Fatigue endurance and viscoelastic hysteresis of short fiber/rubber composites.

Fatigue endurance and viscoelastic hysteresis of short fiber/rubber composites

Composites made with combinations of short fibers and rubber (short fiber-rubber composites or SFRCs), like those made of rubber and continuous cords, exhibit improved properties, such as increased stiffness, over rubber used alone[ref. 1]. And short fibers, which have been studied extensively for a considerable number of years[ref. 1], can be added to rubber more easily than can continuous cords. Therefore, it would be expected that tire companies would increase their use of SFRCs in the construction of pneumatic tires. But, tire manufacturers have not as yet made large volume use of SFRCs. One of the reasons has been that, along with their desirable properties as rubber reinforcements, the presence of short fibers also results in increased viscoelastic hysteresis (VH) and low fatigue resistance in cyclic straining.

We have conducted experiments to determine whether SFRCs can be fabricated that exhibit fatigue resistance and VH under cyclic straining suitable for application in tires. This article describes the experimental procedure and reports our evaluations and conclusions.

The problem

Because rubber in a tire undergoes cyclic straining when the tire rolls, a short fiber-rubber composite must endure the fatigue process in cyclic straining at least as well as unreinforced rubber if the SFRC is to be an effective tire material. Under cyclic straining, when a tire rotates, the difference between the stiffness (modulus) of the fiber and that of the rubber induces a stress concentration in the region near the fiber-matrix (fiber-rubber) interface. This can lead to crack generation in the rubber and/or the breakdown of the fiber-rubber bonding.

Crack propagation, the rate of crack generation, in a failing rubber is accelerated by higher temperature. In an experiment, a temperature rise of 10 [degrees] C was found to double the rate of crack propagation[ref. 4].

The presence of short fibers in rubber can cause heat build-up, resulting in a negative effect on fatigue endurance[ref. 2]. The effect becomes more obvious at high levels of fiber loading and strain amplitude.

It has also been shown that at a higher speed of tire rotation, that is, a higher frequency of cyclic straining, the heat build-up is more severe and can have an adverse effect on fatigue[ref. 3].

This article reports on experiments designed to answer the following two related questions:

* How are the fatigue endurance and viscoelastic hysteresis of an SFRC affected by the composite-construction variables? And in turn,

* What are the criteria of SFRC design that will lead to fatigue endurance of the composite which is comparable or superior to that of unreinforced rubber?

To answer these questions, we:

* Considered the construction parameters of an SFRC that affect its fatigue endurance;

* Prepared SFRC samples, using a number of different fibers, by systematically varying these parameters; and

* Tested the samples for fatigue endurance and viscoelastic hysteresis.

Fatigue resistance

In SFRCs, external stress is transferred to the fibers through the rubber. Because there is a great difference in stiffness, or modulus, between the fiber and rubber, severe stress concentration can occur at the fiber-rubber interface. Such stress concentration can accelerate the fatigue process.

Also, the high viscoelastic hysteresis that occurs under cyclic straining contributes to the acceleration of the fatigue process. Therefore, it is expected that the fatigue resistance of an SFRC under cyclic straining is inferior to that of unreinforced rubber.

Application of shear stress 

A qualitative assessment of the effects of shear stress on an SFRC at the fiber-rubber interface can be deduced from theoretical considerations. Assume a tensile stress is applied in the longitudinal direction of the fiber to a small segment of SFRC in which a piece of short fiber is embedded in rubber (figure 1).

By applying some simplifying assumptions, the maximum shear stress at the fiber-rubber interface is approximated by the following equation: [Mathematical Expression Omitted] where

[Sigma.sub.S] = the maximum shear stress at the fiber-rubber interface

[Sigma.sub.T] = the tensile stress applied in the longitudinal direction of the fiber

E = modulus

D, L and V are diameter, length and volume fraction, respectively

The subscripts f and R refer to fiber and rubber, respectively; and the subscripts S and T refer to shear and tensile, respectively.

Although this equation is an approximation, it provides a good qualitative picture of the relationship between the composite parameters and the shear stress at the fiber-rubber interface. It shows that the shear stress would be higher when the fiber length-to-diameter ration (aspect ratio) is higher, the fiber volume fraction is higher, the shear modulus-to-tensile modulus ratio of rubber is higher and when the fiber-to-rubber modulus ratio is higher.

