Evaluation of Temper Embrittlement of 30 Cr 2 MoV Rotor Steels Using Electrochemical Impedance Spectroscopy Technique

50 ) is commonly used as an indicator parameter to characterize the temper embrittlement. Compared with conventional destructive methods (e.g., small punch test), nondestructive approaches have drawn significant attention in predicting the material degradation in turbine rotor steels without impairing the integrity of the components. In this paper, laboratory experiments were carried out based on a nondestructive method, electrochemical impedance spectroscopy (EIS), with groups of lab-charged specimens for predicting the temper embrittlement (FATT


Introduction
Thermal power stations are the most common electricity sources all over the world due to their low running costs and reliability.However, any failures in the main components (e.g., steam turbine rotor) of aged thermal power plants operating in many areas may cause significant costs, long downtime, and even the loss of life.The precisely predicting of the aging process or the remaining service life of turbine rotor is of great importance for safe operation and life extension [1].
Temper embrittlement in low alloy steels (e.g., Cr-Mo-V) of steamed turbine rotors is one of the typical material degradations (e.g., creep, fatigue, embrittlement, and corrosion) [2,3] and is commonly characterized by fracture appearance transition temperature (FATT 50 ), at which the fracture surface of the material is 50% brittle or cleavage and 50% ductile [1].The turbine rotor steel operated at a high temperature for long time may lose its flexibility and ductility as the segregation of metalloid impurities such as phosphorus (P), tin (Sn), and antimony (Sb), at the grain boundaries which reduces the cohesion at grain boundaries [4][5][6].Among the impurity elements, phosphorus (P) is considered as the main impurity causing temper embrittlement [5,7,8].If the increase of FATT 50 value is not detected in time, the rotor steel can be easily damaged or even broken and causes severe safety accidents [4].Therefore, it is essential to make the accurate predictions and assessments on the temper embrittlement parameters of the turbine rotor material.
As a relatively high-precision nondestructive detecting method, electrochemical approach has drawn significant attention in predicting the material degradation in turbine rotor steels without impairing the integrity of the components.Mao and Zhao investigated the electrochemical behaviors of type 321 austenitic stainless steel in sulfuric acid solution and found that the electrochemical polarization curves can be used to estimate the aging embrittlement degradation [21].Komazaki et al. developed a methodology for thermal aging embrittlement and the results on electrochemical polarization measurements in 1N KOH solution revealed that the peak current density " p " value was found to be increasing linearly with the degree of embrittlement as evaluated by impact absorbed energy at 0 ∘ C [22,23].Anodic and single loop electrochemical potentiokinetic reactivation (SL-EPR) polarization curves of the embrittled specimens have been evaluated; difference in current density (IP2-E-Ipass-E) between active second peak and passive one in an anodic polarization curve of temper-embrittled specimens increases linearly with increase in FATT in the range of mode transfer over transgranular cleavage to intergranular of Charpy impact fracture [24].Zhang et al. developed a genetic programming (GP) for FATT 50 prediction and single loop electrochemical polarization reactivation (EPR) test has been conducted [5].The multiple correlation coefficient between predicted and measured FATT 50 was 0.990, indicating the model obtained by GP can be used in predicting temper embrittlement of new rotor materials with a precision of about ±20 ∘ C [5].Bayesian neural network was proposed to model the temper embrittlement of steam turbine rotor in service, and the FATT 50 was predicted as a function of ratio of the two peak current densities ( p / pr ) tested by electrochemical potentiodynamic reaction method [25].
EIS, as an effective electrochemical method, originally was used to study the electrical response characteristic frequency of linear circuit network and has been used by more and more researchers to study the electrode process which could provide more information of interface structure than other methods [26][27][28].
In this paper, EIS method was employed to study the thermal embrittlement of turbine rotor and a multiple linear regression analysis on interfacial impedance and other relevant parameters was carried out to build a predict model of FATT 50 .The predicted and measured values of FATT 50 were compared and the error was within an acceptable range, indicating an effective and reasonable model was obtained.

Experimental Method
2.1.Principle.The test specimens in this paper were labcharged phosphorus-doped 30Cr2MoV rotor steel and the chemical composition was shown in Table 1.
To simulate the temper embrittlement during the longterm service of turbine rotor, step cooling treatment was used to promote the segregation of phosphorus to the grain boundary.Their FATT 50 values were measured by a stress test according to relevant national standard.The result would be used to verify the subsequent test.Impedance of the specimens was measured in a three-electrode system and analyzed by the equivalent circuit method.A predictive model was built based on the analysis results.

