Effect of Frequency, Environment, and Temperature on Fatigue Behavior of E319 Cast-Aluminum Alloy: Small-Crack Propagation
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Abstract
The influence of test frequency on fatigue-crack propagation behavior of small cracks in E319 cast-aluminum alloy was studied using ultrasonic and conventional test techniques. It was observed that fatigue cracks grow faster at 30 Hz than at 20 kHz in air at both 20 °C and 250 °C. The effect of frequency on the fatigue-crack growth rates was attributed to an environmental effect. For E319 cast-aluminum alloy, fatigue-crack growth rate increases with increasing water exposure (characterized by the ratio of water partial pressure over test frequency, P/f), and this behavior can be estimated using a modified superposition model. The effect of temperature on fatigue-crack growth behavior was primarily attributed to the effect of temperature on Young’s modulus and yield strength. The environmental contribution to fatigue-crack growth rates modestly decreases with increasing temperature.
1 Introduction
Cast-aluminum alloys have been extensively used in the production of fatigue- critical automotive components, including engine blocks and cylinder heads, which experience more than 10^{8} alternating stress cycles during the expected service life, and the very high-cycle fatigue properties are therefore of great interest. Performing fatigue tests in the very high-cycle regime becomes practical with the use of ultrasonic-testing instrumentation, which operates at approximately 20 kHz. Ultrasonic-fatigue techniques can also be used for rapid generation of fatigue-crack growth data and offers the possibility to study very low fatigue-crack growth rates far below the conventional threshold (10^{−10 }m/cycle). However, in actual components of cast-aluminum alloys, the critical locations are subjected to a loading frequency of 20 to 100 Hz, which is two to ten decades lower than the ultrasonic-fatigue testing frequency. Therefore, it is necessary to know if the fatigue properties are significantly influenced by the substantial increase in the cycling frequency.
Fatigue-damage evolution can be divided into crack initiation and crack propagation. It has been widely concluded that, for cast-aluminum alloys, fatigue cracks initiate predominantly from pores located at or close to the specimen surface, and the number of cycles required to initiate a crack is insignificant relative to the total fatigue life. Therefore, the fatigue life is dominated by crack propagation in cast-aluminum alloys[1, 2, 3, 4] and determining the effect of frequency on fatigue-crack propagation is important in understanding the effect of frequency on the S-N behavior.
The effect of frequency on fatigue-crack propagation in aluminum alloys may arise from intrinsic effects, i.e., strain-rate effect, and time-dependent, or extrinsic, effects, such as those attributable to environmentally assisted crack growth or fatigue/creep interaction. It is unlikely that strain rate exerts a significant influence on fatigue-crack propagation in aluminum alloys because plastic deformation of face centered cubic metals has been reported to be relatively insensitive to strain rates.[5, 6, 7] Holper et al.[8,9] investigated the effect of frequency on fatigue-crack growth of aluminum alloys at 20 kHz and 20 Hz in vacuum and found no frequency influence on near threshold fatigue-crack growth in aluminum alloys. Also, cyclic loading near the fatigue limit or fatigue-crack growth near the threshold stress intensity involves only minimal cyclic plastic deformation, thus strain-rate effects should be significantly moderated or absent.[8,9]
When the effect of strain rate is small, a dependence of crack-growth rate on frequency is expected to be related to environmental influences. It has been observed that the fatigue-crack growth threshold decreased and fatigue-crack growth rate increased in the presence of water vapor in atmospheric air for aluminum alloys.[10, 11, 12, 13, 14, 15, 16, 17] Because the duration of crack-tip opening under ultrasonic-frequency loading at 20 kHz is an order of magnitude shorter for each cycle than for conventional fatigue experiments, any environmentally assisted increase in fatigue-crack growth rate is generally presumed to be less pronounced at 20 kHz, leading to lower fatigue-crack growth rate at this frequency. Holper et al.[9] studied the influence of frequency on fatigue-crack growth of aluminum alloys and reported that fatigue cracks propagated at lower growth rates at 20 kHz than at 20 Hz in ambient air if cycled above threshold; however, the test frequency had no influence on the fatigue-crack growth threshold itself.
In this article, the fatigue-crack propagation behavior of a 319-type cast-aluminum alloy (referred to as E319) was studied at ultrasonic and conventional cyclic frequencies at 20 °C and 250 °C to understand the potential effect of frequency and environment at ambient and elevated temperature. In a companion article,[18] the effect of frequency, environment, and temperature on S-N behavior of E319 cast-aluminum alloy will be addressed in detail.
