- Email: [email protected]
Correlation between solid particle erosion of cermets and particle impact dynamics
ARTICLE IN PRESS
Tribology International 41 (2008) 323–330 www.elsevier.com/locate/triboint
Correlation between solid particle erosion of cermets and particle impact dynamics Irina Hussainovaa,, Klaus-Peter Schadeb a
Department of Materials Engineering, Tallinn University of Technology, Ehitajate 5, Tallinn 19086, Estonia SIVUS GmbH, Institute of Process, Environmental and Sensor Technology at the Chemnitz University of Technology, Schulstrasse 38, Chemnitz 09125, Germany
b
Received 8 February 2006; received in revised form 1 February 2007; accepted 4 September 2007 Available online 29 October 2007
Abstract Since the erosion rate depends on energy exchange between particle and material, a reformulation and solution of the equations of two solid bodies collision is presented and adapted to the calculation of the energy absorbed by a material surface during impact of a spherical particle onto a plain target. It has been observed that energy loss is a strong function of dynamic coefficients named as coefficient of velocity restitution after impact, k, and coefficient of dynamic friction, f. The new method and experimental equipment for the coefficients determination are described. It was shown that energy consumption during application may be an appropriate guide for the material selection in the conditions of erosive wear. r 2007 Elsevier Ltd. All rights reserved. Keywords: Particle–wall collision; Coefficient of restitution; Coefficient of dynamic friction; Energy dissipation; Erosion
1. Introduction Solid particle erosion is a serious problem for many industrial components, such as nozzles, valves, turbines, etc. Erosion is a process of material damage caused by hard particles striking the surface, either carried by a gas stream or entrained in a flowing liquid. Mechanisms of material removal differ for ductile and brittle materials. For ductile materials the main mechanism is severe localized plastic strain at the impact site exceeding the material strain—to failure. For brittle materials, the impacting particles typically cause localized cracking on the surface. For particle reinforced composites, mass loss due to solid particle erosion rather depends on intrinsic microstructural features [1]. However, materials response to a wear environment is not just an intrinsic one, but rather a reaction to a complicated combination of stresses imposed by an external system that is defined by the impact variables such as contact geometry, velocity, load, temperature, etc. An empirical power law relationship of the Corresponding author. Tel.: +372 620 33 55; fax: +372 620 91 36.
E-mail address: [email protected] (I. Hussainova). 0301-679X/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.triboint.2007.09.001
erosion rate W and particle velocity v is commonly used as W ¼ kvn, where k is a constant and n has values in a wide range. Value of 2 would be expected based on the particle kinetic energy, given by (1/2)mv2. Until now there is no satisfactory explanation for the deviation of n from 2. For instance, different particle shapes result in different energy of the particle to be transferred to the target. Depending on the specific combination of factors, the mechanism of material removal during erosion can be described as being somewhat between ductile and brittle [1,2]. In an attempt to rank materials based on mechanical properties several models have been developed [3,4]; however, the data obtained for composites [1,5] makes it clear that use of those approaches does not provide a consistent correlation between wear resistance and such composite properties as hardness, fracture toughness and modulus of elasticity. In general, erosion rate is influenced by test conditions such as abrasive particle velocity, angle of particle impingement, mass flux, particle mechanical properties, size and shape and target material properties. Different particles transfer the energy to the target over different volumes, thereby causing different energy densities in the target material and different mechanisms and
ARTICLE IN PRESS 324
I. Hussainova, K.-P. Schade / Tribology International 41 (2008) 323–330
rates of damage. Under other all things being identical, the material properties play the most important role. In that case a simplified assumption that the erosion rate should be proportional to the energy exchange between the erodent and the impacted material surface may be made. Thus, the energy absorbed during particle–target collision can be a useful approach for the evaluation of materials erosion resistance. In impact mechanics, several approaches are applied to study the solid bodies interaction. One of the first approaches was developed by Newton in the 17th century. Classical theory of impact based on Newton’s Second Law continues to be successfully used to model a process of twobody collision. The equations involve the use of the coefficients named as coefficients of velocity restitution after the collision, impulses and momentum. Further, the approaches taken frictional forces into consideration were developed. A comprehensive review of the collision models has been presented in [6]. Depending on the contact conditions and the approach used, the solution of the model equations can involve mathematical methods ranging from linear algebraic to nonlinear differential equations. Since the energy exchange is related to the velocity and angle of impact, these parameters have to be determined with a great care. As dynamic coefficients are not material constants, the coefficients must be evaluated experimentally or analytically related to the contact process. Any change in energy loss due to material properties effects can easily be masked by a small change
in velocity. To clarify the details of two-body interaction, a special test facility equipped with a digital video camera was worked out and used. One of the objectives of this study is the proper use, interpretation and measurement of the dynamic coefficients when solid particle strikes a flat solid surface as it everywhere happens when the particle erosion is mentioned. Another purpose of this study is characterization of the nature of energy absorption during impact of solid particle onto the target material of ceramic–metal composites or cermets. The third goal of the study is evaluation of an energetic approach for assessment of the cermet materials resistance to solid particle erosion. 2. Materials and experimental details The cermets tested in this study were produced by powder metallurgy processing techniques and in the compositions shown in Table 1. Table 1 presents the Vickers hardness values for those materials, also, but omits the values of fracture toughness because of some uncertainties in determination and estimation of this parameter for multi-phase systems [1]. It should be noticed that fracture toughness values measured by Palmgvist method were between 10 MPa m1/2 (for cermet C10S) and 17 MPa m1/2 (for cermet T20). Fig. 1 shows a schematic of the test equipment, which was specially developed by SIVUS GmbH at Chemnitz University of Technology, Germany, for the determination
Table 1 Composition and hardness of materials tested Grade
Composition
Vicker’s hardness, HV10
Notes
W15 C10 C20 CM20 C10S C20S T20
WC–85 wt%+Co–15 wt% Cr3C2–90 wt%+Ni–10 wt% Cr3C2–80 wt%+Ni–20 wt% Cr3C2–80 wt%+NiMo–20 wt% Cr3C2–90 wt%+Ni–10 wt% Cr3C2–80 wt%+Ni–20 wt% TiC–80 wt%+NiMo–20 wt%
1258 1358 1140 1217 1407 1233 1430
14 wt% Ni+6 wt% Mo Reaction sintering Reaction sintering 14 wt% Ni+6 wt% Mo
Fig. 1. Experimental facility.
