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Research on low cycle fatigue properties of TA15 titanium alloy based on reliability theory
Materials Science and Engineering A 430 (2006) 216–220
Research on low cycle fatigue properties of TA15 titanium alloy based on reliability theory Fuguo Li ∗ , Xiaolu Yu, Leikui Jiao, Qiong Wan School of Materials Science and Engineering, Northwestern Polytechnical University, Xi’an 710072, PR China Received 15 July 2005; received in revised form 11 May 2006; accepted 17 May 2006
Abstract This paper introduces a method to determine the symmetric cycle fatigue limit of TA15 alloy at given confidence γ and survival probability P. It gives a general method to calculate the true survival probability of this material fatigue limit. The median and data of the LCF at γ = 95% and P = 99.9% are acquired after studying the LCF properties of aircraft construction material TA15 at the temperature of 25 and 250 ◦ C. The strain–life curve, cyclic stress–strain curve and parameters of LCF are also achieved. These provide reference to analyze the reliability of aircraft construction and estimate the life. © 2006 Elsevier B.V. All rights reserved. Keywords: TA15 alloy; Low cycle fatigue; Reliability
1. Introduction With the requirement of aircraft construction integrity, reliability and durability improving, higher requirement is presented to LCF properties of utilized material. The titanium alloy TA15 is widely applied in large aircraft construction and its nominal composition is Ti–6Al–2Zr–1Mo–1V. This alloy was successfully developed in Russian at 1964. TA15 alloy, which is equivalent to Ti–8Al–1Mo–1V of America in properties, works at the temperature of 500 ◦ C and it is the general alloy of bar stock and sheet material. It is generally considered TA15 is a near␣ titanium alloy of high aluminum equivalency, its strengthen mechanics is mainly solution strength of Al and other elements and it cannot be strengthened by heat treating. So TA15 alloy is used at annealed condition, where the phase composition of the alloy is the matrix ␣ phase and a smaller volume fraction of the  phase. However, it is found the surplus quantity of the strength index is little in the study of large titanium alloy forging, and sometimes it can even not meet the requirement of the standard [1]. This paper measures and analyzes the LCF properties of TA15 according to applicable work condition of certain structure and loading conditions of aircraft, acquires strain–life curve at cyclic loading and determines its cyclic characteristic. These
provide fundamental data to the fatigue design and reliability analysis of structure. 2. Test procedures 2.1. Specimen preparation After related standard comparison and lots of experiment research, the shaped size of the specimen and the machining processing technique are determined in Fig. 1. The surfaces of the samples were in accurately machined condition, the transition circular arcs mechanically polished in order to avoid the influence of geometric discontinuity and surface condition on the experimental results. 2.2. Test equipment The test equipment is MTS-809 electro-hydraulic fatigue testing machine which controls axial strain. The standard scale distance of the test is 10 mm and the ratio of the strain Rε = −1. The waveform of the test is triangle, the loading frequency is 0.083–0.667 Hz. 2.3. Step of the test
∗
Corresponding author. Tel.: +86 29 88474117; fax: +86 29 88492642. E-mail address: [email protected] (F. Li).
0921-5093/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2006.05.102
The test is executed according to GB/T15248-94—axial constant amplitude low cycle fatigue testing method of metal mate-
F. Li et al. / Materials Science and Engineering A 430 (2006) 216–220
217
(1) Determining the fatigue limit medium Determine the fatigue limit medium according to the general fluctuation method and make the subsample fatigue limit medium as the estimated value of the parent’s. The formula is as following: 1 εi ε¯ = n n
(1)
i=1
(2) Calculating the subsample standard deviation The standard deviation of the material’s fatigue limit is calculated according to the following formula: n 1 (xi − x¯ )2 S= (2) n−1 i=1
(3) Verifying the valid sample size Calculate the subsamples’ coefficient of variability, and then use the following formula to verify the valid strain sample size overrunning the minimum size which the test requires. If not meet, penalty run until the valid strain sample size reaches or overruns the minimum size required: tr
Fig. 1. Low cycle fatigue test specimen of TA15 at (a) 25 ◦ C and (b) 250 ◦ C.
