NBSIR 77-1396

Erosion of Brittle Materials By

Solid Particle Impact

B. J. Hockey, S. M. Wiederhorn, and H. Johnson

Inorganic Ma

Institute for \

National Bure

Washington, I

Hockey, B. J., Wiederhorn, S. M., Johnson, H.,

Erosion of brittle materials by solid

particle impact, (Proc. 2nd Int. Symp.

Fract. Mech., State College, PA, July 26-29,

1978 )> Paper in Fracture Mechanics of Ceramics 3, R. C. Bradt, D. P. H 0 Hasselman,

F. F. Lange, Eds., 379-^02 (Plenum Publ.

Corp., New York, NY, 1978).

New-562 NBSIR 77-1396

/ 21ft .

Prepared for The Pennsylvania State University

Department of Material Sciences

201 Mineral Industries Building

University Park, Pennsylvania 1 6802

NBSIR 77-1396

EROSION OF BRITTLE MATERIALS BY

SOLID PARTICLE IMPACT

B. J. Hockey, S. M. Wiederhorn, and H. Johnson

Inorganic Materials Division

Institute for Materials Research

National Bureau of Standards

Washington, D C. 20234

Prepared for The Pennsylvania State University

Department of Material Sciences

201 Mineral Industries Building

University Park, Pennsylvania 16802

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

Dr. Sidney Harman, Under Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director

EROSION OF BRITTLE MATERIALS BY SOLID PARTICLE IMPACT

B. J. Hockey, S. M. Wiederhorn, and H. Johnson

Institute for Materials Research

National Bureau of Standards

Washington, D. C. 20234

ABSTRACT

Results are presented which show, that in addition to fracture,

plastic deformation occurs and plays an important role in the erosion

of brittle materials by solid particle impact. These conclusions are supported by transmission electron microscopy studies of impact

damage produced in a wide variety of brittle materials and by erosive

wear studies on silicon nitride and alumina. The erosive wear

studies also indicate that while erosion resistance is primarily

determined by fracture toughness and hardness, the relative importance of these materials parameters depends on the test conditions

(e.g. temperature and angle of particle impingement).

1. INTRODUCTION

Because most ceramics are inherently brittle, they are susceptible to localized surface cracking in solid particle impact situations. Cracks formed in strong ceramics by a single impact event cause serious strength degradation for modest impact velocities (1).

Moreover, continual, multiple impacts result in appreciable material

loss by erosive wear. Thus, the damage resulting from solid particle

impact leads to a deterioration in performance, and even failure of

vital ceramic components. Despite these practical consequences, very

few comprehensive erosive wear studies have been made on brittle

materials. More importantly, the actual mechanisms that govern the

erosive wear process in brittle materials are not well understood.

Attempts to describe the erosive wear behavior of brittle

materials have tended to be semi -empirical . Nevertheless, considerable insight into this problem has been made by a recognition of
the similarity between quasi-static indentation and dynamic

particle impact in the region of subsonic impact velocities. In this approach, one draws upon the similarity between the damage

produced in both types of contact and uses quasi-static indentation

theory to relate the extent of damage (and thus volume of material

removed) to impact parameters and material properties.

This approach was first applied to an analysis of the

erosive wear of brittle materials by Sheldon and Finnie (2, see also 3), who assumed that particle-target interactions were perfectly elastic. The extent of damage or volume removed was described on the basis of a classical Hertzian analysis of fracture

beneath a spherical indenter. Inherently, this elastic/brittle

treatment leads to the conclusion that the erosive wear of a brittle material depends on the fracture toughness (4) and on the

size and distribution of pre-existing flaws (2,3).

The general assumption made by Sheldon and Finnie, that most

solid particle impact events in brittle materials can be described

as purely elastic contacts can be questioned. In most practical

situations, surfaces are subjected to impact by angular, irregularangul ar-shaped particles. Typical contact situations, therefore,

resemble quasi-static indentation with indenters of small radii

of curvature (i.e. sharp indenters (4)). These indenters are known to cause plastic flow (5,6) in brittle materials. Because

of this, recent treatments of elastic/plastic contacts in brittle

materials have suggested the importance of the flow properties

(hardness) of the material as well as fracture toughness in

determining the extent of fracture and erosive wear (7,8,9).

In this paper, the essential features of the quasi-static

indentation approach to impact and erosive wear are examined on the basis of results from two recent experimental studies.

