00 0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 strain
Fig. 1. Initial stress–strain for SBR with carbon black N220.
On the basis of Fig. 1 we can lay down two questions: (1) Why does the regression line of initial stress– strain dependence not go through origin? (2) Is it really possible to obtain initial tensile modulus E of elastomers from normal tensile testing? To answer these questions a detail analysis of initial tensile behaviour of elastomers was done in this work. 3.2. Initial stress The initial force–time dependence in Fig. 2 has two parts. The first is negative and roughly constant while the second linearly increases with time. For the first 15 positive and increasing force points of force–time dependence in Fig. 2 we obtained parameters kF and qF of the linear regression equation F ¼ kF t þ qF (where F is force and t is time). Parameter kF characterizes here initial rate of force increase (i.e. dF/dt). Division of kF by the initial cross-section area of the sample A0 gives initial rate of stress s increase (as kF =A0 ¼ _ Arithmetic means of the so obtained ds=dt ¼ s). initial ds/dt values for the tested SBR samples are shown in Fig. 3. As expected, the mean value of initial ds/dt for unfilled sample in Fig. 3 is much lower than values for carbon black filled SBR. The mean values of initial ds/dt for carbon black filled samples increase
ARTICLE IN PRESS J. Mala´cˇ / Polymer Testing 25 (2006) 650–655
652
4.0 0.8
3.5 extension (mm)
3.0 force (N)
2.5 2.0 1.5 1.0
0.6 0.4 0.2
0.5 0.0
0.0 -0.5 66.8
66.9
67.0
67.1 67.2 time (s)
67.3
67.4
Fig. 2. Initial force–time for SBR with carbon black N220.
66.8
67.0 67.2 time (s)
67.4
67.6
Fig. 4. Initial extension–time for SBR with carbon black N220.
initial gauge length L0 ¼ 25 mm gives the initial rate of strain e increase (as kL =L0 ¼ de=dt ¼ e_). The problem is that the first 15 positive and increasing values of extension–time and force–time dependencies do not correspond to the same times and, therefore, the first times for force and the first times for extension are shifted. This fact apparently requires some explanation.
1.2 1.0 d (sigma)/dt (MPa/s)
-0.2 66.6
0.8 0.6 0.4
3.4. Initial time lag
0.2 0.0 N220
N330 N550 carbon blacks
no
Fig. 3. Mean values for initial rate of stress increase ds/dt: carbon black filled and unfilled SBR.
with increasing reinforcing effect of the carbon blacks. 3.3. Initial strain from extensometer data The initial extension–time dependence in Fig. 4 also has two parts. The first is negative while the second linearly increases with time. For the first 15 positive and increasing extension values of extension–time dependence in Fig. 4 we obtained parameters kL and qL of the linear regression equation L ¼ kL t þ qL (where L is extension and t is time). Parameter kL characterizes here initial rate of extension increase (i.e. dL/dt). Division of kL by the
If we compare Figs. 2 and 4 (data are from the same tensile test) we see that the force–time dependence crosses the zero level before the extension–time does. Therefore, there is an initial time lag between force–time and extension–time data at the time of crossing zero level, and this initial time lag can simply explain why the stress– strain regression line in Fig. 1 does not go through the origin. Exact values of zero level crossing times were obtained from the parameters of the respective regression equations. For force–time zero level crossing time tF ¼ qF =kF , for extension–time zero level crossing time tL ¼ qL =kL , and initial time lag is Dt ¼ tL 2tF . Arithmetic means of initial time lag Dt values for tested SBR samples are shown in Fig. 5 and the variation coefficients of initial time lag are in Table 1. Because of the initial time lag variations shown in Fig. 5 and Table 1, we are not able to unambiguously assign force–extension and stress–strain data to each other and to directly get precise E values. Hence, random values of initial time lag seem to be
ARTICLE IN PRESS J. Mala´cˇ / Polymer Testing 25 (2006) 650–655
145.5
0.16 crosshead position (mm)
0.14 0.12 time lag (s)
653
0.10 0.08 0.06 0.04 0.02 N330 N550 carbon blacks
no
Fig. 5. Mean values for initial time lag: carbon black filled and unfilled SBR.
N220 N330 N550 No
23.51 24.77 88.09 46.51
143.5 143.0
Fig. 6. Initial crosshead position–time for SBR with carbon black N220.
0.14 0.12 d (epsilon)/dt (1/s)
Variation coefficient of initial time lag (%)
144.0
time (s)
Table 1 Variation coefficients of initial time lag: carbon black filled and unfilled SBR Carbon blacks
144.5
142.5 66.6 66.7 66.8 66.9 67.0 67.1 67.2 67.3 67.4
0.00 N220
145.0
0.10 0.08 0.06 0.04 0.02
a main source of error in E values obtained on the basis of initial strains from extension data. Random initial time lags in Fig. 5 and Table 1 indicate that a mechanical contact extensometer, which is very useful for higher deformations, is probably not sensitive enough to obtain exact data in the region of initial tensile deformations. Therefore, for more reliable initial E values we have to use deformation data from another source. 3.5. Initial strain from crosshead position It would be possible to use a laser extensometer instead of a mechanical contact extensometer but laser extensometers are not that common in contemporary rubber tensile testing. Another possibility is derivation of deformation data from initial crosshead positions. Crosshead position–time dependence in Fig. 6 also has two parts. The first is horizontal and the second linearly increases with time. For the first 15 increasing values of crosshead position–time dependence in Fig. 6 we obtained
0.00 N220
N330 N550 carbon blacks
no
Fig. 7. Mean values for initial rate of strain increase de/dt: carbon black filled and unfilled SBR.