rial. In the tests with different strain amplitude, the loading frequency is adjusted according to the strain amplitude in order to keep the strain rate constant. 3. Test results and analyses The higher and lower test data are needed processing in the processing procedure. Pointing at the effect of the coarse error, the Chauvenet criterion (a mathematical method to abandon dubious data) is used to verify the acquired data, and then test data are determined reserving or abandoning. The steps of utilizing the Chauvenet criterion to verify the dubious data are as following: at first, process data of all strain levels; calculate the medium ε¯ of all strain levels subsample and obtain their standard deviation S. According to the formula di /S = |(εi − ε¯ )/S|, the dubious data of all stain levels can be calculated, and then the dubious data can be reserved or abandoned after looking up the critical criterion d/S of the dubious data in the related table. Given survival probability and confidence, the method of determining material’s symmetric cycle fatigue limit is as following [2]:
δmax 1 n
+ u2p (k − 1) − δmax up k
≥
S ε¯
(3)
where δmax is the error limit and δmax is 5%; n the minimum valid strain sample size; k the modified coefficient of the standard deviation; tr the value of the t distribution, it can be determined by t distribution according to the significance level α = 1 − γ and the test strain sample size n ; S the standard deviation of the material’s fatigue limit; ε¯ the fatigue limit medium; up is the standard normal deviator related to the survival probability and can be checked out in the standard normal deviator table. (4) Calculating the unilateral allowance coefficient k k is approximately calculated as: u2 u2r up − ur ni 1 − 2(n −1) + 2(n p−1) k= (4) r 1 − 2(nu −1) where n is the valid test strain sample size; up the standard normal deviator, which can be checked out in the standard normal deviator table when giving survival probability; ur is the standard normal deviator related to the reliability. (5) Calculating true survival probability The project requires forecasting the survival probability corresponding to the unilateral allowance coefficient method. Literature [3] gives the accurate method to calculate the true survival probability: −(υ+1)/2 tα 1 t2
α= 1 + dt (5) √ υ −∞ υB 21 , υ2
1 where B 21 , υ2 = 0 x−(1/2) (1 − x)(υ−2)/2 dx is beta function and υ = n − 1.
218
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Fig. 2. LCF strain–life curves of TA15 at 25 ◦ C. Fig. 4. LCF cyclic stress–strain curve of TA15 at 25 ◦ C.
Fig. 3. LCF strain–life curves of TA15 at 250 ◦ C.
After reserving and abandoning the dubious data, process the valid fatigue data of reliability γ = 95% and survival probability P = 99.9%, then obtain the strain–life curve (εt /2 − 2Nf , εe /2 − 2Nf , εp /2 − 2Nf logarithm curve), cyclic stress–strain curve (σ/2 − εt /2 curve) which attribute the material’s fatigue characteristic as Figs. 2–5. All strain fatigue parameters (σf , b, εf , c) are in Table 1 (simultaneous equation (5), the true survival probability α is greater than 99.97%, it means that the parameters in Table 1 are valid). The approximate k values calculated from formula (4) can be seen in Table 2. The intersecting point of εe /2 − 2Nf curve and εp /2 − 2Nf curve can be obtained from Figs. 2 and 3. At the temperature of 25 ◦ C, the abscissa of the intersecting point is 2.21 and the
Fig. 5. LCF cyclic stress–strain curve of TA15 at 250 ◦ C.
