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Fatigue Testing
8.5 Combined Strain State
8
Fatigue Testing
8.1
Introduction
117
There are two methodologies used in determining the fatigue life of a material: Testing cycles to failure with constant amplitude oscillations called the stress-life or strain-life method
Measuring the fatigue crack growth rates also under constant cyclic stress or strain conditions.
The discussion of the fatigue crack growth method is left to Chapter 11 and we will cover stress-life and strain-life here. Contrary to the usual practice with metals, strain life will be emphasized over stress-life. Most rubber components that undergo fatigue cycling in service endure a shear or compressive cycle. Bearing failures generally are due to the shear fatigue, which is most often stroke-controlled, rather than compressive fatigue, which is usually load-controlled. The response of the elastomer component to a stroke-controlled loading is most closely approximated by constant amplitude strain cycles. In addition, there is the cost and inconvenience of trying to create a credible constant stress compressive cycle test. The strain-life curve is simply life in cycles vs. strain amplitude (or range). In spite of the fact that the amplitude is the independent variable, by custom the data is usually plotted as range or amplitude vs. cycles on a log-log plot. We shall follow that custom here.
8.2
Parameters Affecting the Strain-Life Curve
These parameters can be loosely classified as mechanical or environmental. Mechanical parameters are stress or strain amplitude, combined stress or strain state, R-ratio, strain rate, frequency, and wave form. The environmental variables are temperature and the fluid environment. Fluids include air, water, oils, etc. There is an important distinction between a test procedure and a test protocol. Procedures include such details as how the test machine is turned on and how the specimen clamps are operated; they are unique to a particular lab. The test protocol states what the test specimen will experience and what parameters will be measured without special attention as to what devices or equipment settings are used. Here, we will make recommendations on protocols for fatigue testing.
118
8 Fatigue Testing
8.2.1
Parameters to Be Specified
In a strain-life or stress-life test, the minimum parameters to be specified are: strain amplitude (or range), R-ratio (or mean strain), wave form, frequency, temperature, environment (i.e., air, water, oil, etc.), and failure criterion (or criteria). In addition, any special handling of the specimen such as preliminary heat or liquid exposure should be clearly prescribed. Of course, an exact description of the specimen design is essential. It is also good practice to detail the type of test machine and any pertinent fixtures. In turn, the results should be reported with all the specifications.
8.2.2
Selecting Strain Amplitude
At a given set of conditions, the cycles to failure at constant strain amplitude follow a power law often written as ⎛ε ⎞ N =⎜ a ⎟ ⎝ ε0 ⎠
k
(8.1)
where N is cycles to failure, ε a the strain amplitude, and ε 0 and k are constants. In selecting a strain amplitude for the first test of a new elastomer, the test engineer should pick an amplitude that will give a relatively short life. This guesstimate can be made by comparison to other tests of similar rubbers, or even just from a textbook example. The procedure is to pick an amplitude to give a failure in an hour or less. Then, a second guess is made, but this time only the slope, k, need be estimated. After the second test the engineer will have two data points to establish the curve. Now the procedure is more exact. The engineer may fill in gaps or extrapolate for high cycle tests as needed.
