Study on observation condition and on simple evaluation method of TypeIV creep damage of Mod.9Cr-1Mo steel

Type IV creep damage is the phenomena that a large number of voids in micron size initiate, grow, coalesce each other and become large cracks. They initiate in welded joints of high chromium steel in power plant. The density of voids, the number of voids per a unit area, is used to evaluate the residual life. The observed density of voids depends on the observation conditions; the observation area and the magnification of observed photograph of metallographic structure, because voids do not distribute uniformly and the small magnification misses the small voids. In previous study, we studied the influence of them with simulated fine-grain HAZ of Mod.9Cr-1Mo steel, and proposed how to determine the appropriate observation area for the temporary allowable error. We also proposed the method to evaluate the start time of initiation of voids, the initiation rate of voids and the growth rate of voids based on the relation between the observed density of voids and the magnification. But the experimental data was short. In this paper we showed new data, but they were yet not sufficient. We used FEM analysis and considered why enough data had been not taken.


Introduction
Type IV creep damage is the phenomena that a large number of voids in micron size initiate, grow, coalesce and become large cracks [1]. They initiate in the fine grain heat affected zone (FGHAZ) in the welded joints that have been exposed to stress and high temperature for years. For reliable use of power plants, the method to evaluate the residual life is demanded. The density of voids is defined as the number of voids per a unit area. It is used as the parameter of the life fraction of the component with Type IV creep damage [2]. The observed density of voids depends on the observation conditions [3] which are the observation area and the magnification of observed photograph of metallographic structure, because voids do not distribute uniformly and the small magnification misses the small voids.
Generally Type IV creep damage initiates under high stress triaxiality. However the influence of the stress and the stress triaxiality on the density of voids has been researched [4] [5], the quantitative conclusion has not been taken yet. One of the reasons is that the influence of the stress and stress triaxiality is hidden by the influence of the observation conditions. In the previous research [6][7] [8], authors proposed the method to determine the appropriate observation area. They showed that the influence of the Heat on the appropriate observation areas was small. In the previous research [7] the linear relation between the mean density of voids and the reciprocal of the magnification also was taken. There was the probability that the relation represents the distribution of the radius of voids. The initiation rate, the growth rate and the start time of initiation of voids might be evaluated with the distribution of the radius. However, data were short to discuss it. In this research we add data and try to evaluate these parameters and to calculate the density of voids. However, they are not enough, either. We use FEM analysis and consider the reason of short data.