transition fatigue life NT calculated is 162.84 reversals; at the temperature of 250 ◦ C, the abscissa of the intersecting point is 2.82 and the calculated NT is 663.98 reversals. The transition fatigue life is a key index of LCF [3]. When the transition fatigue life NT overruns, the contribution of the elastic strain capacity to fatigue is greater than the plastic strain capacity’s, so the plastic strain capacity plays a dominant role on fatigue breakage; per contra, plastic strain capacity plays an important role. Coffin thinks the strength plasticity of material and the test temper-
Table 1 LCF properties of TA15 at 25 and 250 ◦ C Parameters of LCF γ (%)
P (%)
αf (MPa)
αf /E (%)
b
εf (%)
c
25 ◦ C
Median 95
99.9
1386 1254
0.01286 0.01163
−0.08492 −0.07697
1.3993 1.8651
−1.0019 −1.0740
250 ◦ C
Median 95
99.9
1096 1087
0.01012 0.01009
−0.06660 −0.07660
0.2772 0.5428
−0.5797 −0.6899
Strain–life curve
ε/2 = (αf /E)(2Nf )b + εf (2Nf )c
F. Li et al. / Materials Science and Engineering A 430 (2006) 216–220
219
Table 2 The k values with approximate calculation Test number
25 ◦ C, k
Test number
250 ◦ C, k
4 5 8 14 17 19 20 24 25 27 29 34
2.03357 1.92095 1.94001 1.86203 1.94648 1.94567 1.96374 1.92563 1.91871 1.94942 2.05589 1.96087
A1 A2 A25 A26 A33 A35 A40 A45 A47 A52
1.92254 1.92127 1.99389 1.95525 1.92627 1.92627 1.95525 1.95815 1.92979 1.96093
Fig. 6. Stress–strain hysteresis loop-line.
Table 3 Stress amplitude of sample 14 at constant strain test Cycle, N
2 6 12 18 22 28 32 34
Stress (MPa)
Strain (mm/mm)
Max
Min
Max
Min
909.123 891.137 875.096 866.104 862.094 852.979 837.303 811.783
−969.245 −953.206 −939.352 −934.127 −931.453 −929.023 −927.443 −925.377
0.015 0.015 0.015 0.015 0.015 0.015 0.015 0.015
−0.015 −0.015 −0.015 −0.015 −0.015 −0.015 −0.015 −0.015
ature have an important effect on the transition fatigue life NT [4]. The test result indicates that the stress has a trend of gradually reducing at the constant strain conditions. Table 3 is the test result of sample 14 and other test results have the same law with it. The above results indicate that TA15 titanium alloy has the cyclic softening characteristic and it reaches stability after certain circulations. Table 4 compares the theoretical calculated plastic strain value and actual measurement results. The experimental plasTable 4 Calculation and measurement values of plastic strain Test number
4 5 8 14 17 19 20 24 25 27 29 34
25 ◦ C
Test number
Calculated
Measured
0.000180 0.002387 0.002645 0.007021 0.001287 0.007185 0.000117 0.004602 0.004310 0.001343 0.000242 0.000141
0.000020 0.002280 0.002265 0.006930 0.001088 0.007007 0.000037 0.003985 0.004220 0.001106 0.000189 0.000039
A1 A2 A25 A26 A33 A35 A40 A45 A47 A52
250 ◦ C Calculated
Measured
0.006003 0.007962 0.008499 0.001443 0.004140 0.004302 0.002464 0.023110 0.005878 0.000734
0.005824 0.007742 0.008298 0.001381 0.009907 0.004160 0.002081 0.001825 0.005655 0.000569
tics strain values are obtained by stress–strain hysteresis loopline as Fig. 6, which can be achieved from tests. In Fig. 6, E represents elastic modulus, σ represents the range of stress, εt , εe , εp represent the range of total strain, elastic strain and plastic strain, respectively. From Fig. 6, we can have the experimental plastics strain values by the expression shown as below: εp = εt − εe = εt −
σ tan α
(6)
It can be seen there is definite misdistance between the theoretical values and true values and the theoretical values are greater than true values. The reasons include: the first, the samples are affected by the processing stress in the manufacturing procedure; the second, the effect of the loading velocity; the third, inhomogeneous of the material and the four is the artificial error in the test. 4. Conclusion (1) TA15 titanium alloy has the cyclic softening characteristic and it reaches stability after certain circulations. (2) The LCF strain–life curve of TA15 is determined and the relational expression to predict the LCF of TA15 is given. At the temperature of 25 ◦ C, the expression is εt /2 = 0.01163(2Nf )−0.07697 + 1.8651(2Nf )−1.0740 ; at the temperature of 250 ◦ C, the expression is εt /2 = 0.01009 (2Nf )−0.07660 + 0.5428(2Nf )−0.6899 . The relationship between stress and strain when material bears cyclic loading is fitted: at the temperature of 25 ◦ C, the relationship is σ = −920.4055 eε/(−0.0044) + 916.81311 and r2 = 0.09727; at the temperature of 250 ◦ C, the relationship is σ = −715.7165 eε/(−0.0047) + 719.23075 and r2 = 0.097119. (3) The intersecting points of εe /2 − 2Nf curve and εp /2 − 2Nf curve are obtained. At the temperature of 25 ◦ C, the abscissa of the intersecting point is 2.21 and the transition fatigue life NT calculated is 162.84 reversals; at
