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Critical impact velocity in the solid particles impact erosion of metallic materials
Wear 233–235 Ž1999. 468–475 www.elsevier.comrlocaterwear
Critical impact velocity in the solid particles impact erosion of metallic materials Akihiro Yabuki ) , Kazuo Matsuwaki, Masanobu Matsumura Department of Chemical Engineering, Hiroshima UniÕersity, Higashihiroshima 739-8527, Japan
Abstract Solid particles impact erosion of metallic materials proceeds through two kinds of damage processes. One is the removal of material due to repeated plastic deformation, and the other is cutting. These processes occur simultaneously and the ratio of each contribution to the total damage depends not only on the impact angle Žthe predominant parameter. but also on the impact velocity. As the impact velocity goes down, a solid particle tends not to skid on the target material surface, and hence the cutting damage is reduced. At a certain lower velocity, the particle does not skid at all, resulting in no cutting damage but plastic deformation damage only. This velocity was defined as the ‘‘critical impact velocity’’. In this study, the methodology to determine the critical velocity through a measurement of the coefficient of friction was established, that is, the dynamic friction coefficient during skidding and the static friction coefficient during rolling without skidding. In order to measure the coefficient of friction at the moment of particle impact, a rotating target apparatus was developed. The critical impact velocity thus determined depended on the hardness of both material and particle, as well as on the shape and size of the solid particles. q 1999 Elsevier Science S.A. All rights reserved. Keywords: Erosion; Solid particle; Critical impact velocity; Friction coefficient; Impact angle
1. Introduction Components of solid particle-handling machines and equipment suffer some damage by the impact of solid particles, causing plastic deformation which leads to the material removal from the surface. This phenomenon is called abrasive wear or solid particles impact erosion. In case of serious damage, this may influence the service life of these machines. Thus, accelerated erosion tests in laboratories are carried out to predict the amount of damage in the field or to select materials suitable to the machines seeking a way to prolong the service life. It is generally recognized, however, that any experimental result obtained by the accelerated test does not agree with the performance of real equipment. Even the ranking of materials hardly coincides with the order of their service life in the field. This discrepancy between a laboratory test result and the performance of the material in the field is mainly attributed to the fact that erosion of metallic materials proceeds through two kinds of damage processes and the ratio of each contribution to the total damage depends on
)
Corresponding author
many factors, in particular, on the particles impact angle w1,2x. When solid particles impinge almost vertically on a metallic material at a high impact angle, removal of metallic material occurs mainly due to repeated plastic deformation. On the other hand, the removal due to cutting become dominant over plastic deformation damage at a low impact angle. These processes occur simultaneously and the ratio of each contribution to the total damage depends not only on the impact condition Žimpact angle, velocity. but also on the mechanical properties of solid particles Žhardness, shape, size, etc.. as well as the target materials Žhardness, toughness, etc... However, we experienced an unexpected agreement: the erosion–corrosion test results for two kinds of chromium steels in gypsum–sulfuric acid slurry obtained by a laboratory apparatus agreed well with the actual performance in slurry pump, although both impact velocities and angles of solid particles were quite different. To be precise, the particles impact velocity in laboratory test was 1.7 mrs and in the slurry pump it exceeded 10 mrs. The particles impact angle in laboratory test was apparently 908 and in the actual slurry pump it was very low w3x. The reason for this unexpected agreement may be explained as follows. As the impact velocity goes down, a solid particle tends
0043-1648r99r$ - see front matter q 1999 Elsevier Science S.A. All rights reserved. PII: S 0 0 4 3 - 1 6 4 8 Ž 9 9 . 0 0 1 7 0 - 2
A. Yabuki et al.r Wear 233–235 (1999) 468–475
Fig. 1. Relationship between dissolution rate of damaged surface and SiC particle impact velocity on mild steel w4x.
469
machine component. Further, a good agreement is anticipated even in the erosion–corrosion interaction between the field and laboratory. As mentioned above, the critical impact velocity is a very important factor in predicting the erosion behavior of the material. The critical velocities of various combinations of particle and material may be obtained through measuring the dissolution rates of damaged surfaces. A lot of time and work, however, have to be taken in this method. For a material, any suitable dissolving liquid or any method to measure the dissolution rate could not always be found. In this study, the methodology to determine the critical impact velocity through measuring the friction coefficient between a solid particle and material is established, which is of universal application.
2. Principle of measurement not to skid on the target material surface, which accordingly decreases the damage through cutting. At a certain lower velocity, the particle does not skid at all, which results in no cutting damage but plastic deformation damage only. We named this velocity ‘‘critical impact velocity’’. It is interpreted that in the laboratory test the particles impact velocity was lower than the critical velocity because the solid particles impinged on the specimen with a low velocity and at a high impact angle for the cutting process not to occur. On the other hand, the solid particles in the slurry pump were smaller in size and lower in hardness than the particles used in the laboratory test. Even if these particles impinged on the material surface with a high velocity at a low impact angle, the material would not be damaged by cutting. In other words, the critical impact velocity in the slurry pump must be higher than the actual impact velocity, 10 mrs. Then, it was a matter of course that the results of the accelerated laboratory test agreed with the actual performance in slurry pumps because the damage mechanism was repeated plastic deformation only in both cases. To provide proof of the critical impact velocity, an experiment was carried out by allowing silicon carbide particles to fall freely on the mild steel surface which was inclined at an angle. The damaged surface was put into a hydrochloric acid solution of pH 2 and its dissolution rate was measured. The dissolution rates of surfaces damaged at various impact angles gradually converged upon a certain common rate with reducing impact velocity as shown in Fig. 1 w4x. This impact velocity of 1.7 mrs at which dissolution rate came to a common value must be the critical impact velocity because unity of dissolution rate means the unity of damage mechanism. It can be expected that erosion damages in actual machines and equipment occur at the critical impact velocity or less. If so, the test results obtained at an accelerated damage rate but at an impact velocity lower than the critical velocity may agree with the actual performance of
2.1. Friction coefficient The rotating target apparatus in Fig. 2 was used to determine the friction coefficient during the particle impact. A solid particle is allowed to fall from a certain distance down to impinge on the rotating conical target specimen. After the impact, the solid particle rebounds off toward the measuring board. During the impact, the solid particle is affected by a friction force in the tangential direction due to the rotation of the specimen to cause some deviation in its rebound direction. The deviation in angle is determined through the distance between two points which are marked by the particle impact with and without the specimen rotation. The friction coefficient is derived from the angle of deviation, a . The particle impact velocity is controlled through the falling distance, and the impact angle through the half vertical angle, b , as well as the specimen rotating velocity. Four kinds of materials were used as target specimens, these were aluminium, brass, carbon steel and quenched carbon steel. The chemical compositions and the mechani-
Fig. 2. Schematic diagram of the rotating target apparatus for measuring the friction coefficient during particle impact.