ARTICLE IN PRESS I. Hussainova, K.-P. Schade / Tribology International 41 (2008) 323–330
Number of events
120
impact velocity
100
rebound velocity
80 60 40 20 0 4
5
6
7
8
9
10
Particle velocity, m/s
600
Number of events
of dynamic coefficients. The basic element is a centrifugal accelerator consisting of a feeder, a rotating disc and a target holding system. Solid particles are continuously fed into the central hole of the rotating disc and are accelerated through eight radial tubes by the centrifugal force and ejected from the end of the tubes. It has been indicated [7] that particle rotation increases the dynamic energy at impact. To avoid the influence of rotation, special configuration of test equipment was designed. The accelerator is rotated by a circulating belt, which is driven with the help of a high speed DC motor. To fix the particle exit, the tube ends are shut off by an additional belt rotating over the open circuit of the accelerating disc. As a result of the additional belt adjustment only a limited section of the disc circumference is uncovered at a definite period of time. Before ejecting from the outlet of the disc tube, a particle is stopped and leaves the channel at a fixed moment when the outlet of the tube is free from the covering belt. Therefore, the particles emerging from the acceleration tube of the tester have a fixed spatial position and negligible rotation. The specimen target is set near the disc on a holder that has provision for reorientation relative to the direction of particle flow and thus achieves the desired impact angle. Two particle velocities before impact have been used for the tests, which are 10 and 30 m/s, in order to obtain dynamic coefficients over a range of impact velocities. The rotational velocity of the accelerator disc was adjusted to give an exit velocity of the particles at each individual velocity required. The particle concentration in the jet emerging from the tubes in the disc was minimized as far as possible in order to avoid inter-particle collision effect. Tests were carried out at impact angles from 151 up to 851; 125-mm glass beads with a value of Vickers hardness of 540 HV were used as the impacting particles. Particle velocity distribution was determined for a large number of particles under identical conditions. A characteristic distribution of the beads velocity is illustrated in Fig. 2. Because of some deviation from the initial velocity, the number-averaged mean velocity was used for the results interpretation. The view of particle tracks as treated by a computational program is demonstrated in Fig. 3. After the impact test at each impact angle, the area of interaction was changed to avoid any ambiguities in surface quality. An Ar-ion laser beam refracted by cylindrical lens was used to illuminate a working area. The impact event was recorded with a digital video camera and transferred into a PC. The video images were then decomposed into individual frames with software. A calibration procedure has been carried out to eliminate any distortions. A conventional centrifugal four-channel accelerator was used for testing the solid particle erosion according to the procedure outlined elsewhere [5,8]. A comprehensive analysis of particle dynamics within the tester was carried out in [8,9]. The specimen targets are located around the disc on adjustable systems. In the tests, positions of target holders were arranged similar to those applied during the tests for dynamic coefficients determination. Test condi-
325
500
impact velocity
400
rebound velocity
300 200 100 0 15
20
25 Particle velocity, m/s
30
35
Fig. 2. Distribution of initial and rebound particle velocities: (a) in the case of C20 as a target and impact angle of 751, and (b) in the case of W15 and impact angle of 301.
Fig. 3. Particle tracks obtained by video camera: (a) in the case of impact angle of 301, and (b) in the case of impact angle of 601.
tions were as given in Table 2. The device allows testing 15 specimens simultaneously, thus all materials were examined under identical conditions. The number of test specimens of each cermet grades was four. To achieve a steady state erosion rate, all specimens were exposed to pre-testing for 180 min. The particles were fed into the rig
ARTICLE IN PRESS I. Hussainova, K.-P. Schade / Tribology International 41 (2008) 323–330
326
simplified and rewritten as follows:
Table 2 Erosion tests data Particle velocity before impact (m/s)
Impact angle (deg)
10 and 30
14, 30, 45, 60, 75, 85
vn2 ¼ kvn1 ,
(1)
vt2 vt1 ¼ f ð1 þ kÞvn1 ,
(2)
Temperature (1C)
23
and Oo¼
n dc
C
l
dn
t
O
Ft Fn
Fig. 4. Diagram of two-body interaction.
at a feed rate of 250 g/min. At least 10 increments of erosion were used to determine the steady state erosion rate. The erosion rate was calculated from the average mass loss and is equal to the volume of material removed per unit mass of abrasive particle entrained in the stream, and has units of mm3/kg. To quantify weight loss during erosion experiments, the specimens were ultrasonically cleaned in acetone and weighed before and after the erosion tests on an analytical balance to 0.01 mg. In this study, the variation in the measured mass loss among the four test samples of the same type was rarely greater than 15% and was usually much less. Thus, differences in tests results of greater than 15% were attributed to real differences in the wear behaviour of the materials. 3. Impact mechanics with application to energy loss The analysis of the collision between a solid particle and a massive flat surface is given in, for example, [10,11]. Fig. 4 represents the schematic drawing of particle–wall collision. Here, t–n axes are chosen as tangential and normal to the plane surface of a specimen, respectively. In the case of spherical particle impacting the plane target surface, the equations derived in [10] may be
f ð1 þ kÞvn1 l , R
(3)
where vn1 and vt1 are the normal and tangential components of a particle velocity before collision, respectively; vn2 and vt2 are the normal and tangential components, respectively of a particle velocity after collision describing a movement of centre of mass C. O and o are the final and initial angular velocities, respectively, I is the moment of inertia. Eq. (1) contains a coefficient k that expresses the process of a normal velocity restitution of particle at point O. Thus, the coefficient of restitution is related in a simple way to the relative velocities of particle before and after collision. It is obvious that the value of k is between 0 and 1. The coefficient f in Eq. (2) represents the process of tangential velocity restitution and may be treated as a coefficient of dynamic friction. Finally, Eq. (3) is an expression of conservation of the angular momentum about point O, where R is a particle radius and l ¼ R2/j2 ¼ 5/2 (j is the radius of gyration) for a solid sphere. These expressions correspond to sliding movement of spherical particle. The boundary conditions for particle sliding have been discussed in [10,12] and may be given as fp
2 ðvt1 RoÞ . 7 ð1 þ kÞvn1
(4)
Phenomenologically it is well known that part of the kinetic energy of the system could be lost due to various mechanisms, including deformation of contact surfaces and generation of heat and sound. The kinetic energy loss can be expressed in the terms of Eqs. (1)–(3) in nondimensional form [10] as 1 k2 b2 1 f f n K ¼ þ 2 , (5) fc 1 þ b2 1 þ b2 1 þ l f c where b ¼ ðvt1 RoÞ=vn1 and fc represents the maximal value of the coefficient of the dynamic friction: fc ¼
1 b . 1 þ l1 þ k
(6)
Eq. (6) reduces to expression (4) in the case of a solid sphere. In general, the value of the coefficients depends on the properties of the two bodies as well as their velocities and orientations when they collide, and they can be determined either by experiment or by a detailed analysis of the deformation of the two bodies during collision. The main task of this study is an experimental determination of the coefficients of restitution in order to calculate the particle energy loss or the energy absorbed by a target material during the impact.
