Fatigue testing for commercial applications.

This article will illustrate fatigue crack growth (FCG) tests that are available in commercial and independent test labs for evaluation of rubber compounds. These are highly useful for evaluation of developmental alternatives such as polymer and compounding variations, as well as characterization of materials prepared in commercial processes. Because of the high precision possible, they are also capable of evaluating processing variations for specific compounds.

The testing and analyses discussed will be energy based fatigue crack growth and associated data that are available from fully automated testing systems. Examples of data from two proprietary studies will be shown to illustrate the data obtainable, some of the common problems experienced and the high quality comparisons of alternative materials that one can obtain through informed analyses. While details of the compounds and the application can not be disclosed, the types of data and the means to obtain them are the main points of this article.

Background

A short compilation of pertinent papers that review or extend the energetics approach to fatigue and fracture is offered. These include several excellent papers by Lake (refs. 1 and 2), Hamed (refs. 3 and 4), Gent (refs. 5 and 6), Thomas (ref. 7) and Mars (refs. 8-10). Young presented the "Effects of temperature on fatigue and fracture" in 1993 (ref. 11).

Clapson and Lake showed the application to (bias ply) truck tire groove cracking in 1971 (ref. 12). Results of fracture in two ply laminates was reported by Breidenbach and Lake in 1979 (ref. 13). "Dynamic property and FCG of tire sidewall and model compounds" was presented by the author using test methods similar to those herein in 1985 (ref. 14), although the test control and crack growth were manually monitored. This paper also showed the effects of sample preparation and sample thickness. "Fatigue crack growth in high load capacity rubber laminates" was reported by Stevenson in 1986 (ref. 15). Results of FCG of NR truck tire belt skim compounds were reported by Young in 1990 (ref. 16), and FCG of diverse tank track pad compounds in 1991 (ref. 17). Reference 17 was based on a 1991 Akron Rubber Group presentation that also discussed the importance of understanding the mode of deformation (strain, load or energy) that controls the application of interest, since that will have a dominant effect on the types of compounds which perform best. "Strain energy release rates for crack growth in an elastic cylinder subjected to axial shear" were reported by Gent in 1993 (ref. 18). "Fatigue crack propagation in NR/BR rubber blends (for tire sidewalls)" by Lee and Moet in 1993 (ref. 19) and by Kim and Hamed in 2000 (ref. 20). "Fatigue life prediction of bonded rubber cylinders" was reported by Leicht, et al in 2003 (refs. 21 and 22).

While not intended as an exhaustive review of the relevant papers, the above gives a fairly comprehensive idea of the basic science and extremely wide application of the energetics approach to robber fatigue research and development. Clearly, it has been applied successfully to many different elastomers and rubber applications over the past 30+ years.

The surprising thing is that, to the author's knowledge, there have been no papers in the accessible literature that describe the use of modern versions of fatigue crack growth testing employing computer control of all data acquisition and analyses. Major rubber companies are understandably reluctant to divulge such information, but there are independent test labs in the U.S. and U.K. which offer such testing. Further, the automation of such fatigue tests, even when using the generally well behaved "pure shear" sample geometry, is a challenge which requires a working knowledge of rubber FCG data, and not just the application of computer algorithms. This may have led some to conclude that such tests are only viable with a large amount of skilled operator involvement, and hence, are very expensive (or require graduate students). This is no longer true.

Thus, a primary objective of this article is to demonstrate how automated FCG testing can provide precise results under conditions which model field conditions, and do so in an efficient, cost effective manner. Decision making in developmental programs is greatly enhanced as a result.

Experimental

Before describing the experimental specifics of this work, a few comments are offered about the energy balance basis upon which the data analysis relies. In reference 7, Thomas describes the fracture criterion based on the energy balance approach, which he and Rivlin pioneered for elastomers in the early 1950s. The elastic energy available for tearing, or "tearing energy," was denoted as T. For certain sample geometries, the value of T has been determined. One of the most commonly used geometries for fatigue studies is the "pure shear" specimen for which the value of T is simply the elastic energy density in the pure shear region, W, times the unstrained sample height, [h.sub.o]. Thus,

T = [Wh.sub.o] (1)

W is determined in a straightforward manner by integrating the area under the stress-strain curve. In most cases, the unloading curve data are used, since they represent the stored energy, whereas the loading curve data include the hysteretic energy. Thus, in this article, the value of T, which has been calculated from the unloading strain energy density, W, has been titled [T.sub.u]. With modern high-speed computers, the stress-strain data are acquired for each cycle of loading and the value of [T.sub.u] is calculated for each test segment. Note that equation (1) has no term relating to the crack length. Thus, the value of T is independent of the crack growth, which is discussed below.