8.3
Failure Criteria
In order to measure the fatigue life of a test specimen, the instant of failure must be determined. The manner in which “failure” is defined will powerfully influence the cycle count. The problem is to select a clear, easy to establish criterion of failure, which reasonably corresponds to failure of the component in service. In strain-life testing there are several possible criteria. 1. Complete rupture as in metal testing 2. Load drop by some specified percentage 3. Onset of cracking 4. Crack size
8.5 Combined Strain State
119
Complete rupture works quite well in a tension cycle test. There is a sudden drop to zero load which is easily recorded, or the test machine may respond in some fashion, or there may be a load noise, and so on. However, as noted above, rubber components are not usually designed to pass their major fatigue loads in tension. The use of the load drop implies that the failure does not take place as a sudden rupture, but as gradual crack growth, which is evidenced as a drop in load. The method is best employed in a stroke-controlled shear cycle test. In such a test, the mean cyclic load will decline with time or cycles due to cyclic stress-relaxation. The load-cycles curve can be traced on a graphical output or later plotted from a digital output. If the decline is purely stressrelaxation, the curve will be a straight descending line on a log-log plot. The point at which the crack begins to grow will be marked as a departure below the straight line. It is a simple matter to plot the extension of the straight-line curve and a parallel line some fixed percentage below it. Failure then is that point where the actual curve of the cracking specimen intersects the parallel lower curve. It remains only to select what percentage of load drop will be designated as “failure.” Historically, the onset of cracking has often been used to mark the end of fatigue life. It can be used for shear and compressive cycle testing; however, it implies visual tracking by test personnel. As noted above, a departure from the cyclic stress relaxation curve may also be used, but this is less accurate. As the test program calls for lower amplitudes, the length of specimen life may easily exceed 24 hours. While 24 hour-a-day, 7 days-a-week tracking can be aided by taping a television record of the specimen in testing, the method obviously becomes more costly and less convenient. Crack size can be used as a failure criterion. It is, in effect, the same idea as the percent load drop without the need to track the stress relaxation curve. In tensile tests conducted on long “pure shear” specimens it can be practical. As a failure criterion in shear testing, crack size suffers from the same disadvantages that crack onset does.
8.4
R-Ratio
R is the ratio of the minimum strain of the cycle to the maximum. That is R = ε min /ε max
(8.2)
The R-ratio is illustrated in Fig. 8.1. To estimate strain-life, Walkers [1] empirical equation, which converts strain amplitude data taken at various R-ratios to an effective value at R = 0, is covered in detail in Chapter 9.
8.5
Combined Strain State
The most common combined strain state for rubber components is shear with compression. Rubber pads experience this condition in helicopter rotor bearings, bridge and
120
Figure 8.1
8 Fatigue Testing
R-ratios for three strain cycles
building bearings, and offshore piping flexible joint bearings. In these cases, the pad is designed to accept a high compressive load through thickness and shear deflections in the plane of the pad. Pad compression increases the fatigue life significantly and must be accounted for in testing. Once a specimen is deformed by the applied load, the only strains that can be directly measured are those on the surface. That means that determination of the interior strain (or stress) state is left to calculation. The finite element method is by far the best for this purpose. In Chapter 9, the shear fatigue testing of an acrylonitrile is described where the data was taken from pads under compression. In this case, finite element analysis was used to predetermine the maximum bulge shear strain when the specimen was squeezed by a certain measurable displacement. Then a screw clamp was set to compress the specimen by the amount calculated in the finite element analysis and the result reported in terms of the bulge shear strain. It is a recommended method to deal with this particular combined strain state. Another common combined strain state is found in bushings under transverse shear. When the rod at the center of the bushing is displaced radially, the region opposite the displacement experiences biaxial tension, see Fig. 8.2. The additional tensile component must also be accounted for in testing.
Figure 8.2
Center rod in bushing displaced radially downward
8.6 Wave Form
8.6
121
Wave Form
Most fatigue testing employs either a sinusoidal or sawtooth wave. While in metals some testing indicates a sawtooth wave is more “damaging” than a sinusoidal one, there is no corresponding data for elastomers. Nor have other waveforms, such as square waves or slanted sawtooth, been investigated. These shapes are illustrated in Fig. 8.3. Once the wave form is specified, achieving it over the duration of the test, particularly in a load or stress controlled tension tests can be a challenge. The measurement of maxima and minima, and therefore, the amplitude and R-ratio will be greatly affected by cyclic creep changing the unloaded length of the specimen. Thus, to maintain the particular stresses of the intended cycle, the machine stroke settings must be adjusted as the test progresses. However, the majority of the elongation occurs in the first few cycles, generally less than a hundred, so the period of frequent adjustment is usually short. However, adjusting the stroke should be continued throughout the test. The second consideration is to determine on what length to base the strain calculation. The author has found that the most consistent results were obtained when the fresh length taken before the first cycle was used. There is one caveat; in some testing machines, the clamping of a pure shear specimen extrudes enough material out from between the clamps so that the base length for strain computation is changed by clamping. In such cases, the length and the zero displacement position should be established after clamping. The effect of variation in wave form in rubber fatigue is unknown and often unreported. In metal fatigue, some work has been done regarding the effect of cycle waveform on fatigue crack growth, but none has been reported in the literature for rubber. In metals, sharp reversals seem to increase fatigue crack growth somewhat, that is, a sawtooth wave is more destructive than a sinusoidal wave. Given the internal heat generation of elastomers at high strain rates, it may be that at equal frequencies back slanted sawtooth or square
Sinusoidal Black slanted sawtooth
Sawtooth
Trapezoidal Square wave
Figure 8.3
Wave forms
122
8 Fatigue Testing
waves may produce a shorter fatigue life. The author has had experience with sawtooth and sinusoidal waveforms (Fig. 8.3) in rubber fatigue and has not seen an effect. At this point, the effect must be described as unknown but probably small.