2 Experimental
2.1 Material
Yield Strength, Tensile Strength, Elongation, and Dynamic Young’s Modulus of E319 Cast Aluminum at 20 °C, 150 °C, and 250 °C
Temperature (°C) | Yield Strength (MPa) | Tensile Strength (MPa) | Elongation (Pct) | Young’s Modulus (GPa) |
---|---|---|---|---|
20 | 199 | 290 | 2 | 77.5 |
150 | 181 | 223 | 5 | 71 |
250 | 123 | 147 | 7 | 66 |
2.2 Fatigue Testing
For comparison, conventional fatigue tests were conducted at 30 Hz using servohydraulic fatigue-testing equipment under load control. Fatigue testing was conducted under fully reversed tension-compression loading in lab air at 20 °C and 250 °C. Specimens were heated in an electric-resistance furnace during conventional-fatigue testing at 250 °C.
2.3 Fatigue-Crack Growth
A stress amplitude of 95 and 80 MPa was applied for 20 °C and 250 °C, respectively. Cracks were observed with the aid of a QUESTAR^{1} telescope mounted on the test frame. Crack-length measurement was done by acquiring digital images using National Instruments IMAQ^{2} Vision Builder software and processing the images using ADOBE PHOTOSHOP^{3} software. The resolution of the crack-length measurement was close to 1 μm. The crack length projected in the pure-mode I plane was used for analysis.
The cyclic crack-growth rate, da/dN, was determined from the crack length vs number of cycles using a three-point sliding polynomial method described in ASTM E647. The stress-intensity factor range, ΔK, corresponding to a given crack length was calculated using a solution presented by Newman and Raju[24] for a surface crack growing in a finite plate. Only the tensile portion of the applied stress range was used to calculate ΔK.
This study is intended to ascertain the growth rates of small fatigue cracks, indicative of those initiating at pores. The experimental setup used to optically monitor and digitally record crack growth, coupled with the absence of an initiation lifetime, allowed detection of crack growth directly from the notch. Therefore, no precracking was necessary. However, calculations of crack-growth rates were only made when crack lengths exceeded 20 pct of the notch length to avoid artifacts from the stress-concentration field of the notch.
2.4 Environmental Control
Ultrasonic-fatigue specimens were tested at room temperature in various environments, i.e., ambient air with relative humidity (RH) of approximately 20 to 90 pct, distilled water, and dry air (approximate RH of 0.1 to 0.2 pct).
Dry air was generated by cooling the air using liquid nitrogen to temperatures below −50 °C where the water vapor condensed, reducing water-vapor partial pressure to below 5 Pa. The water-vapor partial pressure in the dry air was measured by a hygrometer, which can continuously monitor water-vapor partial pressure from 0.05 to 100 Pa. The dry air was subsequently pumped into the specimen chamber, which was attached to the load train at vibration nodes to avoid damping the vibration. To facilitate optical observation of crack growth, the specimen chamber was equipped with a flat window.
3 Results and Discussion
3.1 Effect of Frequency and Environment on Fatigue-Crack Propagation at 20 °C
Calculated Water Exposure in Various Environments
f (Hz) | P (Pa) | P/f (Pa s) | |
---|---|---|---|
Dry air | 20,000 | 5 | 2.5 × 10^{−4} |
Lab air | 20,000 | 935 | 0.05 |
Water | 20,000 | 10^{5} | 5 |
Lab air | 30 | 935 | 31 |
Lab air | 1 | 935 | 935 |
Three possible mechanisms for hydrogen-assisted cracking have been proposed:[27] hydrogen-enhanced decohesion, adsorption-induced dislocation emission, and hydrogen-enhanced localized plasticity. However, in the current study, it was not possible to determine which mechanism is operative based on the fracture-surface morphologies. The subtle change of fracture-surface morphology with water exposures indicates that, although the fatigue-propagation behavior is influenced by water exposure, the response of fatigue-crack growth rate to the water exposure for the investigated E319-T7 cast-aluminum alloy is not as significant as for those aluminum alloys, which exhibited obvious morphology change of fracture surface in different environments.[25]
3.2 Effect of Frequency and Temperature on Fatigue-Crack Propagation at 250 °C
3.3 Mechanisms and Modeling of Environmental Effect on Fatigue-Crack Propagation
These three steps operate in sequence, and the crack-growth response is governed by the slowest process in the sequence. To determine the rate-limiting step, the time needed for each step can be roughly estimated as follows.