A. Yabuki et al.r Wear 233–235 (1999) 468–475
470
Table 1 Chemical composition and mechanical properties of target specimens
3. Measuring method
Material
Chemical composition Ž%.
Vickers hardness Hvs ŽGPa.
3.1. Friction coefficient
Aluminium Brass
2.4 Mg 58.69Cu–37.85Zn– 3.06Pb–0.25Sn 0.43C–0.63Mn–0.26Si 0.43C–0.63Mn–0.26Si
0.88 1.23
S45C S45C Žquenched.
2.35 4.41
cal properties are listed in Table 1. The half vertical angles of the specimen were 208, 308 and 408. The surface of the specimens were polished with emery paper of a2000. Two kinds of spherical particles and three kinds of angular particles were used as impacting particles. Their mechanical properties are listed in Table 2. The measuring board was made of polyvinyl-chloride resin of which the surface was covered with chalk dust through spraying the so-called developer of the visible dye penetrant testing. The position of the particle impact on the board was recorded through the peeling off of the developer dust. The impact velocity of the solid particle ranged from 1.0 to 5.0 mrs, and the impact angles were 158, 208 and 308. 2.2. Critical impact Õelocity The principle in the derivation of critical impact velocity from the friction coefficients is simple, that is, the dynamic friction coefficient during skidding and the static friction coefficient during rolling without skidding. The value of the dynamic coefficient is generally smaller than that of the static coefficient, and is always constant independent of skidding velocity w5x. Thus, the beginning of the particle skidding on the specimen surface will be easily perceived as a turning point in the friction coefficient vs. impact velocity relationship, and this velocity must be the critical impact velocity.
During the impact of a spherical particle at the impact velocity of V0 on the target specimen which is rotating with the velocity of 2p rn, two forces act on the particle as shown in Fig. 3. One is the friction force F in the tangential direction to the target surface, and the other is the rebounding force W in the normal direction to the target surface ŽFig. 3Ža... F is decomposed into the component in the specimen rotating direction, F cos g , and the component in the specimen ridge direction, F sin g . The particle velocity, V0 , is decomposed into Vt and Vr as shown in Fig. 3Žb., and turned into V0X through the impact. The friction coefficient, m , is defined through the following equation.
ms
F W
.
Ž 1.
The tangent of deviation angle, a , is given as follows. tan a s
Vt VrX
.
Ž 2.
Firstly, we consider the velocity component in the specimen rotating direction. Vt is founded on the friction force in the specimen-rotating direction during the particle impact. Eq. Ž3. is derived from the conservation of momentum in the specimen rotating direction. m Ž Vt y 0 . s F cos g d t.
Ž 3.
H
Substituting Eq. Ž1. into Eq. Ž3., we get mVt s cos g mWd t.
Ž 4.
H
The friction coefficient m varies from time to time during the particle impact, and it is difficult to determine its value
Table 2 Mechanical and physical properties of particles Shape
Material
Mean diameter Dp Žmm.
Density rp Žkgrm3 .
Spherical
Steel shot
7890
8.8
Angular
Brass shot Steel grit
0.6 0.8 3.0 5.0 3.0 0.28 0.88 1.13 0.27 0.29 0.56 0.26 0.34 0.40
8430 7890
2.1 2.9
3170
11.8
2650
35.3
Silicon carbide
Silica sand
Vickers hardness Hvp ŽGPa.
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The rebounding coefficient, e, is defined as a ratio of velocities before and after the impact in the direction vertical to the target surface w7x, Vr sin b X es . Ž 8. V0 sin b Expressing VrX in terms of Vr , b and bX , VrX s Vr cos Ž 1808 y 908 y b y b X . s Vr sin Ž b q b X . .
Ž 9. Substitution of Eqs. Ž2., Ž7. – Ž9. into Eq. Ž6. leads to Vr tan a ms sin Ž b q b X . . Ž 10 . V0 sin b cos g Ž 1 q e . Similarly, we consider the velocity component in the specimen ridge direction. The change in momentum vs. the impulse balance in the specimen ridge direction derives mVr cos b X y mV0 cos b s ym sin g Wd t.
Ž 11 .
H
Substitution of Eq. Ž7. into Eq. Ž11. leads to Vr cos b X y mV0 cos b s ym sin g Ž mVr sin b X q mV0 sin b . . Ž 12 . Combining Eq. Ž8. with Eq. Ž12. leads to the following equation of Vr .
)
1
Vr s V0 sin b e 2 q
tan b
2
y m Ž 1 q e . sin g
.
Ž 13 .