8.7
Creep and Stress Relaxation
In tensile fatigue tests, elastomers respond to a stress-controlled test by a significant elongation with time. The magnitude of this cyclic creep is much greater than for metals and makes it more difficult to conduct the test. As noted above, to create a stress-life curve for a particular elastomer, a test machine whose stroke is continually adjusted to keep the stress cycle approximately constant, must be employed. Hence the machine must be computer controlled by a feed back loop from the load sensor or be continually adjusted by its operator. In constant stroke amplitude shear fatigue tests the maximum cyclic load will decline with the number of cycles. This phenomenon is called cyclic stress relaxation. Cyclic stress relaxation has been shown to follow a power law of the form ⎛N⎞ Pmax = ⎜ ⎟ ⎝C⎠
p
(8.3)
where Pmax is the peak cyclic load, and N is the number of cycles. The empirical constant p is negative, corresponding to a downward slope, and C is the number of cycles with Pmax = 1. Equation 8.3 indicates that in testing one expects that the Pmax vs. N curve will be a downward sloped straight line on a log-log plot. Deviation below this line indicates that cracking is occurring. Stress relaxation can best be estimated from a record of peak stress for constant strain amplitude cycles. Analogously, creep is measured by recording maximum elongation for constant stress or constant load cycles. These measurements need not be made every cycle but can be made every thousand cycles. Since the data is plotted on a log cycles graph and the phenomenon has a log-log relationship, it is logical that an approximate logarithmic increment be used to establish measurement points. For example, make measurements at 10, 30, 100, 300, 1000, 3000, etc. cycles.
8.8
Frequency and Strain Rate
Frequency has a strong effect; however, it cannot be distinguished from simple elevated temperature. In fact, in some testing, control of the test frequency has been employed to refine the specimen temperature during cycling. As cyclic rates increase, rubbers produce heat internally at higher rates. This heat production is due to hysteresis and is thought of
8.9 Effect of Temperature
123
as internal friction opposing deformation. Thus, heat production increases with strain rate. In fatigue testing to date, it has not been possible to distinguish the effect of temperature increase due to the environment from that produced by hysteretic heating. Hence, to deal with this effect in fatigue testing, consider frequency simply a way to elevate temperature.
8.9
Effect of Temperature
Temperature has a powerful effect on cycles to failure. Life can be doubled or halved by a change of only 10 °C. Over modest ranges of temperature change, say less than 100 °C, the cycles to failure at differing temperatures can be correlated. In Chapter 9, three methods are described: the ratio of Arrhenius functions, Nagel’s equation [2], and a simple linear approximation. In the case of shear fatigue it is relatively easy to get accurate measurements. The recommended specimen for shear fatigue is the dual-lap shear specimen with disc pads illustrated in Figure 8.4. Disc pads have uniform compressive bulge so compression can be imposed without creating irregular strains around the rim. Since the bars are made of metal which has great conductivity compared to the rubber, a thermocouple placed in a small hole drilled close to the rubber pad in one of the bars will give an accurate reading.
Figure 8.4
Dual-lap shear with disc specimen
124
8 Fatigue Testing
The dumbbell tensile specimen (Fig. 8.5) presents a greater challenge. If the cycling is stopped to use a thermocouple on the surface, it must be assumed that the specimen will cool somewhat between the time the cycling stops and the temperature probe reaches equilibrium with the specimen. An estimate of the cooling effect can be made by creating a finite element heat transfer model of the specimen, probe, and test chamber air. In testing, experimenters often assume the room or test oven air temperature is the specimen temperature. If the cyclic rate is relatively low and the specimen small in mass, this approximation may be sound. The simplest approach to controlling the specimen temperature during cycling is water immersion.