By comparing t_{1}, t_{2}, and t_{3}, it can be seen that the time for migration of water molecules to crack tip is much longer than that for either surface reaction or hydrogen diffusion. Therefore, migration of water molecules is the rate-limiting step. This is consistent with the results by Wei et al.,[15,29] i.e., for highly reactive gas-metal systems, such as water vapor and aluminum, hydrogen-assisted fatigue-crack growth is controlled by the rate of transport of water molecules to the crack tip.
The environmental contribution to the fatigue-crack growth rate is assumed to be determined by the concentration of hydrogen atoms at the crack tip produced in each loading cycle. The hydrogen concentration can be considered as a bridge that connects the influence of water on surface reaction kinetics and the resultant crack-growth performance. However, the concentration of hydrogen is controlled not by hydrogen diffusion or the fracture-surface reaction but by transport of water to the crack tip. To quantify the concentration of hydrogen, the concentration of water available on the fresh fracture surface has to be determined, and this value is limited by Knudsen flow[30] of water vapor from the surrounding environment to the crack tip.
Interestingly, the dependence of fatigue-crack growth rate on water exposure closely follows the assumed dependence of hydrogen concentration on water exposure, as shown in Figure 7. The observed saturated environmental effect on crack-growth rate and the estimated saturated concentration of hydrogen occur at approximately the same water exposure (P/f = 26 Pa s). This correlation strongly supports the assumption that the increase in crack-growth rate caused by environment is determined by the concentration of hydrogen at the crack tip. Thus, (P/f)_{s} is termed the saturation water exposure, above which hydrogen concentration at the crack tip and fatigue-crack growth rate are independent of P/f.
Wei et al.[15,29] proposed the following superposition model to quantify the effect of water exposure on the fatigue-crack growth rate:
Here, (da/dN)_{tot} is the fatigue-crack growth rate in a deleterious environment and can be described as the sum of two independent components, (da/dN)_{mech} and (da/dN)_{env} (da/dN)_{mech} is the fatigue-crack growth rate in an inert environment (called pure-mechanical fatigue-crack growth rate); (da/dN)_{env} is the environmental contribution to the fatigue-crack growth rate (called environmental fatigue-crack growth rate). When the environmental effect becomes saturated, (da/dN)_{tot} reaches the maximum value, (da/dN)_{sat} (saturated fatigue-crack growth rate). The environmental fatigue-crack growth rate is determined by (da/dN)_{mech}, (da/dN)_{sat}, P/f, and (P/f)_{s}. The values of (da/dN)_{mech} and (da/dN)_{sat} can be estimated based on the experimental observations in Figure 7. At a constant ΔK of 2 MPa \(\sqrt {\text{m}} \), (da/dN)_{mech} was assumed to be 10^{−11 }m/cycle, which is equivalent to the crack-growth rate in dry air at 20 kHz, where the environmental effect is very small and the crack growth can be reasonably considered as “pure-mechanical.” (da/dN)_{sat} was assumed to be 10^{−9 }m/cycle, which is the average fatigue-crack growth rate in ambient air at 30 and 1 Hz where the environmental effect is saturated.
The square-root correlation between (da/dN)_{env} and C_{H} suggests that the response of fatigue-crack growth rate in E319-T7 cast-aluminum alloy to water exposure is less significant than presumed in the superposition model, which has successfully modeled fatigue-crack growth rate for some peak-aged (T6) aluminum alloys.[15,29] In other words, the role of hydrogen concentration in increasing of fatigue-crack growth rates might be different for T7 and T6 heat-treated aluminum alloys. T6 heat treatment promotes localized plastic deformation within a single-slip system in each grain along the crack front, while T7 heat treatment favors a wavy slip mechanism.[26] In ambient air, the single-slip mechanism, which is operative in the peak-aged alloy, is assumed to offer a preferential path for hydrogen-assisted cracking, which leads to a stronger environmental effect. In contrast, in the T7 heat treatment, local hydrogen concentration would be less deleterious to fatigue cracking, as indicated by the square-root dependence.