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327
2 1 1 , 7 1 þ k tan a1
(7)
where a1 is the angle before collision or the impact angle. The coefficients of the velocity restitution k and the dynamic friction f can be calculated from vn (8) k ¼ 2 vn 1 and vt vt 2 1 . f ¼ ð1 þ kÞ vn1
(9)
The experimental data concerning the coefficient variations with the impact velocity and angle are presented in Figs. 5–7. It should be noticed that particle fragmentation would have complicated the energy balance; however, at low velocities applied in this study, the amount of fractured particle have been negligible and tracks of rebounding fractured particles have been eliminated from consideration. For the composite materials coefficient of restitution
W15 C20 C20S
0.110 0.105 0.100 0.095 0.090
W15 C10 C20 CM20 C10S C20S T20
0.9 0.85
15 20 Initial velocity, m/s
25
40 50 60 Impact angle, deg
70
30
0.14 0.12 0.1 W15 C20S C20 C10 T20
0.08 0.06 0.04 0.02 10
30
20
80
0.25
0.8 0.75 0.7 5
10
15 20 Impact velocity, m/s
25
30
0.95
Kn* Kt* K*
0.2 0.15 0.1 0.05 0 0
Restitution coefficient, k
10
Fig. 6. Coefficient of dynamic friction vs. (a) impact velocity (impact angle 601), and (b) impact angle (particle velocity—30 m/s).
0.95 Restitution coefficient, k
0.140 0.135 0.130 0.125 0.120 0.115
5
Normalized energy loss
f cp
Coefficient of dynamic friction, f
The boundary condition for the sliding impact (as based on Eq. (6) and taking into account the equality o ¼ 0 as provided by the experimental set-up) is
Coefficient of dynamic friction, f
4. Results and discussion
0.9 W15
C20 C20S
0.8
20
30
40 50 60 Impact angle, deg
70
80
90
Fig. 7. Effect of impact angle on the normal K n , tangential K t and total K normalized energy absorbed by W15 composite (impact velocity— 30 m/s).
C10
0.85
10
T20
0.75 0.7 0.65 0
10
20
30 40 50 60 Impact angle, deg
70
80
90
Fig. 5. Coefficient of velocity restitution vs. (a) impact velocity (impact angle 601), and (b) impact angle (particle velocity—30 m/s).
slightly decreases with approaching of the impact angle to the normal one and/or increasing the impact velocity. In Figs. 5(b), 6 and 7, there are data for several materials presented. It allows avoiding a mess on the pictures, whereas the common principal trends are similar for all materials tested. In the range of impact angles from 451 to 851 (Fig. 6(b)) the coefficient of dynamic friction decreases with increase in impact angle. At those angles the glass
ARTICLE IN PRESS I. Hussainova, K.-P. Schade / Tribology International 41 (2008) 323–330
Here fc represents a boundary friction coefficient. This expression presents the energy that is normalized by dividing the full particle energy by the initial kinetic energy and, therefore, K* is non-dimensional. The rotational energy loss can be hardly measured by the present experimental set-up. However, rolling after impact usually leads to negligible energy absorption. The variations of the translational kinetic energy loss with the impact angle are plotted in Fig. 7. Figure reveals that the energy loss at the shallow impact angles is due almost exclusively to the tangential forces. Both compressive and tangential losses have the same order of magnitude at the angle of about 601. The compressive effects dominate at the angles approaching the normal one. Energy loss due to inelasticity is insufficient because material hardness exceeds particle hardness and relatively soft but brittle particles are not able to cause significant plastic flow in a hard target. In the case of elastic impact the energy absorbed at oblique impact angles includes a substantial component attributed to the energy dissipation by frictional effects at the particle–target interface and the component of the energy transmitted to the surface depends strongly on the impact angle through the coefficient of dynamic friction. A large portion of the incident energy is dissipated via elastic– plastic deformation and heating in the near surface regions [1]. Fig. 8 shows the normalized energy absorbed by the cermets. Particles of low kinetic energy do not cause a large destruction in the surface of composites. The impact may be treated as almost elastic one. However, repeated impacts can result in surface damage and material removal due to low-cycle fatigue mechanisms operating in the near surface areas [1]. The influence of the impact angle on the erosion
0.35 Normalized energy absorbed
particles start rolling on the surface at the end of contact. At shallow angles, the coefficient f slightly changes and is approximately constant and ranges between 0.12 and 0.135 for all materials. This is the sliding region within which f may be interpreted as a coefficient of friction that obeys Amontons–Coulomb’s law. As was expected, f is a function of both impact angle and initial velocity of particle (Fig. 7). In ductile materials high shear strength is accumulated in the sub-surface areas of a target material because of friction-induced plastic deformation. That results in a high friction coefficient [13]. Cermets mostly show brittle fracture with relatively low resistance to crack extension originating at pre-existing defects. Energy release is more likely achieved through the formation of fracture surfaces rather than through plastic or viscoplastic processes, as compared to the more ductile materials of similar strength level. The energy loss during impact can be estimated according to the equation derived from Eqs. (9)–(13): 2f f 2 2 n K ¼ ð1 kÞ sin a1 þ 2 cos2 a1 ¼ K nn þ K nt . 7fc fc (10)
Impact angle 60
0.3
Impact angle 85
0.25 0.2 0.15 0.1 0.05 0 W15
C20S
C20
CM20
C10
C10S
T20
Fig. 8. Normalized energy absorbed by the materials tested (impact velocity—30 m/s).