Finally, substitution of Eq. Ž13. into Eq. Ž10. leads to the following equation of m. Fig. 3. The locus of an impacting particle on rotating target specimen: Ža. forces applied on a particle; Žb. velocities of particle before and after the impact; Žc. relative impact velocity and angle of particle against target specimen.
)
1
tan a e 2 q
ms
tan b
2
y m Ž 1 q e . sin g
Ž 1 q e . cos g
sin Ž b q b X .
Ž 14 . at each instant. For this reason, the time averaged friction coefficient m is adopted w6x, that is,
HmWd t s mHWd t.
Ž 5.
Combining Eq. Ž5. with Eq. Ž4. leads to the following equation of m ,
ms
mVt
.
Ž 6.
cos g Wd t
H
Secondly, we consider the velocity component in the direction normal to the target surface. Equating the impulse with the change in momentum in the direction normal to the target surface, X
HWd t s mV sin b y Ž ymV sin b . . r
0
Ž 7.
in which b X is the rebounding angle of the particle to the target surface and is given as the following equation by combining Eq. Ž8. with Eq. Ž12.. e sin b tan b X s . Ž 15 . cos b y m Ž 1 q e . sin g sin b The impact velocity V, the impact angle u and the angle g at the impact are given by the following equations referring Fig. 3Žc.. Note that the velocities and the angles in Fig. 3Žc. are referring to a rotating coordinate for easier understanding of the actual impact velocities of particle on the target surface.
(
V s V02 q Ž 2p rn .
u s siny1 g s tany1
ž ž
2
V0 sin b V V0 cos b 2p rn
/ /
Ž 16 . Ž 17 . .
Ž 18 .
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A. Yabuki et al.r Wear 233–235 (1999) 468–475
m is to be calculated from Eqs. Ž14., Ž15. and Ž18. by using the observed angle of deviation a . The impact condition is determined by Eqs. Ž16. and Ž17.. Note that the friction coefficient obtained is the time averaged coefficient during the impact. The rebounding coefficient e is required for the calculation of m. However, the discretional value of e between 0 and 1 was inserted into these equations because m was practically insensitive to e. 3.2. Verification of measurements 3.2.1. Friction coefficient In order to verify the theoretical equation, the observed values of a were put into the equation to derive the friction coefficient for the impact of a spherical particle on the target specimens of the same material but with different vertical angle b : the equation should give the same value of m independent of b so long as the particle impinged under the same impact condition. The so-derived value of m are shown in Fig. 4 for the steel shot of 0.6 mm diameter which impinged on the carbon steel target specimens with the half vertical angles of 208, 308 and 408 at the impact angle of 208. Almost every point fell on a single line proving the equation to be quite reliable. The m exhibited nearly constant value in the range of higher impact velocities, but in the velocity range lower than a certain velocity it rose with the decreasing impact velocity just as expected above. The rise in m with the lowering of the impact velocity, can be explained as follows: the static friction coefficient varies depending on the ratio of force components during the impact, and further m is the average of the dynamic friction coefficient during particle skidding at the beginning of contact and the static friction coefficient during particle rotating after the skidding.
Fig. 5. Optical micrographs of crater formed on mild steel, S45C, by impacting of steel shot of 5 mm, diameter; upper: impact velocity of 1.9 mrs; and lower: impact velocity of 2.5 mrs.
3.2.2. Critical impact Õelocity In order to verify the critical impact velocity, the bottom surface of the craters were carefully observed which originated on the target surface through the impact of a
spherical particle at the impact velocity range where the break appeared on the m vs. impact velocity relationship. The particle was a steel shot of 5 mm diameter which was allowed to impinge on the carbon steel specimen at the impact angle of 308. The impact velocities were 1.9 and 2.5 mrs since the rise in m appeared at 2.0 mrs ŽFig. 5.. In contrast to the scarce difference in the shape between the craters, a clear difference was recognized in the shape of pits which originated on the bottom surface of the craters, that is, circular points at 1.9 mrs as against dashes arranged in the impact direction at 2.5 mrs. This result of observation does not contradict the particle skidding at
Fig. 4. Relationship between friction coefficient and impact velocity for various half vertical angles.
Fig. 6. Relationship between friction coefficient and impact velocity for various impact angles and diameters of steel shot.
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473
various diameters on carbon steel at the impact angles of 158, 208 and 308 were shown in Fig. 6. The friction coefficients and accordingly the critical impact velocities of steel shot of 0.6 mm diameter were same independent of impact angle. The results with various target specimens are shown in Fig. 7. In conclusion, not only the critical impact velocity but also the friction coefficient varied largely depending on the particle diameter and the target material. Both the critical impact velocities and the friction coefficients of brass shot on four kinds of target specimens were shown in Table 3, including other results mentioned above.
4.1.2. Critical impact Õelocity for angular particle The friction coefficient was measured for the impact of steel grid of 0.88 mm mean diameter on carbon steel target. Some dispersion of the friction coefficient was observed even under the same impact conditions. The frequency distributions of the friction coefficient at four different impact velocities are shown in Fig. 8. The distributions at the impact velocities higher than 2.6 mrs were similar to each other, but at 1.9 mrs it was spread wider and the friction coefficient at the maximum frequency rose. This may be interpreted as follows: at a higher impact velocity range, it remains almost constant because of the skidding of the particle on the target surface, or directly speaking, being a dynamic friction coefficient; its dispersion comes from the deviation in the rebounding direction which resulted from the irregular shape of the angular particle. At a lower velocity range, it rose since it is a static friction coefficient accompanied with the dispersion of the same reason, that is, the irregularity in the particle shape.
Fig. 7. Relationship between friction coefficient and impact velocity for various target specimens.
higher impact velocities than 2.0 mrs, and supports no skidding at the velocities lower than that. Consequently, we may take the velocity at the break point for the critical impact velocity.
