Mathematical correlation of viscoelastic properties using two different testers.Rubber, being a viscoelastic Adj. 1. viscoelastic - having viscous as well as elastic properties natural philosophy, physics - the science of matter and energy and their interactions; "his favorite subject was physics" material, has viscous viscous /vis·cous/ (vis´kus) sticky or gummy; having a high degree of viscosity. vis·cous adj. 1. Having relatively high resistance to flow. 2. Viscid. as well as elastic elastic Of or relating to the demand for a good or service when the quantity purchased varies significantly in response to price changes in the good or service. phases. When rubber is deformed de·formed adj. Distorted in form. , energy input is involved, part of which is returned when the rubber returns to its original shape. That part of the energy that is not returned as mechanical energy is dissipated dis·si·pat·ed adj. 1. Intemperate in the pursuit of pleasure; dissolute. 2. Wasted or squandered. 3. Irreversibly lost. Used of energy. in the form of heat in the rubber. Rubber is frequently used for applications in which it undergoes rapid cyclic cyclic /cyc·lic/ (sik´lik) pertaining to or occurring in a cycle or cycles; applied to chemical compounds containing a ring of atoms in the nucleus. cy·clic or cy·cli·cal adj. 1. deformations at a certain frequency or over a range of frequencies. Examples of this are the sidewalls or tread tread injury to the coronet of the horse's hoof by treading on it by the opposite hoof, or by another horse when they are being worked in a team. If the coronary matrix is injured there may be a subsequent crack or deformity. of a tire, and engine mounts that serve the purpose of isolating engine vibration from a chassis Pronounced "chah-see," it is a physical structure that holds everything or that everything is attached to. A computer's cabinet is often called the chassis. or a building. The viscoelastic properties are strongly dependent on temperature, frequency, the presence of fillers and the extent of deformation deformation /de·for·ma·tion/ (de?for-ma´shun) 1. in dysmorphology, a type of structural defect characterized by the abnormal form or position of a body part, caused by a nondisruptive mechanical force. 2. if it is large. For very small deformation, the properties have been found to be independent of the magnitude of the deformation (linear viscoelasticity Viscoelasticity, also known as anelasticity, is the study of materials that exhibit both viscous and elastic characteristics when undergoing deformation. Viscous materials, like honey, resist shear flow and strain linearly with time when a stress is applied. region) (ref. 1). A wide variety of experimental techniques Experimental research designs are used for the controlled testing of causal processes. The general procedure is one or more independent variables are manipulated to determine their effect on a dependent variable. for measuring viscoelastic properties of elastomers has been developed in research laboratories for specific investigations (refs. 2-4). In the rebound rebound (rē´bownd), n/v 1. a recovery from illness. n 2. an outbreak of fresh reflex activity after withdrawal of a stimulus rebound adjective resilience resilience (r  ·zilˑ·yens),n test, the deformation is an indentation in·den·ta·tion n. A notch, a pit, or a depression. due to a single impact. The ratio of the energy returned to the energy applied is termed the resilience. When deformation is an indentation due to a single impact, this ratio is termed the rebound resilience. The value of rebound resilience for a given material is not a fixed quantity, but varies with temperature, strain distribution, strain rate, strain energy and strain history (ref. 5). In the dynamic mechanical analyzer analyzer /ana·ly·zer/ (an´ah-li?zer) 1. a Nicol prism attached to a polarizing apparatus which extinguishes the ray of light polarized by the polarizer. 