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F. Li et al. / Materials Science and Engineering A 430 (2006) 216–220
the temperature of 250 ◦ C, the abscissa of the intersecting point is 2.82 and the calculated NT is 663.98 reversals. When the transition fatigue life NT overruns, the contribution of the elastic strain capacity to fatigue is greater than the plastic strain capacity’s, so the plastic strain capacity plays a dominant role on fatigue breakage.
References [1] [2] [3] [4]
J.-Y. Zhang, Y.-Q. Yang, et al., Trans. Metal Heat Treat. 28 (2003) 46–48. B. Xiang, J.-P. Shi, et al., China Railway Sci. 23 (2002) 72–76. C.R. Williams, Y.L. Lee, J.T. Rilly, Int. J. Fatigue 25 (2003) 427–436. Z. Zhang, Rare Metal Mater. Eng. 23 (1994) 56–60.
Research on low cycle fatigue properties of TA15 titanium alloy based on reliability theory Fuguo Li ∗ , Xiaolu Yu, Leikui Jiao, Qiong Wan School of Materials Science and Engineering, Northwestern Polytechnical University, Xi’an 710072, PR China Received 15 July 2005; received in revised form 11 May 2006; accepted 17 May 2006
Abstract This paper introduces a method to determine the symmetric cycle fatigue limit of TA15 alloy at given confidence γ and survival probability P. It gives a general method to calculate the true survival probability of this material fatigue limit. The median and data of the LCF at γ = 95% and P = 99.9% are acquired after studying the LCF properties of aircraft construction material TA15 at the temperature of 25 and 250 ◦ C. The strain–life curve, cyclic stress–strain curve and parameters of LCF are also achieved. These provide reference to analyze the reliability of aircraft construction and estimate the life. © 2006 Elsevier B.V. All rights reserved. Keywords: TA15 alloy; Low cycle fatigue; Reliability
1. Introduction With the requirement of aircraft construction integrity, reliability and durability improving, higher requirement is presented to LCF properties of utilized material. The titanium alloy TA15 is widely applied in large aircraft construction and its nominal composition is Ti–6Al–2Zr–1Mo–1V. This alloy was successfully developed in Russian at 1964. TA15 alloy, which is equivalent to Ti–8Al–1Mo–1V of America in properties, works at the temperature of 500 ◦ C and it is the general alloy of bar stock and sheet material. It is generally considered TA15 is a near␣ titanium alloy of high aluminum equivalency, its strengthen mechanics is mainly solution strength of Al and other elements and it cannot be strengthened by heat treating. So TA15 alloy is used at annealed condition, where the phase composition of the alloy is the matrix ␣ phase and a smaller volume fraction of the  phase. However, it is found the surplus quantity of the strength index is little in the study of large titanium alloy forging, and sometimes it can even not meet the requirement of the standard [1]. This paper measures and analyzes the LCF properties of TA15 according to applicable work condition of certain structure and loading conditions of aircraft, acquires strain–life curve at cyclic loading and determines its cyclic characteristic. These
provide fundamental data to the fatigue design and reliability analysis of structure. 2. Test procedures 2.1. Specimen preparation After related standard comparison and lots of experiment research, the shaped size of the specimen and the machining processing technique are determined in Fig. 1. The surfaces of the samples were in accurately machined condition, the transition circular arcs mechanically polished in order to avoid the influence of geometric discontinuity and surface condition on the experimental results. 2.2. Test equipment The test equipment is MTS-809 electro-hydraulic fatigue testing machine which controls axial strain. The standard scale distance of the test is 10 mm and the ratio of the strain Rε = −1. The waveform of the test is triangle, the loading frequency is 0.083–0.667 Hz. 2.3. Step of the test
∗
Corresponding author. Tel.: +86 29 88474117; fax: +86 29 88492642. E-mail address: [email protected] (F. Li).
