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PUBLICATIONS

NBSIR 78-1575

Erosion by Solid Particle

Impact

A. W. Ruff and S. M. Wiederhorn

A 1 1 1 3 TTbDDb

National Measurement Laboratory

Center for Materials Science

National Bureau of Standards

January 1 979

» Interim Report

)

-4C

100

,U56

78-1575

C.2

Prepared for The Office of Naval Research

Department of the Navy

Arlington, Virginia
DATE DUE

>

Demco, Inc. 38-293
ATTENTION:

Please note that pages 7 and 8 are missing from this publication.

Content that is similar to NBSIR 78-1575 has been published in the

following source:

A.W. Ruff and S. M. Wiederhom, Erosion by Solid Particle Impact, in:

Treatise on Materials Science and Technology, Vol. 16, ed. C.M. Preece

(Academic Press, New York, 1979) pp 69-126.

See pages 75-77
.
*9*owr Bureau of StawJard* MAY 1 4 10?9

NBSIR 78-1575

EROSION BY SOLID PARTICLE

IMPACT

A. W. Ruff and S. M. Wiederhorn

National Measurement Laboratory

Center for Materials Science

National Bureau of Standards

January 1 979

Interim Report

Prepared for The Office of Naval Research

Department of the Navy

Arlington, Virginia

O

U.s. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS. Ernest Ambler, Director
1
EROSION BY SOLID PARTICLE IMPACT

A. W. Ruff and S. M. Wiederhorn

Center for Materials Science

National Bureau of Standards

Washington, D.C. 20234

Introduction

Single Particle Erosion

A. Metals

1. Methods and Results

2. Interpretations

B. Ceramics

1. Results

2. Interpretations

Multiple Particle Erosion

A. Metals

1. Methods and Results

2. Interpretations

B. Ceramics

1. Results

2. Interpretations

Theories of Erosion

A. Ductile Material Models

B. Brittle Material Models

C. Other Considerations

Significant Parameters

A. Eroding Particle Characteristics

B. Eroded Material Characteristics

C. Environmental Effects

Summary and Recommendations for Future Work

References

EROSION BY SOLID PARTICLE IMPACT

I . INTRODUCTION

The erosion of materials by surface impact of hard particles is one

of several forms of material degradation generally classified as wear. It

is by now well understood that wear is a complex phenomenon, consisting in

fact of several simultaneous and interacting processes, typically involving

mechanical, chemical and material parameters as well as complex mechanisms.

This complexity in many instances seems to defy simplification on the part

of the experimentalist seeking to carefully separate variables and the

theorist attempting to accurately model the wearing system. However, in

recent years considerable progress has been made both in gaining a basic

appreciation of the significant parameters of wear and in applying a

materials methodology to mitigate the problems of wear. While this Chapter

will only address solid particle erosion, it is well to keep in mind that

other wear processes, e.g., abrasive wear and oxidative wear, involve many

similar characteristics and perhaps mechanisms. Progress in understanding any

one of these processes may be applicable to others, and to the development

of more wear resistant materials and systems.

Reviews of the state of information on solid particle erosion have appeared

recently in several sources (Engel, 1976; Preece and MacMillan, 197"'; Hutchings.

1978; Finnie £t a_l, 1978). The state of earlier understanding has been

adequately reviewed in several other articles (Finnie, 1960, 1972; Finnic

et al, 1967; Ritter, 1963; Neilson and Gilchrist, 1968; Sheldon and Finnie.

1966, a, b); that information will not be repeated here. Rather we wish to
establish a framework for considering solid particle erosion, to review

briefly only the central features of previous results, and to emphasize

primarily the microstructural aspects of the problem. It is this latter

area that appears to us to offer promise of further understanding of erosion

(and wear) processes. Other chapters in this book will contain relevant

information on microstructural and environmental effects and should be

consulted for details. The mechanics of erosion, in particular, are addressed

in detail in Chapter 1.

It has been very instructive we believe to examine the effects of

solid particle erosion, first, on the basis of single particle impacts, and

then under multiple impacting conditions. This chapter will review briefly

recent work using that format, and then describe the theoretical situation.

It is hoped that the reader can thereby appreciate what is known as well as

what is yet needed. Significant parameter issues, e.g., surface temperatures

and melting, strain rate effects, will then be described. Finally, our view

of the needed future emphasis in this area will be described.

2
II. SINGLE PARTICLE EROSION

Erosive wear of materials in practice generally involves long times

of exposure under steady state conditions. However, by its nature,

solid particle erosion is a discrete, accumulative process and the

single impact event is clearly worthy of as accurate an understanding

as possible. It is also clear that multiple particle effects are to

be expected; these will be treated later in the Chapter.

Single particle studies can be conducted over a wide size scale

of particles, from millimeters to micrometers, through the use of

quantitative measurement methods involving optical, scanning and

transmission electron microscopes. Recent studies have produced

extremely valuable information on the basic process of particlesurface impact.

3
A. METALS

1. Methods and Results

Two illustrations of eroded surface structures on a ductile metal

are shown in Fig. 1. In one case discrete, isolated impact craters are

seen (Fig. la), the result of a very brief exposure time. At longer

exposure times, the more uniformly eroded surface shown in Fig. lb results.

Through considerable care in designing and using experimental apparatus,

one can control the important parameters of particle orientation and

velocity, and quantitatively investigate single particle erosion. Some

recent studies are described below.

Various experimental techniques have been used to cause single

particles to impact on specimen surfaces under controlled conditions.

Electrostatic acceleration methods were employed by Shelton et al. (1960)

and Hutchings and Winter (1974) in studies of small particle erosion

effects. Explosive acceleration methods have also been reported

(Hutchings and Winter, 1974), however most studies have used some type of

gas-projectile gun. In this method, shown schematically in Fig. 2, a

single projection of one or more erosive particles against the specimen

surface is carried out. Large particles can be directly accelerated while micrometer sized particles are indirectly accelerated using a carrier or sabot

(that does not strike or damage the specimen). Sheldon and Kanhere (1972)

used this latter method to accelerate individual particles of silicon

carbide, steel and glass shot about 3 mm in diameter at various velocities

from about 130m/s to 400 m/s. Both previously eroded and un-eroded

surfaces were exposed and then studied. Erosion weight loss measurements also

were made. Observations of the impact craters showed that the displaced

crater material appeared to have flowed in the direction of particle

4
incidence until the material fractured at high accumulated strains. They

noted considerable evidence of deformation adjacent to the crater in

annealed material. In previously work-hardened specimens, the forward

built-up edge seemed to fracture sooner.

Hutchings and Winter (1974) studied the erosion process using

large (3mm) spherical particles; they placed particular emphasis on the geometry

and mechanisms of metal removal. The characteristic deformation pattern

resulting from particle impact consisted of a depression and a lip or rim

of displaced material. Figure 3a shows the impact crater morphology found

in this work for a steel sphere impacting on aluminum. A

representation of the crater cross section is shown in Fig. 3b. They

reported that smaller particles (down to 1 ym size) produced very similar

patterns of deformation for the velocities studied (about 150 m/ s to

200 m/s) on specimens of copper, mild steel and aluminum.

Studies of the erosion impact craters recently carried out using

50 ym A^O^ particles have revealed similar structures (Ives and

Ruff, 1978 a). Annealed AISI type 310 stainless steel specimens and

copper specimens were impacted by spherical glass particles and also by

angular Al^O^ Part icl es at a velocity of 59 m/s. Two exposure angles of

attack, 20° and 90°, were used in order to examine different modes of

material removal. At the low angle, material was deformed and displaced

from the crater into a lip at the exit end and sides. At 90° incidence,

a more uniform lip of material around the crater was produced. There was

considerable evidence of plastic flow within the impact crater region.

Transmission electron microscopy (TEM) studies were carried out to

investigate the sub-surface damage. Figure 4 shows an impact crater in

5
type 310 stainless steel produced by an irregular 50 pm Al^O^ Particle

that impacted at 90°angle and 59 m/s. The surface appearance (Fig. 4a)

is consistent with the shape and size of the particles. The sub-surface

damage, seen in Fig. 4b, was typical of that found at the craters. It consisted

of a high density of dislocations formed in a well defined zone around the

crater, extending a few micrometers in all directions. Some bands and groups

of dislocations were observed but more usually a random tangle of dislocations around the crater walls was found. There was evidence of deformation

twinning in some cases, and electron diffraction studies indicated polycrystalline regions, perhaps due to recrystallization. The dark central

region in Fig. 4b results from strong electron scattering from the

deformed material adjacent to the crater wall. Outside of the immediate

crater region, the concentration of dislocations dropped sharply. Some

slip plane arrays of dislocations were identified.

Plastic strain measurements were carried out using a selected area

electron channeling method (Ruff, 1976) in order to further measure the

erosion damage. This method which averages the strain over a volume of

3 material of about 10 ym showed that plastic strains greater than about

15% were associated with the impact craters in copper. The

strains decreased rapidly with distance from the crater, and decreased

with depth below the original surface as determined by electrolytic removal

of material.

Studies carried out using 50 ym spherical glass particles

(Ives and Ruff, 1978a) produced crater geometry and deformation patterns

somewhat easier to analyze. The crater shown in Fig. 5a from a type 310

stainless steel specimen produced at an attack angle of 20° and velocity

6
2. Interpretations

Despite the few studies reported so far on single particle

erosion, some essential features of the process have

been identified. Particle shape and orientation at contact are clearly

important parameters along with particle velocity, attack angle, and

particle material properties. A difference in the characteristics of craters

formed on uneroded and on previously eroded surfaces was found. Thus, single

particle experiments alone are not sufficient. Sheldon and Kanhere (1972)

also found a small difference in the velocity dependence of erosion between

uneroded and previously eroded surfaces that is probably significant.

These authors did observe that the displaced lip material appeared to

detach earlier on previously eroded surfaces, reflecting apparently the

higher strain levels in the material.

Hutchings and Winter ( 1973 ) found evidence for a critical particle

velocity above which material is displaced from the crater lip. They

suggested that frictional forces between the surface and the particle may

be important in the crater formation process. Hence, the effect of

environment (including surface films) on surface friction may need further

consideration. These authors (Winter and Hutchings, 1974 ) also studied

angular particle impacts where a micromachining process was identified.

The details depended on particle rake angle and attack angle, as well on

the extent to which particle fragmentation occurred. Figure 7 shows an

interesting section through an impact crater in steel where both the

configuration of displaced material and the pattern of deformation in the

bulk material can be seen. Bands of local, intense shear were observed

in some of the crater lips. Evidence for local heating leading to local

9
thermally affected deformation has been presented (Winter and Hutchings,

1975) and points up the need to consider thermal-mechanical properties of

materials with regard to erosion behavior.

Transmission electron microscope studies of the damage associated

with particle impact in copper and type 310 stainless steel (Ives and

Ruff, 1978a) revealed a zone of high dislocation density typically a few micrometers thick around an impact crater. Strain measurements using the

electron channeling method also showed a localization of damage near the

craters. Deformation twins were formed at large angular particle craters,

suggesting an intense local stress, possibly imposed at a high strain rate.

Experiments using a diamond pyramid indentor to form impressions revealed

similar dislocation patterns as were found near the impact craters,

although deformation twins were not observed at the identations.

