Correlation between mass loss on cavitation erosion and fatigue stress for a martensitic stainless steel.

Voda, Mircea ; Bordeasu, Ilare

1. INTRODUCTION

Production in hydroelectric power plants represents a significant percentage of the electric power obtained all over the world. To maintain the performance of energy systems, it is very important that each turbine unit runs according to optimal parameters. Situations that may require repair work involve cavitation erosion of the blade material or of the turbine runner. The variable and repetitive loads in time produced by the hydrodynamic mass, as well as inertia and related moments applied to the turbine runner, exert a material fatigue effect.

There are literature reports on resistance to cavitation erosion as a function of fatigue resistance (Bedkowski et al., 1999) and under the influence of creep-fatigue (Min et al., 2004; Hong et al., 2002), but there is no information on the cumulative effect of these two types of damage. In this article, we report on experimental research carried out to determine the effect of fatigue on cavitation erosion.

The material under investigation was taken directly from a blade used at the Iron Gates II power plant. The manufacturer's certificate indicates that the material is stainless steel G-X5CrNi 13.4 with the chemical composition and mechanical properties according to EN 1008-3.

2. FATIGUE TESTS

Fatigue tests were performed using an Instron 8516 instrument to measure tensile stress. Figure 1 shows the sample geometry. Samples were subjected to cyclic loading at ambient temperature with sinusoidal waves of a frequency of 20 Hz. For all the tests a stress ratio ([S.sub.min]/[S.sub.max]) of 0.5 was used. The stress applied ranged from 170 to 500 MPa, and thus cycles included the value of 90% of the elastic limit of the steel tested. The force ranges and stress amplitudes used in the fatigue tests are presented in Table 1.

Fracture was not always in the central zone of the sample, but failure was always due to fatigue.

A schematic diagram of sample selection for cavitation tests is shown in Figure 2.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

3. CAVITATION EROSION TESTS

Two types of samples were examined: without fatigue and after fatigue. A vibratory apparatus with a magnetostrictive oscillator was used according to ASTM G32-86.

The samples were cylindrical in shape with a diameter of 14 mm and surface roughness [R.sub.a] of 0.4 [micro]m. Vibrations were produced at a frequency of 7 kHz ([+ or -]3%). The characteristics of the device at this frequency are: one period of vibration 7=14.28 x [10.sup.-5] s, oscillation pulsation [omega]=43.98 x [10.sup.-3] [s.sup.-1], and maximum sonic pressure [p.sub.S max] = 29.187 bar. The liquid used during testing was water at 21 [+ or -] 1[degrees]C. The two types of samples were eroded for 5 min, then for further intervals of 15 min to a maximum duration of 150 min. After exposure to cavitation, the test sample was removed from the vibratory tube bar and weighed on an analytical balance with a sensitivity of 0.01 mg. The rate of cavitation erosion was calculated as the mass loss divided by the test duration. The eroded surface was analysed by optical microscopy and scanning electron microscopy. Measurements of the surface roughness were made with a laser profilometer (Perthometer S3P, Mahr Perten, France); surface profiles and [R.sub.a] values were obtained.

4. RESULTS AND DISCUSSION

The penetration of cavitation erosion was analysed using measurement of the external roughness. Since the displacement of the profilometer sensor cannot exceed 10 mm, we took radial measurements starting from an uneroded part of the surface in the centre of the sample. The penetration depth of cavitations is most significant for samples subjected to fatigue cycles. Figure 3 shows the measurement results for the case [DELTA] [sigma]=198 MPa. [R.sub.a] is 2.21 [micro]m greater and [R.sub.z] is 13 [micro]m greater for the fatigued sample than for the sample subjected to cavitation only.

[FIGURE 3 OMITTED]

It is also evident that the depth of the eroded surface is almost constant for the whole sector for the sample subjected to fatigue cycles, whereas for the case without fatigue, the depth is not homogeneous.

Taking into account the evolution of the experimental results (mass loss vs. time), we examined several analytical functions (exponential, logarithmic curve, polynomial) and selected the one yielding the best correlation for the mass loss. The experimental results were smoothed and the best correlation was obtained with the following exponential function:

m = A [n.summation over (i=1)] [m.sub.i] t (1 - [e.sup.-b x t), (1)

where: m: mass loss [mg]; A: scale parameter of the curve; B: form parameter of the curve; ': time [min].

[FIGURE 4 OMITTED]

The analytical approach proposed in Eq. (1) is adequate for all sample types (Fig. 4), with better smoothing for [DELTA][sigma]=170 MPa and 198 MPa.

This observation suggests that the distribution of residual stress is more homogeneous in the case of loads of 226 and 255 MPa for material not subjected to fatigue.

The evolution of the results for the analytical model according to Eq. (1) shows that the scale parameter A varies, while the shape parameter B remains constant (Table 2).

We note that correlation of the mass loss vs. time and the scale parameter A with the stress amplitude [DELTA][sigma] is described by a similar exponential equation (Fig. 5). The difference between the functions is the parameter A. The dependence of A on Act is defined by:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

[FIGURE 5 OMITTED]

5. CONCLUSIONS

1. Cavitation erosion mass losses are aggravated with increasing fatigue stress amplitude.

2. Fatigue increases the penetration depth of erosion.

3. The period after which erosion becomes stable is shorter for samples subjected to fatigue.

4. Regardless of whether specimens are subjected to fatigue stresses or not, evolution of cavitation erosion in time can be described by the same exponential equation.

5. The slope of the linear section of the characteristic curves (mass loss vs. time) increases with fatigue stress amplitude.

6. The scale parameter A of the exponential equation depends on the fatigue stress amplitude [DELTA][sigma].

7. The model can be used for estimation of cavitation behaviour and we will extend our research for more materials.

6. REFERENCES

Bedkowski, W.; Gasiak, G.; Lachowicz, C.; Lichtarowicz, A.; Lagoda, T. & Macha, E. (1999). Relations between cavitation erosion resistance of materials and their fatigue strength under random loading, Wear 230, pp 201-209

Min, K.S., Kim, K.J. & Nam, S.W. (2004). Investigation of the effect of the types and densities of grain boundary carbides on grain boundary cavitation resistance of AISI 321 stainless steel under creep-fatigue interaction, Journal of Alloys Compounds 370, 2004, pp 223-229

Hong, H.U.; Rho, B.S. & Nam, S.W. (2002). A study on the crack initiation and growth from [delta]-ferrite/[gamma] phase interface under continuous fatigue and crep-fatigue conditions in type 304L stainless steels, International Journal of Fatigue 24,2002, pp 1063-1067

Tab. 1. Test conditions

Test number 1 2 3 4
Force interval (kN) 60-30 70-35 80-40 90-45
Stress amplitude
 ([DELTA][sigma] (MPa) 170 198 226 255

Tab. 2. Evolution of the parameters and mass loss

[DELTA][sigma] (MPa) A B Cumulative mass
 loss (mg)

 0 1.703x[10.sup.-4] 0.053 26.29
 170 2.053x[10.sup.-4] 0.053 30.78
 198 2.243x[10.sup.-4] 0.053 33.64
 226 2.411x[10.sup.-4] 0.053 36.16
 255 2.706x[10.sup.-4] 0.053 40.57