2. (VA4000), dynamic properties were measured at 5% strain and 11 Hz frequency in compression-tension mode. The properties that can be measured in a dynamic mechanical analyzer (VA4000) (ref. 6) are as follows: * Elastic or storage modulus See modulo. , M*, is the real part of the complex modulus M*. It represents the rigidity rigidity /ri·gid·i·ty/ (ri-jid´i-te) inflexibility or stiffness. clasp-knife rigidity of an elastic material (elastic component) and is proportional to the maximum energy stored during a load cycle. * Viscous or loss modulus, M", is the imaginary part Noun 1. imaginary part - the part of a complex number that has the square root of -1 as a factor imaginary part of a complex number complex number, complex quantity, imaginary, imaginary number - (mathematics) a number of the form a+bi where a and b are real of the complex modulus M*. It represents the viscous component and is proportional to the energy dissipated during a load cycle. * Loss factor, tan [delta], is the ratio of the loss modulus M" divided by the storage modulus M'. In the present work, the storage and loss energy of rubber compounds was measured at room temperature as well as at 70 [degrees]C, using two pieces of equipment named the rebound resilience tester (Zwick 5109.01) and the dynamic mechanical analyzer (VA4000). Experimental Seven compounds having different polymer blends A polymer blend, polymer alloy, or polymer mixture is a member of a class of materials analogous to metal alloys, in which two or more polymers are blended together to create a new material with different physical properties. and fillers (major contributing element to viscoelastic properties) were mixed in a laboratory internal mixer mixer, either of two electronic devices in which two or more signals are combined. In the type of mixer used in radio receivers, radar receivers, and similar systems, a signal is translated upward or downward in frequency. of 1.5 litre LITRE. A French measure of capacity. It is of the size of a decimetre, or one-tenth part of a cubic metre. It is equal to 61.028 cubic inches. Vide Measure. capacity and given in table 1. The mixing was done following a power integrator (1) In electronics, a device that combines an input with a variable, such as time, and provides an analog output; for example, a watt-hour meter. (2) See systems integrator. mode of mixing. The discharged compounds from the mixer were sheeted out on a laboratory two-roll mill. The green compounds were cured in an electrically heated laboratory hydraulic curing press of six inches ram diameter. The curing condition maintained for determination of rebound resilience was 141 [degrees]C for 60 minutes, and 141 [degrees]C for 45 minutes for dynamic mechanical properties. The dynamic mechanical properties were measured in a viscoanalyzer VA 4000 following ASTM ASTM abbr. American Society for Testing and Materials D 5992. Phase angle and complex modulus vary with filler fill·er 1 n. One that fills, as: a. Something added to augment weight or size or fill space. b. A composition, especially a semisolid that hardens on drying, used to fill pores, cracks, or holes in wood, plaster, loading, polymer blend ratio and state of cure. Thus, in the present study, the absolute values of storage modulus (M' in MPa) and loss modulus (M" in MPa) were used for calculating storage and loss energy, in percentage, with the help of the following equations: (A) Storage energy (%), [E.sub.s] = {M'/(M' + M")} x 100 (B) Loss energy (%), [E.sub.1] = {M"/(M' + M")} x 100 Where, M' is storage modulus (MPa); and M" is loss modulus (MPa) Rebound resilience was measured using a Zwick rebound resilience tester 5109.01 (ref. 7) taking the help of the following equations: (C) Rebound resilience (RR) = (recovered energy/total energy applied) x 100 (D) 100 - Rebound resilience (RR) = percentage loss