Effect of Hold Time Periods at High Temperature on Fatigue Life In Aluminum Alloy 2024 T4

In s ome a pplications, the alumin um alloy 2024 T4 may be subj ected to an interaction of fatigue and creep effects at high t emperature. This paper investigates the effect of this interact ion by studyi ng the effect of co nstant amplitude fatigue (CAF) and cree p separately, and the n fatigue-creep interaction is introduced by testing the alloy under constant amplitude with some holding time periods through th e test at high tempera ture (150 o C). The results showed that the life time of the alloy decreases due to fatigue-creep interaction as c ompared to creep alone in about 77%, and in about 80% as compared with fatigue alone. This is a result of accumulated fatigue damage superimposed on cree p damage. Creep allows more free spaces for f atigue cracks paths that accelerate failure. A theoretical model to calculate the time to failure due to fatigue-creep interaction has been proposed. This theoretical interaction model predicts ve ry close time to failure values to the experimental results.

The conclusions that derived from this work were the dynamic mechanical properties reduced by a factor of 1.6 to 2.4 and the static mechanical properties reduced by a factor of 1.3 to 1.8.
In the present paper, the effect of creep-fatigue interaction in Al 2024-T4 alloy will be studied.This will be achieved by studying the effect of fatigue, then creep separately, and finally, creep-fatigue interaction.

Experimental Work
This investigation presents firstly the analysis of chemical composition and mechanical properties at room and elevated temperature of the selected material (Al 2024-T4 alloy), then testing its static mechanical properties at room and elevated temperatures and comparing the results.Secondly, preparing the creep and fatigue testing machine and cutting the specimens from a rod of the Al 2024-T4 alloy to a suitable size and number, then arranging a furnace of a suitable size, which can be attached to the testing machine with a thermal controlling system to control the required elevated temperature.Thirdly, testing some of the specimens in creep only, and another group in constant amplitude fatigue only at elevated temperature, then making an interaction between creep and fatigue on the rest specimens.Moreover, for each step of testing, a comparison of results is made with the other steps.

Material
The selected material for the experimental work is 2024-T4 aluminum alloy, which is an aluminum copper alloy of wide industrial use, mainly airplanes and aerospace industries, due to its desired mechanical properties such as light weight and high corrosion resistance [4].
The nominal and experimental chemical composition in percentage weight (%wt) of the selected material is shown in Table (1).
Two static tensile tests are performed, the first is at room temperature (approximately 30 o C), while the second is at elevated temperature (150 o C), which is the creep temperature of the alloy in this investigation [5].
The specimens are prepared for these tests according to the testing machine recommendations.Table (2 The applied constant stresses at the creep temperature for the ten specimens were (300, 275, 260, 250, 225, 210, 200, 175, 160, and 150) MPa.The specimen is considered as a cantilever beam due to type of loading in the testing machine as shown in ), and is equal to (62 GPa); and I is the second moment of inertia of the specimen, which is equal to (12.566mm 4 ).
So δ (yield) is equal to (18.4mm), and from triangular similarity, the real deflection of the specimen is (1.15mm), so the total strain will be (0.0903) as determined by Eqn. ( 5 2).It can be easily noted that the time to failure increases with a decrease in the applied stress.

Constant Amplitude Fatigue Test
In this test, the furnace was heated to about (150 C o ) after fixing it on a rotating bending fatigue tester.Twenty specimens of the alloy were subjected to the following stress amplitudes (300, 275, 260, 250, 225, 210, 200, 175, 160, and 150) MPa, two specimens were tested at each stress.
The recorded value of the number of cycles to failure was an average of two tests at the same stress amplitude.

Constant Amplitude Fatigue-Creep Test
The final test is an interaction test which contains both fatigue and creep effects.This test was achieved by rotating the specimen for n cycles at a stress and (150 C o ), then holding it for a period of time t h at same stress and temperature, then repeating the loading program until failure.The applied stresses at the creep temperature for twenty specimens were (300, 275, 260, 250, 225, 210, 200, 175, 160, and 150) MPa, two specimens were tested at each stress.
n represents the number of cycles required to initiate a crack.It has been suggest that n is approximately 0.9N ff [6], but this value may be different at elevated temperature.Al-Amiri [7] has determined fatigue properties of Al 2024T4 at room and elevated temperature and obtained a factor that takes into account the decrease in life due to increasing test temperature.It can be predicted that the number of cycles required to initiate a crack ( n) Holding time (t h ) i for the applied stress ( σ i ) was determined approximately as the time required for 1% strain and considered constant for each holding period to make the time to failure reasonable under creep-fatigue interaction as follows; where: ω is motor speed of the testing machine which is equal to (2850)rpm; Theory In this article, theoretical relationships between creep and fatigue behaviors will be established to find the interaction effect theoretically which will be compared later with the experimental results.

Creep Calculations
There are three stages of creep.The overall creep behavior can be represented by the following equation [8]: PDF created with pdfFactory Pro trial version www.pdffactory.com The overall strain ε can be calculated by strain energy [9]: ε= (2Tδ)/σ …….. (5) The initial strain ε i in the first creep stage can be determined by [10]: B and m can be determined experimentally.
The third stage is the failure stage and there is no problem in discarding it.