Figure 8.5
8.10
ASTM D412 die “C” specimen
Liquid Immersion
Immersion of the elastomer in a liquid has potentially two effects. One effect is for the liquid is to carry off the hysteretic heat created in cycling and thereby reduce temperature excursions. In fact, to gain control of the specimen temperature at high cyclic rates, water immersion can be the solution. On the other hand, for elastomers operating in some liquids, the liquid can contribute greatly to deterioration of the rubber molecules. Various oils and other substances can break down polymer chain bonds, returning the rubber to a soft sticky state or stiffen and embrittle the material by increasing the crosslinking. Deterioration by liquid immersion can be a major factor in decreasing the useful life of an elastomer part and thus the environment must be included in the testing of the elastomer for such an application. Where the liquid is known to have a deleterious effect on the rubber properties, only testing in that liquid can adequately simulate the environment and produce relevant fatigue life results. One approach to reduce test duration is to run a “hot test.” In such a test the specimens are cycled to failure at the same amplitude and R-ratio at two temperatures.
8.13 Batch Variation
125
The results are then used to establish an activation energy for the Arrhenius function for that process. Employing the Arrhenius equation, the life at a lower temperature can be estimated. The hot test has the advantage of producing a life estimate in much less time than the one needed for testing to failure at the lower operating temperature. This method is shown in Chapter 9.
8.11
Recovery
It is a common experience in testing for the machine to stop for one reason or another. As noted earlier in stress-strain testing, the immediate result of a pause in an extension cycle will be a gradual drop in stress, if the displacement is held and an increase in the stress when the machine resumes the extension. In a stress-strain test where the curve is to be standardized at a particular number of cycles, say five, the test result is thereby invalidated. However, in a fatigue test where there are thousands perhaps millions more cycles to go, the effect of a short halt and temporary recovery of stress is of no importance. Generally, the peak load curve will return to its original path after a pause in cycling of a few minutes.
8.12
Scragging
In some industries, physical testing of rubber is conducted after the specimen has been “scragged.” Scragging means to put the specimen through several cycles of stretching or deformation before measurements are taken. Sometimes no record of stress, strain, or other parameters is made during such a process. Any scragging should at least be standardized and recorded. Generally, there is no need to scrag a fatigue test specimen or to exclude the early cycles of a fatigue test from the record. It is also undesirable to scrag rubber specimens before a stress-strain curve is to be produced. On the other hand, for stress-strain curves, a specific number of controlled extension cycles made before the one to be used in analysis is good practice. The number of such preparatory cycles should be selected so the resulting curve is representative of the service condition.
8.13
Batch Variation
Stress-strain testing of various elastomers frequently shows variation from batch to batch. There is little corresponding data from fatigue testing to show how great batch variation might be. However, the shear fatigue data in the example of Chapter 9 contained two batches and showed no apparent difference between the batches.
126
8 Fatigue Testing
While batch variation in stress-strain testing is significant, it is not known how significant such variation is in fatigue life testing. Nevertheless, specimen should be tracked individually and identified by batch. Since many elastomers will change properties with long term exposure to room temperature, the storage conditions for specimens should be specified.
8.14
Storage
Since specimens can be manufactured on one date and tested weeks or even years later, it is important to report the date of manufacture as well as the date of the test and to describe the conditions of storage.
Acknowledgements The author is grateful to his former associates at Oil States Industries, Arlington, Texas for the use of the test lab and their support and coaching test procedures.
References 1
Walker, K., “The Effect of Stress Ratio During Crack Propagation and Fatigue for 2024-T3 and 7075-T6 Aluminum,” Effects of Environment and Complex Loading History on Fatigue Life, ASTM STP462, American Society for Testing and Materials, Philadelphia, 1970, pp. 1 – 14.
2
Nagel, W.B., “Design with Rubber, Parts 1, 2, 3 and 4: The Design Surface,” Machine Design, Jun 23, 77, Penton Publications.
3
Mott, P. H. and Roland C. M., “Aging of Natural Rubber in Air and Seawater,” Rubber Chemistry and Technology, Vol 74, 2001, pp 79 – 88.