14 Erosion rate, mm3/kg
328
W15 C20 C10S T20
12 10
C10 CM20 C20S
8 6 4 2 0 10
20
30
40 50 60 Impact angle, deg
70
80
90
Fig. 9. Effect of impact angle on the erosion rate (impact velocity—30 m/s).
rate caused by the particles travelling at a velocity of 30 m/s is shown in Fig. 9. Some differences in wear behaviour of the materials tested can be recognized. WC–Co cermet exhibits the maximum erosion rate at an impact angle of 601 while TiC–NiMo one has the poorest erosion resistance at 751. Chromium carbide based cermets tend to even more brittle behaviour and their resistance to erosion damage decreases with increase in impact angle. Moreover, at shallow impact angles the erosion rates of the materials do not differ to a great extent. However, a conditional division of the materials into two groups may be made (Fig. 9). Erosion leads to greater wear rates when the materials have less than about 2.3 times the hardness of the surface. Fig. 10 presents the erosion rates of the cermets under impact velocity of 10 m/s. Fig. 11 shows the erosion rate vs. normalized energy absorbed by the materials studied. Although cermets C20S and CM20 have similar erosion rates, they absorb different amounts of energy. It may be due to redistribution of the stresses and, therefore, energy transmitted to the surface. Presence of defects would be expected to promote easier formation of microcracks in the damaged region around the crater in CM20. In the case of C10S, reaction sintering results in the almost free of the defects composite structure having a strong interface bonding.
ARTICLE IN PRESS I. Hussainova, K.-P. Schade / Tribology International 41 (2008) 323–330 3
Impact angle 15 Impact angle 60 Impact angle 85
2.5 Erosion rate, mm3/kg
329
2 1.5 1 0.5 0 W15
C10
C20
CM20
C10S
C20S
T20
Fig. 10. Effect of impact angle on the erosion rate (impact velocity—10 m/s).
12 Erosion rate, mm3/kg
Impact angle 15
10
Impact angle 60 Impact angle 85
8 6 4 2 0 0.1
0.15
0.2 0.25 0.3 Normalized enegry absorbed
0.35
Fig. 11. Erosion rate of the materials vs. normalized energy absorbed by these materials.
As was recently shown [14], a key point in composite fracture analysis is that friction and imperfect interface effects are the parts of the energy release. The additional energy dissipation is caused by the creation of numerous new surfaces (microcracks). That allows conclusion that microstructural features should be under consideration of concern with the energy consumption by composites. However, the common tendency of increase in erosion rate with increase in the amount of energy absorbed can be clearly observed. The test equipment presented in this paper enables single- or multi-impact tests to be performed at controlled energy. It can be used for reproducing and studying the mechanisms of material damage. Prior to SEM examination, the samples were ultrasonically cleaned up in acetone. SEM micrographs in Fig. 12 show the single-impact sites produced on the surface of W15 and C20 cermets by glass sphere. The isolated impact sites reveal different mechanisms of material failure for different composites. As compared with the relatively ductile WC–Co, impact site of Cr3C2-based cermet shows much more brittle-like response.
Fig. 12. Single impact sites on the surface of (a)—C10 cermet, and (b)— W15 produced by glass bead at the impact angle of 751 and impact velocity of 30 m/s.
5. Conclusions A new test equipment and an experimental procedure has been developed to study single or multi-impacts of controlled energy and to determine parameters of the collision process of a particle impacting a flat surface. The impact mechanics approach provides the simple equations for the impact variables and energy loss that are extremely important for the assessment of the erosion resistance of materials. The magnitude of the energy absorbed during each impact is a function of impact angle and velocity. Frictional effects play an important role in
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the energy release under conditions of two-body interaction. To apply the energy loss expression and study the impact wear dependence on energy absorbed by a surface, two coefficients have to be estimated. These are the classical coefficient of velocity restitution, k, and the dynamic friction coefficient, f. The method and test equipment proposed above allow estimation of coefficients experimentally. Energy absorbed by target material gives evidence on two-body interaction process. Impulse ratio fc is a straightforward parameter to estimate the mode of motion at the contact point, sliding or rolling. The initial stages of the erosion damage can be examined. Energy absorbed by material during particle–target collision seems to be an appropriate guide for the materials selection for the application under erosive conditions. Acknowledgements The authors would like to express their gratitude to Dr. J. Pirso for supplying the test specimens and the DAAD Foundation, Germany, for funding a fellowship for this study. This research was supported by the Estonian Science Foundation under Grant No. 6163 also. References [1] Hussainova I. Microstructure and erosive wear in ceramic-based composites. Wear 2005;258:357–65. [2] Hussainova I. Some aspects of solid particle erosion of cermets. Tribol Int 2001;34:89–93.
[3] Evans AG, Marshall DB. In: Rigney DA, editor. Fundamentals of friction and wear of materials. Metals Park, OH: ASM; 1981. p. 439–52. [4] Axen N, Jacobson S. Wear resistance of multiphase materials. Wear 1994;174:187–96. [5] Hussainova I. Effect of microstructure on the erosive wear of titanium carbide-based cermets. Wear 2003;255:121–8. [6] Mac Sithigh GP. Rigid body impact with friction—various approaches compared. In: Impact mechanics: experiment, theory and calculation. New York, USA: ASME-AMD; 1995. [7] Li J, Deng T, Bingley MS, Bradley MSA. Prediction of particle rotation in centrifugal accelerator type erosion tester and the effect on erosion rate. Wear 2005;258:497–502. [8] Deng T, Bingley MS, Bradley MSA. An investigation of particle dynamics within a centrifugal accelerator type erosion tester. Wear 2001;247:55–65. [9] Deng T, Bingley MS, Bradley MSA. Influence of particle dynamics on erosion test conditions within a centrifugal accelerator type erosion tester. Wear 2001;249:1059–69. [10] Brach RM. Impact dynamics with application to solid particle erosion. Int J Impact Eng 1988;7(1):37–53. [11] Stronge WJ. Swerve during three-dimensional impact of rough bodies. J Appl Mech 1994;61:605–11. [12] Schade K-P, Erdmann H-J, Petrak D. Experimental investigations of the particle–wall collision under particular consideration of the wall roughness. Fluids Eng Div 1996;236:759–66. [13] Sundararajan G. The energy absorbed during the oblique impact of a hard ball against ductile target materials. Int J Impact Eng 1990;9(N3):343–58. [14] Nairn John A. Fracture mechanics of composites with residual stresses, imperfect interfaces, and traction-loaded cracks. Compos Sci Technol 2001;61:2159–67.