Accordingly, the formal structure consists of two parts. In the

first part, optical and transmission electron microscopy observations are used to characterize single particle impact damage in

various brittle materials. In particular, emphasis is placed on illustrating the essential role of plasticity in impact situations

and on demonstrating the correlation between "sharp" particle

impact and quasi-static indentation. In the second part, comparative erosive wear data for alumina and silicon nitride are used

to describe the dependence of erosive wear on particle velocity,

angle of impingement, and temperature. These data are then

discussed in the light of the single particle damage observations,

and also in terms of the relative importance of fracture toughness

and hardness.

2
2. SINGLE2.1PARTICLE IMPACT DAMAGE

Materials

To elucidate the basic mechanisms of erosive wear of brittle

materials and to provide a clearer description of the residual

damage that affects material properties, solid particle impact

damage studies were made on a variety of brittle materials:

silicon; germanium; magnesium oxide; aluminum oxide; silicon

nitride; and silicon carbide. For the most part, these materials

were selected because of their practical importance and because

they represent brittle materials that differ in their atomic

bonding, hardness, and fracture toughness.

2.2

Experimental Procedure

All studies were conducted using an erosion tester previously

described by Wiederhorn and Roberts (10). Sample surfaces were

subjected to a controlled flux of abrasive grit under fixed

conditions of particle velocity, angle of impingement, and temperature (up to 1000°C). To distinguish individual particle damage

events - for a given set of experimental conditions - only small

quantitites of abrasive grit were allowed to impinge on polished

(chemically or mechanically) sections. The polished sections

were then examined optically to characterize the nature and

extent of surface damage. In most cases, the impacted samples were thinned and examined by transmission electron microscopy to

reveal details of the subsurface damage. For these samples, the

thinning procedure closely followed that used in previous indentation and mechanical abrasion studies on ceramics (5,6).

2.3

Results

2.3.1 Impact Surface Damage . Room temperature, normal

incidence impact damage studies were made using measured particle

velocities (11) in the range, 30 to 100 m/sec. 100 mesh (150

micron size) silicon carbide abrasive grit was used in tests on

A1 2 0 3 , SiC and Si 3 N 4 ; whereas 150 mesh (^70 micron size) alumina

grit was used in tests on Ge, Si, and MgO*. Both types of abrasive

grit were composed of irregularly-shaped, angular solid particles,

Fig. 1, which according to the scheme advanced by Lawn and co- workers (1) fall into the "sharp" indenter/particl e category.

*Because the prethinned (^100 to 150 micron) sections of Ge, Si

and MgO necessary for subsequent TEM examination tended to shatter

in tests involving the larger particles, the 150 mesh alumina grit

had to be used on these specimens.

3
Figure 1. Scanning electron micrograph illustrating angular

morphology of silicon carbide particles used in

impact damage and erosive wear studies.

Because the irregular impacting particles can strike the

surface in any arbitrary orientation, individual impact sites were found to differ considerably in their detailed appearance.

Despite this difference, the residual impact damage was found to

closely resemble that produced quasi -statically in brittle

materials using "sharp" indenters. In this regard, particle

impact usually resulted in the formation of a permanent surface

crater (indicative of surface penetration), surrounded by a welldefined, associated crack pattern. As illustrated in Figure 2,

the localized fracture patterns produced by normal -incident

impact were identical in all respects to those produced by quasistatical indentation. The fracture patterns usually contained

both median and lateral cracks. In all materials studied,

material loss from the surface occurred as the result of the

extension of the lateral cracks to form a surface chips, Figure

3. This observation clearly indicates the importance of fracture

to the process of erosion in brittle materials, and therefore

suggests that the fracture toughness is one of the primary

material parameters to be considered in problems of erosive wear.

4
Figure 3. Surface of damage produced in Germanium by 90° impingement impact (70 micron size alumina at 90 m/s). Note

material removal by the extension of lateral -vent type

cracks

.

Figure 2. Comparison of surface damage produced in SiC by: (A)

90° impingement (150 micron size SiC particle at 90 m/s)

and (b) quasi-static indentation (Vickers diamond

pyramid, 400 gram load).

5
2.3.2 Plastic Deformation: Occurrence and Extent . Although

the materials studied in this paper are generally considered to

be brittle, it can be demonstrated that plastic flow is also

important to the erosive wear of these materials. As in previous

studies of indentation sites in brittle materials (5,6), transmission

electron microscopic examination of room temperature impact sites

clearly revealed the occurrence of plastic flow by slip. This

was evidenced not only by a highly deformed zone directly beneath

the area of actual contact, but also by the presence of a residual

dislocation pattern in the adjacent vicinity. Figures 4a and 4b.