energy (calculated) The correlation coefficient Correlation Coefficient A measure that determines the degree to which two variable's movements are associated. The correlation coefficient is calculated as: (ref. 8) was used to determine the relationship between storage and loss energy with the help of the following equation: (E) [rho]x, y = COV COV Composés Organiques Volatiles (French) COV Compuestos Orgánicos Volátiles (Spanish: Volatile Organic Compounds) COV Coefficient of Variation COV City of Villians (game) (x,y) / [[sigma].sub.x] x [[sigma].sub.y] where, x is set of array 1; y is set of array 2; [sigma] is standard deviation In statistics, the average amount a number varies from the average number in a series of numbers. (statistics) standard deviation - (SD) A measure of the range of values in a set of numbers. ; and COV is coefficient coefficient /co·ef·fi·cient/ (ko?ah-fish´int) 1. an expression of the change or effect produced by variation in certain factors, or of the ratio between two different quantities. 2. of variance. Viscoelastic properties were predicted by using linear regression Linear regression A statistical technique for fitting a straight line to a set of data points. analysis and coefficient of regression ([R.sup.2]) (ref. 8). The properties measured using the rebound resilience tester and the dynamic mechanical analyzer VA4000 are mentioned in table 2. The percentage storage energy and percentage loss energy values at room temperature, as well as at 70 [degrees]C, were measured using the rebound resilience tester and the dynamic mechanical analyzer VA4000, and are mentioned in table 3. Calculated correlation coefficient is mentioned in table 4. Prediction of storage energy at room temperature was made using the equation: (F) y = 0.501x + 56.606 Where, y is measured[E.sub.s] (%), x is measured RR (%) and the regression coefficient Regression coefficient Term yielded by regression analysis that indicates the sensitivity of the dependent variable to a particular independent variable. See: Parameter. regression coefficient ([R.sup.2]) is 0.98. The percentage variations of predicted and measured viscoelastic properties were calculated using the following equation: [(Predicted value -measured value)/measured value] x 100. The predicted, measured and percentage variations observed for storage energy at room temperature are summarized in table 5. Prediction of storage energy at 70 [degrees]C temperature was made using the equation: (G) y = 0.4655x + 58.889 Where, y is measured [E.sub.s] (%), x is measured RR (%) and the regression coefficient ([R.sup.2]) is 0.97. The predicted, measured and percentage variations ob served for storage energy at 70 [degrees]C temperature are summarized in table 6. Prediction of loss energy at room temperature was made using the equation: (H) y = 0.501x - 6.7028 Where, y is measured [E.sub.l] (%), x is measured 100-RR (%) and the regression coefficient ([R.sup.2]) is 0.98. The predicted, measured and percentage variations observed for loss energy at room temperature are summarized in table 7. Prediction of loss energy at 70 [degrees]C, was made using the equation: (I) y = 0.4655x - 5.4373 Where, y is measured [E.sub.l] (%), x is measured 100-RR (%) and the regression coefficient ([R.sup.2]) is 0.97. The predicted, measured and percentage variations observed for loss energy at 70 [degrees]C, are summarized in table 8. The predicted, measured and percentage variations observed for loss factor (tan 6) at room temperature and at 70 [degrees]C are summarized in table 9. Results and discussion The correlation coefficient between storage energy and loss energy obtained using both the mentioned testers were calculated and the coefficient of correlation coefficient of correlation n. pl. coefficients of correlation See correlation coefficient. Noun 1. coefficient of correlation value was found to be 0.99 for room