Since a higher stress concentration accelerates the fatigue process, improved fatigue resistance of the SFRC would require that the composite's parameters move in the opposite direction of those indicated in the preceding paragraph. That is, fatigue resistance would improve with a smaller fiber aspect ratio, smaller fiber volume fraction and smaller shear modulus of rubber. Therefore, when considering which fibers would best result in improved fatigue resistance when used in an SFRC, it would be appropriate to consider ones that exhibit these latter properties.

Of course, fiber is used in the composite to reinforce the rubber and raise the modulus; lowering the modulus to a very great degree would improve endurance at the expense of the original purpose of the reinforcement. Therefore, a balance must be struck between these two objectives.

Temperature rise due to viscoelastic hysteresis Tire temperature rises when a tire is rolling, due mainly to the viscoelastic hysteresis of tire components in cyclic straining[ref. 7]. The temperature increase is fairly sensitive to the differences in VH characteristics of tire cord and rubber.

Beringer, et al, defined a "sensitivity coefficient" of tire temperature to the heat generation rate of tire components[ref. 8]. It was shown that, in a bias-ply truck tire, a change in the rubber heat generation rate by 0.0055 cal/cc/sec can cause a temperature increase of about 25 [degrees] C.

A temperature rise accelerates the fatigue process and reduces fatigue resistance in fibers[ref. 6a] as well as in rubber[ref. 6b]. Therefore, if a better fatigue resistance is desired in the SFRC, the VH of the composite under cyclic straining should be as low as possible, preferably lower than that of the unreinforced rubber.

Fiber-matrix adhesion Probably even more important than other factors for the fatigue resistance of SFRC is the fiber-rubber adhesion at the interface. The adhesion depends on the individual characteristics of the fiber and rubber, the adhesive agent used, and the processing conditions. In this study, we used the best available known adhesive for each fiber-rubber combination and prepared the samples by methods currently being practiced. In future work, however, the adhesion characteristics should be studied in depth.

The experiment

Samples of SFRC were prepared by mixing the rubber stock and short fibers, calendering the mixture into sheets, and curing. The rubber stock was made of natural rubber, carbon black, silica and other additives such as bonding agent, salt additive, pine tar, sulfur and sulfonamide curing system. The mixing formulation was varied to prepare three different rubber stocks for tire application: radial belt rubber, tread rubber and carcass rubber. Short fibers of several types were used:

* Low modulus polyamide (nylon 6) fiber;

* Regular modulus polyamide (nylon 6) fiber;

* Cellulosic pulp;

* Aramid fiber;

* Polyester.

Fibers were used in lengths of 1/8-inch, 1/4-inch, 1/2-inch and 1-inch. SFRC samples contained 2, 4, 6 and 8 parts of fiber per hundred parts of rubber. Linear density of samples ranged from 2 to 8 denier per filament. Standard adhesive coating for tire applications was used.

The rubber and the additives were first mixed without sulfur by use of an internal mixer to prepare the master batch. To this, sulfur and short fibers were mixed to prepare the final batch. This mixture was calendered to form sheet which was then cured. The final sample was a 1/4-inch-thick sheet. Anisotropy (measurements that vary with the direction of measurement) in the mechanical properties of the composites indicated that the fibers were to some degree aligned in the mechanical direction of calendering.

Experimental apparatus

We used Allied Fibers' High Strain Viscoelastometer to measure VH and fatigue endurance of the SFRC samples. This instrument was described previously[ref. 5]. In brief, it is a dynamic viscoelastometer which was designed to accommodate tire cords, rubber specimens and cord-rubber composites, subject them to a cyclic straining with strain amplitude and pre-stress level which are typically encountered in a rolling tire, and monitor the stress and strain. The specimen temperature can be varied in a programmed manner. To measure fatigue endurance, the specimen is subjected to cyclic straining until it fails by breaking. The number of cycles to the break is counted by a cycle counter built into the instrument.

Measuring VH

Figure 2 shows the experimental arrangement for measuring VH under cyclic straining. The test specimen was cut out of the cold-cured composite sheet into the size shown in figure 2a. The specimen length direction was taken in the direction of calendering. The effect of the fibers on the VH of the composite is believed to be the greatest when the cyclic straining is applied in this direction.