The transmission electron microscopy studies also revealed distinct

differences in material response to the impacting particles. The

differences appeared to be related to the nature of atomic bonding.

In covalently-bonded Ge and Si, plastic deformation extended only

slightly beyond the region of actual contact. Figure 4a. As a result, the radial dimension of the elastic-plastic zone in these

materials was only slightly larger than the surface impression,

which was small when compared to the associated fracture pattern,

Figure 3. In contrast, particle impact of ionically bonded MgO

resulted in extensive plastic flow. As seen in Fig. 4b, deformation extends far beyond the region of actual contact and often

encompasses the associated fracture pattern.

Observations on A1 2 0 3 and SiC, which possess partial ionic

and covalent bonding, revealed a somewhat intermediate behavior

during room temperature, normal -incidence impact. For these

materials, the radial extent of the deformation was estimated to

be about twice the lateral dimensions of the residual impact

impression. However, under most conditions, the extent of deformation

was considerably smaller than the length of the cracks.

2.3.3 Effect of Temperature . Surface damage produced in

A1 2 0 3 and Si 3 N 4 by solid particle impact at temperatures up to

1000°C was investigated by optical microscopy. Impact damage in

A1 2 0 3 was also examined by transmission electron microscopy. Over

the temperature range studied, no difference was found in the

general morphology of the impact fracture patterns. Figures 5a and

5b. For normal -incidence impact, localized fracture, consisting of

lateral and median vent cracks, remained evident, thus indicating

that material removal still occurred predominantly by surface

chipping.

Transmission electron microscopy observations on A1 2 0 3 , 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 ° was found to be comparable to the radial

extent of fracture, (which appeared unchanged between 25° and

1000°C). In addition, impact at 500°C and above resulted in a significant increase in deformational twinning. As a result, high

6
m

Figure 4. Transmission electron micrographs illustrating subsurface damage produced in (a) silicon and (b) MgO under

similar impact conditions (90 micron size alumina

particle at 90 m/s).

7
Figure 5. Normal -impingement impact damage produced in AI 0 O 3 at

(a) 25°C and (b) 1000°C.

8
temperature impact also resulted in numerous interactions between

slip bands, twins, and grain-boundaries outside the region of

contact.

2.3.4 Effect of Angle of Impingement . Observations on the various brittle materials included in this study showed that

both the nature and extent of impact damage depends upon the angle

of particle impingement. Characteristic changes that evolve as the angle of impingement is reduced to 15° are illustrated in

Figures 6 a and 6 b. Predictably, the most obvious change is a considerable reduction in the extent of localized surface cracking.

In addition, cracks produced during low angle impact were predominantly of the lateral vent type; median vent crack formation appeared

to have been almost completely surpressed under these conditions.

Another characteristic of low or oblique angle impact. Figure

6a, is the formation of shallow, residual surface impressions,

typically elongated along the horizontal component of particle

motion. Again, transmission electron microscopy studies on Si C and

A1 2 0 3 confirmed that these surface impressions are the result of

plastic flow, Figure 6 b. Thus, oblique angle impact of the brittle

materials investigated in this study is seen to result in the

ploughing of material parallel to the surface. This finding

suggests that at low angles of impingement plastic flow plays an important role in the erosion process and, as will be discussed,

may dominate the erosion process under certain conditions (Section

4).

3.0 Erosive Wear Studies

The observations described above will now be correlated with

studies of the erosive wear of hot-pressed silicon nitride and two

grades of alumina ( A1 2 0 3 ) that differed microstructural ly. One

grade of alumina was a large-grained (^30 ym), sintered product;

the other was a fine-grained (^5 ym), hot-pressed product. In this

section, erosive wear data, describing the dependence of erosion on particle velocity, temperature, and angle of impingement are presented and compared.

3.1 Experimental Procedure

The erosive wear tests were conducted using the hot erosion

tester described by Wiederhorn and Roberts (10). In this study,

bulk samples (typically 1/2 x 1/2 in by 1/4 in thick) were eroded

by the action of 100 mesh SiC abrasive grit (^150 ym particle

size). Fig. 1. Tests were conducted on each of the materials at

temperatures ranging from 25°C to 1000°C. Angles of particle

impingement were varied from 15° to 90°. In all tests at oblique

angles of impact, the leading edge of the test samples were protected to avoid extraneous edgewear. Rates of erosive wear were determined by measuring sample weight loss after long-term exposure.

9
Figure 6. (a) Optical micrograph showing series of shallow surface

impressions produced in A1 2 0 3 by 15° impingement impact,

(b) Transmission electron micrograph showing region

beneath shallow surface impressions produced under similar

impact conditions in SiC. Presence of dislocations

emerging from contact zone and absence of cracks confirm

fully plastic nature of impact event.

