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Nickel base single crystal superalloy Larson

1 preface

nickel base single crystal superalloy has been successfully used as the hot end components of advanced aircraft engines, such as turbine blades, and has become the key material of aircraft engines. In order to meet the requirements of the continuous development of aeroengines, it is very necessary to develop nickel base single crystal superalloys with good high temperature strength and other comprehensive properties, especially good durability and phase stability

the development of new nickel base single crystal superalloy is time-consuming and cost-effective, so as to avoid many problems caused by the increase of thickness. The practice shows that the time and cost of developing single crystal superalloy can be saved by using the alloy design method. Recently, we have proposed a new design method for nickel base single crystal superalloys, including the high temperature endurance life, oxidation resistance, corrosion resistance, heat treatment window, the design of alloy yield strength and the prediction of phase stability. Among them, the design of single crystal superalloy yield strength and the prediction of phase stability have been reported [1]. This paper further studies the design of endurance life of nickel base single crystal superalloy, that is, the prediction of Larson Miller curve of single crystal superalloy

the key of alloy design is the design of endurance life, but the prediction of endurance life of alloy has always been a difficult problem, and the understanding of creep mechanism is not unified, including dislocation climb theory, dislocation cut order theory, recovery theory, diffusion creep theory, etc. [2 ~ 4]. Therefore, only on the basis of existing tests, a reasonable data model can be established to predict the endurance life of the alloy. However, the test conditions for the endurance life of nickel base single crystal superalloys reported at present are different [5 ~ 7], which brings some difficulties to the data modeling. Based on the Monkman grant equation [8], a reasonable data model equation is established and applied to the prediction of Larson Miller curve of nickel base single crystal superalloy

2 theoretical basis

the main design goal of single crystal superalloy is the endurance property of the alloy, and the effective endurance life tr mainly depends on the steady-state creep rate s. The relationship between them conforms to the Monkman grant equation [8] (1)

where: B is a constant related to the alloy composition

generally speaking, the apparent equation of steady-state creep rate can be expressed as [8]:

(2)

, where: A is the structural constant; Is creep stress; E (T) is the young's modulus of elasticity of pure nickel; QE is the apparent activation energy; R is the gas constant; T is Kelvin temperature; N is the stress index, generally 3 ~ 5

combine equations (1) and (2), and get:

(3)

take logarithm on both sides of equation (3), then there is:

(4)

where: e is the base of natural logarithm

at constant temperature, for the same alloy, a, B, e (T) and QE are constant, so let:

(5)

, then (4) formula becomes:

lntr=c-nln (6)

3 prediction method

in formula (5), a, B, e (T) and QE are functions of alloy composition and structure at a certain temperature, ignoring the influence of structural factors, and at a certain temperature, C is only a function of alloy composition. Here, it is assumed that C has a linear relationship with the alloy composition, that is:

(7)

where: C0 is a constant; Ki is the coefficient of alloy element I; Cai is the concentration of alloy element I in single crystal alloy, at%

in order to calculate the coefficient in formula (7), the C value of the alloy at 982 ℃ is calculated according to the endurance life test values of 160 single crystal alloys with more than 160 components in literature [5, 6, 7, 9]. The composition of some single crystal alloys and their endurance life and C value at 982 ℃ are listed in the table below. According to equation (7), the coefficient in equation (7) is obtained statistically. The standard error of statistics is 0.7%, which shows that the error is very small, which just shows the rationality of the assumption of formula (7)

table some single crystal alloy components and their 982 ℃/248.2mpa endurance life TR and C

Table composition, creep fracture lives tr at 982 ℃/248.2mpa

and C of some available single crystal superalloys

(1) single crystal alloy components are converted into atomic concentration, and the constant C of 982 ℃ alloy is calculated according to formula (7)

(2) the endurance life of the alloy under different external stresses at 982 ℃ is calculated by formula (6)

(3) calculate the p value under different stress from formula (8) [9], and draw the Larson Miller curve

t (lgtr+20) =p (8)

where: P is a constant dependent on external stress

in order to verify the feasibility of this method, this method is applied to predict the Larson Miller curves of Rene N5 and CMSX-4 alloys

4 calculation results and discussion

Fig. 1 and Fig. 2 show the Larson Miller curves of CMSX-4 and Rene N5 single crystal alloys respectively. The solid line is the experimental value [10, 11], and the dotted line is the calculated value. Obviously, the calculated Larson Miller curve is in good agreement with the experimental curve. It shows that this method is feasible for predicting the endurance life and Larson Miller curve of single crystal alloys

Fig. 1 Comparison of calculated and experimental Larson Miller curves of CMSX-4 alloy and test results

fig.1 comparison of calculated and experimental Larson Miller curves of cmsx-4

Fig. 2 Comparison of calculated and experimental Larson Miller curves of Rene N5 alloy and test results

fig.2 comparison of calculated and experimental Larson Miller curves of Rene n is based on plastic textile 5

it can be seen from formula (6) that at constant temperature, C is a constant. Figures 3 and 4 show the lgtr LG diagrams of Rene N6 and CMSX-4 alloys, and the test values of endurance life are from the Larson Miller curve in literature [10, 11]. It can be seen from the figure that under constant temperature, lgtr and LG have a linear relationship, and the lgtr and LG lines at different temperatures are parallel to each other. It is further explained that at constant temperature, C is a constant that achieves a fast drying performance comparable to that of polyester sweat absorbing fast drying silk, and N is independent of temperature. The currently reported nickel base single crystal superalloys basically have a rupture life value of 982 ℃. Although their loading stresses are different, the C value at this temperature can be obtained through formula (6), and the C value is only related to temperature and alloy composition. In this way, the C value has a good experimental basis, which ensures the accuracy of statistical analysis, thus ensuring the accuracy of this method in predicting single crystal superalloys

Figure 3 lgtr LG map of Rene N6 alloy

fig.3 lgtr LG map of Rene n6

Figure 4 lgtr LG map of CMSX-4 alloy

fig.4 lgtr LG map of cmsx-4

5 conclusion

based on the Monkman grant equation, the proposed prediction method of Larson Miller curve of nickel base single crystal superalloy has good prediction accuracy and can successfully predict the growth of nickel base single crystal superalloy.Larson Miller curve

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