The recent results of Hutchings (1977a, 1978) clearly establish

several modes of particle impact deformation. Particle shape was significant. Since angular particles either displace more material into

the crater lip where it becomes vulnerable to further erosion or actually

detach material from the surface (depending on particle rake angle at

contact)^ the erosion efficiency of angular particles relative to round

particles can be explained. In combination with these experiments,

a theoretical model was developed to describe the particle interaction

with the impacted surface. Calculations of the particle position and

orientation with time were in good agreement with the experimental

photographs of actual impact events. The limited range of rake angles,

0° to -17°, over which actual cutting was observed confirmed the

calculations. It was pointed out that such impact conditions are

infrequent, perhaps only occurring about once out of six impacts on a

10
random basis. Thus the crater lip formation process appears to be the

dominant mode of impact damage, and loss of metal takes place primarily

through subsequent impacts with the lip material. Recent observations on

debris particles recovered from eroded 1015 steel surfaces support this

picture (Ruff, 1978).

11
B. CERAMICS

1. Results

Erosion of ceramic materials has been generally viewed as a

brittle process. This view is based on the observation that material

removal occurs mainly by chipping. A more modern view of ceramic erosion

is based on the assumption that plastic deformation plays a crucial role

in the chipping process. In this section, the microscopic processes

that occur during impact of brittle materials are described.

The morphology of fractures formed in ceramic materials

during impact can be divided into two classes, depending on whether the

impacting particle is blunt or sharp (Lawn and Wilshaw, 1975, Lawn and

Marshall, 1978). Blunt particles, typified by spheres, result in the

formation of cone-shaped cracks (Hertzian cracks) , which initiate from

pre-existing flaws that lie just outside the area of contact between the

particle and the target surface (Fig. 8). The entire process of Hertzian

crack formation is an elastic one that can be described by linear elastic

fracture mechanics. Hertzian cracks form for a wide range of impact

loads; however, as the contact forces increase above a level that is

determined by the hardness of the material, plastic deformation occurs

beneath the impacting particle, and a second set of cracks are observed

to form normal to the impacted surface (Fig. 9, also see Evans and Wilshaw,

1976, 1977). This second set of cracks, termed radial, are more typical

of the type that form as a result of sharp particle impact. Their

formation suggests that the same plastic processes that govern crack

formation for sharp particles become active when blunt particles impact

at high loading levels. This point is clearly illustrated in the work of

Evans and his colleagues (1978) who investigated the morphology of cracks formed

by high velocity impact with solid particles. Thus, the distinction

12
between blunt and sharp particle impact is a distinction that depends on

the role of plastic deformation in the impact process. The particle

velocity that characterizes the transition between the formation of Hertzian

cracks and the formation of radial cracks depends on the hardness, fracture

toughness, and surface structure of the target material. In glass, for

example, this transition occurs at ^30 m/s for unabraded surfaces impacted

with 0.8 mm radius steel or tungsten carbide spheres (Wiederhorn and Lawn, 1977).

The transition occurs at lower velocities for pre-abraded glass surfaces.

Because Hertzian cracks initiate from pre-existing surface

flaws, a minimum threshold stress (corresponding to a minimum impact velocity)

is required for Hertzian crack formation (Evans, 1973, Wiederhorn and Lawn,

1977, Kirchner and Gruver, 1977). The threshold stress for crack formation

is governed by the radius of the impacting particle, and the fracture

resistance of the material (the critical stress intensity factor) . The

size of the flaw that initiates the Hertzian crack plays a secondary role

in Hertzian crack formation (Lawn and Langitan, 1969).

Impact by sharp particles (angular rather than round) results in

a distinctly different type of crack pattern in the target surface. Two

types of cracks are observed: the first type is a radial set of cracks

oriented primarily perpendicular to the target surface; the second type is

a lateral set of cracks oriented primarily parallel to the target surface

(Fig. 10). The radial set of cracks are primarily responsible for strength

degradation, whereas the lateral set are responsible for erosive wear. As

can be ascertained from static indentation tests (Lawn and Swain, 1975,

Evans and Wilshaw, 1976), radial cracks form during the loading portion of

the impact cycle, whereas lateral cracks form as the particle leaves the

13
target surface. Once radial cracks have initiated, the driving force for

fracture is the wedging action of the impacting particle. By contrast,

lateral cracks are formed as a result of residual plastic deformation at

the point of contact. Lateral cracks usually curve and propagate to the

target surface, resulting in chip formation and loss of material from the

target surface.

The threshold velocity for crack formation is considerably lower

for sharp particles than for blunt particles. For example, 30 mesh

abrasive SiC particles (^0.6 mm sieve opening) dropped from a height of 1 cm

(velocity ^.4 m/s at contact) onto the surface of glass results in a significant decrease in strength due to crack formation (Wiederhorn and Lawn,

1979). By contrast, velocities of ^30 m/s are required for Hertzian crack

formation caused by 0.4 mm diameter tungsten carbide spheres (Wiederhorn

and Lawn, 1977). Theoretical estimates of the load for radial crack formation have been presented by Lawn and Evans (1977) using an elastic-plastic

analysis. They indicate that the critical load depends on both the hardness

and the critical stress intensity factor of the target material.

Direct evidence for plastic flow during impact has been obtained

from transmission electron microscope studies of surfaces that have been

impacted with hard particles (Hockey at al_. , 1978) . These studies were

conducted on a group of brittle crystalline materials with very different

properties. Microstructural features were very similar to those observed in

static indentation studies (Hockey, 1971, Hockey and Lawn, 1975). Dense

tangles of dislocations were observed at the impact site for all materials;

the density of dislocations was similar to that observed in metals. The

dislocation and crack morphology in ceramics depended on the crystal structure.

For MgO (Fig. 11) , dislocation arrays propagated on (110) planes well beyond

the impact area, a behavior that is consistent with the ease of deformation

14
of ionic crystals on (110) planes. Cracks also propagated on (110)

planes in this crystal, but were contained within the dislocation arrays.

Silicon and germanium, which are covalent, also exhibited dense arrays

of dislocations at the contact site, but now the dislocations were

tightly bound to the immediate vicinity of the contact site (Fig. 12).

Cracks that were generated during impact propagated well beyond the

immediate contact site often resulting in extensive surface chipping.

Materials that possess partial covalent and partial ionic behavior

(A^O^, SiC) exhibited a somewhat intermediate behavior during impact

(Fig. 13). Both dislocations and cracks propagated well beyond the

contact area during impact.

Temperature has the effect of increasing dislocation mobility in

crystalline materials, so that a material dependent critical temperature

should exist for transition from elastic-plastic to plastic impact conditions.

In an attempt to investigate temperature effects on erosion, Hockey £t al

.

,

(1978) exposed A^O^ crystals to erosive particles at 1000°C. Optical

microscopy investigations of the target surface revealed little change in

the erosion crack morphology: material removal from the Al ,0 , surface at

1000°C was still primarily by chipping (Fig. 14). Consistent with this

observation is the fact that temperature had little effect on bulk erosion

rates of A^O^ (Hockey e£ al

.

, 1978) . Transmission electron microscopy

observations, however, did reveal a considerable increase in the relative

extent of the deformation associated with impact at high temperatures. In

contrast to room temperature results, the radial extent of deformation by

slip at 1000°C was found to be comparable to the extent of fracture. In

15
addition, impact at 1000°C resulted in a significant increase in the amount of

twinning over that occurring at room temperature. High temperature impact

resulted in numerous interactions between slip bands, twins, and grain

boundaries outside of the immediate area of contact. Nevertheless, this

deformation was not sufficient to prevent chipping at the impact site.

Apparently, temperatures greater than 1000°C are needed to obtain completely

ductile erosion for a material such as A^O^-

The amount of cracking of ceramic materials during impact can be

modified significantly by reducing the angle of impact (Hockey e_t al. ,

1978). At 15° impact, cracking on ceramics is largely eliminated. The

cracking that is observed is primarily of the lateral type. Shallow

residual impressions in the ceramic surface are observed (Fig. 15). These

are elongated in the direction of particle motion (in the same way as for

metals) suggesting a shear deformation mechanism of erosion at low impact

angles. Indeed, examination of the contact area by transmission electron

microscopy (Fig. 16) confirms the absence of cracks and the predominance of

plastic deformation in the contact area. Thus at low impact angles, ceramic

materials appear to erode by plastic deformation; in this regard their behavior

is similar to that found in metals.

2. Interpretation

From the above discussion it is clear that a deeper understanding

of single particle impact in ceramics requires a distinction to be made

between completely elastic impact events and elastic-plastic impact events.

In this section, theories of crack formation during impact are reviewed.

In succeeding sections the results of these theories are used to develop

models that predict rates of erosion during multiple particle impact.

16
As mentioned above, impact with blunt particles requires a

minimum threshold velocity for crack formation. Evans (1973), and

Wiederhorn and Lawn (1977) used linear elastic fracture mechanics to

describe the size of the Hertzian crack formed during impact. A quasistatic approximation is used to convert impact velocity to maximum

impact force. The kinetic energy is assumed to be completely converted

into elastic energy during impact. The maximum impact force is then

calculated from the stored elastic energy at deepest penetration of the

particle into the target surface. The maximum impulse load, F , depends

on the elastic constants of the target material and particle, and on the

density, p, radius, r, and velocity, v

q

, of the particle:

F = [(125 7r 3 /48)

1/5

(E/k) 2/5

p 3/5

r

2

] v^/5 m o

E is Young's modulus of the target and k = 9/16 [ (l-v

2

) + (l-v ' 2

) (E/E ' )] is

a dimensionless quantity that depends on Poissons ratio, v of the target,

and v' of the particle, and on Youngs modulus, E of the target, and E' of

the particle.

The critical load, F, for crack growth during impact is

determined from the size of the critical flaw in the target surface.

For the case of quasi-static impact, Lawn and Wilshaw (1975), and Frank

and Lawn (1967) developed the requisite fracture mechanics equations for

crack growth. Because Hertzian stress fields are not homogeneous, a

single, simple analytical expression cannot be derived for the critical

load as a function of flaw size. It is, however, possible to show that

simple limit expressions can be given for very small flaws (c^. 0.01a),

and for large flaws (c° > 0.01a)j where a is the contact radius between the

sphere and the surface at maximum penetration. For most practical

situations, the critical load, F, is given by the large flaw approximation.

( 1 )

17
for which Auerbach's law (1891) is valid (Lawn and Marshall, 1978); F = Ar

,

where A is a constant that is determined by the critical stress intensity

2 * * factor, K

c

, of the target material (A = K

c k/E0 ; 0 is a dimensionless,

material constant whose values are obtained experimentally) . By substituting

F into Auerbach's law, the critical velocity, v , is obtained for Hertzian

crack formation (Wiederhorn and Lawn, 1977)

v - (48/125,

3

) 176 (k/E) 7/6

K

5 / 3 /p1 / 2 r5 / V5/5

. c c For particle velocities less than this critical velocity,

fracture, and hence erosion, will not occur. Above v , the crack size

is determined by a second equation that was derived by Roesler (1956) , who

used a Griffith type energy balance in combination with a dimensional

analysis

:

F/R3/2

= 8 K . R c F is the impulse load, R is the base radius of the cone crack formed

during impact, and 8 is a constant that is usually determined empirically.

Substituting equation (1) into equation (3) (i.e. F = F ), the following

equation is obtained for the size of the cone crack that forms as a

result of impact:

R - [(125*3

/48) 2/15

(E/k) 4/15

p 2/5

r 4/3

/ B 2/3K

2/3 ]v

k >\

R c o The cone crack radius, R, can be used to estimate strength

degradation resulting from impact. Assuming the effective flaw size for

fracture, c^, is proportional to R, c^ = fi R, then strength degradation

is determined by substituting Eq. (4) into the Griffith equation,

a = K /( ttc ) c f 1/2

a - [(48/125 „ 10 - 5

) 1/15

(k/E) 2/1 \

1/3 K^7 V/2

p 1/5

r 2/3

]v

o

-2/5

.