0921-5093/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2006.05.102
The test is executed according to GB/T15248-94—axial constant amplitude low cycle fatigue testing method of metal mate-
F. Li et al. / Materials Science and Engineering A 430 (2006) 216–220
217
(1) Determining the fatigue limit medium Determine the fatigue limit medium according to the general fluctuation method and make the subsample fatigue limit medium as the estimated value of the parent’s. The formula is as following: 1 εi ε¯ = n n
(1)
i=1
(2) Calculating the subsample standard deviation The standard deviation of the material’s fatigue limit is calculated according to the following formula: n 1 (xi − x¯ )2 S= (2) n−1 i=1
(3) Verifying the valid sample size Calculate the subsamples’ coefficient of variability, and then use the following formula to verify the valid strain sample size overrunning the minimum size which the test requires. If not meet, penalty run until the valid strain sample size reaches or overruns the minimum size required: tr
Fig. 1. Low cycle fatigue test specimen of TA15 at (a) 25 ◦ C and (b) 250 ◦ C.
rial. In the tests with different strain amplitude, the loading frequency is adjusted according to the strain amplitude in order to keep the strain rate constant. 3. Test results and analyses The higher and lower test data are needed processing in the processing procedure. Pointing at the effect of the coarse error, the Chauvenet criterion (a mathematical method to abandon dubious data) is used to verify the acquired data, and then test data are determined reserving or abandoning. The steps of utilizing the Chauvenet criterion to verify the dubious data are as following: at first, process data of all strain levels; calculate the medium ε¯ of all strain levels subsample and obtain their standard deviation S. According to the formula di /S = |(εi − ε¯ )/S|, the dubious data of all stain levels can be calculated, and then the dubious data can be reserved or abandoned after looking up the critical criterion d/S of the dubious data in the related table. Given survival probability and confidence, the method of determining material’s symmetric cycle fatigue limit is as following [2]:
δmax 1 n
+ u2p (k − 1) − δmax up k
≥
S ε¯
(3)
where δmax is the error limit and δmax is 5%; n the minimum valid strain sample size; k the modified coefficient of the standard deviation; tr the value of the t distribution, it can be determined by t distribution according to the significance level α = 1 − γ and the test strain sample size n ; S the standard deviation of the material’s fatigue limit; ε¯ the fatigue limit medium; up is the standard normal deviator related to the survival probability and can be checked out in the standard normal deviator table. (4) Calculating the unilateral allowance coefficient k k is approximately calculated as: u2 u2r up − ur ni 1 − 2(n −1) + 2(n p−1) k= (4) r 1 − 2(nu −1) where n is the valid test strain sample size; up the standard normal deviator, which can be checked out in the standard normal deviator table when giving survival probability; ur is the standard normal deviator related to the reliability. (5) Calculating true survival probability The project requires forecasting the survival probability corresponding to the unilateral allowance coefficient method. Literature [3] gives the accurate method to calculate the true survival probability: −(υ+1)/2 tα 1 t2
α= 1 + dt (5) √ υ −∞ υB 21 , υ2
1 where B 21 , υ2 = 0 x−(1/2) (1 − x)(υ−2)/2 dx is beta function and υ = n − 1.