temperature and 0.98 for 70 [degrees]C temperature. A maximum of 12% variation was observed between the measured and the predicted values. Conclusion Storage and loss energy values measured by both testers show excellent correlation (coefficient of correlation = 0.99 at room temperature testing and 0.98 when tested at 70 [degrees]C temperature). The measurement of viscoelastic properties with a rebound resilience tester will also serve the purpose of predicting the viscoelastic properties measured with a dynamic mechanical analyzer (VA4000) and vice versa VICE VERSA. On the contrary; on opposite sides. . This was confirmed as a maximum of 12% variation existed between the predicted and the measured value using any of the above mentioned testers. The dynamic mechanical analyzer (VA4000) is a very costly tester as compared to the rebound resilience tester, and it is very difficult for a small-scale rubber producer to measure the viscoelastic properties through the dynamic mechanical analyzer (VA4000). Therefore, the above experiment will assist in predicting the viscoelastic properties measured by the dynamic mechanical analyzer (VA4000) by simply measuring through a comparatively much less expensive tester like the rebound resilience tester. S.L. Agrawal, S.K. Mandot, S. Bandyopadhyay and R. Mukhopadhyay, Hair Shankar Singhania Elastomer elastomer (ĭlăs`təmər), substance having to some extent the elastic properties of natural rubber. The term is sometimes used technically to distinguish synthetic rubbers and rubberlike plastics from natural rubber. and Tyre Tyre (tīr), ancient city of Phoenicia, S of Sidon. It is the present-day Sur in Lebanon, a small town on a peninsula jutting into the Mediterranean from the mainland of Syria S of Beirut. Research Institute, and A.S. Deuri, J.K. Tyre References (1.) P.R.S. Shaktawat, et al, "Correlation between tan delta and heat build up of tire components, "paper presented in Rubtech 2000, New Delhi New Delhi (dĕl`ē), city (1991 pop. 294,149), capital of India and of Delhi state, N central India, on the right bank of the Yamuna River. , India. (2.) L.E. Nielsen, "Mechanical properties of polymers and composites, "ch. 4, Dekker, New York New York, state, United States New York, Middle Atlantic state of the United States. It is bordered by Vermont, Massachusetts, Connecticut, and the Atlantic Ocean (E), New Jersey and Pennsylvania (S), Lakes Erie and Ontario and the Canadian province of , 1974. (3.) A.C. Edwards and G.N.S. Ferrand, in The Applied Science of Rubber (W.J.S. Nauton, ed.), ch. 8, Arnold, London, 1961. (4.) J.R. Scott, "Physical testing of rubbers, "p. 181, MacLaren, London, 1965. (5.) SS-ISO 4662, 1986 (E), "Rubber--determination of rebound resilience of vulcanizates. "' (6.) Dynatest software user manual, Reference: PTEC PTEC Pinellas Technical Education Centers (Clearwater, FL) PTEC Pharmacy Technician Educators Council PTEC Psychiatric Technician PTEC Plastics Technical Evaluation Center PTEC Page Table Edit Control 97/NUT/025/A0 from Metravib R.D.S D.S Drainage Structure (flood protection) ., France. (7.) Instruction manual for rebound resilience tester 5109.01 from Zwick GmbH & Co., Germany. (8.) Richard I Richard I, Richard Cœur de Lion (kör də lyôN`), or Richard Lion-Heart, 1157–99, king of England (1189–99); third son of Henry II and Eleanor of Aquitaine. . Levin lev·in n. Archaic Lightning. [Middle English levene, levin; see leuk- in Indo-European roots.] and David S. Rubin, Statistics for Management, 7th Edition, 1998.
Table 1--polymer blends and fillers used
Ingredients A B C D E F G
NR RMA4 - 55.00 - 92.50 70.00 70.00 100.00
NR SMR20 - - - - - 30.00 -
SBR1502 50.00 - - - - - -
SBR1712 50.00 - 70.00 - - - -
BR - 45.00 30.00 7.50 30.00 - -
N220 - 55.00 - - - - -
N234 80.00 - - - - - -
N330 - - - - - - -
N339 - - - 49.00 - - -
N550 - - - - 60.00 45.00 40.00
HD ppt silica - - 65.00 - - - -
- 6.00 - - - - -