The results included herein are from two different laboratories that conducted tests on compounds for the same application: Axel Products, Ann Arbor, MI, and Experimental Services, Akron, OH. They will be identified as Lab 1 and Lab 2, respectively, which is the order in which the testing occurred. All tests employed the pure shear specimen geometry, also known as the planar tension geometry. As noted above, the key advantage of this geometry is that the tearing energy, T, remains constant if the peak strain levels remain constant. This is a great convenience when conducting fatigue testing in that the test can be continued until there are clearly enough data to precisely describe the crack growth rate ([DELTA]c/[DELTA]n) for that condition. In this case, [DELTA]c is simply the amount of crack growth measured for a given test segment, and An is the number of extension cycles in that segment. One can continue testing for as many segments as necessary to get consistent data, since the severity of the test condition is independent of the crack length.

While pure shear samples with a dumbbell shaped cross section (gripping beads) have often been employed, the samples used in these studies were all flat and relatively thin (<1 mm). The reason for this is that a major aim of these studies was to evaluate the performance of compounds that had been fabricated into commercial parts. This required skiving the parts to yield flat samples suitable for testing. The advantage of being able to test such thin materials is that variables such as differences in cure state as one goes from the surface to the interior of a thick part can be readily investigated.

It should be understood that using thin samples (T <1 mm) is not recommended if one is trying to get material properties which are independent of thickness, since there is a well known thickness effect on such data when T is <1.5 mm. However, if the results are compared on equal thickness specimens of the same elastomer, the thickness effect can generally be ignored for developmental purposes.

Comments on key testing variables Temperature

Usually the highest typical level that can be experienced in field service is employed. That was 50[degrees]C for the application investigated. However, lower temperatures may be chosen if needed to simulate higher strain rates than are achievable with a given servohydraulic test system. This requires knowledge of the WLF shift factors which are usually obtained from other studies. The lower temperature, 35[degrees]C, employed at Lab 2 was chosen on this basis.

Strain level

This is the most critical control variable. Usually one tries to bracket the range of lowest-to-highest strains experienced in service. The strain range used in this work was 5-9%. High strains are seldom a problem; low strains are constrained by the amount of time (cycles) that one is willing to test, and by the sensitivity of the crack length monitoring system.

Strain rate

High speed servohydraulics usually allow modeling the strain rates that are experienced in service. The rates obtainable at Lab 1 allowed this for the current work; those at Lab 2 did not; hence the use of a lower test temperature.

Haversine pulse frequency

This is usually the means of achieving the strain rates desired. The average strain rate is easily calculated from the total amount of deformation divided by V2 the period of the pulse. Using a haversine pulse has the experimental advantage of minimizing the bumping and noise at the start and end of each pulse. In the case of Lab 1, although a haversine pulse was used, the maximum crosshead speed was used for each strain condition. Thus, the effective "pulse frequency" was not constant.

Overall cycle frequency

This determines the number of pulses per unit time and the rest interval between pulses. This allows time for viscoelastic recovery, thereby avoiding excessive growth. It also allows control of the amount of energy input per unit time, and provides time for heat transfer to avoid unwanted heating of the sample.

Oxidative environment

Air is the most common environment and the one used for all the current work. However, other environments are quite feasible with an environmental chamber (e.g., [O.sub.3] or [N.sub.2]) and are often helpful if evaluating components Such as truck tire belt skims that are exposed to only limited amounts of air.

Fully relaxed or preloaded

Depending on the service conditions and the type of elastomer employed, this can have a major effect. Fully relaxed conditions were used herein. This allows for a significant amount of sample recovery between strain pulses.