4. Results and discussion 4.1. Measurement of critical impact Õelocity 4.1.1. Critical impact Õelocity for spherical particle The critical impact velocities for spherical particles were determined from the measurement of the friction coefficients for various impact conditions changing the impact angle, particle diameter and target material. The friction coefficient during the impact of steel shots of Table 3 Critical impact velocity and friction coefficient under various impact conditions Particle Shape
Material
Mean diameter Dp Žmm.
Spherical
Steel shot
3.0 3.0 0.6 0.8 3.0 5.0 3.0 3.0 3.0 3.0 3.0 0.28 0.88 1.13 0.27 0.29 0.56 0.26 0.34 0.40
Brass shot
Angular
Steel grit
Silicon carbide
Silica sand
Target specimen
Critical impact velocity Vc Žmrs.
Friction coefficient m Žy.
Aluminium Brass S45C S45C S45C S45C S45CŽquenched. Aluminium Brass S45C S45CŽquenched. S45C S45C S45C S45C S45C S45C S45C S45C S45C
0.8 0.9 1.4 1.2 1.9 2.0 3.0 1.0 1.2 1.5 1.3 3.0 2.1 1.7 2.7 2.3 2.3 2.5 2.3 2.1
0.22 0.19 0.18 0.17 0.14 0.13 0.12 0.26 0.22 0.17 0.15 0.36 0.28 0.23 0.39 0.39 0.38 0.29 0.26 0.25
474
A. Yabuki et al.r Wear 233–235 (1999) 468–475
Fig. 8. Normalized frequency distributions of friction coefficient during impact of angular particle for various impact velocities.
The interpretation above leads to the adoption of the coefficient at the maximum frequency as the representative value at that impact velocity. The points obtained in the above mentioned procedure were connected with a line in a similar manner as is in the case of aluminium specimen ŽFig. 7. to give the critical impact velocity of 2.2 mrs as shown in Fig. 9. The results of silicon carbide particle and silica sand of various diameters on carbon steel target specimen were shown in Table 3. Relationship between the critical impact velocities and the particle diameter for spherical particle as well as angular particles are shown in Fig. 10. In the case of spherical particle, the larger the diameter, the higher the critical impact velocity. In the case of the angular particle, the larger the particle diameter, the lower the critical impact velocity. Thus, the particle shape effect is clearly reflected in the particle size vs. impact velocity relationship.
Fig. 9. Relationship between friction coefficient and impact velocity during impact of angular particle.
Fig. 10. Influence of particle diameter on critical impact velocity for spherical particle Žsteel shot. and angular particles Žsteel grid, silicon carbide and silica sand..
4.2. Correlation with material properties The correlation between the critical impact velocities determined through the friction coefficient and the material properties was investigated. It is well known that the amount of damage in solid particles impact erosion largely depends on the ratio of particle hardness to the specimen hardness w8x. The relationship between the critical impact velocities and the ratio of specimen hardness ŽHvs . to particle hardness ŽHvp . is shown in Fig. 11 for two kinds of spherical particles. In both cases the critical velocities rose with the rise of hardness ratio. These relationships, however, could not be unified into a single line, which means that the hardness ratio is not the universal parameter. The relationships between the critical impact velocity and the dynamic friction coefficient are shown in Fig. 12 where the critical impact velocity of spherical particles are
Fig. 11. Correlation between critical impact velocity and ratio of Vickers hardness of particle and target specimen.
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2. The methodology to determine the critical impact velocity through the friction coefficient during the impact of solid particles was established. 3. The critical impact velocities depended on the mechanical properties of solid particle and specimen. 4. The critical impact velocities of spherical particles were correlated partly with the friction coefficient and the hardness of solid particle and specimen, however, the shape of solid particle have to be taken into account to estimate the critical impact velocity for angular particles. Acknowledgements Fig. 12. Correlation between critical impact velocity and friction coefficient for various impact conditions.
correlated with the dynamic friction coefficient but those of angular particles are not. All of the foregoing experimental results indicated that the critical impact velocity could be related partly with the mechanical properties such as hardness and dynamic friction coefficient. However, no single parameter nor combined parameters could correlate the velocity for every combination of solid particle and target material. Moreover, it was obvious that the effect of the particle shape must be taken into account to determine the critical impact velocity for angular particles. The theoretical equation of the critical impact velocity in which these parameters were all included will be presented in the next paper w9x.
5. Conclusions 1. The methodology to determine the friction coefficient through a rotating target apparatus was established.
This research was supported in part by a Grant from the Ministry of Education, grant-in aid for scientific research on primary areas ŽNo. 07455292.. The authors wish to express their gratitude to Messrs. H. Ishibashi, S. Kawase, Y. Nishino, T. Kawabata, J. Shimazumi, Y. Tabata, M. Kakimi, T. Katsuki and F. Takenaga for their assistance with the experiments. References w1x J.G.A. Bitter, Wear 6 Ž1963. 5 and 169. w2x M. Matsumura, Y. Oka, M. Yamawaki, Proc. 7th Int. Conf. on Erosion by Liquid and Solid Impact, paper 40, Cambridge, 1987. w3x Y. Oka, M. Matsumura, M. Yamawaki, M. Sakai, ASTM STP 946 Ž1987. 141. w4x M. Matsumura, Corros. Rev. 12 Ž1994. 321. w5x C.A. Coulomb, Memoires de Mathematique et de Physique de l’Academie Royal de Sciences, 1785, p. 161. w6x F.P. Bowden, P.A. Persson, Proc. R. Soc. A 260 Ž1960. 433. w7x A.D. Salman, A. Verba, Zs. Lukenics, M. Szabo, Period. Polytech. Chem. Eng. 35 Ž1991. 43. w8x K. Wellinger, H. Uetz, Wear 1 Ž1957. 225. w9x A. Yabuki, K. Matsuwaki, M. Matsumura Ž1998. Žpaper is WEA 8260..