Materials, creep test and observation
The creep tests were conducted with simulated FGHAZ and the samples with Type IV creep damage were obtained.
The material was KA SFVAF28, which was forged Mod.9Cr-1Mo steel. Table 1 shows the chemical composition of this material. It was normalized at 1045 C for 3.5 hours and tempered at 760 C for 5.5 hours. After that it was cut to the bars. To reproduce the metallographic structure of FGHAZ, the Heat 1 and the Heat 2 were heated at 910 C for 1 second one time and three times, respectively. After that the test pieces were machined from the bars.
To simulate the Post Weld Heat Treatment (PWHT), and to remove the residual strain, the test pieces were heated for 2 hours at 740 C after the machining. Table 2 shows the Vickers hardness measured with 9.807N and the average grain size after PWHT.
Tests were conducted with notched test pieces and a smooth test piece. Figure 1 (a) shows the notched test piece of Heat 1 with M18 screws. The shape of smooth test piece of Heat 1 was the same as figure 1 except for the notch. Figure 1  The test temperature was 650 C. The fracture time of notched test piece of Heat 1 and that of Heat 2 were 1487 hours and 2302 hours, respectively. The smooth test piece of Heat 1 didn't fracture and the notch factor is unknown. The similar notched test pieces need from 1.3 to 1.4 times larger net section stress to the same fracture time as the smooth test piece [9].
The stress and TF, the triaxiality factor, were analyzed with FEM with ANSYS Academic Teaching Introductory. Young's modulus of 157 GPa and Poisson's ratio of 0.314 were used. Equation where  is creep rate and  is stress.  For the example, figure 2 (a) and (b) show the distributions of stress and TF on the cross section of the bottom of the notch, respectively. They distribute uniformly in the area with the radius of less than 1 mm, and we observed this area. The creep damage of the centre of this cross section (radius r=0 mm) and that of the bottom of the notch (r=3.75 mm) were calculated with the time fraction rule shown with equation (3).
where c D , i t and ri t are the creep damage, the period during that the principal stress is i  and the creep fracture time for i  . ri t is calculated with equations (4) and (5).  Figure 4 shows the observed cross sections. Table 3 shows the test time, the stress and TF of the observed cross section. Only the cross section f was on the smooth test piece. Other cross sections were on notched test pieces.
The cross sections were etched with Nital. Figure 5 shows the example of metallographic structure. The observed photographs of metallographic structure were taken and printed with a optical microscope, a digital camera and a printer. The magnification of them, O , were approximately 1000, 500 and 250.  The pictures were connected to be the circle with the radius of 1mm where the stress distributed uniformly ( figure 6). The circle was divided to rectangles. A is the area of each rectangles. Except for cross section a and b, A is 0.04mm 2 when O is 500 or 1000 and 0.08mm 2 when O is 250, respectively. In cross section a, A is 0.10mm 2 , 0.07mm 2 and 0.06mm 2 when O is 250, 500 and 1000, respectively. In cross section b, A is 0.09mm 2 when O is 250 and 0.04mm 2 when O is 500 or 1000. Figure 7 shows the examples.
The size of observed area, s , is the same as A, or is twice or four times as large as A. i is the density of voids of each s . The distribution of i was taken. The mean and the standard deviation of i are represented with u i and s i , respectively. . Figure 9 is the relation between the density of voids i and the confidence level  that is the probability of i being in the allowable error. Figure 10 shows that the confidence level increases with the increase of s . The area appropriate for the confidence level of 0.8 is shown in figure 11. It is function of u i . The grain size of Heat 2 is about twice as large as that of the Heat 1, and the summation of grain boundary length per unit area of Heat 2 is shorter than that of Heat 1. But, in figure 11, there is not the difference between the Heat 1 and Heat 2. The reason may be that at the same u i the influence of the grain size is cancelled.  Mean of the density of voids i u (/mm 2 )

Heat1
Heat2 Heat1 cross secsion f  Figure 12 shows the relation between O and u i . Figure 12 (a) shows the cross sections of Heat 1 observed with 3 magnifications. Figure 12 (b) shows the cross sections of Heat 2 with the distance of 1.85mm from the bottom of notch.   Table 4 shows the results. The density of voids calculated with equation (7) and the variables in table 4 are compared to the observation in figure 13. Errors of observation are large. The reason of that is thought to be not enough observation area. In this study observation area of u i is about 2 mm 2 , which is the area of the largest square in circle with radius of 1 mm. As shown in figure 11, because u i of Heat 2 is small, observation area might be need more than 2 mm 2 .  Figure 13 Calculated density of voids compared with the test results.  Though there is the error, equation (7) well expresses the relation of u i and 1  O . So the calculated variables are thought to be valid.

Evaluation method of initiation and growth of voids
It is not clear whether there are differences among variables of three cross sections. In the next test, we should use the test piece with the observation areas with various TF or observation areas of high creep damage (in other words, large density of voids) at fracture time.
In some conditions, u i might not be liner to 1  O . In that case we should study   t G and   t H that are not constant but functions of time.

Conclusions
The observation area appropriate for the assumed allowable error of with the confidence level of 0.8 is determined. The appropriate area is small if the density of voids is large. The influence of Heat on the appropriate area is thought to be small.
The method that estimates the voids' initiation rate, growth rate and the initiation start time is proposed. It needs the observation more than two times with more than two magnifications. This method will be used to estimate the influence of TF on Type IV creep damage.