Number of loading cycles per test segment

This is determined by the number of cycles required to get a measurable amount of crack growth. Since this changes by orders of magnitude from low to high strain levels, one usually picks a convenient number, e.g., 100 cycles. The result may be little apparent growth for long periods at very low strain levels, but very fast growth at highest strain levels.

Table 1 gives the test conditions employed in the two laboratory programs. Variables monitored by the data acquisition systems for each segment of each test condition included:

* Peak stress and peak strain levels;

* minimum stress and strain levels;

* dynamic modulus;

* loading, unloading and hysteretic loss energies;

* crack length; and

* number of loading cycles per segment and cumulative.

All of these are acquired by proprietary computer programs and imaging systems on a continuous basis as the test proceeds. This allows accomplishment of many test cycles in a relatively short time with minimal operator involvement.

Data analyses, post test, consisted of:

* Review of the crack appearance from a digital photo supplied with the data table. Almost all were quite straight and horizontal, with varying degrees of apparent roughness and crack tip blunting.

* Calculation of average levels of key parameters for each test segment (strain condition), including peak strain, modulus and unloading tearing energy, [T.sub.u].

* Plot of crack length vs. cycles of testing; careful review and elimination of any data which did not meet objective criteria for pure shear FCG results.

* Linear regression analysis to obtain the slope, dc/dn, and the regression coefficient, [R.sub.2] , for each strain case.

* Plots for each sample, and then combined for all samples, of a given compound:

--dc/dn vs. [T.sub.u]

--dc/dn vs. peak strain

--modulus vs. peak strain

Since linear plots were used for convenience, the regression lines for the dc/dn vs. [T.sub.u] or peak strain plots were second order power law formulations, since these data are known to follow such relationships.

Results and discussion

Program no. 1--tests of skived samples taken from commercial parts

The results of the dc/dn vs. peak strain analysis for compound A are shown in figure 1. There is some scatter as occurs in most fatigue studies, but considering that these were skived samples, which introduce some additional (thickness) variations and possible stress concentrations, the agreement among runs is quite good. The use of a second order power law regression formula provides a good representation in this experimental region.

[FIGURE 1 OMITTED]

When the results of compound B are added in figure 2, there is clearly a significant difference shown between the FCG performance of A vs. B. Compound B exhibits consistent FCG rates that are two to three times higher than those of compound A. There is almost no overlap of the data.

[FIGURE 2 OMITTED]

The application in which these compounds are employed is predominantly strain controlled. This is why the plot of FCG vs. peak strain was shown first. In fact, the strain level most typical of this application is approximately 6%. If one uses the best fit regression lines to calculate the dc/dn levels at 6% for both of these compounds, it is found that the FCG rate of compound B is 2.74 times that of compound A.

The reason these two compounds were tested, using skived samples from commercial parts is that the field performance of each had been independently assessed. This showed that compound A provided at least 2.2 times the number of cycles of flexing in the field before cracking vs. compound B. This level of validation is felt to be excellent for a fatigue evaluation of skived samples vs. actual field performance.

To complete the analysis for these compounds, illustrating some of the other data that are obtained, plots of FCG vs. unloading tearing energy, [T.sub.u], and modulus vs. peak strain are shown in figures 3 and 4, respectively.

[FIGURES 3-4 OMITTED]

Figure 3 shows that compound A still performs better at a given [T.sub.u] level than does compound B, however, the differences are smaller than they were in figure 2 at a given strain level. Figure 4 shows why. The modulus of compound B, at any given strain, is significantly higher than that of compound A, and this is especially true at the lower strain levels. It is well known, and logical, that a higher modulus compound will perform more poorly in a strain controlled environment than will a lower modulus one, all other things being equal.

The reason is that a higher modulus results in a higher strain energy level at any given strain. However, the FCG vs. [T.sub.u] plot, figure 3, should normalize out this bias. As seen in figure 3, compound A remains better, regardless of the modulus effect, indicating that A has inherently better FCG resistance compared with B.

Please note the excellent behavior of the modulus vs. peak strain data in figure 4. This is typical of data obtained routinely in the FCG test using the pure shear sample. This high quality stress-strain, modulus and tearing energy data could be valuable for other uses, such as material models required for finite element studies and compound property databases. These data are obtained at no extra cost using conditions that simulate as closely as possible those encountered in the field.