The validity of this approach to Hertzian crack formation has

been checked recently on several ceramic materials. Wiederhorn and Lawn

(1977) have shown that the theory predicts the effect of particle velocity.

( 2 )

(3)

(4)

(5)

18
particle density, and particle size on the strength of glass impacted by

steel and tungsten carbide spheres. Evans (1973) has shown that strength

data obtained by Ashford (1968) on SiC is explained by the above theory.

Although Kirchner and Gruver (1977) also obtained reasonable predictions

of strength degradation of glass impacted with glass spheres, they

never-the-less found that the crack size formed during impact was significantly less than that calculated from theory. From these results it can

be concluded that the theory for predicting crack formation in the

elastic impact situation is generally supported by experimental data.

Clearly, additional work is needed to fully evaluate the theory, which

does not completely account for the shape of the cracks formed on impact.

Loading history appears to play some role in determining the crack

shape, as evidenced by small rims that are observed to form along the

edge of the Hertzian cracks as the particle leaves the surface (Chandhri

and Walley, 1978). The formation of these rims may be the result of

elastic wave generation during crack formation, residual plasticity at

the impact site, or rebound of the surface as the sphere leaves the

target. Despite some differences between experiment and theory, the

theory does explain most major observations of spherical particle impact.

Sharp particle impact theories require a greater number of

assumptions than blunt particle impact theories because plastic deformation occurs during impact. As noted by Lawn and Evans (1977) in

their model for crack initiation in elastic-plastic indentation fields,

crack initiation is determined by the stresses set up by the plastic

zone that forms on impact. Their model can be applied to explain crack

initiation for the case of quasi-static impact. Pre-existing flaws at

the impact site are assumed to be the sources of crack formation. These

19
flaws grow as a result of the plastic stress field formed during impact.

The hardness, H, and the contact radius (or an equivalent parameter), a,

are convenient scaling parameters used to establish the stress in the

vicinity of the flaw. Applying fracture mechanics theory, Lawn and

* * Evans derive a critical crack size, c , and a critical load, F , for

fracture, both of which depend on the hardness and critical stress

intensity factor of the target material:

c* = (1.767/0

2

) (K /H)

2 c

F* = (54.57 a/n

2 04

) (K /H)

3 K . c c

a is a constant that depends on the indenter geometry (a = 2/tt for a

Vickers diamond pyramid indenter) ; 0 is a dimensionless constant that

relates hardness to the maximum stress beneath an indenter; n is another

dimensionless constant that relates the depth of the maximum stress to

the size of the hardness impression. From equation 6 we note that

k

unless a critical flaw larger than c is located in the vicinity of the

indenter, fracture will not occur during indentation. The critical load

k

for fracture, F , calculated by Lawn and Evans (1977) is shown to vary

for a variety of materials, from 0.003 N (silicon) to 40 N (NaCl) . The

k

value obtained for glass, F = 0.02N, is considerably less than that

obtained for any practical sphere size. A 0.4 mm radius sphere, for

example, requires a load of 98.5 N to form a crack, whereas a sphere of

approximately 0.1 pm would be required to generate a crack under a load of

t

%0.02 N. Thus, the theory by Lawn and Evans demonstrates the greater

sensitivity of ceramic materials to sharp particle erosion than to blunt

particle erosion.

Assuming a crack can be generated during impact, it is necessary

to develop a mechanism of load transfer from the narticle to the target

t Spheres of this radius are, of course, "sharp” from a microscopic

point of view.

20
surface in order to estimate the final crack size resulting from the

impact. The problem of load transfer arises because a complete elasticplastic solution of the indentation process is not available. Hence the

rate of particle deceleration, and consequently, the change in particle

momentum at the target surface is not known. Two models have been

proposed to estimate the contact force during impact. In one (Wiederhorn

and Lawn, 1979), the kinetic energy of the particle is assumed to be

completely dissipated by plastic flow as the particle contacts the

surface. The contact force is calculated from the hardness of the

target material and the maximum depth of penetration during contact.

The maximum load, F^, during contact is determined by the mass, m, of

the particle, the hardness, H, of the target, the particle velocity, v ,

and several geometric constants that are governed by particle shape:

w tt 1 / 3 2/3 4/3

F ^ H m v

m

The size of the crack formed during impact is then determined by substituting

* Eq. (8) into Eq. (3) , which is tantamount to assuming that a crack

formed during impact depends on the load in the same way as one formed

during static indentation:

4/9 2/9 8/9 „ -2/3

c m H v K

r c Evans, Gulden, and Rosenblatt (1978) included dynamic effects

in their calculation of the contact force during impact. In contrast to

the assumptions made by Wiederhorn and Lawn (1979), plasticity as represented by the hardenss is assumed to play a minor role in the fracture

process. A spherical particle is assumed to penetrate into the target

surface without distortion, and the contact pressure is assumed to be

the dynamic pressure set up when the particle first hits the surface.

The depth of penetration is determined from the time of contact, and the

mean interface velocity, both of which are calculated from a one dimensional

( 8 )

(9)

*Eq. (3) has been shown by Lawn and Fuller (1975) to be valid for the formation

of radial cracks in brittle materials.

21
impact analogue. The final expression obtained by Evans et al . , (1978)

for the contact force is considerably different from that obtained by

Wiederhorn and Lawn:

2 2 F v R p (10) m

Here R is the particle radius and p is its density. The size of the

crack formed during impact is obtained by substituting Eq. (10) into

Eq. ( 3

) *

:

c r

- [(v r)

2 /Kj 2/3

p 2/3

. (]])

By comparing Eq. (11) with Eq. (9) we see that the two theories

result in different expressions for radial crack formation. However,

-2/3 both expressions suggest that crack formation depends on K . The

c theory by Evans ejt a_l. suggests a stronger dependence of crack size on A/3 8/9 velocity (v ) than does the theory by Wiederhorn and Lawn (v ) .

Furthermore, the theory by Wiederhorn and Lawn takes into account the

hardness of the target material, whereas the theory by Evans et_ aj_. does

not. Evans e£ al. compared their theory with data giving crack size as

a function of particle velocity, particle shape and size, and target

properties. In all cases good agreement was obtained between theory and

experiment. In a more limited but similar set of experiments on glass,

Wiederhorn and Lawn also obtained good agreement between theory and

experiment. Additional experimental data and a detailed comparison of

the two theories with the data will be needed to decide which of them

better describes the impact process in terms of particle/ target parameters.

*In comparing Eq. (11) with experimental data, Evans £t al_. (1978) discovered

a weak dependence of c on p . Consequently, Evans et_ al_. deleted p from

Eq. (11) for further theoretical analysis. However since p enters the theory

again in estimating the erosion rate, it was felt best to use Eq . (11) as it

appears above. As a consequence the erosion rate (Eq. (20)) based on the

above theory differs from that published by Evans e_^ al .

22
Evans, Gulden and Rosenblatt ( 1978 ) also developed a theoretical

description of lateral crack formation. The theory takes into account

both the depth at which the lateral cracks form and the size to which

they propagate. The depth, h, at which lateral cracks form is assumed

to be proportional to the plastic zone depth at full penetration of the

impacting particles. The problem of estimating the penetration depth

had been addressed for a variety of impact conditions by Goodier (1965) .

Using Goodier's results and experimental data on depth of crack formation,

Evans et_ al .

,

( 1978 ) relate the depth of crack formation, h, to the

particle size, r, particle velocity, v , particle density, p, and

target hardness, H:

(h/r)

2 v

o (p/H)

1/^ 2

The size of lateral cracks formed during impact is found experimentally

to be proportional to the size of the radial cracks formed during impact.

Thus, the semi-empirical model proposed by Evans et_ a_l. , (1978) provides

a quantitative description of lateral crack formation during impact.

23
III. MULTIPLE PARTICLE EROSION

Technological concern with the erosion of materials involves

multiple particle impacts, usually in a steady state long term

regime (National Research Council, 1977). Simple consideration of

the effects of a flux of particles incident on a surface for some

length of time suggests that many new, complex aspects are added to

the basic problem. These include particle impacts within the incident

stream, a wide range of simultaneous attack angles, particle fragmentation,

surface shielding due to rebounding particles, and particle embedding

effects among others. (Some of these effects, e.g., fragmentation and

embedding also occur on single particle impact). Clearly multiple

particle erosion exposures must be conducted in order to measure

meaningful erosion rates of materials for application purposes. A

second reason for such experiments would involve a search for new,

significant effects due to multiple particles. One such effect has

recently emerged concerning particle embedding in the specimen surface.

Another important effect is that of subsurface damage due to multiple

impacts. This section will review principally the recent work in this

area

.

24
A. METALS

1. Methods and Results

Two basic types of equipment design have been used to expose

solid specimens to a stream of erosive particles. In one design the

specimen is moved at a controllable velocity, usually on a rotating arm

fixture, through a slowly moving erosive stream. The exposure may be intermittent but can continue for a long time period. The relative particlespecimen velocity can be accurately determined since the principal velocity

component is that of the specimen (in the laboratory system) . A variation

on this design allows the erosive particles to be spun from a rotating disk

to strike a fixed specimen. The alternative design involves propelling a

stream of particles at a fixed specimen. The specimen may be completely

immersed in the stream, or perhaps only a portion of the specimen exposed.

In this scheme some method of measuring or calculating particle velocity must be

used. The particle concentration in the stream and the nature of the carrier

gas (fluid) can be chosen as appropriate. Some type of nozzle or flight tube

is involved in order to properly confine the erosive stream. Velocities of 300 s

larger have been reported using this method (for example. Grant and Tabakoff, 1975).

Quantitative measurements of erosion rate require careful attention to

the experimental system and the parameters of exposure. For example, wear

of the abrasive delivery nozzle can greatly alter the stream shape and velocity

profile. Turbulance within a flight tube or caused by the presence of the

specimen itself in the stream can significantly affect particle flux and

particle velocity as experienced by the test specimen. Consideration of the

particle trajectories within the incident stream, particularly near the specimen,

are important (Tilly, 1969). Since, as we shall see. the erosion rate can vary

as high as the third power of the particle velocity, accurate knowledge of

25
particle impact velocity is essential.

The variation of erosion, usually measured in mass or volume loss from

the specimen per unit mass of impacting abrasive, as a function of angle of

attack of the particles is shown schematically in Fig. 17 for brittle and for

ductile materials. Many workers have reported this general behavior. For

ductile materials the peak erosion loss occurs at around 20°. For brittle

materials the peak erosion loss occurs at around 90° (normal incidence) . The

dependence of erosion rate on particle velocity has been measured for many

materials over at least three orders of magnitude in velocity. The erosion

2 3 rate is found to increase as v to v in most cases (see for example, Sheldon

and Kanhere, 1972; Finnie et_ al, 1967). The velocity exponent has been reported

not to depend on the type of material (Fig. 18), however, detailed studies have

shown some dependence of the velocity exponent on attack angle (Fig. 19) and a

dependence on the temperature of erosion (Fig. 20).

The dependence of erosion on particle size has also been studied by

several workers. In a detailed study, Goodwin e£ al^, (1969) examined the erosion

of steel by quartz particles over a large size range. As shown in Fig. 21, an

increase in erosion with increasing particle size was found up to a limiting size,

above which the erosion remained constant.* A theory explaining this result has

been developed (Tilly, 1973) and will be discussed later. Much interest has been

centered on the possible erosion effects of very small particles e.g., less than

5pm in diameter. There have been conflicting reports in the literature on the

size effect for such small particles. Recent studies have shown significant

erosion of metals by particles as small as 2pm (Goebel et_ al_, 1976) .