10
The erosion rates are expressed here in terms of the normalized

quantity: sample weight loss per unit weight of abrasive actually

striking the surface.

3.2 Results

Representative wear data, pertinent to a general description

of the observed erosive wear behavior, are shown in Figures 7, 8,

9, and 10. Figures 7, 8, and 9, illustrate the dependence of

erosion rate on particle velocity and temperature for the different

materials. Figures 10, a and b, illustrate the dependence of

erosion rate on angle of impingement at 25° and 1000°C, respectively.

In each plot, the data points represent average values obtained

from a minimum of three determinations; usually, however, five or more tests were made for each condition. Finally, Figures 11, a and b, illustrate the change in surface morphology that occurs

when the angle of particle impingement is reduced from 90° to 15°.

3.2.1 Dependence on Particle Velocity . For all test

conditions, erosive wear increases with increased particle velocity.

As indicated in Figures 7 and 8, erosion rate, E, could be expressed

as a simple power function of the particle velocity, V: E ^ V.

On the basis of a linear least squares fit of each set of data,

values of the velocity exponent, n, were found to range from 1.7

to 2.7, depending on temperature, angle of impingement, and the

material tested. Although the value of n was found to increase

with temperature, a consistent relationship could not be established

between n and other experimental variables.

3.2.2 Temperature Dependence . A significant effect of

temperature on the erosive wear of the materials studied was only

apparent in the data for oblique angles of incidence (i.e. a=15°

and 30°). This is illustrated in Figure 7 and in Figure 8, where

90° and 15° impingement data for each material are compared.

As seen in Figure 7, erosive wear rates at 90° impingement

are, for all practical purposes, independent of temperature

between 25° and 1000°C. For each material, changes in rate of wear or slope, n, with temperature were too small to be considered

statistically significant. The 90° impingement data, moreover

shows that hot-pressed silicon nitride is more resistant to erosion

than the hot-pressed alumina (by a factor of ^1.5 on a volume loss

basis), which in turn, is more resistant than the sintered alumina

(by a factor of ^2-3)

.

In contrast to the results described above, data obtained

using particle impingement angles of 30° and 15° both* indicated

*For brevity, the data obtained for 30° impingement are not presented

in this paper.

11
12

Figure

7.

Erosive

wear

rate

as

a

function

of

particle

velocity

and

temperature

for

90°

impingement:

(a)

Sintered

alumina;

(b)

Hot-pressed

alumina;

(c)

Hot-pressed

silicon

nitride.
that erosion is affected significantly by temperature for oblique

angles of impact. Under these conditions the erosive wear data

for each material exhibited a substantial increase in slope, n, as the temperature was increased from 25°C to 1000°C. This increase

can be seen in Figures 8a, 8b, and 8c, where 15° impingement data

at 25°C and 1000°C are compared for each material. For hotpressed silicon nitride, Figure 8a, the value of n increased from

1.7 at 25° to 2.7 at 1000°C. Although the erosion behavior of the

hot-pressed alumina was similar to that of the hot-pressed silicon

nitride, the increase in n from 2 to 2.6 was not as great as for

'the hot-pressed silicon nitride. A similar observation is made

fo»^ the sintered alumina, for which n increased from 2.1 to 2.6 over the same temperature range. The erosion behavior of the

sintered material, however, is seen to differ significantly from

that of the hot-pressed materials, in that erosive wear rates are lower at 1000°C than at 25°C over most of the range of particle

velocities used in these tests (Figure 8c).

The net effect of temperature on erosion wear at oblique

angles of impingement is illustrated in Figure 9 for the 15° data.

At 25°C, Figure 9a, hot-pressed silicon nitride exhibits better

erosion resistance than the two types of alumina, while the

hot-pressed alumina exhibits better erosion resistance than the

sintered alumina. At both 15° and 30° impingement, the room temperature erosion behavior of the materials was comparable to

that found at 90° impingement. In contrast to these results at

25°C, results obtained at 1000°C for both 30° and 15° impingement,

Figure 9b, show little difference in the erosive wear of these

materials. Thus at 1000°C, the erosion behavior at oblique angles

of impingement differs significantly from that found at a=90°

.

This change in erosive behavior at high temperatures and oblique

angles of impingement appears to be related to an increase in the

role of plastic flow in the erosion process (see Sections 3.2.3

and 4.0)

.