Program no. 2--tests of cast samples prepared in the lab Following the success of program no. 1, a study was undertaken at another laboratory to assess the effects of processing variations on compounds being considered for this application. In this case, the samples were cast in the laboratory, as is standard practice for materials being evaluated in development studies for this application. However, they were then skived to the same thickness as the samples used in program 1. The processing variation is proprietary, but was deemed significant by the client. Compounds C and D are the same formulation otherwise, but labeled to reflect the difference in processing.

Since it was known that the available crosshead speeds were much lower in lab 2 vs. lab 1, a lower temperature, 35[degrees]C, was selected. Other studies had shown that this would increase the effective strain rate by a factor of roughly 100. This provided strain rates at 35[degrees]C, using a pulse frequency of 10 Hz, that were comparable to those in lab 1 at 50[degrees]C using a much faster actuator. Preliminary experiments showed that results for compounds A and B were obtained at lab 2 which were in good agreement with those shown earlier for lab 1.

Figure 5 shows the results of FCG (dc/dn) rates vs. peak strain. There is some scatter in the dc/dn rates at a given strain, which is not surprising, since these were also skived samples, but the agreement among the replicates is generally good (for fatigue crack growth data). Note the excellent consistency of the peak strain levels. This was a side benefit of operating at a lower crosshead speed. The peak strains were right on, or within +/- 0.01% of the target level, in all cases. This makes comparison of replicate results much more straightforward as the testing progresses.

[FIGURE 5 OMITTED]

Figure 6 shows the comparison of the FCG performance of compound C vs. compound D. Compound C has higher FCG rates at all strain levels. Using the regression equations, the best-fit results for compounds C and D were calculated at specific strain levels and compared. Compound C had higher FCG rates that ranged from 1.73x to 1.23x those of compound D, as peak strain levels increased from 5 to 9%. At 6% strain, the typical operating level for this application, the ratio was 1.56x for C vs. D.

[FIGURE 6 OMITTED]

While the data in figure 6 seem to show a consistent benefit for D vs. C in lower FCG, a ratio of performance of 1.56 is marginal with respect to what will be realistically seen in field performance under a variety of commercial operating conditions for this application. However, the results shown above were supported by other comparisons of similar pairs of compounds, both cast and skived, that were included in this study. Thus, the client was able to conclude that the processing variations studied were indeed meaningful, and worth pursuing to maintain the highest possible levels in FCG performance of their materials.

The related analyses are shown in figures 7 and 8. In figure 7, it is seen that compound C is also higher in FCG vs. [T.sub.u] than compound D. The difference is smaller than it was for FCG vs. strain, and the reason is again that the modulus of compound C is somewhat higher than for compound D. In this case, the difference is only about 4%. However, the fact that a processing variation could cause a modulus difference of 4% was another notable fact for this application.

[FIGURES 7-8 OMITTED]

Scrutiny of FCG data to eliminate artifacts

Having shown that high quality data can be obtained in fully automated tests, it is now important to show the types of results that sometimes need to be carefully reviewed to ensure that the dc/dn data are appropriate for pure shear specimens before using them in analyses. This is an especially important aspect of this article, since it is mostly concerned about the testing, per se, and not the particular results that have been used to illustrate the testing capabilities. Four major examples will be given, all of which are drawn from the data generated in program no. 2.

Data which are non-linear

As stated initially, a plot of [DELTA]c vs. [DELTA]n for data acquired at constant strain using a pure shear sample should be linear.

However, there are two deviations from linearity that are occasionally seen. First is the case of a new crack that is growing more rapidly, initially, than the rate it will finally maintain under the low strain testing condition (assuming this is run first). This is shown in figure 9.

[FIGURE 9 OMITTED]

Although the data for the first 1,000 cycles had already been ignored, the plot shows that the results for 1,000 to 2,000 cycles exhibit a steeper slope than those from 2,000 to 10,000. If used in the regression calculation, this would have skewed the line at the low end, resulting in a steeper slope (dc/dn) calculation. By eliminating the data before 2,000 cycles, a more appropriate estimate of the dc/dn value for this sample is obtained, as shown in figure 10. If one is interested in accurate data at low strains, representative of the application, it is sometimes necessary to eliminate this early data to avoid a significant (unnecessary) bias.