Tribology International 41 (2008) 323–330 www.elsevier.com/locate/triboint
Correlation between solid particle erosion of cermets and particle impact dynamics Irina Hussainovaa,, Klaus-Peter Schadeb a
Department of Materials Engineering, Tallinn University of Technology, Ehitajate 5, Tallinn 19086, Estonia SIVUS GmbH, Institute of Process, Environmental and Sensor Technology at the Chemnitz University of Technology, Schulstrasse 38, Chemnitz 09125, Germany
b
Received 8 February 2006; received in revised form 1 February 2007; accepted 4 September 2007 Available online 29 October 2007
Abstract Since the erosion rate depends on energy exchange between particle and material, a reformulation and solution of the equations of two solid bodies collision is presented and adapted to the calculation of the energy absorbed by a material surface during impact of a spherical particle onto a plain target. It has been observed that energy loss is a strong function of dynamic coefficients named as coefficient of velocity restitution after impact, k, and coefficient of dynamic friction, f. The new method and experimental equipment for the coefficients determination are described. It was shown that energy consumption during application may be an appropriate guide for the material selection in the conditions of erosive wear. r 2007 Elsevier Ltd. All rights reserved. Keywords: Particle–wall collision; Coefficient of restitution; Coefficient of dynamic friction; Energy dissipation; Erosion
1. Introduction Solid particle erosion is a serious problem for many industrial components, such as nozzles, valves, turbines, etc. Erosion is a process of material damage caused by hard particles striking the surface, either carried by a gas stream or entrained in a flowing liquid. Mechanisms of material removal differ for ductile and brittle materials. For ductile materials the main mechanism is severe localized plastic strain at the impact site exceeding the material strain—to failure. For brittle materials, the impacting particles typically cause localized cracking on the surface. For particle reinforced composites, mass loss due to solid particle erosion rather depends on intrinsic microstructural features [1]. However, materials response to a wear environment is not just an intrinsic one, but rather a reaction to a complicated combination of stresses imposed by an external system that is defined by the impact variables such as contact geometry, velocity, load, temperature, etc. An empirical power law relationship of the Corresponding author. Tel.: +372 620 33 55; fax: +372 620 91 36.
E-mail address: [email protected] (I. Hussainova). 0301-679X/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.triboint.2007.09.001
erosion rate W and particle velocity v is commonly used as W ¼ kvn, where k is a constant and n has values in a wide range. Value of 2 would be expected based on the particle kinetic energy, given by (1/2)mv2. Until now there is no satisfactory explanation for the deviation of n from 2. For instance, different particle shapes result in different energy of the particle to be transferred to the target. Depending on the specific combination of factors, the mechanism of material removal during erosion can be described as being somewhat between ductile and brittle [1,2]. In an attempt to rank materials based on mechanical properties several models have been developed [3,4]; however, the data obtained for composites [1,5] makes it clear that use of those approaches does not provide a consistent correlation between wear resistance and such composite properties as hardness, fracture toughness and modulus of elasticity. In general, erosion rate is influenced by test conditions such as abrasive particle velocity, angle of particle impingement, mass flux, particle mechanical properties, size and shape and target material properties. Different particles transfer the energy to the target over different volumes, thereby causing different energy densities in the target material and different mechanisms and
ARTICLE IN PRESS 324
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rates of damage. Under other all things being identical, the material properties play the most important role. In that case a simplified assumption that the erosion rate should be proportional to the energy exchange between the erodent and the impacted material surface may be made. Thus, the energy absorbed during particle–target collision can be a useful approach for the evaluation of materials erosion resistance. In impact mechanics, several approaches are applied to study the solid bodies interaction. One of the first approaches was developed by Newton in the 17th century. Classical theory of impact based on Newton’s Second Law continues to be successfully used to model a process of twobody collision. The equations involve the use of the coefficients named as coefficients of velocity restitution after the collision, impulses and momentum. Further, the approaches taken frictional forces into consideration were developed. A comprehensive review of the collision models has been presented in [6]. Depending on the contact conditions and the approach used, the solution of the model equations can involve mathematical methods ranging from linear algebraic to nonlinear differential equations. Since the energy exchange is related to the velocity and angle of impact, these parameters have to be determined with a great care. As dynamic coefficients are not material constants, the coefficients must be evaluated experimentally or analytically related to the contact process. Any change in energy loss due to material properties effects can easily be masked by a small change
in velocity. To clarify the details of two-body interaction, a special test facility equipped with a digital video camera was worked out and used. One of the objectives of this study is the proper use, interpretation and measurement of the dynamic coefficients when solid particle strikes a flat solid surface as it everywhere happens when the particle erosion is mentioned. Another purpose of this study is characterization of the nature of energy absorption during impact of solid particle onto the target material of ceramic–metal composites or cermets. The third goal of the study is evaluation of an energetic approach for assessment of the cermet materials resistance to solid particle erosion. 2. Materials and experimental details The cermets tested in this study were produced by powder metallurgy processing techniques and in the compositions shown in Table 1. Table 1 presents the Vickers hardness values for those materials, also, but omits the values of fracture toughness because of some uncertainties in determination and estimation of this parameter for multi-phase systems [1]. It should be noticed that fracture toughness values measured by Palmgvist method were between 10 MPa m1/2 (for cermet C10S) and 17 MPa m1/2 (for cermet T20). Fig. 1 shows a schematic of the test equipment, which was specially developed by SIVUS GmbH at Chemnitz University of Technology, Germany, for the determination
Table 1 Composition and hardness of materials tested Grade
Composition
Vicker’s hardness, HV10
Notes
W15 C10 C20 CM20 C10S C20S T20
WC–85 wt%+Co–15 wt% Cr3C2–90 wt%+Ni–10 wt% Cr3C2–80 wt%+Ni–20 wt% Cr3C2–80 wt%+NiMo–20 wt% Cr3C2–90 wt%+Ni–10 wt% Cr3C2–80 wt%+Ni–20 wt% TiC–80 wt%+NiMo–20 wt%
1258 1358 1140 1217 1407 1233 1430
14 wt% Ni+6 wt% Mo Reaction sintering Reaction sintering 14 wt% Ni+6 wt% Mo
Fig. 1. Experimental facility.