*An increase in erosion was noted for particle sizes greater than about 500pm.

26
The effect of particle size as measured using flat test specimens

may not be applicable in all geometries as shown by the recent work of Mills

and Mason (1977) . In studying erosion in 90° tube bends due to the conveying

of abrasive sands, they reported that depth of penetration for 70 ym particles

was much greater than for 230 ym particles. Further a different surface

morphology resulted and a different angle of maximum penetration was found.

The effects of increasing temperature on erosion have been studied in

more detail in the last few years. The environment in which high temperature

erosion takes place usually has a very significant effect on erosion rate

but will not be considered here (see, however, Chapter 8 for this question).

Depending on the material being eroded, the temperature range, and the

environment, different effects due to temperature have been reported (Young

and Ruff, 1976). The results in one specific instance shown in Fig. reveal

a large increase in erosion of type 310 stainless steel on going from 25°C

to 975°C. A recent study of erosion of aluminum and type 310 stainless steel

(Finnie et al. , 1978) also reported increased erosion for increased temperature*

although a complicated dependence on erosion angle was reported (Fig. 22 ).

In work on other alloys, however (Smeltzer et. a_l . , 1970), decreases in erosion

with increasing temperature have been reported.

One material parameter that has been of particular interest in connection with the understanding of ductile material erosion is indentation

hardness. Numerous correlation studies have been attempted to determine the

relation of hardness to erosion rate. In Fig. <0 some results due to

Finnie _et _al • » (1967) are shown. Clearly the erosion rate of different

ductile metals decreases as the reciprocal of material hardness. However,

when those authors studied the effect of hardness variation for one alloy

(varied through thermal treatments of a tool steel) they found little effect

on erosion rate. Other differences between the materials studied such as the

27
crystal structure, slip systems, flow stress, and strain rate sensitivity,

appear to be the determining parameters. Sheldon (1977) has recently proposed

that the indentation hardness of a work-hardened surface would be a more

appropriate measure to utilize.

The influence of other erosion parameters such as particle concentration

in the erosive stream, particle hardness, and particle strength, have only

been examined in a few instances. In the case of particle concentration,

divergent findings have been reported as summarized by Uuemois and Kleis (1971).

It would seem that relative erosion (specimen mass loss divided by impacting

erosive mass) should be independent of particle concentration so long as each

particle event is equally effective. At higher concentrations, where particl

interference (shielding) effects occur at the specimen surface, the relative

erosion should be expected to decrease and this has been reported (Uuemois and

Kleis, 1975; Young and Ruff, 1977). Only limited studies of the effects of

particle hardness, strength, and frangibility on the erosion of a given particle

material have been reported (Tilly, 1973; Uuemois and Kleis, 1975). The

interpretation of those results is complicated by the need for more extensive

characterization of the particles before and after erosion. Recently, Maj i and

Sheldon (1978) have studied the effects of different mechanical conditions of

spherical steel shot that were used as erosive particles. They examined the

erosion of aluminum alloy tubes and flat plates using 270um shot and found

considerably more erosion for brittle than for ductile shot. Evidence for the

removal of additional specimen material upon the fracture of an incident particle,

so-called secondary erosion, was presented. At elevated temperatures, the hot

hardness and high temperature toughness of both the specimen and the eroding

28
materials would be important to consider.

There has been attention given recently to the effect of particle

embedding during erosion. Further, the effects of specimen microstructure

on erosion behavior has been examined. Ives and Ruff (1978) have studied

surface and subsurface erosion damage in copper exposed at room temperature

and found evidence for significant particle embedding. As seen in Fig. 2'-,

the initial erosion effect involves a mass gain of the specimen due to the

added particulate matter. This results in an initial "incubation" period

before the usual steady state erosion rate develops; this effect has been

reported previously (Neilson and Gilchrist, 1968). Studies of the eroded

copper specimens selected after various periods of exposure revealed a layer

of deformed copper and abrasive (A^O^) fragments that had developed at the

surface, as seen in Fig. 25 . In these experiments an electrodeposit of

copper was used to preserve the true surface structure during the preparation

of cross-sections. Transmission electron microscopy studies of the effects

of particle embedding were also reported; a region around one such particle

is shown in Fig. 26 . Embedding was more pronounced at a 90° attack angle

than at 20°, the other angle studied. A recent study by Zahavi et al .

(1978) has also emphasized the occurrance of particle embedding during erosion

studies of three different ductile alloys by natural sand particles.

It is possible to recover eroded material (metal and abrasive particles)

after appropriately designed experiments. Preliminary studies have been

carried out using mild steel (type 1015) specimens eroded at room temperature

at 30° angle of attack using 50 ym Al^O.^ particles (Ruff, 1978). Magnetic

recovery methods were applied in this case to collect the metallic debris.

Examples of recovered debris are shown in Fig. - where the aggregation of

29
individual particles is due to the impressed magnetic field used in

recovery. The eroded surface structure is also shown. The majority

of eroded metal particles are equiaxed and average about 3 ym in size.

Many small metal particles were found less than 1 ym in size. Very

few examples of particles of "cutting-like" morphology (ribbon or wirelike appearance) were found. A significant proportion of particles having

a plate-like shape were seen. A good correspondence could be achieved

between the observed metallic debris morphology and certain features

of the metal surface topography. It appears that the metal debris

was removed primarily from the exposed portions of surface impact

crater features that were formed from plastic deformation associated

with particle impacts. From the debris size and shape it does not appear

that the metal debris particles were formed in a single cutting process

but perhaps after several successive impact events. Examples were also

found of abrasive particle fragments within the metallic debris clusters

indicating transferred or adherent metal layers on the abrasive. Further

studies of recovered metal and abrasive debris are in progress.

30
2. Interpretations

Review of the literature of erosion testing indicates many different methods and apparatus that have been used with considerable success.

Frequently, multiple particle equipment is designed with some potential

application geometry in mind. Perhaps a quantitative inter-comparison

between different testing systems* would reveal some advantageous design

in terms of the ability to reproduce the more critical parameters from test

to test, but such information is not presently available. It is acknowledged

that considerable care must be taken in accurately measuring the many

parameters of erosion testing. Two critical experimental quantities can

be mentioned here, particle velocity and particle attack angle. Several

particle velocity measurement methods have been reported; photographic

(Finnie et fiL. , 1967), rotating disk (Ruff and Ives, 1975) and laser doppler

(Goebel and Pettit, 1976). Particle velocity calculations have also been used

in place of detailed measurements in some studies. The particle attack angle

can ordinarily be measured accurately, however, for small particles (< 10 pm)

flow pattern disturbances can produce large deviations from the nominal attack

angle and must be considered. Such deviations near the peak erosion angle for

ductile materials can lead to significant errors. Particle divergence within

a stream and the effect of fragmentation on impact must also be considered

carefully

.

Results of multiple particle erosion studies on various materials have

shown the effect of the principal parameters involved. Existing theoretical

*An inter-laboratory comparative measurement series involving solid particle

erosion is presently beginning within the ASTM Committee G2 on Erosion and Wear.

31
models and calculations that consider these results will be described in

the next section. The peak erosion angle of about 20° for ductile materials

is ascribed to ploughing and cutting deformation processes with consideration

also of particle fragmentation on impact. Brittle material erosion peaks at

90° incidence are related to the efficiency of crack formation around the

impact crater. The particle velocity dependence of erosion, variously measured

2 3 as proportional to v to v is still the subject of detailed investigation.

In ductile materials the specific manner of deformation and cutting may determine the precise exponent value. Recent theoretical results of Hutchings

(1978) and Finnie and McFadden (1978) address this matter.

The effects of particle size on erosion rate also need further study.

For example, relatively little effort has been made to study particle size

distributions before and after erosion and to characterize the erosion

debris. Particle fracture and fragmentation phenomena have been reported;

however, the importance of such issues is not agreed upon. Recently,

Hutchings (1977) has proposed that the particle size effect (Fig. 21 ) is due

to the variation in imposed strain rate on impact with particle size.

The role of embedded particles (or fragments) on steady state erosion

also needs more study. It appears that a layer of deformed metal and

embedded particles forms as a result of the erosion of ductile material

(Ives and Ruff, 1978). The sizes of the embedded particles are generally

much smaller than the incident particles, as a result of fragmentation

upon collision at the specimen surface. The mechanical properties of this

mixed material surface layer and of the underlying material then determine

the overall erosion behavior. Characterization of the subsurface damage

produced during erosion below this mixed layer is also needed. It seems

32
possible that in some systems a degree of protection may even result

from the embedding or adhesion of incident material in this manner.

The detailed deformation and fracture processes that take place

as a result of particle impact on metals are not yet adequately understood.

It appears from limited studies of erosion debris (Ruff, 1978) that, even

at low (30°) attack angles, little metal may be removed by direct cutting

impacts. Rather, plowing-type interactions producing extensive plastic

deformation and displaced material create a surface topography (Fig. 27a)

from which metal may be removed by subsequent particle impacts. In

view of the complex topography of eroded surfaces it will be necessary

to further examine the theoretical models that presently describe the

erosion process.

Recent studies of erosion microstructures in metals by Levy and coworkers

1978) have also shown some interesting subsurface structures resulting from defori

tion processes. Erosion of an aluminum alloy specimen using spherical particles

produced a surface structure comprised of rounded hills of rippled appearance.

A deformed surface layer of material was found that appeared to detach

from the surface by a delamination type of process. Studies of this

mechanism are reportedly continuing.

33
B. CERAMICS

1. Results;

The main parameter that controls the rate of erosion of materials

is the particle velocity. A number of studies indicate that the erosion rate

can be expressed as a power function of the particle velocity. As with

metals (Finnie et al. , 1967, Sheldon and Kanhere, 1977), velocity exponents

generally range from %2 to ^3 (Hockey _et al_ . , 1978, Sheldon 1970). Higher

exponents have, however, been reported: 6 for glass impacted with steel spheres

(Finnie, 1960); 4 for MgF£ impacted with quartz, or silicon carbide (Gulden,

1978); 4 for silicon nitride impacted with quartz, or silicon carbide

(Gulden, 1978). The value obtained for the velocity exponent of a given

material apparently bears little relation to composition or microstructure of

that material. Thus, castable refractories, which are ^30 percent porous

and have a multiphase structure, exhibit the same range of velocity exponents

(2.3 to 3.9, Wiederhorn et_ aJ, 1977) as dense, relatively homogeneous ceramics

such as glass, hot-pressed silicon nitride, and high density aluminum oxide

(Hockey et_ al., 1978). In dense ceramic materials, grain size also has

little apparent effect on the velocity exponent, even though it has a

significant influence on the absolute rate of erosion. This insensitivity to

composition and structure means that the velocity exponent is not a useful

indicator for evaluating microstructural effects on erosion, or distinguishing

between mechanisms of erosion.

Studies on both ceramics and metals suggest that impingement

angle is a more satisfactory indicator of erosion mechanism. As noted

earlier in this chapter, ductile materials (metals) exhibit a maximum in

the erosion rate at an angle of impingement of approximately 20° (Fig. 17).