Critical impact velocity in the solid particles impact erosion of metallic materials Akihiro Yabuki ) , Kazuo Matsuwaki, Masanobu Matsumura Department of Chemical Engineering, Hiroshima UniÕersity, Higashihiroshima 739-8527, Japan
Abstract Solid particles impact erosion of metallic materials proceeds through two kinds of damage processes. One is the removal of material due to repeated plastic deformation, and the other is cutting. These processes occur simultaneously and the ratio of each contribution to the total damage depends not only on the impact angle Žthe predominant parameter. but also on the impact velocity. As the impact velocity goes down, a solid particle tends not to skid on the target material surface, and hence the cutting damage is reduced. At a certain lower velocity, the particle does not skid at all, resulting in no cutting damage but plastic deformation damage only. This velocity was defined as the ‘‘critical impact velocity’’. In this study, the methodology to determine the critical velocity through a measurement of the coefficient of friction was established, that is, the dynamic friction coefficient during skidding and the static friction coefficient during rolling without skidding. In order to measure the coefficient of friction at the moment of particle impact, a rotating target apparatus was developed. The critical impact velocity thus determined depended on the hardness of both material and particle, as well as on the shape and size of the solid particles. q 1999 Elsevier Science S.A. All rights reserved. Keywords: Erosion; Solid particle; Critical impact velocity; Friction coefficient; Impact angle
1. Introduction Components of solid particle-handling machines and equipment suffer some damage by the impact of solid particles, causing plastic deformation which leads to the material removal from the surface. This phenomenon is called abrasive wear or solid particles impact erosion. In case of serious damage, this may influence the service life of these machines. Thus, accelerated erosion tests in laboratories are carried out to predict the amount of damage in the field or to select materials suitable to the machines seeking a way to prolong the service life. It is generally recognized, however, that any experimental result obtained by the accelerated test does not agree with the performance of real equipment. Even the ranking of materials hardly coincides with the order of their service life in the field. This discrepancy between a laboratory test result and the performance of the material in the field is mainly attributed to the fact that erosion of metallic materials proceeds through two kinds of damage processes and the ratio of each contribution to the total damage depends on
)
Corresponding author
many factors, in particular, on the particles impact angle w1,2x. When solid particles impinge almost vertically on a metallic material at a high impact angle, removal of metallic material occurs mainly due to repeated plastic deformation. On the other hand, the removal due to cutting become dominant over plastic deformation damage at a low impact angle. These processes occur simultaneously and the ratio of each contribution to the total damage depends not only on the impact condition Žimpact angle, velocity. but also on the mechanical properties of solid particles Žhardness, shape, size, etc.. as well as the target materials Žhardness, toughness, etc... However, we experienced an unexpected agreement: the erosion–corrosion test results for two kinds of chromium steels in gypsum–sulfuric acid slurry obtained by a laboratory apparatus agreed well with the actual performance in slurry pump, although both impact velocities and angles of solid particles were quite different. To be precise, the particles impact velocity in laboratory test was 1.7 mrs and in the slurry pump it exceeded 10 mrs. The particles impact angle in laboratory test was apparently 908 and in the actual slurry pump it was very low w3x. The reason for this unexpected agreement may be explained as follows. As the impact velocity goes down, a solid particle tends
0043-1648r99r$ - see front matter q 1999 Elsevier Science S.A. All rights reserved. PII: S 0 0 4 3 - 1 6 4 8 Ž 9 9 . 0 0 1 7 0 - 2
A. Yabuki et al.r Wear 233–235 (1999) 468–475
Fig. 1. Relationship between dissolution rate of damaged surface and SiC particle impact velocity on mild steel w4x.
469
machine component. Further, a good agreement is anticipated even in the erosion–corrosion interaction between the field and laboratory. As mentioned above, the critical impact velocity is a very important factor in predicting the erosion behavior of the material. The critical velocities of various combinations of particle and material may be obtained through measuring the dissolution rates of damaged surfaces. A lot of time and work, however, have to be taken in this method. For a material, any suitable dissolving liquid or any method to measure the dissolution rate could not always be found. In this study, the methodology to determine the critical impact velocity through measuring the friction coefficient between a solid particle and material is established, which is of universal application.
2. Principle of measurement not to skid on the target material surface, which accordingly decreases the damage through cutting. At a certain lower velocity, the particle does not skid at all, which results in no cutting damage but plastic deformation damage only. We named this velocity ‘‘critical impact velocity’’. It is interpreted that in the laboratory test the particles impact velocity was lower than the critical velocity because the solid particles impinged on the specimen with a low velocity and at a high impact angle for the cutting process not to occur. On the other hand, the solid particles in the slurry pump were smaller in size and lower in hardness than the particles used in the laboratory test. Even if these particles impinged on the material surface with a high velocity at a low impact angle, the material would not be damaged by cutting. In other words, the critical impact velocity in the slurry pump must be higher than the actual impact velocity, 10 mrs. Then, it was a matter of course that the results of the accelerated laboratory test agreed with the actual performance in slurry pumps because the damage mechanism was repeated plastic deformation only in both cases. To provide proof of the critical impact velocity, an experiment was carried out by allowing silicon carbide particles to fall freely on the mild steel surface which was inclined at an angle. The damaged surface was put into a hydrochloric acid solution of pH 2 and its dissolution rate was measured. The dissolution rates of surfaces damaged at various impact angles gradually converged upon a certain common rate with reducing impact velocity as shown in Fig. 1 w4x. This impact velocity of 1.7 mrs at which dissolution rate came to a common value must be the critical impact velocity because unity of dissolution rate means the unity of damage mechanism. It can be expected that erosion damages in actual machines and equipment occur at the critical impact velocity or less. If so, the test results obtained at an accelerated damage rate but at an impact velocity lower than the critical velocity may agree with the actual performance of
2.1. Friction coefficient The rotating target apparatus in Fig. 2 was used to determine the friction coefficient during the particle impact. A solid particle is allowed to fall from a certain distance down to impinge on the rotating conical target specimen. After the impact, the solid particle rebounds off toward the measuring board. During the impact, the solid particle is affected by a friction force in the tangential direction due to the rotation of the specimen to cause some deviation in its rebound direction. The deviation in angle is determined through the distance between two points which are marked by the particle impact with and without the specimen rotation. The friction coefficient is derived from the angle of deviation, a . The particle impact velocity is controlled through the falling distance, and the impact angle through the half vertical angle, b , as well as the specimen rotating velocity. Four kinds of materials were used as target specimens, these were aluminium, brass, carbon steel and quenched carbon steel. The chemical compositions and the mechani-
Fig. 2. Schematic diagram of the rotating target apparatus for measuring the friction coefficient during particle impact.