The specimen was held by clamps at two ends and placed in a temperature-controlled chamber (figure 2b). One of the clamps was connected to the eccentric wheel of the viscoelastometer, which subjects the specimen to cyclic straining; the other clamp was connected to the force transducer. A strain transducer was also connected to the eccentric wheel to monitor the strain. Both transducers were connected to an oscilloscope as well as to an integrator to determine the cyclic hysteresis, that is, the area of the stress-strain loop displayed by the oscilloscope (figure 2c).

The specimen was installed and subjected to a controlled pre-tension. Cyclic straining was then initiated under a prescribed strain amplitude set by use of the eccentric wheel. The specimen temperature was controlled to vary from room temperature up to 160 [degrees] C. VH was measured as a function of temperature.

Measuring fatigue endurance

Fatigue endurance under cyclic straining was measured using the same viscoelastometer setup that was used to measure VH (figure 2). When installing the specimen with clamps, a thin rubber pad was placed between the specimen and clamp surface to protect the specimen from being damaged by the clamp and to increase the likelihood that fatigue failure would occur at the specimen's middle section, away from the clamps. Even then, failure occurred at the clamped section in some cases; when this happened, the tests were discarded.

The fatigue endurance test was conducted at 130 [degrees] C under a strain amplitude of 8.5% and a frequency of 10 Hz to accelerate the fatigue process. For the several tests in which specimen failure occurred in the specimen's middle section, the number of cycles to failure observed was averaged.

Results and discussion

In preliminary analysis of the effect of fiber length and fiber content in the composite on fatigue resistance, fiber length of 1/4-inch and fiber content of 6 pph were found to be optimum. When fiber length and loading were higher, fatigue resistance fell; when the two factors were lower, the mechanical strength of the composite declined.

Among the three rubber stocks, the belt rubber, which has the greatest stiffness, provided the best fatigue resistance for the composite.

To limit the number of subsequent experiments, these preliminary results were used to fix the fiber length, fiber content and rubber stock parameters.

VH under cyclic straining

In measuring VH under cyclic straining, a pre-tension of 5 kg was applied in the direction of the specimen length. This pretension level is within the range of tension that rubber experiences in the circumferential direction in a tire tread near its belt. The strain amplitude in cyclic straining was set at 2%. Like the pre-tension level, this corresponds to the strain amplitude of rubber in the region of a tire near its belt. The cycling frequency was set at 10 Hz, which corresponds to approximately 50 miles per hour (80 km/hour) in the case of a typical size passenger car.

During the measurement of VH under cyclic straining of the various composites, the dynamic modulus was also measured. By a method which was previously reported[ref. 9], the measured dynamic modulus was used to determine the heat generation rate under the same cyclic stress loading.

The results are shown in figures 3 and 4. Figure 3 shows the dynamic modulus as a function of temperature and figure 4 shows the heat generation rate due to VH corrected for the effect of dynamic modulus.

From these figures, the following observations can be made:

* There are considerable differences in the dynamic modulus of composites made with different fibers. The composite made with aramid fiber yields the highest values of dynamic modulus, particularly at high temperatures.

* The heat generation rate due to adjusted VH also shows some differences. At low temperatures, all composites exhibit a lower heat generation rate than the unreinforced rubber used as a control. At higher temperatures, above 80 [degrees] C, the composite with nylon 6 still exhibits lower heat generation than the control rubber, while the composites with other fibers exhibit greater heat generation than the rubber. These results suggest that if an SFRC is used in a tire, the contribution to tire-temperature increase under comparable cyclic stress loading would be the highest with the PET fiber and lowest with nylon 6 fibers.

Fatigue endurance under cyclic straining

Results of the fatigue endurance tests are shown in table 1. Fiber modulus data are also shown for comparison. In general, the composite made with a higher-modulus fiber provided lower fatigue resistance.

The SFRC made with both types of nylon 6 fibers, regular and low modulus, exhibited fatigue endurance comparable to, or better than, the unreinforced rubber used as a control. Composites made with the other fibers exhibited fatigue endurance much lower than that of rubber.

It seems that nylon 6, with lower fiber modulus, greater extensibility of fiber, a lower heat generation rate, and probably better adhesion to rubber (adhesion, however, needs to be studied in depth), is more "compatible" with rubber in the fatigue straining environment than are other fibers.