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Number of events
120
impact velocity
100
rebound velocity
80 60 40 20 0 4
5
6
7
8
9
10
Particle velocity, m/s
600
Number of events
of dynamic coefficients. The basic element is a centrifugal accelerator consisting of a feeder, a rotating disc and a target holding system. Solid particles are continuously fed into the central hole of the rotating disc and are accelerated through eight radial tubes by the centrifugal force and ejected from the end of the tubes. It has been indicated [7] that particle rotation increases the dynamic energy at impact. To avoid the influence of rotation, special configuration of test equipment was designed. The accelerator is rotated by a circulating belt, which is driven with the help of a high speed DC motor. To fix the particle exit, the tube ends are shut off by an additional belt rotating over the open circuit of the accelerating disc. As a result of the additional belt adjustment only a limited section of the disc circumference is uncovered at a definite period of time. Before ejecting from the outlet of the disc tube, a particle is stopped and leaves the channel at a fixed moment when the outlet of the tube is free from the covering belt. Therefore, the particles emerging from the acceleration tube of the tester have a fixed spatial position and negligible rotation. The specimen target is set near the disc on a holder that has provision for reorientation relative to the direction of particle flow and thus achieves the desired impact angle. Two particle velocities before impact have been used for the tests, which are 10 and 30 m/s, in order to obtain dynamic coefficients over a range of impact velocities. The rotational velocity of the accelerator disc was adjusted to give an exit velocity of the particles at each individual velocity required. The particle concentration in the jet emerging from the tubes in the disc was minimized as far as possible in order to avoid inter-particle collision effect. Tests were carried out at impact angles from 151 up to 851; 125-mm glass beads with a value of Vickers hardness of 540 HV were used as the impacting particles. Particle velocity distribution was determined for a large number of particles under identical conditions. A characteristic distribution of the beads velocity is illustrated in Fig. 2. Because of some deviation from the initial velocity, the number-averaged mean velocity was used for the results interpretation. The view of particle tracks as treated by a computational program is demonstrated in Fig. 3. After the impact test at each impact angle, the area of interaction was changed to avoid any ambiguities in surface quality. An Ar-ion laser beam refracted by cylindrical lens was used to illuminate a working area. The impact event was recorded with a digital video camera and transferred into a PC. The video images were then decomposed into individual frames with software. A calibration procedure has been carried out to eliminate any distortions. A conventional centrifugal four-channel accelerator was used for testing the solid particle erosion according to the procedure outlined elsewhere [5,8]. A comprehensive analysis of particle dynamics within the tester was carried out in [8,9]. The specimen targets are located around the disc on adjustable systems. In the tests, positions of target holders were arranged similar to those applied during the tests for dynamic coefficients determination. Test condi-
325
500
impact velocity
400
rebound velocity
300 200 100 0 15
20
25 Particle velocity, m/s
30
35
Fig. 2. Distribution of initial and rebound particle velocities: (a) in the case of C20 as a target and impact angle of 751, and (b) in the case of W15 and impact angle of 301.
Fig. 3. Particle tracks obtained by video camera: (a) in the case of impact angle of 301, and (b) in the case of impact angle of 601.
tions were as given in Table 2. The device allows testing 15 specimens simultaneously, thus all materials were examined under identical conditions. The number of test specimens of each cermet grades was four. To achieve a steady state erosion rate, all specimens were exposed to pre-testing for 180 min. The particles were fed into the rig
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326
simplified and rewritten as follows:
Table 2 Erosion tests data Particle velocity before impact (m/s)
Impact angle (deg)
10 and 30
14, 30, 45, 60, 75, 85
vn2 ¼ kvn1 ,
(1)
vt2 vt1 ¼ f ð1 þ kÞvn1 ,
(2)
Temperature (1C)
23
and Oo¼
n dc
C
l
dn
t
O
Ft Fn
Fig. 4. Diagram of two-body interaction.
at a feed rate of 250 g/min. At least 10 increments of erosion were used to determine the steady state erosion rate. The erosion rate was calculated from the average mass loss and is equal to the volume of material removed per unit mass of abrasive particle entrained in the stream, and has units of mm3/kg. To quantify weight loss during erosion experiments, the specimens were ultrasonically cleaned in acetone and weighed before and after the erosion tests on an analytical balance to 0.01 mg. In this study, the variation in the measured mass loss among the four test samples of the same type was rarely greater than 15% and was usually much less. Thus, differences in tests results of greater than 15% were attributed to real differences in the wear behaviour of the materials. 3. Impact mechanics with application to energy loss The analysis of the collision between a solid particle and a massive flat surface is given in, for example, [10,11]. Fig. 4 represents the schematic drawing of particle–wall collision. Here, t–n axes are chosen as tangential and normal to the plane surface of a specimen, respectively. In the case of spherical particle impacting the plane target surface, the equations derived in [10] may be
f ð1 þ kÞvn1 l , R
(3)
where vn1 and vt1 are the normal and tangential components of a particle velocity before collision, respectively; vn2 and vt2 are the normal and tangential components, respectively of a particle velocity after collision describing a movement of centre of mass C. O and o are the final and initial angular velocities, respectively, I is the moment of inertia. Eq. (1) contains a coefficient k that expresses the process of a normal velocity restitution of particle at point O. Thus, the coefficient of restitution is related in a simple way to the relative velocities of particle before and after collision. It is obvious that the value of k is between 0 and 1. The coefficient f in Eq. (2) represents the process of tangential velocity restitution and may be treated as a coefficient of dynamic friction. Finally, Eq. (3) is an expression of conservation of the angular momentum about point O, where R is a particle radius and l ¼ R2/j2 ¼ 5/2 (j is the radius of gyration) for a solid sphere. These expressions correspond to sliding movement of spherical particle. The boundary conditions for particle sliding have been discussed in [10,12] and may be given as fp
2 ðvt1 RoÞ . 7 ð1 þ kÞvn1
(4)
Phenomenologically it is well known that part of the kinetic energy of the system could be lost due to various mechanisms, including deformation of contact surfaces and generation of heat and sound. The kinetic energy loss can be expressed in the terms of Eqs. (1)–(3) in nondimensional form [10] as 1 k2 b2 1 f f n K ¼ þ 2 , (5) fc 1 þ b2 1 þ b2 1 þ l f c where b ¼ ðvt1 RoÞ=vn1 and fc represents the maximal value of the coefficient of the dynamic friction: fc ¼
1 b . 1 þ l1 þ k
(6)
Eq. (6) reduces to expression (4) in the case of a solid sphere. In general, the value of the coefficients depends on the properties of the two bodies as well as their velocities and orientations when they collide, and they can be determined either by experiment or by a detailed analysis of the deformation of the two bodies during collision. The main task of this study is an experimental determination of the coefficients of restitution in order to calculate the particle energy loss or the energy absorbed by a target material during the impact.