By contrast, brittle materials (ceramics) exhibit a maximum in the

34
erosion rate at an angle of 90°. This type of behavior has been used to

classify materials as either brittle or ductile with regard to erosion

(Bitter, 1963, Neilson and Gilchrist, 1968, Sheldon 1970). Actually, most

materials exhibit behavior that is neither completely ductile nor completely

brittle, and quantitative procedures have been developed to evaluate the

relative amounts of brittle and ductile erosion that occurs for a given

material-particle system. Recent studies on ceramic materials indicate

a strong contribution of ductile behavior in these primarily brittle

materials

.

Sheldon and Finnie (1966 a) were the first to demonstrate a

ductile-to-br ittle transition in ceramic materials. They showed that at

a fixed velocity (^150 m/s) the erosion behavior depended on the size of

the impacting particle. Studies on glass, high-density magnesium oxide,

and graphite indicated brittle type of erosion behavior for 127pm

silicon carbide particles, whereas a change to a more ductile type of

behavior was observed when the particle size was reduced to 9pm. This

change in behavior was quite dramatic for glass, which exhibited a

strong maximum in the erosion rate at an impact angle of ^25°, as illustrated in Fig. 28. Moreover, microscopic studies of the eroded surfaces

showed that the 127pm particles produced a chipped surface topography,

wherease 9pm particles produced a ripple pattern, typical of ductile

erosion, (Fig. 29). High density aluminum oxide, on the other hand,

exhibited brittle erosion behavior for all particle sizes. These results

indicate a significant effect of target material properties, even among

materials that generally behave mechanically in a brittle fashion.

In a more recent discussion of the erosion behavior of materials,

Sheldon (1970) noted the importance of tangential forces in the wear
process. For normal impact the erosion of brittle materials is proportional to v^, where is the particle velocity and b is the power exponent.

If only brittle behavior were occurring at an oblique impact angle, then

the erosion rate, w, might be expected to be proportional to (v

q sin a)*

5

,

where a is the impact angle. By plotting In w as a function of In

(sin a), Sheldon determined that, although the data fit straight lines, the

power function b was not the same as that determined from velocity studies

using normal impact angles. He concluded from these results that tangential

forces contribute to the wear of brittle materials.

In a study of the effect of temperature on erosion. Hockey et_ a_l. ,

(1978) also demonstrated that plastic flow processes occur during the erosion of

brittle materials. The erosion rate of glass, silicon nitride, and

aluminum oxide was measured as a function of temperature and impingement

angle using ^150ym silicon carbide particles as the erosion agent.

Although a low angle maximum in the erosion rate was not observed in

these studies, there did seem to be a significant enhancement of the

erosion rate at low angles of impingement. Fig. 30. These findings were

consistent with those reported earlier by Sheldon (1970) . It was concluded

that wear generally occurs by a mixed mode of erosion, with the ductile

processes becoming increasingly more important with decreasing angle of impingement .

The above conclusions on ductile behavior are also supported

by optical and scanning microscopy studies of erosion surfaces. Ceramic

materials eroded at an impingement angle of 90° exhibit a rough, chipped

surface indicative of material removal by a fracture process (Fig. 31).

By contrast, erosive wear at 15° results in relatively smooth surfaces

that are characterized by furrows, or wear scars, which indicate material

36
removal by a plowing mechanism, Fig. 32. Lateral cracks form at the

margins of the wear scars, undoubtedly contributing to the wear process.

This evidence for ductile erosion is consistent with single particle

impact experiments (described above) , which show extensive deformation

in the impact area and a significant decrease in the incidence of fracture

for low angles of particle impingement.

2. Interpretation

The results presented in the previous section point to the

importance of plastic deformation in the erosion process. Subsurface

plastic deformation at the impact site results in residual stresses that

cause lateral crack formation and surface chipping, so that erosion

appears to occur primarily by a brittle fracture process. The role of

plastic deformation, relative to fracture, is enhanced by reducing the

impact load during erosion. This can be accomplished by reducing the

impact velocity, the particle size, or the angle of impingement. When

the impact load falls below a critical value, fracture does not occur,

and erosion occurs by plastic deformation processes. In this section,

a discussion is presented of the theories that have been used to explain

plastic processes in ceramic materials; these theories are applied to

explain effects of particle size, impingement angle and temperature on

erosion. Conditions that define the brittle to ductile transition for

erosion of ceramics are also discussed.

Sheldon and Finnie (1966 a) were the first to provide a theoretical framework for understanding the transition from brittle to ductile

erosion in ceramic materials. For impact that can be approximated by

quasi-static loading under Hertzian loading conditions, they noted that

fracture of brittle materials is described by Auerbach's law. From

these relations, the condition for fracture can be expressed in terms

of the maximum radius of contact and the impact load. Plastic flow

37
during impact is determined by the impact load and the hardness of the

material. Two equations were obtained by Sheldon and Finnie (1966 a).

Both related the contact load to the impact radius: one equation was

3/2 2 for fracture (F °c a ) ; the other was for plastic deformation (F a ) . m m

At high impact loads (i.e. high particle velocities; large particle

mass), the equations predict a lower load for fracture than for deformation; thus fracture dominates the impact process at high impact loads.

At low impact loads the reverse is true; plastic deformation dominates

the impact process. A maximum load for ductile impact was determined by

setting the equations equal to one another. Following this procedure,

Sheldon and Finnie (1966 a) estimated that fracture of glass occurred when

the contact radius during impact was greater than vlOym. This estimate

was about one order of magnitude greater than that observed experimentally.

A more realistic investigation of the impact problem was

conducted by Evans, Gulden and Rosenblatt (1978). For sharp particle

contact, Eq. (7) provides a relation between the critical load

for fracture and the material parameters K

c and H. Evans et al. (1978)

converted the impact load to an impact velocity using a dynamic treatment

of the impact event. They showed that the critical velocity for fracture,

v , was related to K

c and H through the following equation:

v

c

> (0/4 tt) (K

c

2 /r H

3/2

) (1+Z

t /Z

p

) /[ Pp (Z

t /Z

p

)]

1/2

where 0 is a constant' (v0.2), r is the particle radius, is the

particle density, and and are the elastic impedances of the target

and particle respectively. Although Eq. (13) is only applicable

to radial crack formation, the dependence of the fracture threshold on K ,

H, p, etc., probably also applies for lateral crack formation.

The procedure used by Evans et_ al

.

can also be applied to the

elastic-plastic theory discussed by Wiederhorn and Lawn (1977) (also

(13)

38
see Chapter 1) to obtain the following equation for the velocity threshold:

v = (2.25Trtan^)” 1/4(54 . 47/q

2 0

2

) 3/4

(a/m) 1/2 K

3 H~

5/2

(14)

c c where n , 0 and a are constants discussed above (see eqn. 6 and 7), and

2\p is the included angle of the contacting point of the impacting particle,

(Wiederhorn and Lawn, 1979). Although these two equations are functionally

different, both predict a dependence of the threshold velocity on the

hardness and critical stress intensity factor of the target material,

and on the size and density of the impacting particle. Both theories

predict an increase in the threshold velocity for cracking as the particle

size is made smaller. This prediction is in qualitative agreement with

the data of Sheldon and Finnie discussed above (1966 a) , which showed

that a transition from brittle to ductile erosion occurs as the size of

the silicon carbide particles is decreased. A closer comparison of

theory and experiment is not possible, however, because Eq. (13) and

(14) give threshold conditions for radial crack formation. To predict

threshold conditions for erosion, a similar equation would have to be

derived for lateral crack formation. Nevertheless, it is probable that

the threshold velocity for lateral crack formation has a similar dependence

on target and particle properties and thus also depends on stress intensity

factor, hardness, and particle size and density in a way that is similar

to that given in Eq. (13) and (14).

Equations (13) and (14) are useful for discussing the dependence

of erosion on temperature. The critical stress intensity factor and the

hardness are the only materials variables in Eq. (13) and (14) that

depend on temperature; therefore, the effect of temperature on the

brittle-to-ductile transition will be determined by the behavior of

these variables as the temperature is increased.

Investigations of the effect of temperature on K. suggest modest

changes in K as the temperature is increased. Studies on sapphire (Wiederhorn,

39
Hockey and Roberts, 1973), for example. Indicate a decrease in K from

c 1/2 1/2

a-2.4 MPa-m to ol.8 MPa-m as the temperature is increased from room

temperature to 800°C. Similar results are obtained for chemical borosilicate glass (C7740) and for silica glass (C7940) (Wiederhorn, Johnson,

Diness and Heuer, 1974), which showed very little change in K as the

c temperature is increased from room temperature to o600°C. On the other hand,

hot pressed silicon nitride (HS-130) exhibits a substantial change in K

c as the temperature exceeds 1200°C (Evans and Wiederhorn, 1974), but this

increase in has been shown to be strain-rate dependent. Thus under

impact loading conditions, has almost the same value at 1300°C as at

room temperature (Mendiratta et_ al_. , 1977, Gonazy and Johnson, 1978). A

similar finding was obtained on single crystal silicon for which the

ductile-to-brittle transition (determined by K

c measurements) increased

from 'WOO°C to n-950°C as the loading rate increased from 5x10 ^ cm/min

_2

to 5x10 cm/min (St, John, 1976). These results again suggest that for the

dynamic loading conditions expected during impact, the critical stress

intensity factor of ceramic materials is not dependent on temperature.

Measurements of the hardness of ceramic materials, however, do

indicate a substantial decrease in hardness as the temperature is increased.

2 The hardness of aluminum oxide, for example, decreases from ^2000 Kg/mm

2 at room temperature to ^500 Kg/mm at 500°C (Westbrook, 1966) . Similarly,

2 the hardness of magnesium oxide decreases from rv-800 Kg/mm*" at room

2 temperature to ^100 Kg/mm at 1000°C while that of quartz decreases from

2 2 vllOO Kg/mm at room temperature to ^200 Kg/mm at 900°C (Westbrook, 1966) .

Similar results are obtained on other materials as the temperature is increased.

Assuming that remains constant as the temperature is increased, these changes

40
in the hardness would have significant effects on the ductile- to-brittle

transition for erosion. Depending on the properties of the target

material, and the theory used to predict the transition velocity,

expected increases in v^ at 1000°C range from 10 to 100 times that

predicted at room temperature. These increases in v^ are of the same

magnitude as would be expected if the particle size were reduced by a

factor of 10, as in the experiments by Sheldon and Finnie (1966 a)

.

Studies of the erosion of ceramic materials do not support the predicted

increase in v . For the materials investigated, temperature appears to

have a small effect on the erosion rate of dense ceramic materials (Hockey,

et al

.

, 1978). Furthermore, direct examination of impact sites by

transmission electron microscopy gives little indication of a significant

enhancement of the plastic zone at the contact site as the temperature

is increased (Hockey, et al

.

, 1978). From this evidence we conclude

that the significant parameter in Eq. (13) and (14) is not the static

hardness just discussed, but the dynamic hardness (i.e., hardness measurements made using impulse load conditions)

.

Except for one study on soda-lime-silicate glass (Gunasekera

and Hollaway, 1973), dynamic hardness measurements have not been made on

ceramic materials. The study by Gunasekera and Hollaway on soda-limesilicate glass was conducted at room temperature using load durations

-3 5 ranging from olO to ol0 s. Over this range, the hardness of freshly

cleaved glass surfaces was found to increase from 0-3.5 GPa for a 10

sec. load duration to 08 . 5 GPa for a 10 sec. load duration. When one

considers that the impulse time for small particles impacting glass

surfaces is of the order of microseconds, then the importance of dynamic

hardness to the erosion process becomes apparent.