[FIGURE 10 OMITTED]

The second case of non-linearity which occasionally occurs, but less frequently, is when the crack has been growing at a steady rate under a constant peak strain condition, but then slows down for no apparent reason near the end of the test segment. If this occurs, the non-linear data are eliminated before fitting the regression line, similar to what was done in figure 10 vs. figure 9. There were no examples of this in the current data set, but it occasionally occurs and must be eliminated to achieve best accuracy of results. This may be a special case of the effect discussed in the section, "Data exhibiting an apparent slow-down and then jump in crack length," which is presented later.

Data exhibiting very slow crack growth

If one is attempting to test at very low strains to obtain data at one or two strain conditions that are below the normal operating condition of the application (maximum), it is possible that the crack growth rate will be so slow that even 10k cycles will produce only three or four changes in crack length. Although the crack is growing very slowly and steadily, the crack length monitoring system has a finite lower limit of detecting changes. In this case, that was 0.04 mm. Thus, the crack appears to be at a steady length for 1-2k cycles, and then jumps to another level where it remains steady for another 1 or 2k cycles. Figure 10 shows this behavior. If an even lower strain condition had been attempted for this compound, such as 4.5%, the rate of crack growth would have been so slow that the crack might have only grown by two or three (detectable) levels in 10k cycles or more. The choices are to run the test for very long periods, or accept that the data obtained at a condition like that of figure 10, is adequate and move on to the higher strain conditions. This was not a problem in the program shown, but in cases where very low modulus compounds are being tested, it has sometimes been a problem requiring careful review and decision making. Thus, the interaction of test capability, choice of test condition, and compound modulus and fracture toughness are factors which must be thoughtfully balanced when choosing test conditions in various stages of each program to avoid wasting testing time (or including marginal data).

Data exhibiting an apparent slow-down and then jump in crack length

Figure 11 shows this behavior. This occasionally happens and is believed to be an artifact of the kind of crack measurement that is typically used. Since a light is shone through the sample to detect the crack tip, any change in the crack front that is not perpendicular to the face of the sample will appear to result in a crack slow-down. In cases like figure 11, where the slope of the FCG function is not affected by much, it is usually ignored. Otherwise, the data must be carefully edited. In this case, the author believes that it is sometimes better to accept the whole data set intact rather than attempt to edit it, provided that the slope of the results before and after the apparent jump in crack length is very similar.

[FIGURE 11 OMITTED]

Data exhibiting a periodic waviness in [DELTA]c/[DELTA]n

Occasionally, data will be obtained which show a distinct waviness in the plot of crack length vs. cycles, as shown in figure 12. This is believed due to the dynamics of the crack growth process for a given compound as it interacts with the practical aspects of automated crack growth measurement (as discussed above). The important lesson here is that one must use testing segments that are sufficiently long that a good averaging of the gradual rise and fall in (apparent) rates is obtained.

[FIGURE 12 OMITTED]

Finally, the examples above of some non-linear effects that can be observed in automated testing should not mislead the reader. In the vast majority of data sets that the author has reviewed, the plots of crack length vs. cycles are clearly linear. Figure 13 gives an example of a typical set. While there are a few minor perturbations, these data illustrate the kind of linear relationship one should expect. Of course, the usual caveat applies of needing to use test segments of sufficient cycles that any such perturbations are clearly averaged out. The elegance of the pure shear testing protocol is that the expected result is a linear response. If, for any reason, that is not observed for a given range of loading cycles one has two choices: 1) run more cycles, or 2) start over and rerun the testing segment at that strain. Both are valid, since the sample remains reasonably stable unless very high strains have been imposed. In the author's experience, the number of test segments that have had to be repeated (on the same sample) is less than 5% in recent work. This is for an application where the strain range of interest and test conditions was previously defined. When one is just beginning an FCG test program for a new application, where the peak strain levels that will cause meaningful cracking are unknown, the number of repeats might be higher, however. The discussions above illustrate why it is important for a knowledgeable person, who is not actually doing the test, to monitor the daily progress and provide input to ensure that the quality of results is high and consistent with the developmental use intended.