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Table 1 Chemical composition and mechanical properties of target specimens
3. Measuring method
Material
Chemical composition Ž%.
Vickers hardness Hvs ŽGPa.
3.1. Friction coefficient
Aluminium Brass
2.4 Mg 58.69Cu–37.85Zn– 3.06Pb–0.25Sn 0.43C–0.63Mn–0.26Si 0.43C–0.63Mn–0.26Si
0.88 1.23
S45C S45C Žquenched.
2.35 4.41
cal properties are listed in Table 1. The half vertical angles of the specimen were 208, 308 and 408. The surface of the specimens were polished with emery paper of a2000. Two kinds of spherical particles and three kinds of angular particles were used as impacting particles. Their mechanical properties are listed in Table 2. The measuring board was made of polyvinyl-chloride resin of which the surface was covered with chalk dust through spraying the so-called developer of the visible dye penetrant testing. The position of the particle impact on the board was recorded through the peeling off of the developer dust. The impact velocity of the solid particle ranged from 1.0 to 5.0 mrs, and the impact angles were 158, 208 and 308. 2.2. Critical impact Õelocity The principle in the derivation of critical impact velocity from the friction coefficients is simple, that is, the dynamic friction coefficient during skidding and the static friction coefficient during rolling without skidding. The value of the dynamic coefficient is generally smaller than that of the static coefficient, and is always constant independent of skidding velocity w5x. Thus, the beginning of the particle skidding on the specimen surface will be easily perceived as a turning point in the friction coefficient vs. impact velocity relationship, and this velocity must be the critical impact velocity.
During the impact of a spherical particle at the impact velocity of V0 on the target specimen which is rotating with the velocity of 2p rn, two forces act on the particle as shown in Fig. 3. One is the friction force F in the tangential direction to the target surface, and the other is the rebounding force W in the normal direction to the target surface ŽFig. 3Ža... F is decomposed into the component in the specimen rotating direction, F cos g , and the component in the specimen ridge direction, F sin g . The particle velocity, V0 , is decomposed into Vt and Vr as shown in Fig. 3Žb., and turned into V0X through the impact. The friction coefficient, m , is defined through the following equation.
ms
F W
.
Ž 1.
The tangent of deviation angle, a , is given as follows. tan a s
Vt VrX
.
Ž 2.
Firstly, we consider the velocity component in the specimen rotating direction. Vt is founded on the friction force in the specimen-rotating direction during the particle impact. Eq. Ž3. is derived from the conservation of momentum in the specimen rotating direction. m Ž Vt y 0 . s F cos g d t.
Ž 3.
H
Substituting Eq. Ž1. into Eq. Ž3., we get mVt s cos g mWd t.
Ž 4.
H
The friction coefficient m varies from time to time during the particle impact, and it is difficult to determine its value
Table 2 Mechanical and physical properties of particles Shape
Material
Mean diameter Dp Žmm.
Density rp Žkgrm3 .
Spherical
Steel shot
7890
8.8
Angular
Brass shot Steel grit
0.6 0.8 3.0 5.0 3.0 0.28 0.88 1.13 0.27 0.29 0.56 0.26 0.34 0.40
8430 7890
2.1 2.9
3170
11.8
2650
35.3
Silicon carbide
Silica sand
Vickers hardness Hvp ŽGPa.
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The rebounding coefficient, e, is defined as a ratio of velocities before and after the impact in the direction vertical to the target surface w7x, Vr sin b X es . Ž 8. V0 sin b Expressing VrX in terms of Vr , b and bX , VrX s Vr cos Ž 1808 y 908 y b y b X . s Vr sin Ž b q b X . .
Ž 9. Substitution of Eqs. Ž2., Ž7. – Ž9. into Eq. Ž6. leads to Vr tan a ms sin Ž b q b X . . Ž 10 . V0 sin b cos g Ž 1 q e . Similarly, we consider the velocity component in the specimen ridge direction. The change in momentum vs. the impulse balance in the specimen ridge direction derives mVr cos b X y mV0 cos b s ym sin g Wd t.
Ž 11 .
H
Substitution of Eq. Ž7. into Eq. Ž11. leads to Vr cos b X y mV0 cos b s ym sin g Ž mVr sin b X q mV0 sin b . . Ž 12 . Combining Eq. Ž8. with Eq. Ž12. leads to the following equation of Vr .
)
1
Vr s V0 sin b e 2 q
tan b
2
y m Ž 1 q e . sin g
.
Ž 13 .