41
Dynamic hardness measurements have been made on indium as a

function of temperature (Silverio, 1963). A ballistic pendulum was used

-2

for impact times of ^10 sec. and a falling ball for impact times of

-4

^10 sec. His study showed that for the temperature range -196°C to

130°C, the hardness increased as the load duration decreased. For times

-4

of ^10 sec., a maximum value of the hardness was approached regardless

-4

of the temperature. Thus, for times less than ^10 sec. the dynamic

hardness was found to be independent of temperature. If this result

could be generalized, then the ductile-to-brittle transition for the

erosion of ceramics would not depend on temperature, since neither K , c nor H in Eq. (13) and (14) would depend on temperature. Clearly,

additional experimental work on dynamic and H is needed to fully

characterize the effect of material parameters on the erosion of ceramics.

42
IV. THEORIES OF EROSION

A. DUCTILE MATERIAL MODELS

The earliest consideration of ductile processes of erosion is due to

Finnie (1960), who considered a micro-machining mechanism as a model. He

treated the problem by assigning a plastic response character to the material

through a flow stress, o^. The trajectory of a particle cutting and removing

material was calculated, and the eroded volume, V, was determined to be given

by the expression:

2

T7 mV

V = o opra- « <“> (15)

where m is the particle mass, v

q

the impact velocity, K the ratio of vertical

force to horizontal force on the particle, and d the depth of cut. g(ot) is a

function describing the effect of attack angle a. This approach was quite

successful in explaining many features of solid particle erosion. However,

quantitative discrepancies arose concerning the effect of flow stress, the

velocity exponent, and the applicability of the model itself for attack angles

near a = 90°. Recent refinements of the original analysis by Finnie and

McFadden (1978)^ in which the interaction force between the particle and the

target surface is modif iedjhave led to velocity exponents of about 2.5, which arc

more closely those found by experiment. Earlier, Bitter (1963) considered an

indentation deformation process to occur near a = 90°, as well as the

cutting process embodied in Finnie' s model. By considering the energies

involved in these processes. Bitter was able to develop an expression to

better account for erosion at all attack angles. This theory, as well as that

43
of Nielson and Gilchrist (1968) requires experimentally determined parameters

for complete application. Tilly (1973) has proposed a two stage mechanism

of erosion recognizing explicitly that particles impacting at near-normal

incidence may fragment and the fragments may subsequently erode exposed

surface features. He was able to account for a reported decrease of erosion

with decreasing particle size and introduced the concept of a minimum particle

size for effective erosion.

As previously described, Sheldon and Kanhere (1972) have examined the

mechanism of single particle erosion of ductile materials. They then developed

a method to describe the deformation and machining actions observed using

indentation theory and an energy balance equation. Their results differ from

previous calculations, giving the erosion volume as

V

,3 3 , ,3/2

d v (p ) o P H

3/2

( 16 )

where d is the (spherical) particle diameter, the particle density, and

H the Vickers hardness value of the material. This theory leads to a greater

2 velocity dependence than expected from energy arguments (proportional to v )

.

Recent studies by Winter and Hutchings (1975) and Hutchings (1977),

1978) into the mechanisms of single particle erosion have led to suggestions

of several significant impact processes and materials parameters. One

important mechanism they report involves adiabatic shear (thermally localized

deformation) . Titanium in particular appeared sensitive to local thermal

effects due to particle energy release. As a result, detachment of small meta]

chips took place more frequently from the ploughed metal at the impact crater

in titanium than in steel specimens similarly impacted. A second consideration

involves the deformation strain rate applied to a material as a result of

particle impact. For small particles (<100|jm) they found that high strain

44
rates (e) are an important consequence of impact. Calculations showed that

e

11 (particle radius) \ reaching values of the order of 10^ sec ^ for

5ym particles and a velocity of the order of 100 m/sec. Material response

at such high strain rates is not well known; such data are needed for an

improved understanding. Based on single particle impact observations,

Hutchings (1978) has developed a formulation of the deformation process.

The two curves shown in Fig. 6 are predictions of that numerical theory using

one material parameter, the indentation pressure. The original papers should

be consulted for further details. It is an interesting feature of this theory

2 that the velocity dependence of erosion varies from v^ to slightly higher

values depending on the detailed mechanism assumed.

Recent studies of eroded specimen structures that have been discussed

in prior sections of this article show that erosive impact and wear are complex

processes. It would appear that results from studies currently underway may

lead to new or modified erosion models involving a more accurate understanding

of the physical processes involved. An improved theoretical capability for

erosion prediction should then result.

45
B. BRITTLE MATERIAL MODELS

Two models of erosion have been developed for brittle materials:

one is based on the assumption that erosion occurs entirely by crack

propagation and chipping (Sheldon and Finnie, 1966 b) ; the other is

based on the assumption that plastic deformation contributes to the

process of crack formation and surface chipping (Evans, Gulden and

Rosenblatt, 1978). Erosion rates are predicted in terms of both target

(fracture toughness, hardness, flaw density, etc.) and particle (velocity,

density, size, etc.) properties. The models assume that particle impact

is normal to the target surface, and that erosion is the result of

cumulative damage of non-interacting, single particle impacts. As will

be shown below, these theories predict various aspects of erosion data

for ceramic materials.

The model proposed by Sheldon and Finnie (1966 b) assumes that

erosion occurs as the result of Hertzian contact stresses during impact.

These stresses cause cracks to grow from preexisting flaws in the target

surface. The load at which crack propagation occurs is related to the

distribution of surface flaws through the Weibull statistics. The

approximate area. A, of cracked material is calculated for a particle

penetration depth of h, and the volume removed per impact is set

* proportional to Ah. The final equation for the erosion rate , W, is

expressed in terms of the particle size, r, the particle velocity, v ,

and Weibull constants, m and o :

W = rV5 (17)

*Sheldon and Finnie (1966 b) expressed their results in terms of grams

lost per gram of impacting particle.

46
where the exponents a and b are given by:

a = 3(m-0. 67) / (m-2) for round particles

a = 3 . 6 (m-0. 67) / (m-2) for angular particles

b = 2. 4 (m-0. 67) /(m-2) for either shape

For particles much stiff er than the target, the constant, , is given

by:

, 0. 8(m+l) /(m-2) 1 . 2 (m-0. 67) / (m-2) -2m/ (m-2) (18) k =E p a

1 o

where E is the modulus of elasticity of the target and p is the density

of the particle.

Sheldon and Finnie (1966 b) compared the experimentally determined

exponents, a and b, with theoretically predicted exponents and obtained

satisfactory agreement for several brittle materials (glass, MgO, Al-,0^,

graphite). In a later paper, Sheldon (1970) compared experimental and

theoretical value of k^ and again found reasonable agreement between

theory and experiment; however, the agreement was not as good as that for the

exponents a and b. Although the theory by Sheldon and Finnie (1966 b)

provides a reasonable description of erosion in brittle materials, its

physical basis must be questioned because it assumes Hertzian crack formation,

whereas lateral crack formation is the main cause of material removal during

erosion. The recent theory by Evans e_t a^. (1978) explains erosion in

terms of experimental crack behavior during single particle impact

events, and thus takes into account lateral crack formation during

erosion

.

The erosion model developed by Evans et^ al . assumes that the

erosion rate is proportional to the amount of material removed by each

impact event. The volume, V, lost per impact is calculated from the

depth, h, of penetration and the maximum size of the lateral cracks

47
formed during impact. Since the lateral crack size is proportional to

the radial crack size c

r

, V is given by the following equation:

„ 2 , V ^ ire h v r

Substituting semi- empirical expressions for c , Eq. (11), and h,

Eq. (12), into Eq. (19), the following equation is obtained for the

erosion rate:

( 19 )

„ 19/6 11/3 19/12 -4/3 -1/4

V a v r p K H

o c

The elastic-plastic theory used by Wiederhorn and Lawn (1979)

can also be applied to the development of an erosion theory. Assuming that

the lateral crack size is proportional to the radial crack size, and that

the depth of the lateral cracks is proportional to the maximum particle

1/3 2/3 -1/3 penetration, h (<* m v

q

H ), then the following expression for the

wear rate can be derived from Eq. (9) and (19):

( 20 )

v « v 22/9r ll/3 11/9k-4/3h

1/9

o c

( 21 )

The velocity and particle size exponents of Eq . (17). (20) and

(21) are compared with experimental data in table 1. The predicted particle

size exponent is approximately the same for the three theories, the exponent

for the elastic theory being slightly larger than the other two. The velocity

exponents for the three theories also have similar values, the elastic theory

exponent (Eq. (17)) having a value intermediate between those of the two elasticplastic theories. The elastic-plastic theories assume the two exponents

to be independent of target and particle properties, whereas the elastic contact

theory predicts a dependence of the exponents on the Weibull parameter,

m. The elastic-plastic theories also predict a dependence of erosion rate

on target hardness and toughness, which are assumed to be the pertinent

48
material parameters for erosion. In contrast, the elastic theory uses

the Weibull constant, a , and the modulus of elasticity as the pertinent

material parameters. Evans et^ a!L. (1978) have presented some experimental

evidence to show that the erosion of ceramic materials depends on ,

and H in the manner described by equation 20. Similarly, Sheldon (1970)

and Sheldon and Finnie (1966b) presented evidence to support the elastic

theory of erosion. Although the erosion theories discussed above are

supported by erosion data, the functional dependence of these theories

on material properties differ significantly, so that additional experimental

testing should enable one to differentiate among the three and provide

evidence as to which one more accurately describes the erosion process.

Considering the complexities of the erosion process and the simplifying

assumptions used to derive models of erosion, additional theoretical and

experimental work will be needed to further our understanding of brittle erosion

processes

.

49
c. OTHER CONSIDERATIONS

Other processes can take place upon particle impact and should be discussed

in connection with erosion mechanisms. One involves the possibility of surface

melting as a result of localized energy release on impact. Smeltzer et al. (1970)

studies eroded metal specimens using replica electron microscopy and reported

surface structures and metal particle shapes suggesting the occurrence of

local melting. Recently, Jennings et_ cil. (1976) reported observations of

surface and particle morphologies that suggested melting had occurred in

erosion studies of several metals at particle velocities of 145 m/s. In addition,

Christman (1977) has studies the effects of single projectile impacts on

aluminum alloys. He concludes from metallographic examination that localized

deformation producing intense shear bands is a characteristic feature. Studies

of the surfaces of ejected metal chips revealed, in a few cases, structures

suggesting that local melting (Fig. 33) was involved in the separation process

for particle velocities of 185 m/s. In this example, melting was localized in

the immediate area where the chip separated from the specimen surface. While

high velocity particle impacts might be expected to produce such effects, this

finding has not been reported by other workers in lower velocity ranges, below

100 m/s. Hutchings (1978) has estimated the expected local temperature rise

based on observations of impact crater geometry. He concludes that increases of

up to 500°C could occur at velocities of 100 m/s but that actual melting would

appear unlikely. Such a phenomena would of course be more probable under

conditions of high temperature erosion provided that surface films were

penetrated

.

50
Reports of correlations between erosion rate and other physical

properties of materials have also appeared. Ascarelli (1971) introduced

a quantity "thermal pressure" which is proportional to the product BK’AT.

Here 6 is the linear thermal expansion coefficient, K is the bulk modulus,

and AT the difference between the exposure temperature and the melting

temperature of the material being eroded. He reported an inverse proportionality of this quality with volume erosion rates of many metals.

Hutchings (1975) has noted a similar correlation for the quantity C pAT

where is the material specific heat and p the density. There are not

sufficient data available on alloys to test either of these correlations

further, and possible mechanisms involving such parameters have not been

developed

.