8
Fatigue Testing
8.1
Introduction
117
There are two methodologies used in determining the fatigue life of a material: Testing cycles to failure with constant amplitude oscillations called the stress-life or strain-life method
Measuring the fatigue crack growth rates also under constant cyclic stress or strain conditions.
The discussion of the fatigue crack growth method is left to Chapter 11 and we will cover stress-life and strain-life here. Contrary to the usual practice with metals, strain life will be emphasized over stress-life. Most rubber components that undergo fatigue cycling in service endure a shear or compressive cycle. Bearing failures generally are due to the shear fatigue, which is most often stroke-controlled, rather than compressive fatigue, which is usually load-controlled. The response of the elastomer component to a stroke-controlled loading is most closely approximated by constant amplitude strain cycles. In addition, there is the cost and inconvenience of trying to create a credible constant stress compressive cycle test. The strain-life curve is simply life in cycles vs. strain amplitude (or range). In spite of the fact that the amplitude is the independent variable, by custom the data is usually plotted as range or amplitude vs. cycles on a log-log plot. We shall follow that custom here.
8.2
Parameters Affecting the Strain-Life Curve
These parameters can be loosely classified as mechanical or environmental. Mechanical parameters are stress or strain amplitude, combined stress or strain state, R-ratio, strain rate, frequency, and wave form. The environmental variables are temperature and the fluid environment. Fluids include air, water, oils, etc. There is an important distinction between a test procedure and a test protocol. Procedures include such details as how the test machine is turned on and how the specimen clamps are operated; they are unique to a particular lab. The test protocol states what the test specimen will experience and what parameters will be measured without special attention as to what devices or equipment settings are used. Here, we will make recommendations on protocols for fatigue testing.
118
8 Fatigue Testing
8.2.1
Parameters to Be Specified
In a strain-life or stress-life test, the minimum parameters to be specified are: strain amplitude (or range), R-ratio (or mean strain), wave form, frequency, temperature, environment (i.e., air, water, oil, etc.), and failure criterion (or criteria). In addition, any special handling of the specimen such as preliminary heat or liquid exposure should be clearly prescribed. Of course, an exact description of the specimen design is essential. It is also good practice to detail the type of test machine and any pertinent fixtures. In turn, the results should be reported with all the specifications.
8.2.2
Selecting Strain Amplitude
At a given set of conditions, the cycles to failure at constant strain amplitude follow a power law often written as ⎛ε ⎞ N =⎜ a ⎟ ⎝ ε0 ⎠
k
(8.1)
where N is cycles to failure, ε a the strain amplitude, and ε 0 and k are constants. In selecting a strain amplitude for the first test of a new elastomer, the test engineer should pick an amplitude that will give a relatively short life. This guesstimate can be made by comparison to other tests of similar rubbers, or even just from a textbook example. The procedure is to pick an amplitude to give a failure in an hour or less. Then, a second guess is made, but this time only the slope, k, need be estimated. After the second test the engineer will have two data points to establish the curve. Now the procedure is more exact. The engineer may fill in gaps or extrapolate for high cycle tests as needed.
8.3
Failure Criteria
In order to measure the fatigue life of a test specimen, the instant of failure must be determined. The manner in which “failure” is defined will powerfully influence the cycle count. The problem is to select a clear, easy to establish criterion of failure, which reasonably corresponds to failure of the component in service. In strain-life testing there are several possible criteria. 1. Complete rupture as in metal testing 2. Load drop by some specified percentage 3. Onset of cracking 4. Crack size
8.5 Combined Strain State
119
Complete rupture works quite well in a tension cycle test. There is a sudden drop to zero load which is easily recorded, or the test machine may respond in some fashion, or there may be a load noise, and so on. However, as noted above, rubber components are not usually designed to pass their major fatigue loads in tension. The use of the load drop implies that the failure does not take place as a sudden rupture, but as gradual crack growth, which is evidenced as a drop in load. The method is best employed in a stroke-controlled shear cycle test. In such a test, the mean cyclic load will decline with time or cycles due to cyclic stress-relaxation. The load-cycles curve can be traced on a graphical output or later plotted from a digital output. If the decline is purely stressrelaxation, the curve will be a straight descending line on a log-log plot. The point at which the crack begins to grow will be marked as a departure below the straight line. It is a simple matter to plot the extension of the straight-line curve and a parallel line some fixed percentage below it. Failure then is that point where the actual curve of the cracking specimen intersects the parallel lower curve. It remains only to select what percentage of load drop will be designated as “failure.” Historically, the onset of cracking has often been used to mark the end of fatigue life. It can be used for shear and compressive cycle testing; however, it implies visual tracking by test personnel. As noted above, a departure from the cyclic stress relaxation curve may also be used, but this is less accurate. As the test program calls for lower amplitudes, the length of specimen life may easily exceed 24 hours. While 24 hour-a-day, 7 days-a-week tracking can be aided by taping a television record of the specimen in testing, the method obviously becomes more costly and less convenient. Crack size can be used as a failure criterion. It is, in effect, the same idea as the percent load drop without the need to track the stress relaxation curve. In tensile tests conducted on long “pure shear” specimens it can be practical. As a failure criterion in shear testing, crack size suffers from the same disadvantages that crack onset does.