Finally, substitution of Eq. Ž13. into Eq. Ž10. leads to the following equation of m. Fig. 3. The locus of an impacting particle on rotating target specimen: Ža. forces applied on a particle; Žb. velocities of particle before and after the impact; Žc. relative impact velocity and angle of particle against target specimen.
)
1
tan a e 2 q
ms
tan b
2
y m Ž 1 q e . sin g
Ž 1 q e . cos g
sin Ž b q b X .
Ž 14 . at each instant. For this reason, the time averaged friction coefficient m is adopted w6x, that is,
HmWd t s mHWd t.
Ž 5.
Combining Eq. Ž5. with Eq. Ž4. leads to the following equation of m ,
ms
mVt
.
Ž 6.
cos g Wd t
H
Secondly, we consider the velocity component in the direction normal to the target surface. Equating the impulse with the change in momentum in the direction normal to the target surface, X
HWd t s mV sin b y Ž ymV sin b . . r
0
Ž 7.
in which b X is the rebounding angle of the particle to the target surface and is given as the following equation by combining Eq. Ž8. with Eq. Ž12.. e sin b tan b X s . Ž 15 . cos b y m Ž 1 q e . sin g sin b The impact velocity V, the impact angle u and the angle g at the impact are given by the following equations referring Fig. 3Žc.. Note that the velocities and the angles in Fig. 3Žc. are referring to a rotating coordinate for easier understanding of the actual impact velocities of particle on the target surface.
(
V s V02 q Ž 2p rn .
u s siny1 g s tany1
ž ž
2
V0 sin b V V0 cos b 2p rn
/ /
Ž 16 . Ž 17 . .
Ž 18 .
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m is to be calculated from Eqs. Ž14., Ž15. and Ž18. by using the observed angle of deviation a . The impact condition is determined by Eqs. Ž16. and Ž17.. Note that the friction coefficient obtained is the time averaged coefficient during the impact. The rebounding coefficient e is required for the calculation of m. However, the discretional value of e between 0 and 1 was inserted into these equations because m was practically insensitive to e. 3.2. Verification of measurements 3.2.1. Friction coefficient In order to verify the theoretical equation, the observed values of a were put into the equation to derive the friction coefficient for the impact of a spherical particle on the target specimens of the same material but with different vertical angle b : the equation should give the same value of m independent of b so long as the particle impinged under the same impact condition. The so-derived value of m are shown in Fig. 4 for the steel shot of 0.6 mm diameter which impinged on the carbon steel target specimens with the half vertical angles of 208, 308 and 408 at the impact angle of 208. Almost every point fell on a single line proving the equation to be quite reliable. The m exhibited nearly constant value in the range of higher impact velocities, but in the velocity range lower than a certain velocity it rose with the decreasing impact velocity just as expected above. The rise in m with the lowering of the impact velocity, can be explained as follows: the static friction coefficient varies depending on the ratio of force components during the impact, and further m is the average of the dynamic friction coefficient during particle skidding at the beginning of contact and the static friction coefficient during particle rotating after the skidding.
Fig. 5. Optical micrographs of crater formed on mild steel, S45C, by impacting of steel shot of 5 mm, diameter; upper: impact velocity of 1.9 mrs; and lower: impact velocity of 2.5 mrs.
3.2.2. Critical impact Õelocity In order to verify the critical impact velocity, the bottom surface of the craters were carefully observed which originated on the target surface through the impact of a
spherical particle at the impact velocity range where the break appeared on the m vs. impact velocity relationship. The particle was a steel shot of 5 mm diameter which was allowed to impinge on the carbon steel specimen at the impact angle of 308. The impact velocities were 1.9 and 2.5 mrs since the rise in m appeared at 2.0 mrs ŽFig. 5.. In contrast to the scarce difference in the shape between the craters, a clear difference was recognized in the shape of pits which originated on the bottom surface of the craters, that is, circular points at 1.9 mrs as against dashes arranged in the impact direction at 2.5 mrs. This result of observation does not contradict the particle skidding at
Fig. 4. Relationship between friction coefficient and impact velocity for various half vertical angles.
Fig. 6. Relationship between friction coefficient and impact velocity for various impact angles and diameters of steel shot.
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various diameters on carbon steel at the impact angles of 158, 208 and 308 were shown in Fig. 6. The friction coefficients and accordingly the critical impact velocities of steel shot of 0.6 mm diameter were same independent of impact angle. The results with various target specimens are shown in Fig. 7. In conclusion, not only the critical impact velocity but also the friction coefficient varied largely depending on the particle diameter and the target material. Both the critical impact velocities and the friction coefficients of brass shot on four kinds of target specimens were shown in Table 3, including other results mentioned above.
4.1.2. Critical impact Õelocity for angular particle The friction coefficient was measured for the impact of steel grid of 0.88 mm mean diameter on carbon steel target. Some dispersion of the friction coefficient was observed even under the same impact conditions. The frequency distributions of the friction coefficient at four different impact velocities are shown in Fig. 8. The distributions at the impact velocities higher than 2.6 mrs were similar to each other, but at 1.9 mrs it was spread wider and the friction coefficient at the maximum frequency rose. This may be interpreted as follows: at a higher impact velocity range, it remains almost constant because of the skidding of the particle on the target surface, or directly speaking, being a dynamic friction coefficient; its dispersion comes from the deviation in the rebounding direction which resulted from the irregular shape of the angular particle. At a lower velocity range, it rose since it is a static friction coefficient accompanied with the dispersion of the same reason, that is, the irregularity in the particle shape.
Fig. 7. Relationship between friction coefficient and impact velocity for various target specimens.
higher impact velocities than 2.0 mrs, and supports no skidding at the velocities lower than that. Consequently, we may take the velocity at the break point for the critical impact velocity.