[FIGURE 13 OMITTED]

Conclusions

* High quality fatigue crack growth (FCG) results can be obtained using modern, automated test systems.

* Results obtained can closely model the field experience of cyclically loaded elastomer compounds.

* Skived samples from actual parts can provide a direct evaluation of the compound as it was fabricated in the commercial process.

* High precision and good repeatability in these tests allow one to define subtle effects from processing as well as compounding variations.

* Automated testing systems can sometimes result in artifacts in the data. This requires that a knowledgeable person review each data set to ensure accuracy and avoid misleading results.

* This is a powerful, cost effective technology for developing new elastomers, compounds and processes for commercial rubber applications.

* A bonus from conducting such tests is that high quality stress-strain, modulus and energy data are obtained under dynamic conditions which can meet the needs of material models and databases.

References

(1.) G.J. Lake, Rubber Chem. Technol. 45, 309 (1972).

(2.) G.J. Lake, Rubber Chem. Technol. 68, 435 (1995).

(3.) G.R. Hamed, Rubber Chem. Technol. 64, 493 (1991).

(4.) G.R. Hamed, Rubber Chem. Technol. 67, 529 (1994).

(5.) A. Ahagon, A.N. Gent, H.J. Kim and Y. Kumagai, Rubber Chem. Technol. 48, 896 (1975).

(6.) A.N. Gent, Rubber Chem. Technol. 56, 1,011 (1983).

(7) A.G. Thomas, Rubber Chem. Technol. 67, 050 (1994).

(8.) W.V. Mars, Rubber Chem. Technol. 75, 001 (2002).

(9.) W.V. Mars, Rubber Chem. Technol. 76, 1,241 (2003).

(10.) W.V. Mars, Rubber Chem. Technol. 77, 391 (2004).

(11.) D.G. Young, Rubber Chem. Technol. 67, 137 (1994).

(12.) B.E. Clapson and G.J. Lake, Rubber Chem. Technol. 44, 1,186 (1971).

(13.) R.F Breidenbach and G.J. Lake, Rubber Chem. Technol. 52, 96 (1979).

(14.) D.G. Young, Rubber Chem. Technol. 58, 785 (1985).

(15.) A. Stevenson, Rubber Chem. Technol. 59, 208 (1986).

(16.) D.G. Young, Rubber Chem. Technol. 63, 567 (1990).

(17.) D.G. Young, Rubber World, April, 1991.

(18.) A.N. Gent and C. Wang, Rubber Chem. Technol. 66, 712 (1993).

(19.) M.P. Lee and A. Moet, Rubber Chem. Technol. 66, 304 (1993).

(20.) H.J. Kim, and G.R. Hamed, Rubber Chem. Technol. 73, 743 (2000).

(21.) D.C. Leicht, O.H. Yeoh, A.N. Gent, J. Padovan and R.L Mullen, Rubber Chem. Technol. 76, 160 (2003).

(22.) D.C. Leicht, C. Rimnac and R.L. Mullen, Rubber Chem. Technol. 76, 365 (2003).

Donald G. Young, consultant, Cranford, NJ

Table 1--test conditions employed

Program:                                  Lab 1               Lab 2
Pure shear sample
 Height, mm                                12.7                12.9
 Width, mm                                  152                 152
Thickness, mm                      0.86 typical        0.86 typical
Sample source                 Skived from parts    Skived from pads
Test oven temp., [degrees]C                  50                  35
Strain levels, %                         5 to 9              5 to 9
Test environment                            Air                 Air
Loading waveform                Haversine pulse     Haversine pulse
Pulse frequency, Hz                      NA (1)                  10
Strain rates, [sec.sup.-1]                  174          1.0 to 1.8
Overall cycle freq., Hz                      10                   4
Crack measurements                    Automated           Automated
Loading cycles/condition, k     Varied: 2 to 71                  10
Initial stress level          Zero (no preload)   Zero (no preload)

1--Crosshead speed was 2,200 mm/sec.