As such, for E319-T7, the superposition model was then modified as follows:
These results indicate that a significant effect of frequency on fatigue-crack growth can be expected when E319 cast-aluminum alloy is tested in ambient air at ultrasonic frequency (20 kHz) and conventional frequency (10 to 100 Hz). Fatigue-crack growth rates increase with increasing water exposure and then become independent of water exposure when the environmental effect saturates. In ambient air, fatigue testing at 20 kHz represents water exposure of 0.05 Pa s. In this condition, a hydrogen-assisted increase of fatigue-crack growth rate would occur, but the extent of environmental effect on crack-growth rate is moderate because the water exposure in this condition is well below the exposure for saturated environmental effect. On the other hand, fatigue testing at conventional frequencies (approximately 10 to 100 Hz) represents water exposure of approximately 9 to 94 Pa s, which is within, or very close to, the regime of saturated environmental effect. Since ultrasonic fatigue in ambient air represents less water exposure than conventional fatigue, the concentration of hydrogen responsible for an increase in crack-growth rate is less and, thus, the environmental fatigue-crack growth rate at ultrasonic frequency is lower than that at conventional frequency. The observed fatigue-crack growth rate is assumed to be the sum of the pure-mechanical fatigue-crack growth rate and the environmental fatigue-crack growth rate. Therefore, the observed crack-growth rate at ultrasonic frequency is lower than that at conventional frequency.
The correlation of fatigue-crack growth rate with water exposure provides a method to account for the influence of frequency that is caused by an environmental effect. Crack-growth behavior in vacuum (very low water exposure) and in air at low testing frequency (very high water exposure) can be treated, respectively, as the lower bound and the upper bound of crack-growth rates in environment. With these two bounds as references, crack-growth rates at any given frequency or water partial pressure can be estimated. When specimens are tested at 20 kHz in laboratory air, the relative humidity might fluctuate from 20 to 90 pct. In this case, the water exposure varies from 0.02 to 0.1 Pa s, and the corresponding crack-growth rate changes within a factor of 2. When specimens are tested at 30 Hz in laboratory air, water exposure varies from 16 to 70 Pa s, and the fatigue-crack growth rates are close to the saturation fatigue-crack growth rate when the relative humidity fluctuates from 20 to 90 pct. Therefore, at both ultrasonic frequency and conventional frequency, fluctuation of humidity in laboratory air does not significantly influence the fatigue-crack growth results.
In Engler-Pinto, Jr. et al.,[16,35] it was reported that the higher the yield strength, the greater the influence of the water on crack propagation for some cast Al-Si alloys. This is possibly because the higher-yield strength is obtained from peak-aged (T6) heat treatment, and the peak-aged aluminum alloy was found to be more sensitive to environmental effect than the overaged alloy.[26] For these peak-aged alloys, the superposition model proposed by Wei et al.[15,29] would be expected to give a better prediction of the effect of frequency on fatigue-crack growth rate. As shown in Figure 14, by assuming a linear correlation between (da/dN)_{env} and hydrogen concentration, the fatigue-crack growth rates in ambient air at 20 and 30 Hz differ by two orders of magnitude.
Because the crack-growth rate in environment, (da/dN)_{tot}, is a function of temperature and Young’s modulus when other parameters are constant, this model is also applicable for predicting environmental effect at elevated temperature. This issue is addressed in Section D.
3.4 Mechanisms And Modeling of Temperature Effect on Fatigue-Crack Propagation
Because the crack-growth rates have been observed to be influenced by the presence of water vapor in laboratory air, a question arises: is the effect of temperature on crack-growth rates related to an influence of temperature on the mechanical properties or to the temperature dependence of an environmental effect? The modified superposition model provides a basis to separately investigate the effect of temperature and environment. When temperature increases, the pure-mechanical fatigue-crack growth rates are expected to increase because of greater cyclic plasticity, greater accumulated fatigue damage, and, thus, lower cyclic strength of aluminum alloys. The environmental fatigue-crack growth rates are also expected to change with increasing temperature. Based on Eq. [18], the environmental contribution to fatigue-crack growth rate is proportional to (\( {\sqrt {E{\sqrt T }} }\))^{−1}. Therefore, (da/dN)_{env} decreases with increasing temperature, which can be explained by the lower concentration of hydrogen available. At higher temperature, the molecular density of water vapor at a constant pressure is decreased due to volume expansion, and the number of water-vapor molecules that are transported through the crack by Knudsen flow is decreased. Thus, the concentration of water vapor and the concentration of hydrogen produced are decreased. On the other hand, Young’s modulus decreases with increasing temperature, and this will increase crack-opening displacement and, in turn, make it easier for water molecules to migrate to the crack tip. Therefore, (da/dN)_{env} is expected to decrease with increasing temperature, but the decrease is offset by the simultaneously decreased Young’s modulus.