218
F. Li et al. / Materials Science and Engineering A 430 (2006) 216–220
Fig. 2. LCF strain–life curves of TA15 at 25 ◦ C. Fig. 4. LCF cyclic stress–strain curve of TA15 at 25 ◦ C.
Fig. 3. LCF strain–life curves of TA15 at 250 ◦ C.
After reserving and abandoning the dubious data, process the valid fatigue data of reliability γ = 95% and survival probability P = 99.9%, then obtain the strain–life curve (εt /2 − 2Nf , εe /2 − 2Nf , εp /2 − 2Nf logarithm curve), cyclic stress–strain curve (σ/2 − εt /2 curve) which attribute the material’s fatigue characteristic as Figs. 2–5. All strain fatigue parameters (σf , b, εf , c) are in Table 1 (simultaneous equation (5), the true survival probability α is greater than 99.97%, it means that the parameters in Table 1 are valid). The approximate k values calculated from formula (4) can be seen in Table 2. The intersecting point of εe /2 − 2Nf curve and εp /2 − 2Nf curve can be obtained from Figs. 2 and 3. At the temperature of 25 ◦ C, the abscissa of the intersecting point is 2.21 and the
Fig. 5. LCF cyclic stress–strain curve of TA15 at 250 ◦ C.
transition fatigue life NT calculated is 162.84 reversals; at the temperature of 250 ◦ C, the abscissa of the intersecting point is 2.82 and the calculated NT is 663.98 reversals. The transition fatigue life is a key index of LCF [3]. When the transition fatigue life NT overruns, the contribution of the elastic strain capacity to fatigue is greater than the plastic strain capacity’s, so the plastic strain capacity plays a dominant role on fatigue breakage; per contra, plastic strain capacity plays an important role. Coffin thinks the strength plasticity of material and the test temper-
Table 1 LCF properties of TA15 at 25 and 250 ◦ C Parameters of LCF γ (%)
P (%)
αf (MPa)
αf /E (%)
b
εf (%)
c
25 ◦ C
Median 95
99.9
1386 1254
0.01286 0.01163
−0.08492 −0.07697
1.3993 1.8651
−1.0019 −1.0740
250 ◦ C
Median 95
99.9
1096 1087
0.01012 0.01009
−0.06660 −0.07660
0.2772 0.5428
−0.5797 −0.6899
Strain–life curve
ε/2 = (αf /E)(2Nf )b + εf (2Nf )c
F. Li et al. / Materials Science and Engineering A 430 (2006) 216–220
219
Table 2 The k values with approximate calculation Test number
25 ◦ C, k
Test number
250 ◦ C, k
4 5 8 14 17 19 20 24 25 27 29 34
2.03357 1.92095 1.94001 1.86203 1.94648 1.94567 1.96374 1.92563 1.91871 1.94942 2.05589 1.96087
A1 A2 A25 A26 A33 A35 A40 A45 A47 A52
1.92254 1.92127 1.99389 1.95525 1.92627 1.92627 1.95525 1.95815 1.92979 1.96093
Fig. 6. Stress–strain hysteresis loop-line.