8.4
R-Ratio
R is the ratio of the minimum strain of the cycle to the maximum. That is R = ε min /ε max
(8.2)
The R-ratio is illustrated in Fig. 8.1. To estimate strain-life, Walkers [1] empirical equation, which converts strain amplitude data taken at various R-ratios to an effective value at R = 0, is covered in detail in Chapter 9.
8.5
Combined Strain State
The most common combined strain state for rubber components is shear with compression. Rubber pads experience this condition in helicopter rotor bearings, bridge and
120
Figure 8.1
8 Fatigue Testing
R-ratios for three strain cycles
building bearings, and offshore piping flexible joint bearings. In these cases, the pad is designed to accept a high compressive load through thickness and shear deflections in the plane of the pad. Pad compression increases the fatigue life significantly and must be accounted for in testing. Once a specimen is deformed by the applied load, the only strains that can be directly measured are those on the surface. That means that determination of the interior strain (or stress) state is left to calculation. The finite element method is by far the best for this purpose. In Chapter 9, the shear fatigue testing of an acrylonitrile is described where the data was taken from pads under compression. In this case, finite element analysis was used to predetermine the maximum bulge shear strain when the specimen was squeezed by a certain measurable displacement. Then a screw clamp was set to compress the specimen by the amount calculated in the finite element analysis and the result reported in terms of the bulge shear strain. It is a recommended method to deal with this particular combined strain state. Another common combined strain state is found in bushings under transverse shear. When the rod at the center of the bushing is displaced radially, the region opposite the displacement experiences biaxial tension, see Fig. 8.2. The additional tensile component must also be accounted for in testing.
Figure 8.2
Center rod in bushing displaced radially downward
8.6 Wave Form
8.6
121
Wave Form
Most fatigue testing employs either a sinusoidal or sawtooth wave. While in metals some testing indicates a sawtooth wave is more “damaging” than a sinusoidal one, there is no corresponding data for elastomers. Nor have other waveforms, such as square waves or slanted sawtooth, been investigated. These shapes are illustrated in Fig. 8.3. Once the wave form is specified, achieving it over the duration of the test, particularly in a load or stress controlled tension tests can be a challenge. The measurement of maxima and minima, and therefore, the amplitude and R-ratio will be greatly affected by cyclic creep changing the unloaded length of the specimen. Thus, to maintain the particular stresses of the intended cycle, the machine stroke settings must be adjusted as the test progresses. However, the majority of the elongation occurs in the first few cycles, generally less than a hundred, so the period of frequent adjustment is usually short. However, adjusting the stroke should be continued throughout the test. The second consideration is to determine on what length to base the strain calculation. The author has found that the most consistent results were obtained when the fresh length taken before the first cycle was used. There is one caveat; in some testing machines, the clamping of a pure shear specimen extrudes enough material out from between the clamps so that the base length for strain computation is changed by clamping. In such cases, the length and the zero displacement position should be established after clamping. The effect of variation in wave form in rubber fatigue is unknown and often unreported. In metal fatigue, some work has been done regarding the effect of cycle waveform on fatigue crack growth, but none has been reported in the literature for rubber. In metals, sharp reversals seem to increase fatigue crack growth somewhat, that is, a sawtooth wave is more destructive than a sinusoidal wave. Given the internal heat generation of elastomers at high strain rates, it may be that at equal frequencies back slanted sawtooth or square
Sinusoidal Black slanted sawtooth
Sawtooth
Trapezoidal Square wave
Figure 8.3
Wave forms
122
8 Fatigue Testing
waves may produce a shorter fatigue life. The author has had experience with sawtooth and sinusoidal waveforms (Fig. 8.3) in rubber fatigue and has not seen an effect. At this point, the effect must be described as unknown but probably small.