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327
2 1 1 , 7 1 þ k tan a1
(7)
where a1 is the angle before collision or the impact angle. The coefficients of the velocity restitution k and the dynamic friction f can be calculated from vn (8) k ¼ 2 vn 1 and vt vt 2 1 . f ¼ ð1 þ kÞ vn1
(9)
The experimental data concerning the coefficient variations with the impact velocity and angle are presented in Figs. 5–7. It should be noticed that particle fragmentation would have complicated the energy balance; however, at low velocities applied in this study, the amount of fractured particle have been negligible and tracks of rebounding fractured particles have been eliminated from consideration. For the composite materials coefficient of restitution
W15 C20 C20S
0.110 0.105 0.100 0.095 0.090
W15 C10 C20 CM20 C10S C20S T20
0.9 0.85
15 20 Initial velocity, m/s
25
40 50 60 Impact angle, deg
70
30
0.14 0.12 0.1 W15 C20S C20 C10 T20
0.08 0.06 0.04 0.02 10
30
20
80
0.25
0.8 0.75 0.7 5
10
15 20 Impact velocity, m/s
25
30
0.95
Kn* Kt* K*
0.2 0.15 0.1 0.05 0 0
Restitution coefficient, k
10
Fig. 6. Coefficient of dynamic friction vs. (a) impact velocity (impact angle 601), and (b) impact angle (particle velocity—30 m/s).
0.95 Restitution coefficient, k
0.140 0.135 0.130 0.125 0.120 0.115
5
Normalized energy loss
f cp
Coefficient of dynamic friction, f
The boundary condition for the sliding impact (as based on Eq. (6) and taking into account the equality o ¼ 0 as provided by the experimental set-up) is
Coefficient of dynamic friction, f
4. Results and discussion
0.9 W15
C20 C20S
0.8
20
30
40 50 60 Impact angle, deg
70
80
90
Fig. 7. Effect of impact angle on the normal K n , tangential K t and total K normalized energy absorbed by W15 composite (impact velocity— 30 m/s).
C10
0.85
10
T20
0.75 0.7 0.65 0
10
20
30 40 50 60 Impact angle, deg
70
80
90
Fig. 5. Coefficient of velocity restitution vs. (a) impact velocity (impact angle 601), and (b) impact angle (particle velocity—30 m/s).
slightly decreases with approaching of the impact angle to the normal one and/or increasing the impact velocity. In Figs. 5(b), 6 and 7, there are data for several materials presented. It allows avoiding a mess on the pictures, whereas the common principal trends are similar for all materials tested. In the range of impact angles from 451 to 851 (Fig. 6(b)) the coefficient of dynamic friction decreases with increase in impact angle. At those angles the glass
ARTICLE IN PRESS I. Hussainova, K.-P. Schade / Tribology International 41 (2008) 323–330
Here fc represents a boundary friction coefficient. This expression presents the energy that is normalized by dividing the full particle energy by the initial kinetic energy and, therefore, K* is non-dimensional. The rotational energy loss can be hardly measured by the present experimental set-up. However, rolling after impact usually leads to negligible energy absorption. The variations of the translational kinetic energy loss with the impact angle are plotted in Fig. 7. Figure reveals that the energy loss at the shallow impact angles is due almost exclusively to the tangential forces. Both compressive and tangential losses have the same order of magnitude at the angle of about 601. The compressive effects dominate at the angles approaching the normal one. Energy loss due to inelasticity is insufficient because material hardness exceeds particle hardness and relatively soft but brittle particles are not able to cause significant plastic flow in a hard target. In the case of elastic impact the energy absorbed at oblique impact angles includes a substantial component attributed to the energy dissipation by frictional effects at the particle–target interface and the component of the energy transmitted to the surface depends strongly on the impact angle through the coefficient of dynamic friction. A large portion of the incident energy is dissipated via elastic– plastic deformation and heating in the near surface regions [1]. Fig. 8 shows the normalized energy absorbed by the cermets. Particles of low kinetic energy do not cause a large destruction in the surface of composites. The impact may be treated as almost elastic one. However, repeated impacts can result in surface damage and material removal due to low-cycle fatigue mechanisms operating in the near surface areas [1]. The influence of the impact angle on the erosion
0.35 Normalized energy absorbed
particles start rolling on the surface at the end of contact. At shallow angles, the coefficient f slightly changes and is approximately constant and ranges between 0.12 and 0.135 for all materials. This is the sliding region within which f may be interpreted as a coefficient of friction that obeys Amontons–Coulomb’s law. As was expected, f is a function of both impact angle and initial velocity of particle (Fig. 7). In ductile materials high shear strength is accumulated in the sub-surface areas of a target material because of friction-induced plastic deformation. That results in a high friction coefficient [13]. Cermets mostly show brittle fracture with relatively low resistance to crack extension originating at pre-existing defects. Energy release is more likely achieved through the formation of fracture surfaces rather than through plastic or viscoplastic processes, as compared to the more ductile materials of similar strength level. The energy loss during impact can be estimated according to the equation derived from Eqs. (9)–(13): 2f f 2 2 n K ¼ ð1 kÞ sin a1 þ 2 cos2 a1 ¼ K nn þ K nt . 7fc fc (10)
Impact angle 60
0.3
Impact angle 85
0.25 0.2 0.15 0.1 0.05 0 W15
C20S
C20
CM20
C10
C10S
T20
Fig. 8. Normalized energy absorbed by the materials tested (impact velocity—30 m/s).