Studies of erosion at elevated temperatures have been carried out to

a limited extent in recent years. However, it has not yet proven possible

to develop an adequate theory giving the temperature dependence of erosion

rate. In most cases environmental reactions also take place, producing surface

films on the material or otherwise complicating the analysis. Further

experimental work will be required in relatively simple systems in order to

clarify this issue. In particular, microscopic characterization of the

subsurface deformation structures should be revealing, particularly in

comparison to the structures found on room temperature erosion (Ives and

Ruff, 1978 a, b) . It is also apparent that the erosion dependence on

attack angle, particle velocity and other parameters may be signif icant ly

different at elevated temperatures than at 20°C (Finnie et_ a_l. , 1978) .

51
As indicated earlier in this review, erosion is one form of material

wear and as a result there may be similar processes involved in other types

of wear. In particular, two-body abrasive wear theories have previously

invoked the occurrence of similar particle cutting and plowing

processes (Rabinowicz, 1970) to those thought to be involved in erosion.

Geometrically, however, abrasive wear involves only tangential interactions

between the particles and contact surface. Comparative studies of wear

debris, wear surface and subsurface structures produced by different wear

modes have not been reported, although such comparisons would be of interest.

A current study of erosion and abrasion in mild steel (Ruff, 1978) has

indicated some potential connections. Figure 34 shows the structure of an

abraded surface and the recovered wear debris resulting from dry, two-body

abrasion using 50pm Afi^O^ particles. These results can be compared with

those from solid particle erosion shown in Fig. 27 involving the same metal

using the same abrasive. It appears that in both cases, much of the wear

debris is produced from plastically displaced material associated with the

impact craters and the abrasion grooves on the exposed surfaces. Subsurface

structure comparisons are being conducted for these same exposures.

52
V. SIGNIFICANT PARAMETERS

The general question of material parameters, of both eroded and eroding

materials, and their effect on erosion rate is of considerable interest.

Indentation hardness of the eroded material is a commonly used and yet

apparently insufficient parameter. Recent interest has turned to more

thorough studies of all involved material characteristics, and hopefully

some improved understanding will soon emerge. The additional complexities of

environmental reactions and elevated temperature exposures, where surface

film formation is a significant, competitive process, are presently under

investigation in several laboratories.

53
A. ERODING PARTICLE CHARACTERISTICS

Many of the important properties of the eroding particles that determine

erosion rates have been mentioned in earlier sections. However, the relative

importance of various parameters are not yet agreed upon in the literature

and a listing here with brief comment seems valuable. The particle characteristics that seem to be most important to the erosion process are as following

(see also Finnie, 1972, Uuemois and Kleis, 1975):

1. Particle shape — For both ductile and brittle materials, more

effective erosion is generally found to be associated with angular

particles (Finnie, 1960). Some basic understanding of rake angle

effects is emerging for ductile materials (Hutchings, 1977a).

2. Particle size — For ductile materials, relative erosion is essentially

independent of particle size for sizes greater than a critical

value. Smaller sizes are less effective and a lower threshold

size (^5pm) for any erosion has been suggested.

For brittle materials, a strong

dependence of erosion rate and strength degradation on particle

size is predicted and some confirmation of these predictions

has been obtained. Further work is required to fully

characterize the effect of particle size on the erosion of

brittle materials.

3. Particle hardness — For ductile solids, so long as the target

surface hardness is much less than the particle hardness, little

effect is expected except indirectly through particle fragmentation, or

other changes. Theories of brittle erosion assume the particle

to be harder than the target; however, for many ceramic materials,

this assumption is not valid. Experimental data by Gulden (1978)

suggest that particle hardness may be an important variable that

54
must be considered when characterizing the wear of brittle

materials.

4. Particle frangibility — For ductile materials, the effect of

particle fragmentation to provide additional erosion loss has

been described by Tilly (1973) and recently studied by Maji and

Sheldon (1978) . The increased erosion potential of abrasives

due to water or impurity content may derive from an altered

tendency to fragment (Uuemois and Kleis, 1975). Particle

frangibility has not been considered as variable in the erosion

of brittle materials, although it is known to occur in these

materials (Evans and Wilshaw, 1977).

B. ERODED MATERIAL CHARACTERISTICS

Many of the material parameters considered for the erosion behavior of

materials are equally involved in other modes of wear. These include:

1. Surface hardness — the single parameter most often chosen to

describe ductile material erosion rate variation (see Fig. 13).

Within one alloy system, indentation hardness is frequently not a

valid parameter to describe erosion differences. However,

Sheldon (1977) has suggested that fully abraded surface hardness

may be a more suitable quantity. As noted in this review, dynamic

hardness is probably the more appropriate variable for characterizing the erosion of either ductile or brittle materials.

2. Strain-rate sensitivity — recent single particle studies on metals

(Winter and Hutchings, 1975; Hutchings, 1977) indicate that the

high strain rates associated with particle erosion may lead to

different deformation modes in different materials. This

material characteristic has not been examined thoroughly

for either ductile or brittle materials.

55
3. Grain orientation and grain size effects — no systematic

studies of the details of these characteristics are available

for solid particle erosion processes. However, Preece ejt al_. (1978)

have recently studied such microstructural effects on cavitation

erosion.

4. Surface thermal parameters — correlations between erosion rates

on the one hand, and thermal conductivities and specific heats on

the other hand, have been noted, but detailed explanations are

not available.

5. Toughness — Because brittle materials erode by elasticplastic processes, the dynamic toughness (dynamic K-^) plays

an important role in the wear of brittle materials. Measurements

of dynamic are needed, both to rank brittle materials and to

develop a better understanding of the process of brittle erosion.

56
c. ENVIRONMENTAL EFFECTS

Some remaining significant considerations are;

1. Impact energy release, surface heating and possible local

melting — temperature effects on deformation may be

important in many cases. Otherwise thermal effects may

only be significant for high temperature erosion.

2. Abrasive bonding to the eroded surface — the possibility of

chemical reaction and bonding to the eroded surface has been

noted in the literature for high temperature erosion processes.

This effect can significantly effect the erosion rate, offering

protection from mechanical damage at the possible expense of

chemical attack on the exposed surface.

3. Atmospheric reaction — the formation of substantial films on

exposed surfaces due to chemical reaction would be expected

in actual elevated temperature exposures. It has been reported

that such films can alter erosion rates, particularly for

smaller particle sizes that are of the same order as the film

thickness. This factor is discussed in Chapter 7.

57
VI. SUMMARY AND RECOMMENDATIONS

The aim of this review has been to examine briefly the current state

of information on solid particle erosion phenomena. Most recently, careful studies of single particle impact processes and of the microstructure of the impacted, deformed region have produced new information

that suggest basic erosion mechanisms. It is clear that except for the

simplest conditions, many different processes are involved; plastic deformation over a wide range of strain rates, thermal effects, crack growth,

environmental effects, and others. However, an improved understanding of

the important aspects of the erosion problem seems to be emerging. That

understanding should greatly aid materials designers, even though some

applications problems may always require empirical and statistically based

approaches. Analytical prediction capability of erosion rates under

small variation of conditions may reasonably be expected in the near future.

In a rapidly developing field it is difficult to recommend detailed

areas for concentrated activity. New information is accumulating too

rapidly for useful recommendations at this time. However, some areas can

be mentioned that either have lacked much attention or have yielded such

valuable information as to be worthy of continued examination.

These would include: — the dynamic effects of impact on materials — the response of complex material microstructures to impact — the effects of substantial surface films on erosion — the role of material toughness and plastic flow properties — the effect of environment on erosion

58
Acknowledgements

Discussions with several staff members at NBS, particularly B. Hockey

and L. K. Ives, on the subject of materials erosion are gratefully acknowledged. One of the authors (SMW) gratefully acknowledges support of the

Office of Naval Research.

59

Table 1. Comparison of velocity and particle size exponents for

various brittle erosion theories

, a b w = k r v

o

Theory a b

Elastic (Eq.(17)) ^4-4.2 %2.6 ~

Elastic-Plastic 3.7 3.2

(E q . ( 20) )

Elastic-Plastic 3.7 2.4

(Eq. (21))

Experiment 3-4 2 -

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Tilly, G. P. (1973). Wear 23, 87-96.

Uuemois, H. and Kleis, I. (1975). Wear 31 , 359-371.

Westbrook, J. H. (1966), Rev. Hautes Temper, et Refract. , _3, 47-57.

Westbrook, J. H. and Conrad, H., editors, (1973), The Science of Hardness

Testing and Its Research Applications . American Society of Metals, Metals

Park, Ohio.
Wiederhorn, S. M. , Hockey, B. J. , and Roberts, D. E. (1973), Phil . Mag

.

, 28 ,

783-96.

Wiederhorn, S. M., Johnson, H., Diness, A. M., and Heuer , A. H. (1974),

J. Am. Ceram. Soc . 57 , 336-41.

Wiederhorn, S. M. , and Lawn, B. R. (1977), J . Am. Ceram. Soc

.

, 60 , 451-8.

Wiederhorn, S. M. , Fuller, E. R. , Jr., Bukowski, J. M. , and Robbins, C. R.

(1977), Trans ASME Journal of Engineering Materials and Technology , 99 ,

143-46.

Wiederhorn, S. M. , and Lawn, B. R. (1979), J. Amer . Ceram. Soc. , January/Februu:

issue

.

Winter, R. E. and Hutchings, I. M. (1974). Wear 29 , 181-194.

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99, 121-125.

Zahavi, J., Wagner, H. J., and Posnansky, A. (1978). Proceedings of ASTM

Symposium "Erosion: Prevention and Useful Applications ," STP 664.

FIGURE CAPTIONS

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

. (a) Erosion impact craters on steel surface. (Ives e^t al. ,

1975).

(b) AISI 310 steel surface after erosion at 25°C at 40 m/s.

(Ives , 1976)

.

. Schematic diagram of particle accelerator device. (Ives and

Ruff, 1978a).

. (a) Damage in aluminum caused by 3 min. steel sphere impacting

at 18.5°, 220 m/s. (Hutchings and Winter, 1974).

(b) Section through crater formed at 40°, 270 m/s. (Hutchings

and Winter, 1975).

. Impact craters in 310 stainless steel produced by 50ym Al^O^

particles at 59 m/s. (a) SEM and (b) TEM micrographs of

crater produced at 90° attack angle. (Ives and Ruff, 1978a).

. (a) Impact crater in 310 stainless steel produced by 50ym glass

sphere at 20° attack angle at 59 m/s.

(b) Dislocation arrangement at rim of impact crater above.

(Ives and Ruff, 1978a).

. Indentation volume for 30° impact on steel. Lines are theoretical

(see text). (Hutchings, 1978).

. (a) Impact geometry and crater produced in steel. Velocity and

rake angle are shown.

(b) Etched section of the crater above. Note the clear boundarv

between the deformed and undeformed material. (Winter and Hutchings.

1974) .
Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

FigFig.

Fig.

8. Schematic diagram of the type of damage that occurs when a

sphere is pressed against the surface of a brittle material

(Lawn and Wilshaw, 1975)

.

9. Fracture damage resulting when a sphere is pressed against

a glass surface (Courtesy of K. Phillips, Reported by Lawn

and Wilshaw, 1975)

.

10. Schematic diagram of crack growth during sharp particle impact.

+ sign indicates loading; - sign indicates unloading. (Lawn

and Swain, 1975)

.

11. Impact site in MgO produced by 65 pm A^O^ particles at a

velocity of 90 m/s and 90° impact angle TEM micrograph demonstrating dense tangles of dislocations at the impact site (Hockey

et al. , 1978)

.