Table 3 Stress amplitude of sample 14 at constant strain test Cycle, N
2 6 12 18 22 28 32 34
Stress (MPa)
Strain (mm/mm)
Max
Min
Max
Min
909.123 891.137 875.096 866.104 862.094 852.979 837.303 811.783
−969.245 −953.206 −939.352 −934.127 −931.453 −929.023 −927.443 −925.377
0.015 0.015 0.015 0.015 0.015 0.015 0.015 0.015
−0.015 −0.015 −0.015 −0.015 −0.015 −0.015 −0.015 −0.015
ature have an important effect on the transition fatigue life NT [4]. The test result indicates that the stress has a trend of gradually reducing at the constant strain conditions. Table 3 is the test result of sample 14 and other test results have the same law with it. The above results indicate that TA15 titanium alloy has the cyclic softening characteristic and it reaches stability after certain circulations. Table 4 compares the theoretical calculated plastic strain value and actual measurement results. The experimental plasTable 4 Calculation and measurement values of plastic strain Test number
4 5 8 14 17 19 20 24 25 27 29 34
25 ◦ C
Test number
Calculated
Measured
0.000180 0.002387 0.002645 0.007021 0.001287 0.007185 0.000117 0.004602 0.004310 0.001343 0.000242 0.000141
0.000020 0.002280 0.002265 0.006930 0.001088 0.007007 0.000037 0.003985 0.004220 0.001106 0.000189 0.000039
A1 A2 A25 A26 A33 A35 A40 A45 A47 A52
250 ◦ C Calculated
Measured
0.006003 0.007962 0.008499 0.001443 0.004140 0.004302 0.002464 0.023110 0.005878 0.000734
0.005824 0.007742 0.008298 0.001381 0.009907 0.004160 0.002081 0.001825 0.005655 0.000569
tics strain values are obtained by stress–strain hysteresis loopline as Fig. 6, which can be achieved from tests. In Fig. 6, E represents elastic modulus, σ represents the range of stress, εt , εe , εp represent the range of total strain, elastic strain and plastic strain, respectively. From Fig. 6, we can have the experimental plastics strain values by the expression shown as below: εp = εt − εe = εt −
σ tan α
(6)
It can be seen there is definite misdistance between the theoretical values and true values and the theoretical values are greater than true values. The reasons include: the first, the samples are affected by the processing stress in the manufacturing procedure; the second, the effect of the loading velocity; the third, inhomogeneous of the material and the four is the artificial error in the test. 4. Conclusion (1) TA15 titanium alloy has the cyclic softening characteristic and it reaches stability after certain circulations. (2) The LCF strain–life curve of TA15 is determined and the relational expression to predict the LCF of TA15 is given. At the temperature of 25 ◦ C, the expression is εt /2 = 0.01163(2Nf )−0.07697 + 1.8651(2Nf )−1.0740 ; at the temperature of 250 ◦ C, the expression is εt /2 = 0.01009 (2Nf )−0.07660 + 0.5428(2Nf )−0.6899 . The relationship between stress and strain when material bears cyclic loading is fitted: at the temperature of 25 ◦ C, the relationship is σ = −920.4055 eε/(−0.0044) + 916.81311 and r2 = 0.09727; at the temperature of 250 ◦ C, the relationship is σ = −715.7165 eε/(−0.0047) + 719.23075 and r2 = 0.097119. (3) The intersecting points of εe /2 − 2Nf curve and εp /2 − 2Nf curve are obtained. At the temperature of 25 ◦ C, the abscissa of the intersecting point is 2.21 and the transition fatigue life NT calculated is 162.84 reversals; at
220
F. Li et al. / Materials Science and Engineering A 430 (2006) 216–220
the temperature of 250 ◦ C, the abscissa of the intersecting point is 2.82 and the calculated NT is 663.98 reversals. When the transition fatigue life NT overruns, the contribution of the elastic strain capacity to fatigue is greater than the plastic strain capacity’s, so the plastic strain capacity plays a dominant role on fatigue breakage.
References [1] [2] [3] [4]
J.-Y. Zhang, Y.-Q. Yang, et al., Trans. Metal Heat Treat. 28 (2003) 46–48. B. Xiang, J.-P. Shi, et al., China Railway Sci. 23 (2002) 72–76. C.R. Williams, Y.L. Lee, J.T. Rilly, Int. J. Fatigue 25 (2003) 427–436. Z. Zhang, Rare Metal Mater. Eng. 23 (1994) 56–60.