4. Results and discussion 4.1. Measurement of critical impact Õelocity 4.1.1. Critical impact Õelocity for spherical particle The critical impact velocities for spherical particles were determined from the measurement of the friction coefficients for various impact conditions changing the impact angle, particle diameter and target material. The friction coefficient during the impact of steel shots of Table 3 Critical impact velocity and friction coefficient under various impact conditions Particle Shape
Material
Mean diameter Dp Žmm.
Spherical
Steel shot
3.0 3.0 0.6 0.8 3.0 5.0 3.0 3.0 3.0 3.0 3.0 0.28 0.88 1.13 0.27 0.29 0.56 0.26 0.34 0.40
Brass shot
Angular
Steel grit
Silicon carbide
Silica sand
Target specimen
Critical impact velocity Vc Žmrs.
Friction coefficient m Žy.
Aluminium Brass S45C S45C S45C S45C S45CŽquenched. Aluminium Brass S45C S45CŽquenched. S45C S45C S45C S45C S45C S45C S45C S45C S45C
0.8 0.9 1.4 1.2 1.9 2.0 3.0 1.0 1.2 1.5 1.3 3.0 2.1 1.7 2.7 2.3 2.3 2.5 2.3 2.1
0.22 0.19 0.18 0.17 0.14 0.13 0.12 0.26 0.22 0.17 0.15 0.36 0.28 0.23 0.39 0.39 0.38 0.29 0.26 0.25
474
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Fig. 8. Normalized frequency distributions of friction coefficient during impact of angular particle for various impact velocities.
The interpretation above leads to the adoption of the coefficient at the maximum frequency as the representative value at that impact velocity. The points obtained in the above mentioned procedure were connected with a line in a similar manner as is in the case of aluminium specimen ŽFig. 7. to give the critical impact velocity of 2.2 mrs as shown in Fig. 9. The results of silicon carbide particle and silica sand of various diameters on carbon steel target specimen were shown in Table 3. Relationship between the critical impact velocities and the particle diameter for spherical particle as well as angular particles are shown in Fig. 10. In the case of spherical particle, the larger the diameter, the higher the critical impact velocity. In the case of the angular particle, the larger the particle diameter, the lower the critical impact velocity. Thus, the particle shape effect is clearly reflected in the particle size vs. impact velocity relationship.
Fig. 9. Relationship between friction coefficient and impact velocity during impact of angular particle.
Fig. 10. Influence of particle diameter on critical impact velocity for spherical particle Žsteel shot. and angular particles Žsteel grid, silicon carbide and silica sand..
4.2. Correlation with material properties The correlation between the critical impact velocities determined through the friction coefficient and the material properties was investigated. It is well known that the amount of damage in solid particles impact erosion largely depends on the ratio of particle hardness to the specimen hardness w8x. The relationship between the critical impact velocities and the ratio of specimen hardness ŽHvs . to particle hardness ŽHvp . is shown in Fig. 11 for two kinds of spherical particles. In both cases the critical velocities rose with the rise of hardness ratio. These relationships, however, could not be unified into a single line, which means that the hardness ratio is not the universal parameter. The relationships between the critical impact velocity and the dynamic friction coefficient are shown in Fig. 12 where the critical impact velocity of spherical particles are
Fig. 11. Correlation between critical impact velocity and ratio of Vickers hardness of particle and target specimen.
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2. The methodology to determine the critical impact velocity through the friction coefficient during the impact of solid particles was established. 3. The critical impact velocities depended on the mechanical properties of solid particle and specimen. 4. The critical impact velocities of spherical particles were correlated partly with the friction coefficient and the hardness of solid particle and specimen, however, the shape of solid particle have to be taken into account to estimate the critical impact velocity for angular particles. Acknowledgements Fig. 12. Correlation between critical impact velocity and friction coefficient for various impact conditions.
correlated with the dynamic friction coefficient but those of angular particles are not. All of the foregoing experimental results indicated that the critical impact velocity could be related partly with the mechanical properties such as hardness and dynamic friction coefficient. However, no single parameter nor combined parameters could correlate the velocity for every combination of solid particle and target material. Moreover, it was obvious that the effect of the particle shape must be taken into account to determine the critical impact velocity for angular particles. The theoretical equation of the critical impact velocity in which these parameters were all included will be presented in the next paper w9x.
5. Conclusions 1. The methodology to determine the friction coefficient through a rotating target apparatus was established.
This research was supported in part by a Grant from the Ministry of Education, grant-in aid for scientific research on primary areas ŽNo. 07455292.. The authors wish to express their gratitude to Messrs. H. Ishibashi, S. Kawase, Y. Nishino, T. Kawabata, J. Shimazumi, Y. Tabata, M. Kakimi, T. Katsuki and F. Takenaga for their assistance with the experiments. References w1x J.G.A. Bitter, Wear 6 Ž1963. 5 and 169. w2x M. Matsumura, Y. Oka, M. Yamawaki, Proc. 7th Int. Conf. on Erosion by Liquid and Solid Impact, paper 40, Cambridge, 1987. w3x Y. Oka, M. Matsumura, M. Yamawaki, M. Sakai, ASTM STP 946 Ž1987. 141. w4x M. Matsumura, Corros. Rev. 12 Ž1994. 321. w5x C.A. Coulomb, Memoires de Mathematique et de Physique de l’Academie Royal de Sciences, 1785, p. 161. w6x F.P. Bowden, P.A. Persson, Proc. R. Soc. A 260 Ž1960. 433. w7x A.D. Salman, A. Verba, Zs. Lukenics, M. Szabo, Period. Polytech. Chem. Eng. 35 Ž1991. 43. w8x K. Wellinger, H. Uetz, Wear 1 Ž1957. 225. w9x A. Yabuki, K. Matsuwaki, M. Matsumura Ž1998. Žpaper is WEA 8260..