Constant Amplitude Fatigue Calculation
The fatigue curve of a material is obtained by many constant amplitude fatigue tests, and can be presented by the following equation [11]; Where i is the number of test, or (i=1, 2, 3,… h), and h is total number of tests and it is equal to (10) in this case.

Constant Amplitude Fatigue-Creep Effect Calculation
In this case, two effects contribute to the life of the specimen, these are fatigue and creep.The interaction allows the use of Miner ' s rule for material fatigue life evaluation [12].By converting the fatigue damage part in Eqn. ( 13) to time damage, the equation becomes: Thus, the total time to failure t f can be calculated theoretically as: The theoretical time to failure due to fatigue-creep interaction ( t f,the ) can be predicted by Eqn. ( 21).The main parameters needed for such prediction are t h , t fc , and t r at each stress amplitude.Besides, the damage value D is also needed.Trials of different values for D will be attempted to select the most appropriate value.The experimental damage D exp at an applied stress σ i can be calculated as follows:

Results and Discussion
Three principal results will be outlined and discussed.These include the results of creep tests, constant amplitude fatigue tests, and the interaction tests.

Creep Results
The failure in this test is defined as the yield failure, [9] i.e. failure occurs when the deflection of the specimen reaches yield deflection. Table (3) shows all the creep statistics obtained from the experimental results and Fig. (3) shows the strain rate-stress relationship for the alloy.The last three readings were obtained by extrapolation to reduce the time of experimental work.Hence, the creep behavior of Al 2024-T4 can be expressed as:

Constant Amplitude Fatigue-Creep Interaction Results
The results of the tests are outlined in Table (4).The theoretical values of the time to failure due to fatiguecreep interaction (Eqn.( 21)) have been calculated with three different D values, namely 1.0, 0.7 and 0.45.Table (5) shows the main parameters needed for such prediction; t h , t fc , and t r at each stress amplitude.In addition, the experimental damage value (D exp ) is also listed.The experimental S-N curve from interaction tests can be described by the following equation; ) shows the tensile properties from the two tests with the standard values of the alloy at room temperature.Each value is an average of three tests.Creep Test Ten specimens were subjected to creep tests at different constant stresses after fixing a small furnace (up to 250 C o ) on a creep tester.An extensometer was used for strain measurement.The furnace was heated to a temperature of (150 C o ) as the creep temperature for Al 2024 T4 alloy [5].

Fig
PDF created with pdfFactory Pro trial version www.pdffactory.comwhere, δ (yield) is yield deflection, and it is determined experimentally;T (yield) is the applied load at the yield stress, and it is equal to (10.5N);L is the moment arm length as shown in Fig.(1), which is equal to (160mm) E is the modulus of elasticity at (150 C o ) The experimental results of creep tests are shown by (stress-time) diagram in Fig. (

(
13) agrees the design criteria of Bhoje and Chllapandi [3], which assumed that the damage D is larger than the accumulated fatigue and creep damages as compared with Miner ' s rule.

Fig. ( 5 )
Compares the time to failure due to creep only, the theoretical values due to fatigue-creep interaction (Eqn.21) and the experimental values under fatiguecreep interaction tests.PDF created with pdfFactory Pro trial version www.pdffactory.comIt is evident that the introduction of fatigue cycling to creep tests accelerates crack initiation and propagation and hence reduces the time to failure; i.e. promotes early failure [1].The theoretical interaction model (Eqn.21), with a D-value of 0.45, predicts almost identical time to failure values to the experimental results.The theoretical predictions can be used in safe design calculations.Therefore, dependent on the degree of the required safety, the value of D is: 0 < D ≤ 0.45 …… (25) In fact, the value of the experimental damage ( D exp ) at all the constant stress amplitudes used in this investigation was found to be in the range: 0.430 ≤ D exp ≤ 0.442 …. (26) With an average value of 0.435.Therefore, the use of Miner rule, which assumes a D value of unity [13], is unsafe since it predicts longer lives (time to failure) than the actual live.Fig.(6) shows the effect of the hold times at high temperature on the number of cycles to failure as compared to constant amplitude fatigue only.It is clear that hold times at high temperatures accelerate failure by allowing the crack, which is initiated by fatigue cycling for n cycles, to propagate through holding time period by increasing space distances between grains of the material microstructure [14].The second fatigue cycling period and holding time period accelerates propagation of an already existing crack and the process continues until final failure occurs.
lower lives and the fatigue limit is decreased to (128 MPa) at 3.5x10 7 cycles due to the interaction.Fig.(7)  shows the safe and unsafe zones for safer design (D=0.45)depending on theoretical damages values as compared with Miner's assumption.ConculusionsThe following conclusions can be drawn from this investigation concerning fatigue-creep interaction at 150 °C in the Aluminum alloy 2024-T4: 1. Hold times at high temperatures at a constant stress during a constant amplitude fatigue test reduces the number of cycles to failure.2. There is a significant reduction in the time to failure during a fatigue-creep interaction test as compared to a pure creep test, especially at low applied stresses.3. A theoretical interaction model has been proposed which predicts very close time to failure values to the experimental results.

Figure
Figure (1) the Testing Machine