These results show that, to obtain an SFRC with fatigue endurance characteristics that would make it useful for tire applications, a fiber with a moderate modulus level should be chosen. This would certainly affect the mechanical properties of the composite, and therefore modulus must not be reduced too greatly. The results we have thus far, however, indicate that the composite can benefit from fiber reinforcement with the use of low modulus nylon 6 fibers.

Potential for SFRC in tire applications

Reinforcement of rubber with short fibers is easier to accomplish than reinforcement with continuous fibers. And, as long as the SFRC can endure the fatigue in rolling tires as well as rubber can, there should be many areas of the tire where the composite can be used to enhance the rubber's mechanical properties.

Results of a finite element analysis to examine the use of SFRC in tires[ref. 10], show that the placement of an SFRC "gum strip" at the belt edge of a passenger car tire helps to reduce the stress concentration significantly, suggesting the possible reduction of the probability of failure.

SFRCs may also alter the wear characteristics of tire tread, improve their resistance to cuts or cracks, and modify their damping characteristics[ref. 11].

Conclusions

Comparing the VH characteristics and fatigue endurance of the SFRCs made with various fibers, it is found that a good fatigue endurance of the composite under cyclic straining is obtained with the use of fibers that exhibit:

* Relatively low modulus; and

* A lower rate of heat generation from the composite due to VH under cyclic straining.

Among the fibers we compared, the low modulus nylon 6 fiber is found to meet these requirements best and seems to be more "compatible" with rubber than other fibers.

Finite element analysis of the use of SFRC in tires suggests that the stress concentration in a tire's belt edge can be reduced significantly by placing an SFRC gum strip in that region. [Figure 1 to 4 Omitted] [Tabular Data 1 Omitted]

References

[1]L.A. Goettler and K.S. Shen, "Short fiber reinforced elastomers," Rubber Chemistry and Technology, Vol. 56, (1983), p. 619. [2]J.W. Dally and L.J. Broutman, "Frequency effects on the fatigue of glass-reinforced plastics," Composite Materials, Vol. 1 (1967) p. 424. [3]L.C. Cessna, J.A. Levens and J.B. Thomson, "Flexural fatigue of glass-reinforced thermoplastic," Polymer Engineering Science, Vol. 9 (1969) p. 339. [4]Y.D. Kwon and D.C. Prevorsek, "Role of viscoelastic properties of tire components in the performance of pneumatic tires rolling at high speeds," Kautschuck + Gummi. Kunstoffe, Vol. 38 (1985), No. 1, pp. 21-27. [5]Y.D. Kwon, et al., "Measurement of nonlinear viscoelastic properties of polymers in cyclic deformation under relatively large strain amplitude," Advances in Chemistry Series, ACS, Washington, D.C., 1979, p. 35. [6](a) D.C. Prevorsek and W.J. Lyon, "Endurance of polymeric fibers in cyclic tension," Rubber Chemistry and Technology, Vol. 44 (1971) p. 271. [6](b) H.W. Greensmith and A.G. Thomas, "Rupture of rubber III. Determination of tear properties," Journal of Polymer Science, Vol. 18 (1955) p. 189. [7]D.C. Prevorsek, C.W. Beringer and Y.D. Kwon, "Design of tire cords: Optimization of viscoelastic properties," Macromolecular Secretariat, Organic Coatings and Plastic Division, American Chemical Society, August 28-September 2, 1983, Washington, D.C. [8]C.W. Beringer, Y.D. Kwon and D.C. Prevorsek, "Sensitivity of temperature rise in a rolling tire to the viscoelastic properties of tire components," Tire Science and Technology, Vol. 15 (1987) No. 2, pp. 123-133. [9]D.C. Prevorsek, Y.D. Kwon, R.K. Sharma and C.W. Beringer, "Analysis of tire deformation in operation from the data of temperature rise," SAE Technical Paper Series, No. 800181, SAE meeting of February, 1980. [10]K. Sarkar and D. Stevans, "Three dimensional thermal mechanical analysis of tires by finite element method," presented at meeting of Tire Society, March, 1989. [11]Y.D. Kwon and D.C. Prevorsek, "Formation of standing waves in radial tires," Tire Science and Technology, Vol. 12, (1-4) (1984), p. 44.

Y.D. Kwon, C.W. Beringer, M.A. Feldstein and D.O. Prevorsek, Allied Fibers Division, Allied-Signal Inc.