8.7
Creep and Stress Relaxation
In tensile fatigue tests, elastomers respond to a stress-controlled test by a significant elongation with time. The magnitude of this cyclic creep is much greater than for metals and makes it more difficult to conduct the test. As noted above, to create a stress-life curve for a particular elastomer, a test machine whose stroke is continually adjusted to keep the stress cycle approximately constant, must be employed. Hence the machine must be computer controlled by a feed back loop from the load sensor or be continually adjusted by its operator. In constant stroke amplitude shear fatigue tests the maximum cyclic load will decline with the number of cycles. This phenomenon is called cyclic stress relaxation. Cyclic stress relaxation has been shown to follow a power law of the form ⎛N⎞ Pmax = ⎜ ⎟ ⎝C⎠
p
(8.3)
where Pmax is the peak cyclic load, and N is the number of cycles. The empirical constant p is negative, corresponding to a downward slope, and C is the number of cycles with Pmax = 1. Equation 8.3 indicates that in testing one expects that the Pmax vs. N curve will be a downward sloped straight line on a log-log plot. Deviation below this line indicates that cracking is occurring. Stress relaxation can best be estimated from a record of peak stress for constant strain amplitude cycles. Analogously, creep is measured by recording maximum elongation for constant stress or constant load cycles. These measurements need not be made every cycle but can be made every thousand cycles. Since the data is plotted on a log cycles graph and the phenomenon has a log-log relationship, it is logical that an approximate logarithmic increment be used to establish measurement points. For example, make measurements at 10, 30, 100, 300, 1000, 3000, etc. cycles.
8.8
Frequency and Strain Rate
Frequency has a strong effect; however, it cannot be distinguished from simple elevated temperature. In fact, in some testing, control of the test frequency has been employed to refine the specimen temperature during cycling. As cyclic rates increase, rubbers produce heat internally at higher rates. This heat production is due to hysteresis and is thought of
8.9 Effect of Temperature
123
as internal friction opposing deformation. Thus, heat production increases with strain rate. In fatigue testing to date, it has not been possible to distinguish the effect of temperature increase due to the environment from that produced by hysteretic heating. Hence, to deal with this effect in fatigue testing, consider frequency simply a way to elevate temperature.
8.9
Effect of Temperature
Temperature has a powerful effect on cycles to failure. Life can be doubled or halved by a change of only 10 °C. Over modest ranges of temperature change, say less than 100 °C, the cycles to failure at differing temperatures can be correlated. In Chapter 9, three methods are described: the ratio of Arrhenius functions, Nagel’s equation [2], and a simple linear approximation. In the case of shear fatigue it is relatively easy to get accurate measurements. The recommended specimen for shear fatigue is the dual-lap shear specimen with disc pads illustrated in Figure 8.4. Disc pads have uniform compressive bulge so compression can be imposed without creating irregular strains around the rim. Since the bars are made of metal which has great conductivity compared to the rubber, a thermocouple placed in a small hole drilled close to the rubber pad in one of the bars will give an accurate reading.
Figure 8.4
Dual-lap shear with disc specimen
124
8 Fatigue Testing
The dumbbell tensile specimen (Fig. 8.5) presents a greater challenge. If the cycling is stopped to use a thermocouple on the surface, it must be assumed that the specimen will cool somewhat between the time the cycling stops and the temperature probe reaches equilibrium with the specimen. An estimate of the cooling effect can be made by creating a finite element heat transfer model of the specimen, probe, and test chamber air. In testing, experimenters often assume the room or test oven air temperature is the specimen temperature. If the cyclic rate is relatively low and the specimen small in mass, this approximation may be sound. The simplest approach to controlling the specimen temperature during cycling is water immersion.