3.2.3 Dependence on Angle of Impingement . Measurements of

the effect of impingement angle on the erosion rate were also made

to investigate mechanisms of erosion. Past studies (12,13) have

shown that erosion by a brittle mode is characterized by a maximum

in erosion rate at 90° impingement and by a relatively rapid

decrease in erosion rate as the impingement angle is decreased.

Ductile erosion, by contrast, is characterized by a peak in the

erosion rate at an angle of impingement of ^15-20° with a decrease

in the erosion rate at higher and lower angles of impingement. It

is generally recognized that most metals undergo combined modes of

erosion. In the present investigation, the observed variation in

rate of erosion with impingement angle for each material also

indicates a combined mode of erosion.

13
(8/8) 3J.VH N0IS0H3

14

Figure

8.

Erosive

wear

rate

as

a

function

of

particle

velocity

for

15°

impingement

at

25°

and

at

1000

C:

(a)

hot-pressed

silicon

nitride;

(b)

hot-pressed

alumina;

(c)

sintered

alumina.
OJV)

IS) CD

s-CL

15

Figure

9.

15°

impingement

erosive

wear

data

for

hot-pressed

silicon

nitride,

hotalumina,

and

sintered

alumina

compared

at:

(a)

25°C

and

(b)

1000°C.
In Figures 10a and b, erosive wear rates for silicon nitride

are plotted as a function of impingement angle for temperatures of

25°C and 1000°C respectively. For both temperatures, the data are compared with a theoretical treatment of brittle erosion that will

be discussed below (Section 4). As can be seen in Figure 10a,

erosion rate follows the theoretical curve for angles as low as 30°. However, at 15° impingement, the rate of erosion is approximately 5 times that predicted by theory. At 1000°C, Figure 10b,

this same type of comparison also indicates a large difference

between measured and predicted erosion rate but now this difference

is observed over a wider range of impingement angles. At 15°, the

measured erosion rate is approximately 7 times the predicted rate,

while at 30° impingement the measured erosion rate is approximately

2 times the predicted rate. At 45° impingement, the measured

erosion rate is still 1.6 times the predicted rate. Similar

differences between measured and predicted wear were also found in

the data for both types of alumina. These deviations between

measured and predicted behavior suggest that wear of the materials

studied occurs by a mixed mode of erosion, with the ductile mode

becoming important at low angles of impingement. On this basis.

ANGLE OF IMPINGEMENT, a

b

Figure 10. Erosive wear rate of hot-pressed silicon nitride plotted

as a function of angle of particle impingement a. Fullline curves represent predicted dependence for purely

brittle behavior (see text).

16
the data also indicates that as the temperature is increased, the

role of plastic flow becomes increasingly more important in the

erosion process.

The above conclusions are supported by optical and scanning

electron microscopy studies of the erosion surfaces. Under

erosion conditions where there is good agreement between measured

and predicted wear, (i.e. a = 90° to 30° at 25°C, and a = 90° to

^45° at 1000°C, Figure 10) the resultant surfaces are similar and

clearly indicate that material has been removed primarily by a brittle chipping process, Figure 11a. By contrast, erosive wear

at lower angles of impingement (i.e. a = 15° at 25°C and a = 15°

and 30° at 1000°C), results in relatively smooth surfaces,

Figure lib. These surfaces, moreover, are characterized by numerous smooth furrows or wear scars indicative of material

removal by a ductile ploughing process. While lateral venting is

also observed along the edges of the wear scars, and obviously

contributes to material removal, it is nevertheless clear that,

for these conditions, the mechanism of erosion more closely

resembles the ductile mode of wear, normally attributed only to

metals. These observations, moreover, are consistent with the

single particle impact damage results discussed in Section 2.

4. DISCUSSION

The results presented in this paper all point to the importance of plastic deformation in the erosion of materials that

otherwise exhibit brittle behavior. Plastic flow appears to enter

the erosion process in two distinct ways: by subsurface deformation that enhances surface chipping; and by shear deformation

wherein fracture is minimal and material is removed primarily by

a plastic cutting process.

In the chipping mode of erosion, material removal occurs primarily by the extension of lateral vent type cracks (as in

Figure 3). The nature of these cracks and the way in which they

grow during quasi-static indentation has been described by Lawn

and Swain (14) for glass, and by Hockey and Lawn ( 6 ) and Evans and

Wilshaw (7) for crystalline materials. These studies have shown

that lateral vent cracks are peculiar to "sharp indenter" contact

situations and that they fully develop only after removal of the

applied load. Previous studies by transmission electron microscopy (5,6) have shown that the indentation of brittle materials

(e.g. A1 2 0 3 and SiC) also results in intense deformation, which is

generally constrained within the region of contact. As a consequence, large residual stresses are produced. These stresses are believed to provide the driving force for lateral -vent crack

formation. Based on results obtained in the present study, a similar explanation is advanced for the formation of lateral vent

cracks during solid particle impact events. Accordingly, the

17
Figure 11. Scanning electron micrographs showing surface morphology

of sintered alumina test samples after erosion at 1000°C:

(a) 90° impingement angle and (b) 15° impingement angle.