12. Impact site in Si produced by 65 ym A^O^ particles at a velocity

of 90 m/s and 90° impact angles. Although most of the deformed

region has chipped out of the specimen surface, the TEM micrograph reveals residual dislocations and cracks associated with

the impact site (Hockey et_ ad . , 1978) .

13. Impact site in SiC produced by 150 ym SiC particles at a velocity

of 94 m/s and a 90° impact angle. (Courtesy of Hockey).

14. Optical micrograph showing normal impact damage in Al^O^ produced

at (2) 25°C and (b) 1000°C. (Hockey et al . , 1978).

15. Optical micrograph showing a series of shallow surface impressions

produced in A^O^ by 15° impingement. (Hockey et^ al. , 1978).

16. Transmission electron micrograph in SiC by 15° impingement:. Absence:

of cracks and presence of dislocations confirm fully plastic nature

of impact event (Hockey et_ cil . , 1978) .
Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

17. Schematic representation of erosion rate on attack angle, (Ives

and Ruff, 1978a).

18. Influence of velocity on erosion for different materials (Goodwin

et. al, , 1969).

19. Collected erosion measurements on copper. (Ives and Ruff, 1978b).

20. Velocity dependence of erosion at 975°C and 25°C. (Ives, 1977).

21. Influence of particle size on erosion of an 11 percent chromium

steel (Goodwin et . al

.

, 1969)

.

22. Erosion of 1100-0 Aluminum at a velocity of 30.5 m/s as a function

of impingement angle and temperature. Homologous temperature =

T/T(melting) . (Finnie et . al

.

, 1978).

23. Volume removal as a function of VHN for metals eroded at a=20 deg

and velocities of 250 and 450 ft/sec. (No data were taken for

nickel at 450 ft/sec.) All metals except cadmium were in annealed

condition. (Finnie et . al

.

, 1967).

24. Copper specimen mass change for accumulated exposures. (Ives

and Ruff, 1978b).

25. Cross section of copper surfaces eroded at 90° and 20 m/s

(a) induction period (b) steady state. (Ives and Ruff, 1978b).

26. Al^O^ particle embedded in copper surface eroded at 90"' and 60 rr s.

(Ives and Ruff, 1978a).

27. Scanning electron micrographs of (a) the surface of eroded 101^

steel and (b) steel debris particles recovered after erosion at

40 m/s and 30° attack angle using 50pm A1,0,. (Ruff, 197S)

.
Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

Fig.

28. Weight loss from plate glass as a function of impingement angle, a,

and particle size (Sheldon and Finnie, 1968a).

29. Surface of plate glass after erosion by silicon carbide particles

at an angle of 30° and a velocity of ^150 m/s (Sheldon and Finnie,

1968a)

.

30. Erosive wear of hot-pressed silicon nitride as a function of

impingement angle. Curves represent erosion dependence for

purely brittle behavior (Hockey e_t al. , 1978).

31. Scanning electron micrograph of surface morphology of sintered

aluminum oxide after erosion at 1000°C, 90° impingement (Hockey

et_ al. , 1978) .

32. Furrow formation in sintered aluminum oxide eroded at 1000°C, 15°

impingement (Hockey et_ al^. , 1978) .

33. Surface morphology on eroded aluminum alloy chips. (Christman,

1977) .

34. Scanning electron micrographs of (a) the surface of abraded

1015 steel and (b) steel debris particles recovered after wear

under dry conditions at 2.2 N load. (Ruff, 1978).
Fig. 1. (a) Erosion impact craters on steel surface. (Ives ot_ a

l

.

1975)

.

(b) AISI 310 steel surface after erosion at 15°C at 40 m s

(Ives , 1976)

.

Specimen P m

Particles —

Sobot -

Rupture

Disk

Compressed

Gas

Fig 2 . Schematic diagram of particle accelerator device.

Ruff , 1978a) .

(Ives and

-1

Fig. 3. (a)

at

(b)

Damage in aluminum caused by 3 min.

18.5°, 220 m/s. (Hutchings and Winter

Section through crater formed at 40°

steel sphere

, 1 Q 74) .

, 270 m/s.

impact ing

(Hutch ings

U

and Winter, 1975).

ig. 4 . Impact craters in 310 stainless steel produced by "’Ov.m

particles at 59 m/s. (a) SEM and (b) TEM micrographs of

crater produced at 90° attack angle. (Ives and Rut t , ba'' .

Fig. 5. (a) Impact crater in 310 stainless steel produced by 50 in glass

sphere at 20° attack angle at 59 m/s.

(b) Dislocation arrangement at rim of impact crater above.

(Ives and Ruff, 1978a).

d

Fig. 6. Indentation volume for 30° impact on steel. Lines are theoretical

(see text). (Hutchings, 1978).

\+— 5 mm'H

Fig. 7. (a) Impact geometry and crater produced in steel. Velocity and

rake angle are shown.

(b) Etched section of the crater above. Observe the clear boundary

between the deformed and undeformed material. (Winter and Hutchings, 0 4^.

Fig. 8. Schematic diagram of the type of damage that occurs when

a sphere is pressed against the surface of a brittle

material (Lawn and Wilshaw, 1975)

.

(A)

(B)

(C)

(D)

9. Fracture damage resulting when a sphere is pressed against

a glass surface (Courtesy of K. Phillips, Reported by

Lawn and Wilshaw, 1975)

.

(d)

(e)

(f)

Schematic diagram of crack growth during sharp particle

impact. + sign indicates loading; - sign indicates unloading.

(Lawn and Swain, 1975).

Fig. 10.

Fig. 11. Impact site in MgO produced by 150 pm SiC particles at a velocity

of 90 m/s and 90° impact angle TEM micrograph demonstrating dense

tangles of dislocations at the impact site (Hockey ejt a_l.

Fig. 12. Impact site in Si produced by 90 pm Al o 0^ particles at a velocity

of 90 m/ s and 90° impact angles. Although most of the deformed

region has chipped out of the specimen surface, the TEM micrograph reveals residual dislocations associated with the impact

site (Hockey e^. al . , 1978)

Fig. 13. Impact site in SiC produced by 150 pm SiC particles at a voice it.

of 94 m/s and a 90° impact angle. (Courtesy of Hockey).

Fig. 14. Normal impact damage in Al^O^ produced at (a) 25°C and (b) 1000°C.

(Hockey jrt _al. , 1978)

Fig. 1

F ig.

5. Optical micrograph

produced in Al^O^

showing a series

by 15° impingement

of shallow surface impressions

(Hockey et. al_ . , 1978) .

16. Transmission electron micrograph showing region beneath shallow

surface impressions produced in SiC by 15° impingement. Absence

of cracks and presence of dislocations confirm tullv plastic natai

of impact event (Hockey e t a 1

.

» 19/8).
L
o

cn

0)o»c

<

JCo

o

<

oo

9|Dy uojsojg

Schematic

representation

of

erosion

rate

on

attack

angle,

(Ive

Fig. 18. Influence of velocity on erosion for different materials

et. al., 1969).
J
Moss

Loss,

mg

/Mass

Abrassive

,

T T T T i i i—

i

r i i i r i t 1 1 1 1 1 iri m

IxlO

IxlO"

IxlO

-2 h

IxlO

-3

10 50 100 150 200

Velocity , m/s

Fig. 19. Collected erosion measurements on copper. (Ives and Ruff. l^'Sb)

.

tiii

rf



x o a 90° impact

Fig. 21. Influence of particle size on erosion of an 11 percent chre :

steel (Goodwin e t . a 1 .

,

1969).

o

<J)

o

co

O

ro

in

O

O

co

LJ

UJ

QCCO

UJQ

UJ

UJ

CO2

OL

Lt. o

UJ_J

CO<

g _0I * (0 !S 1M V/IV1MU)

U

P

3

U_1

CT3

C/5 3

cn6

m

oco

O

Sou

o

—

H

o

>

CO

COE

3

C

O

I o

o

OTo

i_ u

n

CNI

II

of

impingement

angle

and

temperature.

Homologous

temperature

Volume removal as a function of VHN for metals eroded at x=-0 dec

and velocities of 250 and 450 ft/sec. (No data were taken tor

nickel at 450 ft/sec.) All metals except cadmium were in annealed

condition. (Finnie e t . a 1

.

, 1967).

Fig. 24. Copper specimen mass change for accumulated exposures. (I vo

and Ruff, 1978b).

Fig. 25. Cross section of copper surfaces eroded .it 90 " and 20 m s

(a) induction period (b) steady state. (Ives and Ruff, 1° Sb''

.

(Ives and Ruff, 1978a).

Scanning electron micrographs of (a) the sui t ace ot eroc.cc.

steel and (b) steel debris particles recovered after erosion at

AO m/s and 30° attack angle using 50lim Al^O,. (Ruff, 1^7S).

ANGLE oc , degrees

Fig. 28. Weight loss from plate glass as a function of impingement angle,

and particle size (Sheldon and Finnie, 1968a).

Fig. 29. Surface of plate glass after erosion by 1000 mesh grit silicon

carbide particles at an angle of 10° and a velocity of ISO ~

width of field M . 7 mm (Sheldon and Finnie, 19b8a).
.
EROSION

RATE

(g/g)

ANCLE OF IMPINGEMENT, n

a

ANCLE OF IMPINGEMENT. .

b

Fig. 30. Erosive wear of hot-pressed silicon nitride as a function of

impingement angle. Curves represent erosion dependence for

purely brittle behavior (Hockey et al., 1978).

*\

Fig. 31.

o

Scanning electron micrograph

aluminum oxide after erosion

of surface morphology of sintered

at 1000°C, 90° impingement (Hockey

et al. , 1978)

w

*

Fig. 32. Furrow formation in sintered aluminum oxide, eroded at 10.W,

15° impingement (Hockey et^ aJL. , 1978) .

Fig. 33. Surface morphology on eroded aluminum alloy chips. (Chi'irU

1977) .

Fig. 34. Scanning electron micrographs of (a) the surface of abraded

1015 steel and (b) steel debris particles recovered after

wear under dry conditions at 2.2 N load. (Ruff, 1978).

NBS-1 14A (REV. 7-73)

U.'_ DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. 2. Gov’t Accession

78-1575 No.

3. Recipient’s pient's Accession A No.

4. TITLE AND SUBTITLE 5. Publication Date

Erosion by Solid Particle Impact

January 1979

6. Performing Organization Code

7. AUTHOR(S)

A. W. Ruff and S. M. Wiederhorn

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Taslc/Torlc Uni- No. 564Q134

11. Contract/Grant No.

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP) 13. Type of Report & Period Covered

14. Sponsoring Agency C

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.) (NOT TO BE PUBLISHED)

A review of the methods and findings associated with solid particle impact erosior

of metals and ceramics is presented. Modern theories of particle erosion and critical!

reviewed experimental observations are brought together and compared. Conclusions

regarding the present state of understanding of erosion are given.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first kev nerd ur.tess ’ e~e name; separated by semicolons

Abrasives; ceramics; erosion; impact; metals; particle erosion; wear.

18. AVAILABILITY QQj Unlimited

For Official Distribution. Do Not Release to NT1S

Order From Sup. of Doc., U.S. Government Printing Office Washington, D.C. 20402, SD Cat. No, Cl 3

[~X] Order From National Technical Information Service (N 1 1S1 Springfield, Virginia 22151

19. SECURITY CL ASS

(THIS REPORT!

UNCI ASSIEIEP

21. NO. OF P \CF:

20. SECURITY CLASS

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UNCLASSIFIED

tt;22. Pace

i

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