To investigate the combined influence of temperature and frequency on crack propagation of E319 cast-aluminum alloy, Eqs. [18] and [19] were modified as follows to take into account the effect of temperature on fatigue-crack growth behavior:
It would be helpful if (da/dN)_{mech} and (da/dN)_{sat} at 250 °C were known. However, this information is not available. So we assume that (da/dN)_{mech} and (da/dN)_{sat} obtained at room temperature apply for all temperatures after normalization of the stress-intensity factor range by Young’s modulus and yield strength; i.e., at equivalent levels of ΔK/(Eσ_{ys}), \( {\left( {\frac{{da}} {{dN}}} \right)}^{{{\text{250}}^{{\text{o}}} {\text{C}}}}_{{{\text{mech}}}} = {\left( {\frac{{da}} {{dN}}} \right)}^{{{\text{20}}^{{\text{o}}} {\text{C}}}}_{{{\text{mech}}}}\), and \( {\left( {\frac{{da}} {{dN}}} \right)}^{{{\text{250}}^{{\text{o}}} {\text{C}}}}_{{{\text{sat}}}} = {\left( {\frac{{da}} {{dN}}} \right)}^{{{\text{20}}^{{\text{o}}} {\text{C}}}}_{{{\text{sat}}}}\).
4 Conclusions
- 1.
The crack-growth rate of E319 cast-aluminum alloy in laboratory air at 20 kHz is lower than at 30 Hz at both 20 °C and 250 °C. The difference in fatigue-crack growth rates in air between 20 kHz and 30 Hz is attributable to an environmental effect.
- 2.
The presence of water in air was found to increase the fatigue-crack growth rate. At a given stress-intensity factor range, ΔK, fatigue-crack growth rate increases with water exposure, P/f, until it reaches the maximum value when saturation of the environmental contribution occurs. Fatigue testing at 30 Hz in air represents higher water exposure than fatigue testing at 20 kHz, and, therefore, the crack-growth rates at 30 Hz are higher than that at 20 kHz. The dependence of crack-growth rate on water exposure closely follows the dependence of hydrogen concentration on water exposure, which supports the assumption that the enhancement of crack-growth rate caused by environment is determined by the concentration of hydrogen in the plastic zone.
- 3.
The effect of frequency and environment on fatigue-crack growth rate is characterized by a modified superposition model. In this model, hydrogen-induced increase of fatigue-crack growth rate is assumed to be proportional to the square root of hydrogen concentration, which is determined by the transport rate of water molecules from the surrounding environment to the crack tip. Based on this model, fatigue-crack growth rates over the entire range of ΔK in various environments with different water exposure can be predicted, and the predictions generally agree well with the experimental observations.
- 4.
The fatigue-crack growth rate at all temperatures can be successfully described by a universal version of the modified superposition model, in which crack-growth rate is a function of normalized stress-intensity factor range, ΔK/(Eσ_{ys}). This model provides a framework to separately characterize the intrinsic effect of temperature on mechanical properties and the effect of environment at elevated temperature. The effect of temperature on fatigue resistance primarily results from the intrinsic effect of temperature on Young’s modulus and yield strength. The environmental contribution to fatigue-crack growth rates modestly decreases with increasing temperature.
- 5.
These results show that environmental effects need to be considered when ultrasonic fatigue is used to generate fatigue data for modeling the fatigue property of the aluminum-alloy components that operate under conventional loading frequency in service. A modified superposition model was proposed to characterize the hydrogen-induced increase of fatigue-crack growth rates in E319 cast-aluminum alloy. Although based on numerous assumptions, this model provides a basis for investigation of frequency effect on fatigue behavior due to environmental effect at both room temperature and elevated temperature.
Footnotes
Notes
Acknowledgments
Financial support provided by the United States National Science Foundation (Grant No. DMR 0211067) and Ford Motor Company is gratefully acknowledged. The authors thank C.J. Torbet for his assistance with environmental control, A. Shyam for his advice on small crack-growth testing, and J. Yi for helpful discussions.
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