18
erosion of brittle materials by surface chipping should depend

both on resistance to crack extension (fracture toughness) and on resistance to plastic flow (hardness).

Recently, Evans et a 1 . (8,9) have presented a theoretical

treatment for the erosion of brittle materials by "sharp" particle

impact. They estimate the erosion rate from the depth of penetration of the incoming particle and the size of the lateral cracks

that form during the impact event. Accordingly, this treatment

incorporates both the hardness, H, and the critical stress intensity

factor, K

f

, in the equation that describes the amount of material

removed per impact v^

v. ^ I, 2.5 q 4 0.3 u-0-3,/ -1 -5

1 “ v

0

R

P

p

P H Kc

( 1 )

where V is the incoming particle velocity; Rp is the particle

radius, and p p is the particle density. The exponents in this

equation are obtained in part through a mathematical analysis of

the impact problem, and in part through an experimental investigation of the extent of damage that occurs in materials during

impact. In applying this expression to multiple impact situations,

it is assumed that interactions between adjacent impacts are negligible and that each impact event is similar. The theory is

the first to describe the erosion of brittle materials in terms of

an elastic-plastic phenomenon and provides a good basis for discussing the erosion data presented in this paper.

Several aspects of the data in this paper can be described in

terms of the theory developed by Evans and his colleagues. First

and foremost, the theory assumes that plastic flow occurs in the

region beneath the contact area. The results of Section 2,

provide direct evidence to support this assumption. Furthermore,

as discussed earlier in this Section, the formation of lateral

vent cracks appears to be directly related to the occurrence of

plastic deformation and the development of large residual stresses.

A second experimental parameter that can be compared with the

theory developed by Evans et al. is the exponent of the impact

particle velocity. In the present study, velocity exponents

ranging from 1.7 to 2.7 were obtained; the lower values being

representative of room temperature data at low impingement angles,

the high values being representative of the high temperature data.

The theory developed by Evans et al . predicts an exponent of 2.5,

which differs slightly but significantly from the values obtained

in this study. The difference between the predicted and experimental

values of the velocity exponent can be traced to the assumption

used to predict the amount of material removed during multiple

impacts. The erosion rate per particle impacting the surface was assumed to be proportional to the depth of the plastic zone and

19
the square of the size of the lateral cracks. Minor variations in

this assumed proportionality with velocity would lead to a velocity

exponent that differed from the one given by Evans et al . Thus, a dependence on velocity of lateral crack shape or the depth from which the

cracks originate could significantly alter the value of the

velocity exponent. Furthermore, the theory assumes that all

particles hitting the surface cause the same amount and type of

damage. Because of a spread in the velocity of particles in an erosion experiment, the arbitrary orientation of particles as they

contact the surface, and the surface roughness that develops

during the erosion process, this assumption can not be satisfied

rigorously. As a consequence, the velocity exponent might be

expected to differ from the value of 2.5 predicted from the theory.

Considering the difficulty of incorporating these various parameters

into the theory, modification of the theory to handle these

parameters may not be possible.

A final comparison between theory and experiment can be made

by considering the relative erosion rates of alumina and silicon

nitride at normal angles of impact. Based on volume loss, the

erosion rate of the sintered aluminum oxide is approximately four

times that of the silicon nitride at 25°C. Since the room temperature hardness of these two materials are about the same relative

differences in the erosive wear of the two materials should depend

only on the critical stress intensity factors of the two materials.

Specifically, the ratio of erosion rates should be given by ratio

of the two K

c values raised to the 1.5 power, i.e.,

;

i (Al2 03

)/v

i (Si3

N 4

) - [K

c (Al

2

0

3 )/Kc (Si3

N

4

)]

1 ' 3 (2)

Given that K for A1 2 0 3 is 2.5 MN/m 3 / 2 (15) and K for Si 3 N 4 is

5 MN/m 3/ 2

( 1 § ) , the predicted ratio of erosion weir is ^2.9*.