Experiment.
FATT 50 values of specimens were measured by stress test and the result is shown in Table 2.
To measure the impedance of the specimens, a threeelectrode system was employed.As shown in Figure 1, the specimen was cut into cube with side length of 12 mm and was welded on a piece of copper wire.The specimen cube acts as the working electrode in the experiment.In order for the reaction area of the working electrode to remain fixed, five sides of the cube, including some parts of the copper wire, were sealed with epoxy resin; the remaining side was covered with anticorrosion tape with a hole (diameter = 5 mm) after being grinded with sandpaper step by step to 2000#.
Platinum electrode was selected as auxiliary electrode and saturated calomel electrode was used as reference electrode.Electrolyte was made of 0.01 M Na 2 MoO 4 with phosphoric deployed to the pH value of 5.5.The three-electrode system was placed in a water bath filled with circulating hot water of 25 ∘ C to maintain a constant temperature.
The three-electrode system was connected to the corresponding position of electrochemical workstation (model of PARTAT 2273).A computer equipped with software of that workstation was used to record measurements.
All specimens were anodic polarized; the result showed that those corrosion potentials are basically the same.In order to measure the EIS, AC potential with amplitude of 5 mV was applied to working electrode at the corrosion potential as input signal.Sixty frequencies were logarithmic sweeply selected from 100 kHz to 100 mHz.Impedance under that condition could be measured by comparing the measured output current with the input potential.

Results and Discussion
Figure 2 shows the Nyquist plot of measured impedance of specimen.The impedance was represented by a complex.The abscissa of plot in Figure 2 is the real part of the impedance, and the ordinate is the imaginary part.The results showed that the Nyquist plot of all specimens is similar.In the high frequency region, the plots were arcs in the first quadrant, but the centers of arcs were in the fourth quadrant.Some studies claimed that high frequency region was dynamics control district and the diameter of the arc represents the size of charge transfer resistance of the electrode reaction.The higher the diameter of arc, the more difficult the charge transfer in electrode reaction, and the slower the reaction.In the low frequency region, the plots were straight lines of different lengths.This region was considered mass transfer controlled district.If the line in this region was very long, the electrode reaction could be considered as led by mass transfer.An equivalent circuit based on impedance plots was shown in Figure 3.
is the solution impedance between working electrode and auxiliary electrode.CPE is constant-phase-element which could be expressed by parameters  0 and . ct is the charge transfer impedance of the electrode reaction. is mass transfer impedance and can be expressed by parameter   0 .The impedance of the equivalent circuit could be calculated by (1) as follows: . ( The impedance value calculated by the formula matched well the experimental results.Figure 4 showed the calculated and measured curves, and the fitting error of each equivalent circuit component parameter was less than 5%.
By analyzing the component parameter values of equivalent circuit, it could be found that the solution impedance of specimens was essentially unchanged, but the interface impedance varied greatly.Figure 5 shows the linear relationship of interfacial impedance of specimen and its FATT 50 at a frequency of 100 kHz.The abscissa of Figure 5 was interfacial impedance value in ohms; ordinate was FATT 50 value in degree Celsius.Their fitting formula was in the upper left corner.The  in formula represented FATT 50 and  interfacial impedance.The  in formula is the correlation coefficient, and it was calculated as 0.836 by  2 = 0.6983. min , the correlation coefficient threshold, could be looked up from corresponding table as 0.567 [29].Since  was greater than  min , it could be believed that there was a close linear relationship between the interfacial impedance and FATT 50 , and the FATT 50 could be described by linear equations.
In addition to the interfacial impedance, FATT 50 also has linear correlationship with other parameters [29] which were shown in Table 3.
By multivariate linear regression analysis using excel software, the regression equation could be expressed by (2), where Z was interfacial impedance.One has (2) Significant test using Excel software showed that the equation was credible and there was significant linear relationship between FATT 50 and other variables.Table 3 shows that the residuals of predicted value were ±15 ∘ C, the error was small, and the model was reasonable and effective.

Conclusions
In this work, the EIS of turbine rotor at the corrosion potential in 0.01 M Na 2 MoO 4 was studied through laboratory experiments, and the following conclusions are obtained.The electrode reaction of rotor in electrolyte could be represented by an equivalent circuit.The total impedance of the circuit    includes two parts: solution impedance between working electrode and auxiliary electrode and interfacial impedance between the rotor and electrolyte.At higher frequency, there is a linear relationship between the interfacial impedance and its FATT 50 .The larger the interfacial impedance value, the lower the FATT 50 .An effective predictive model could be built by a series of parameters, and the error is small enough indicating the model is reasonable and effective.

Figure 1 :
Figure 1: A three-electrode system for measuring the impedance of the specimens.

Figure 2 :
Figure 2: Nyquist diagrams of the impedance of different samples.

Figure 5 :
Figure 5: Relationship of interface impedance and FATT 50 values.

Table 2 :
The FATT 50 values of different rotor samples.