Figure 8.5
8.10
ASTM D412 die “C” specimen
Liquid Immersion
Immersion of the elastomer in a liquid has potentially two effects. One effect is for the liquid is to carry off the hysteretic heat created in cycling and thereby reduce temperature excursions. In fact, to gain control of the specimen temperature at high cyclic rates, water immersion can be the solution. On the other hand, for elastomers operating in some liquids, the liquid can contribute greatly to deterioration of the rubber molecules. Various oils and other substances can break down polymer chain bonds, returning the rubber to a soft sticky state or stiffen and embrittle the material by increasing the crosslinking. Deterioration by liquid immersion can be a major factor in decreasing the useful life of an elastomer part and thus the environment must be included in the testing of the elastomer for such an application. Where the liquid is known to have a deleterious effect on the rubber properties, only testing in that liquid can adequately simulate the environment and produce relevant fatigue life results. One approach to reduce test duration is to run a “hot test.” In such a test the specimens are cycled to failure at the same amplitude and R-ratio at two temperatures.
8.13 Batch Variation
125
The results are then used to establish an activation energy for the Arrhenius function for that process. Employing the Arrhenius equation, the life at a lower temperature can be estimated. The hot test has the advantage of producing a life estimate in much less time than the one needed for testing to failure at the lower operating temperature. This method is shown in Chapter 9.
8.11
Recovery
It is a common experience in testing for the machine to stop for one reason or another. As noted earlier in stress-strain testing, the immediate result of a pause in an extension cycle will be a gradual drop in stress, if the displacement is held and an increase in the stress when the machine resumes the extension. In a stress-strain test where the curve is to be standardized at a particular number of cycles, say five, the test result is thereby invalidated. However, in a fatigue test where there are thousands perhaps millions more cycles to go, the effect of a short halt and temporary recovery of stress is of no importance. Generally, the peak load curve will return to its original path after a pause in cycling of a few minutes.
8.12
Scragging
In some industries, physical testing of rubber is conducted after the specimen has been “scragged.” Scragging means to put the specimen through several cycles of stretching or deformation before measurements are taken. Sometimes no record of stress, strain, or other parameters is made during such a process. Any scragging should at least be standardized and recorded. Generally, there is no need to scrag a fatigue test specimen or to exclude the early cycles of a fatigue test from the record. It is also undesirable to scrag rubber specimens before a stress-strain curve is to be produced. On the other hand, for stress-strain curves, a specific number of controlled extension cycles made before the one to be used in analysis is good practice. The number of such preparatory cycles should be selected so the resulting curve is representative of the service condition.
8.13
Batch Variation
Stress-strain testing of various elastomers frequently shows variation from batch to batch. There is little corresponding data from fatigue testing to show how great batch variation might be. However, the shear fatigue data in the example of Chapter 9 contained two batches and showed no apparent difference between the batches.
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8 Fatigue Testing
While batch variation in stress-strain testing is significant, it is not known how significant such variation is in fatigue life testing. Nevertheless, specimen should be tracked individually and identified by batch. Since many elastomers will change properties with long term exposure to room temperature, the storage conditions for specimens should be specified.
8.14
Storage
Since specimens can be manufactured on one date and tested weeks or even years later, it is important to report the date of manufacture as well as the date of the test and to describe the conditions of storage.
Acknowledgements The author is grateful to his former associates at Oil States Industries, Arlington, Texas for the use of the test lab and their support and coaching test procedures.
References 1
Walker, K., “The Effect of Stress Ratio During Crack Propagation and Fatigue for 2024-T3 and 7075-T6 Aluminum,” Effects of Environment and Complex Loading History on Fatigue Life, ASTM STP462, American Society for Testing and Materials, Philadelphia, 1970, pp. 1 – 14.
2
Nagel, W.B., “Design with Rubber, Parts 1, 2, 3 and 4: The Design Surface,” Machine Design, Jun 23, 77, Penton Publications.
3
Mott, P. H. and Roland C. M., “Aging of Natural Rubber in Air and Seawater,” Rubber Chemistry and Technology, Vol 74, 2001, pp 79 – 88.