14 Erosion rate, mm3/kg
328
W15 C20 C10S T20
12 10
C10 CM20 C20S
8 6 4 2 0 10
20
30
40 50 60 Impact angle, deg
70
80
90
Fig. 9. Effect of impact angle on the erosion rate (impact velocity—30 m/s).
rate caused by the particles travelling at a velocity of 30 m/s is shown in Fig. 9. Some differences in wear behaviour of the materials tested can be recognized. WC–Co cermet exhibits the maximum erosion rate at an impact angle of 601 while TiC–NiMo one has the poorest erosion resistance at 751. Chromium carbide based cermets tend to even more brittle behaviour and their resistance to erosion damage decreases with increase in impact angle. Moreover, at shallow impact angles the erosion rates of the materials do not differ to a great extent. However, a conditional division of the materials into two groups may be made (Fig. 9). Erosion leads to greater wear rates when the materials have less than about 2.3 times the hardness of the surface. Fig. 10 presents the erosion rates of the cermets under impact velocity of 10 m/s. Fig. 11 shows the erosion rate vs. normalized energy absorbed by the materials studied. Although cermets C20S and CM20 have similar erosion rates, they absorb different amounts of energy. It may be due to redistribution of the stresses and, therefore, energy transmitted to the surface. Presence of defects would be expected to promote easier formation of microcracks in the damaged region around the crater in CM20. In the case of C10S, reaction sintering results in the almost free of the defects composite structure having a strong interface bonding.
ARTICLE IN PRESS I. Hussainova, K.-P. Schade / Tribology International 41 (2008) 323–330 3
Impact angle 15 Impact angle 60 Impact angle 85
2.5 Erosion rate, mm3/kg
329
2 1.5 1 0.5 0 W15
C10
C20
CM20
C10S
C20S
T20
Fig. 10. Effect of impact angle on the erosion rate (impact velocity—10 m/s).
12 Erosion rate, mm3/kg
Impact angle 15
10
Impact angle 60 Impact angle 85
8 6 4 2 0 0.1
0.15
0.2 0.25 0.3 Normalized enegry absorbed
0.35
Fig. 11. Erosion rate of the materials vs. normalized energy absorbed by these materials.
As was recently shown [14], a key point in composite fracture analysis is that friction and imperfect interface effects are the parts of the energy release. The additional energy dissipation is caused by the creation of numerous new surfaces (microcracks). That allows conclusion that microstructural features should be under consideration of concern with the energy consumption by composites. However, the common tendency of increase in erosion rate with increase in the amount of energy absorbed can be clearly observed. The test equipment presented in this paper enables single- or multi-impact tests to be performed at controlled energy. It can be used for reproducing and studying the mechanisms of material damage. Prior to SEM examination, the samples were ultrasonically cleaned up in acetone. SEM micrographs in Fig. 12 show the single-impact sites produced on the surface of W15 and C20 cermets by glass sphere. The isolated impact sites reveal different mechanisms of material failure for different composites. As compared with the relatively ductile WC–Co, impact site of Cr3C2-based cermet shows much more brittle-like response.
Fig. 12. Single impact sites on the surface of (a)—C10 cermet, and (b)— W15 produced by glass bead at the impact angle of 751 and impact velocity of 30 m/s.
5. Conclusions A new test equipment and an experimental procedure has been developed to study single or multi-impacts of controlled energy and to determine parameters of the collision process of a particle impacting a flat surface. The impact mechanics approach provides the simple equations for the impact variables and energy loss that are extremely important for the assessment of the erosion resistance of materials. The magnitude of the energy absorbed during each impact is a function of impact angle and velocity. Frictional effects play an important role in
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the energy release under conditions of two-body interaction. To apply the energy loss expression and study the impact wear dependence on energy absorbed by a surface, two coefficients have to be estimated. These are the classical coefficient of velocity restitution, k, and the dynamic friction coefficient, f. The method and test equipment proposed above allow estimation of coefficients experimentally. Energy absorbed by target material gives evidence on two-body interaction process. Impulse ratio fc is a straightforward parameter to estimate the mode of motion at the contact point, sliding or rolling. The initial stages of the erosion damage can be examined. Energy absorbed by material during particle–target collision seems to be an appropriate guide for the materials selection for the application under erosive conditions. Acknowledgements The authors would like to express their gratitude to Dr. J. Pirso for supplying the test specimens and the DAAD Foundation, Germany, for funding a fellowship for this study. This research was supported by the Estonian Science Foundation under Grant No. 6163 also. References [1] Hussainova I. Microstructure and erosive wear in ceramic-based composites. Wear 2005;258:357–65. [2] Hussainova I. Some aspects of solid particle erosion of cermets. Tribol Int 2001;34:89–93.
[3] Evans AG, Marshall DB. In: Rigney DA, editor. Fundamentals of friction and wear of materials. Metals Park, OH: ASM; 1981. p. 439–52. [4] Axen N, Jacobson S. Wear resistance of multiphase materials. Wear 1994;174:187–96. [5] Hussainova I. Effect of microstructure on the erosive wear of titanium carbide-based cermets. Wear 2003;255:121–8. [6] Mac Sithigh GP. Rigid body impact with friction—various approaches compared. In: Impact mechanics: experiment, theory and calculation. New York, USA: ASME-AMD; 1995. [7] Li J, Deng T, Bingley MS, Bradley MSA. Prediction of particle rotation in centrifugal accelerator type erosion tester and the effect on erosion rate. Wear 2005;258:497–502. [8] Deng T, Bingley MS, Bradley MSA. An investigation of particle dynamics within a centrifugal accelerator type erosion tester. Wear 2001;247:55–65. [9] Deng T, Bingley MS, Bradley MSA. Influence of particle dynamics on erosion test conditions within a centrifugal accelerator type erosion tester. Wear 2001;249:1059–69. [10] Brach RM. Impact dynamics with application to solid particle erosion. Int J Impact Eng 1988;7(1):37–53. [11] Stronge WJ. Swerve during three-dimensional impact of rough bodies. J Appl Mech 1994;61:605–11. [12] Schade K-P, Erdmann H-J, Petrak D. Experimental investigations of the particle–wall collision under particular consideration of the wall roughness. Fluids Eng Div 1996;236:759–66. [13] Sundararajan G. The energy absorbed during the oblique impact of a hard ball against ductile target materials. Int J Impact Eng 1990;9(N3):343–58. [14] Nairn John A. Fracture mechanics of composites with residual stresses, imperfect interfaces, and traction-loaded cracks. Compos Sci Technol 2001;61:2159–67.