Considering the approximations involved in the theory, and the

uncertainties of the experimental values of K , the predicted

ratio is considered to be in good agreement w^fth the experimental

value. As predicted by the theory, normal -impingement erosion

seems to be controlled by the resistance of the material to crack

propagation.

A similar prediction of the erosion rate can be made from the

high temperature erosion data. However, since the hardness of

*Because 30 urn gain A1 2 0 3 was used in these studies, the contact”

area during impact was usually confined to a single grain. Therefore, single crystal values of K

c were used in this comparison.

20
Si 3 N 4 has not been measured at elevated temperatures , the prediction

must be considered more approximate than the room temperature

prediction. Assuming the hardness of aluminum oxide and silicon

nitride are equal at 1000°C, and using measured values of the

critical stress intensity factors for the two materials (^1.8

MN/m 3 /

2 for single crystal A1 2 0 3 at 800°C; %5 MN/m 3 /

2 for Si 3 N 4 at

1000°C), the erosion rate of the aluminum oxide is expected to be

^4.6 times the erosion rate of silicon nitride. The ratio, ^3, of

the two erosion rates obtained experimental ly is in qualitative

agreement with the predicted value.

A similar qualitative comparison of data between the hotpressed aluminum oxide and the other two materials cannot be made

because the critical stress intensity factor for this material was

not measured. However, because of the small grain size of hotpressed aluminum oxide, a polycrystal 1 ine value of K would have

to be used to describe the erosion rate. Since polySrystal 1 ine

values of K are typically higher than single crystal values, the

erosive weaf' of the hot-pressed aluminum oxide would be expected

to be less than that of the sintered aluminum oxide. This expectation is confirmed by experimental observation.

Considering all of the data presented in this paper on erosion at normal incidence of impact, the elastic/plastic treatment developed by Evans et al.(8) seems to provide a good semiquantitative description of the erosion process. Plastic flow is

always observed beneath the contact area; the dependence of

erosion rate on particle velocity agrees qualitatively with the

predicted dependence; and the relative erosion resistance of the

three materials studied is roughly that expected from the tneory.

However, consideration of the observed variation in erosive wear

with impingement angle indicates other factors influence the

erosion process. By modifying the theory presented by Evans et

al . to include oblique angles of impact, it can be shown that

erosion at low angles of impact involves shear deformation as well

as brittle fracture.

Although the theory of Evans et al. was developed for normal

particle incidence, it can be extended to oblique angles of incidence by assuming that lateral crack extension and penetration is

determined only by the normal component of the particle velocity.

Based on this assumption, the erosion equation of Evans et al . is

modified by substituting the normal component for the particle

velocity, V = V sin a, into equation 1. Thus, the dependence of

erosion rate on angle of impingement should be given by:

^i

« (V

Q

sin a

)

n

, (3)

21
where V is the particle velocity, a is the angle of impingement,

and whe?e the experimental velocity exponent, n, has been substituted

for the value of 2.5 given in equation 1.

Equation 3 is compared in Figures 10a and b with erosion data

for hot-pressed Si 3 N 4

. At 25°C, n was found to have a value of ^2

for normal -impingement erosion. The data is, therefore compared

with a plot of the rate of erosion for normal impact times sin 2 a

in Figure 10a. The comparison of the theoretical and experimental

values of the erosion rate is satisfactory for impingement angles

greater than 30°. However at 15° impingement, the measured rate

of erosion is approximately five times the predicted value. A

similar comparison of experimental with predicted erosion rates is

given in Figure 10b, for data obtained on hot-pressed silicon

nitride at 1000 C C. At this temperature, t^e^value of n obtained

for normal impact was ^2.5. A plot of sin a times the erosion

rate for normal impact is found to agree with the experimental

data only for 60° impact. At lower impact angles, the erosion

rate is larger than expected.

The deviation of experiment from theory described above can

be attributed to the increased importance of a shear mechanism of

erosion at low impact angles. Particles impacting upon the

target surface remove material primarily by ploughing in a manner described in much of the erosion literature on metals. In view of

the microscopic evidence for plastic flow underneath the impact

sites, it is reasonable to suggest that the mechanism of material

removal in the plowed area is by ductile flow. However considering

the fact that some lateral venting also occurs, a contribution of

fracture to erosion at oblique angles cannot be dismissed. If

plastic ploughing is the primary mechanism of erosion, then the

erosion rate should depend more on the resistance to deformation

(i.e. hardness), than on fracture toughness. Therefore, materials

that have the same hardness, but different fracture toughness are expected to have the same erosion rate for similar erosion conditions. This conclusion is supported by the results shown in

Figure 9b, which compares the 15° impingement data obtained at

1000°C. Little difference is seen between the data for the three

materials. Had the erosion data been presented in terms of the

volume loss rather than the weight lost per weight of impacting

particles, the comparison would have been even closer. In con- trast, distinct differences in the room temperature erosion

behavior for oblique angles of impact. Figure 9a, suggests that at room temperature fracture still plays a role in the erosion process.