parameters kH and qH of the linear regression equation H ¼ kH t þ qH (where H is crosshead position and t is time). The main advantage is that the first 15 increasing crosshead position values are measured at identical times as the first 15 positive and increasing values of force, and so force–position and stress–strain relations are here unambiguously assigned. Parameter kH of the linear regression equation characterizes initial crosshead rate (i.e. dH/dt). Division of kH by the initial gap between the crosshead and fixed member H 0 ¼ 60 mm gives the initial rate of strain e increase (as kH =H 0 ¼ de=dt ¼ e_). Arithmetic means of initial de/dt values so obtained for tested SBR samples are shown in Fig. 7.
ARTICLE IN PRESS J. Mala´cˇ / Polymer Testing 25 (2006) 650–655
654
The horizontal line in Fig. 7 holds for strain rate obtained from the predetermined crosshead speed of 500 mm/min (which is 8.333 mm/s) by dividing it by initial gap between crosshead and fixed member, 60 mm. The result is 0.1389 s1. In Fig. 7 we expected the mean rates de/dt for all samples to be roughly equal to the strain rate for the predetermined crosshead speed. In reality the mean rates de/dt in Fig. 7 are rather lower than the strain rate from the predetermined crosshead speed and increase slightly with decreasing initial modulus of the tested samples. 3.6. Initial E modulus Arithmetic mean values of initial E modulus obtained from initial rate of stress and initial rate of _ e) for the strain increase (from relation E ¼ s=_ carbon black filled and unfilled SBR compounds are given in Fig. 8. As expected, the mean value of initial E modulus for the unfilled sample in Fig. 8 is much lower than values for carbon black filled SBR. The mean values 10
E modulus (MPa)
8 6 4 2
of carbon black filled samples increase with increasing reinforcing effect of carbon blacks. Variation coefficients of initial E modulus in Table 2 are reasonably low. Values of initial E modulus from crossheadposition strains seem to be exact enough to be used also for evaluation of different theoretical models of filler reinforcement. 3.7. Initial ED modulus As we saw in Fig. 1, the initial tensile stress–strain dependence of elastomers is fairly linear but the regression line does not go through origin. Nevertheless, the slope of the regression line for the first 15 positive stress–strain values can be used to obtain directly initial ED modulus. As we have already shown the values of initial ED modulus are influenced by the initial time lag and therefore are not equal to the initial E modulus obtained in paragraph 3.6. Arithmetic mean values of initial modulus ED are given in Fig. 9. If we compare the mean values of E modulus in Fig. 8 with mean values of ED modulus in Fig. 9 we can see that the ED modulus is rather less sensitive to the reinforcing effect of carbon blacks. Because of the initial time lag effect in case of ED the variation coefficients of ED in Table 3 should be higher than variation coefficients of E in Table 2. As expected, some values of variation coefficient in Table 3 are significantly higher and the explanation of the higher variation coefficients is probably random initial time lag causing errors in the ED modulus.
0 N550 N330 carbon blacks
8
no
Fig. 8. Mean values of initial E modulus: carbon black filled and unfilled SBR.
Table 2 Variation coefficients of initial E modulus: carbon black filled and unfilled SBR Carbon blacks
Variation coefficient of initial E modulus (%)
N220 N330 N550 No
5.92 5.62 2.54 6.67
7 ED modulus (MPa)
N220
6 5 4 3 2 1 0 N220
N330 N550 carbon blacks
no
Fig. 9. Mean values for initial ED modulus: carbon black filled and unfilled SBR.
ARTICLE IN PRESS J. Mala´cˇ / Polymer Testing 25 (2006) 650–655 Table 3 Variation coefficients of initial ED modulus: carbon black filled and unfilled SBR Carbon blacks
Variation coefficient of initial ED modulus (%)
N220 N330 N550 No
1.68 14.94 12.04 5.85
655
Initial tensile modulus from crosshead position has lower variation coefficients than initial tensile modulus from mechanical contact extensometer data. Values of initial tensile modulus from crosshead position seem to be exact enough to be used also for testing the initial structure of particle network in samples and for evaluation of different theoretical models.
4. Conclusions
References
Initial stress–strain dependencies were linear in tensile tests on unfilled and carbon black filled vulcanised SBR samples. The initial stress–strain dependencies do not go through origin, probably because of initial time lag between force and extension times at crossing the zero point. Random values of initial time lag at zero crossing influence the variation coefficients of initial strains from mechanical contact extensometer data. Initial strain values from the crosshead position have lower variation coefficients than strains from mechanical contact extensometer data.
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