0
Research Papers: Multiphase Flows

Incubation Time and Cavitation Erosion Rate of Work-Hardening Materials

[+] Author and Article Information
Jean-Pierre Franc

 LEGI, BP 53, 38041 Grenoble Cedex 9, Francejean-pierre.franc@hmg.inpg.fr

This difference in shape between the theoretical and experimental evolutions of MDPR with exposure time may be the reason for a poorer comparison between theory and experiment for the incubation period compared with MDPR (see Fig. 1).

J. Fluids Eng 131(2), 021303 (Jan 15, 2009) (14 pages) doi:10.1115/1.3063646 History: Received October 19, 2007; Revised August 28, 2008; Published January 15, 2009

A phenomenological analysis of the cavitation erosion process of ductile materials is proposed. On the material side, the main parameters are the thickness of the hardened layer together with the conventional yield strength and ultimate strength. On the fluid side, the erosive potential of the cavitating flow is described in a simplified way using three integral parameters: rate, mean amplitude, and mean size of hydrodynamic impact loads. Explicit equations are derived for the computation of the incubation time and the steady-state erosion rate. They point out two characteristic scales. The time scale, which is relevant to the erosion phenomenon, is the covering time—the time necessary for the impacts to cover the material surface—whereas the pertinent length scale for ductile materials is the thickness of the hardened layer. The incubation time is proportional to the covering time with a multiplicative factor, which strongly depends on flow aggressiveness in terms of the mean amplitude of impact loads. As for the erosion rate under steady-state conditions, it is scaled by the ratio of the thickness of hardened layers to the covering time with an additional dependence on flow aggressiveness, too. The approach is supported by erosion tests conducted in a cavitation tunnel at a velocity of 65 m/s on stainless steel 316 L. Flow aggressiveness is inferred from pitting tests. The same model of material response that was used for mass loss prediction is applied to derive the original hydrodynamic impact loads due to bubble collapses from the geometric features of the pits. Long duration tests are performed in order to determine experimentally the incubation time and the mean depth of penetration rate and to validate the theoretical approach.

Copyright © 2009 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Work-hardening progress

Grahic Jump Location
Figure 2

Behavior of a virgin material after being loaded by a hydrodynamic impact of amplitude σ¯. (a) Case of the superficial layer. (b) Case of a layer at depth x.

Grahic Jump Location
Figure 3

Material response during the incubation period

Grahic Jump Location
Figure 4

Typical example of the variation of the incubation period with the amplitude of impact loads σ¯. Case of stainless steel 316 L. The values of the material constants are given in Eqs. 2,4. The abscissa represents the nondimensional amplitude of impact loads defined by (σ¯−σY)/(σU−σY), whereas the ordinate is the incubation time T made nondimensional using the covering time τ.

Grahic Jump Location
Figure 5

Material behavior after the incubation period during steady-state erosion

Grahic Jump Location
Figure 6

Principle of the computation of mass loss

Grahic Jump Location
Figure 7

Typical example of the variation in the MDPR with the mean amplitude of impact loads. Case of stainless steel 316 L (see Eqs. 2,4 for values of constants). MDPR is made nondimensional using the characteristic erosion rate L/τ, whereas the nondimensional amplitude of impact loads is defined as in Fig. 4.

Grahic Jump Location
Figure 8

View of the cavitation erosion tunnel

Grahic Jump Location
Figure 9

Schematic view of the test section together with an eroded target. The size of the eroded surface shown is 13×1.5 mm2. The operating conditions are Vc=65.3 m/s, pu=21.3 bars, pd=10.1 bars, and σ=0.9. Test duration: 30 min.

Grahic Jump Location
Figure 10

Typical 3D view of the surface after a pitting test. The size of the volume shown is 2 mm×4 mm×2.8 μm. Same operating conditions as in Fig. 9. Exposure time: 5 min.

Grahic Jump Location
Figure 11

Sketch showing the definition of pit depth, diameter, and volume

Grahic Jump Location
Figure 12

Pit depth versus pit diameter. Each point represents a pit. The total number of pits is 797.

Grahic Jump Location
Figure 13

Cumulative distribution and probability density functions of pit density per unit time and unit surface area. Same operating conditions as in Fig. 9. Total number of pits: 797. Analyzed surface: 59.9 mm2.

Grahic Jump Location
Figure 14

Cumulative distribution and probability density functions of the fraction of eroded surface. Same conditions as in Fig. 1.

Grahic Jump Location
Figure 15

Cumulative distribution and probability density functions of the fraction of eroded volume. Same conditions as in Fig. 1.

Grahic Jump Location
Figure 16

Photograph of an eroded sample after an exposure time of 104 h. The external diameter of the sample is 100 mm. Operating conditions: Vc=65.3 m/s, pu=21.3 bars, pd=10.1 bars, and σ=0.9.

Grahic Jump Location
Figure 17

Influence of the exposure time on radial profiles of erosion for the sample presented in Fig. 1. For each time, two profiles are presented: (i) light gray: raw data with a step of 10 μm; (ii) thick black: moving average data on 100 points or 1 mm. (The origins of horizontal and vertical scales are arbitrary.)

Grahic Jump Location
Figure 18

Mean depth of penetration (in black, left scale) and mean depth of penetration rate (in gray, right scale) versus exposure time. The gray curve is the time derivative of the thick black curve.

Grahic Jump Location
Figure 19

Pit depth versus amplitude of impact load for stainless steel 316 L. The two branches correspond to Eq. 21 if σ<σU and Eq. 23 if σ>σU.

Grahic Jump Location
Figure 20

Comparison between theory and experiments for (a) MDPR and (b) incubation time. The theoretical prediction depends on the number of pits used to estimate the erosive potential of the cavitating flow. Prediction can be considered as stabilized above a few hundred pits.

Grahic Jump Location
Figure 21

Relation between nondimensional MDPR and inverse of nondimensional incubation time for stainless steel 316 L. The curve has been obtained by varying the flow aggressiveness in terms of mean amplitude of impact load σ¯.

Grahic Jump Location
Figure 22

Influence of depth threshold on the treatment of a pitting test (same surface as in Fig. 1)

Grahic Jump Location
Figure 23

Influence of depth threshold on predicted incubation period and erosion rate

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In