5. SUMMARY

In this paper, results are presented which show that plastic

flow plays an important role in the erosion of brittle materials.

22
At high impact angles, the occurrence of plastic flow provides an explanation for the growth of cracks that result in material

removal from the target surface. At oblique angles of impingement, impact damage is often free of cracks suggesting that material

removal occurs by a shear deformation process. Erosive wear data

obtained in this study further support the importance of plastic

deformation to the erosion process. The experimental data presented

in this paper also provides support for the elastic-plastic erosion

theory proposed recently by Evans et al . (8), which describes

material removal in terms of the penetration and extension of

lateral vent-type cracks. At oblique angles of impingement,

however, material removal also occurs by a shear deformation

process of the type usually used to describe the erosion of metals.

By increasing the target temperature from 25°C to 1000°C, deformation of the target materials during impact is enhanced, and material

removal by shear deformation occurs at higher impact angles.

Since both brittle and ductile modes of material removal occur,

erosive wear is determined by both hardness and fracture toughness.

Acknowl edgement

The authors wish to acknowledge the support of the Office of

Naval Research.

REFERENCES

1. Lawn, B. R., and Marshall, D. B., this volume.

2. Sheldon, G. L., and Finnie, I., Trans. ASME 88B, 393 (1966).

3. Oh, H. L., Oh, K. P. L., Vaidyanathan , S., and Finnie, I.,

"The Science of Ceramic Machining and Surface Finishing".

NBS Special Publication 348, edited by S. J. Schneider and

R. W. Rice, p. 119 (1972).

4. Lawn, B. R., and Wilshaw, T. R., J. Mater. Sci. KD, 1049

(1975).

5. Hockey, B. J., J. Amer. Ceram. Soc., 54, 223 (1971).

6. Hockey, B. J., and Lawn, B. R., J. Mater. Sci., KD, 1275

(1975).

7. Evans, A. G., and Wilshaw, T. R. , Acta Met. 24, 939 (1976).

8. Evans, A. G., Gulden, M.E., Rosenblatt, M.; to be published

in Proc. Roy. Soc.

9. Evans, A. G., this volume.

23
10 . Wiederhorn, S. M., and Roberts, D. E., Bull. Am. Ceram. Soc.

55^ 185 (1 976).

11. Ruff, A. W., and Ives, L. K. Wear, 35, 195 (1975).

12. Sheldon, G. L., and Finnie, I., Trans. ASME 89B , 387 (1966).

13. Sheldon, G. L., Trans. ASME 92D, 619 (1970).

14. Lawn, B. R. , and Swain, M. V., J. Mater. Sci. 1_0, 1 13 (1975).

15. Wiederhorn, S. M., Hockey, B. J., and Roberts, D. E., Phil,

mag. 28, 783 (1973).

16. Evans, A. G., and Wiederhorn, S. M. , J. Mater. Sci. 9_, 276

(1974).

24
1)5-1 I4A (REV. 7-73)

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BIBLIOGRAPHIC DATA

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1. PUBLICATION OR REPORT NO.

77-1396

2. Gov’t Accession

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3. Recipient’s Accession No.

1. TITLE AND SUBTITLE

Erosion of Brittle Materials by Solid Particle Impact

5. Publication Date

6. Performing Organization Code

7. AUTHOR(S)

B. J. Hockey, S. M. Wiederhorn, and H. Johnson

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. 3130150

11. Contract/Grant No.

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

The Pennsylvania State University

Department of Material Sciences

201 Mineral Industries Building

University Park, Pennsylvania 16802

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Covered

14. Sponsoring Agency Code

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.)

Results are presented which show, that in addition to fracture, plastic deformation

occurs and plays an important role in the erosion of brittle materials by solid

particle impact. These conclusions are supported by transmission electron microscopy

studies of impact damage produced in a wide variety of brittle materials and by

erosive wear studies on silicon nitride and alumina. The erosive wear studies also

indicate that while erosion resistance is primarily determined by fracture toughness

and hardness, the relative importance of these materials parameters depends on the

test conditions (e.g. temperature and angle of particle impingement).

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons)

Ceramics; erosion; fracture; plastic flow; solid particle impact; transmission

electron microscopy.

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