Table 2--properties of tire compounds measured by rebound
resilience tester and dynamic mechanical analyzer (VA4000)
Rebound resilience Dynamic mechanical analyzer,
equipment VA 4000 equipment
M" at
Compound RR (%) RR (%) at Mat RT 70[degrees]C
Identification at RT 70[degrees]C (Mpa) (Mpa)
A 31.1 41.4 8.40 5.92
B 46.6 50.1 5.38 4.46
C 48.7 59.1 7.29 5.08
D 52.8 62.2 5.67 4.74
E 57.6 65.3 5.11 4.35
F 65.1 72.0 4.07 3.67
G 66.3 75.0 3.96 3.77
Dynamic mechanical analyzer, VA 4000 equipment
M" at Tan
Compound M" at RT 70[degrees]C Tan [delta] [delta] at
Identification (Mpa) (Mpa) at RT 70[degrees]C
A 3.33 1.80 0.397 0.305
B 1.29 0.86 0.240 0.193
C 1.71 0.74 0.235 0.145
D 1.19 0.69 0.210 0.145
E 0.78 0.51 0.153 0.118
F 0.53 0.30 0.132 0.082
G 0.47 0.28 0.118 0.074
Table 3--percentage storage energy & percentage loss energy of tire
compounds measured by rebound resilience' tester and dynamic
mechanical analyzer (VA4000)
[E.sub.S]
Compound RR (%) [E.sub.S] RR (%) at (%) at
Identification at RT (%) at RT 70[degrees]C 70[degrees]C
A 31.1 71.6 41.4 76.7
B 46.6 80.7 50.1 83.8
C 48.7 81.0 59.1 87.3
D 52.8 82.7 62.2 87.3
E 57.6 86.8 65.3 89.5
F 65.1 88.5 72.0 92.4
G 66.3 89.4 75.0 93.1
100-RR [E.sub.I]
Compound 100-RR [E.sub.I] (%) at (%) at
Identification (%) at RT (%) at RT 70[degrees]C 70[degrees]C
A 68.9 28.4 58.6 23.3
B 53.4 19.3 49.9 16.2
C 51.3 19.0 40.9 12.7
D 47.2 17.3 37.8 12.7
E 42.4 13.2 34.7 10.5
F 34.9 11.5 28.0 7.6
G 33.7 10.6 25.0 6.9
Table 4--coefficient of correlation for % storage energy and % loss
energy
% storage % storage % loss % loss
energy at energy at energy at energy at
RT 70[degrees]C RT 70[degrees]C
Correlation 0.99 0.98 0.99 0.98
coefficient
Table 5--prediction of storage energy at room temperature
Sample RR (%) RR (%) %
Id. measured predicted variation
A 31.1 29.9 -3.77
B 46.6 48.1 3.20
C 48.7 48.7 -0.02
D 52.8 52.1 -1.36
E 57.6 60.3 4.63
F 65.1 63.7 -2.21
G 66.3 65.5 -1.27
Sample [E.sub.S] (%) [E.sub.S] (%) %
Id. measured predicted variation
A 71.6 72.2 0.82
B 80.7 80.0 -0.93
C 81.0 81.0 0.01
D 82.7 83.1 0.43
E 86.8 85.5 -1.54
F 88.5 89.2 0.81
G 89.4 89.8 0.47
Table 6--prediction of storage energy at 70[degrees]C
Sample RR (%) RR (%) %
Id. measured predicted variation
A 41.1 38.3 -7.58
B 50.1 53.5 6.82
C 59.1 61.0 3.27
D 62.2 61.0 -1.88
E 65.3 65.8 0.70
F 72.0 72.0 -0.01
Sample [E.sub.S] (%) [E.sub.S] (%) %
Id. measured predicted variation
A 76.7 78.2 1.90
B 83.8 82.2 -1.90
C 87.3 86.4 -1.03
D 87.3 87.8 0.62
E 89.5 89.3 -0.24
F 92.4 92.4 0.01
93.8 0.75
Table 7--prediction of loss energy at room, temperature
Sample 100-RR (%) 100-RR (%) %
Id. measured predicted variation
A 68.9 70.1 1.69
B 53.4 51.9 -2.81
C 51.3 51.3 0.01
D 47.2 47.9 1.50
E 42.4 39.7 -6.31
F 34.9 36.3 4.11
G 33.7 34.5 2.48
Sample [E.sub.I] (%) [E.sub.I] (%) %
Id. measured predicted variation
A 28.4 27.8 -2.06
B 19.3 20.1 3.89
C 19.0 19.0 -0.01
D 17.3 16.9 -2.06
E 13.2 14.5 10.15
F 11.5 10.8 -6.24
G 10.6 10.2 -3.95
Table 8--prediction of loss energy at 70[degrees]C
Sample 100-RR (%) 100-RR (%) %
Id. measured predicted variation
A 58.6 61.7 5.35
B 49.9 46.5 -6.85
C 40.9 39.0 -4.74
D 37.8 39.0 3.08
E 34.7 34.2 -1.33
F 28.0 28.0 0.03
Sample [E.sub.I] (%) [E.sub.I] (%) %
Id. measured predicted variation
A 23.3 21.8 -6.26
B 16.2 17.8 9.82
C 12.7 13.6 7.10
D 12.7 12.2 -4.26
E 10.5 10.7 2.05
F 7.6 7.6 -0.04
Table 9--prediction of loss factor at room temperature an at
70[degrees]C
Tan [delta] Tan [delta]
Sample measured predicted %
Id. at RT at RT variation
A 0.397 0.385 -2.94
B 0.240 0.251 4.49
C 0.235 0.235 -0.20
D 0.210 0.204 -2.85
E 0.153 0.170 11.19
F 0.132 0.121 -8.45
0.118 0.113 -3.94
Tan [delta] Tan [delta]
Sample measured at predicted at %
Id. 70[degrees]C 70[degrees]C variation
A 0.305 0.279 -8.38
B 0.193 0.216 12.13
C 0.145 0.157 8.57
D 0.145 0.138 -4.54
E 0.118 0.120 1.71
F 0.082 0.082 0.26
0.074 0.066 -10.68
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