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Erosion damage in structural ceramics
Materials Science and Engineering, 71 (1985) 195-201
195
Erosion Damage in Structural Ceramics* JOHN E. RITTER
Mechanical Engineering Department, University of Massachusetts, Amherst, MA 01003 (U.S.A.) (Received October 30, ]984)
ABSTRACT
The erosion damage (material removal and strength degradation) in a variety of structural ceramics (Al20 s, SiC, SizN 4 and MgO) as a function of kinetic energy o f the impacting particle is compared. Based on this data an erosion damage model is developed by assuming that the kinetic energy of the impacting particle goes into grain boundary cracking and the subsequent grain fall-out creates a hemispherical pit with an annular crack o f about a grain diameter in size. The model predicts that, as kinetic energy increases, larger pits are formed; however, the ratio of the annular crack to pit size decreases, causing the stress intensity factor for this pit-crack defect to become insensitive to the size o f the pit. Thus, strength degradation is predicted to level o f f at high kinetic energies. The dependence of the erosive wear data on the kinetic energy of the impacting particle and the grain size and toughness of the target material agreed well with the model, as well as the strength degradation results o f sintered AlzO s. However, the post-erosion strength of sintered SiC showed an increase at high impacting kinetic energies. This discrepancy was thought to be related to the fact that, in SiC, relatively shallow, rather than hemispherical, pits were formed on erosion.
1. INTRODUCTION Erosion of ceramic materials by hard sharp particles is a co mp l ex process in which material is lost from the target surface by brittle fracture. The sizes and types of cracks that *Paper presented at the International Symposium on Engineering Ceramics, Jerusalem, Israel, December 16-20, 1984. 0025-5416/85/$3.30
form in the target surface during impact can lead to erosive wear as well as to strength degradation, causing a deterioration in performance or even worse failure of ceramic components. Thus, when ceramic materials are considered for structural applications, their response to particle impact during service must be understood. Ceramic materials eroded at an impingem ent angle of 90 ° exhibit a rough chipped surface indicative of material removal by a fracture process [1, 2]. Figure 1 shows a typical isolated impact site for sintered A120 3. The damage zone is characterized by a relatively deep pit formed primarily through intergranular chipping with no evidence of any radial or lateral cracking around this zone. Figure 2 similarly shows a pit created by particle impact of sintered SiC. It is possible t hat t he cont act stresses generated by these impacts did not exceed the threshold for elastic-plastic fracture; however, the estimated impact loads are at least an order of magnitude greater than those necessary to initiate indentation cracks with a Vickers indenter. It is also i m p o r t a n t to note that other researchers [2, 3] have observed similar surface damage m o r p h o l o g y after erosion of polycrystalline ceramics. On the basis of the microstructural observations of the nature of the impact damage produced in polycrystalline A1203, erosive wear and strength degradation have been explained by assuming that the kinetic energy of the impacting particles is absorbed by the target material through grain boundary cracking adjacent to the impact site [1]. The subsequent grain fall-out produces a pit surrounded by an annular crack with a length equal to about a grain diameter. While this view of erosion damage may be oversimplified considering the com pl exi t y of the process, it can be used to model the damage and to de© Elsevier Sequoia/Printed in The Netherlands
196 [ 1] of impact damage in explaining erosive wear and strength degradation results of structural ceramics.
2. EXPERIMENTAL PROCEDURE
Fig. 1. An isolated impact site produced in sintered A1203 by grit size 46 impacting at 75 m s-1 (90°; 23 °C): (a) overall pit; (b) interior of pit.
velop equations that predict erosive wear and strength degradation as a function of projectile kinetic energy and target parameters. The purpose of this paper is to demonstrate the general applicability of this pit-crack model
Sintered A1203 (AD995, Coors Porcelain Co., Golden, CO) and SiC (Hexoloy SA, Carborundum Co., Niagara Falls, NY) were used as the target material. The A1203 samples were manufactured from the same powder lot in the form of discs 38.1 mm in diameter and 2.54 mm in thickness. The faces of the specimens were polished by the manufacturer to a 2.54 pm r.m.s, surface finish. The SiC sample discs were 38.1 mm in diameter and 15.0 mm in thickness. They were given a stress relief anneal (1500 °C for 2 h) and then lightly polished with grade 600 SiC grit paper. The eroding particles were a commercial grade SiC abrasive grain (type RA, Carborundum Co., Niagara Falls, NY). Three different grit sizes were used: 16, 46 and 150. The particle size distribution for each grit size was determined by sieve analysis. The average particle diameters for the three grits were 1530 pm, 400 pm and 90 pm respectively. The m a x i m u m particle sizes, corresponding to the largest 5% of the particles in the distribution, were 1850 pm, 510 pm and 130 pm respectively. Erosion tests were conducted in air using a slinger-type erosion apparatus similar in design to that described by Kosel et al. [4]. In this apparatus, abrasive particles are fed into the center of a tubular rotor 50.8 cm in diameter rotating in a horizontal plane, accelerate to the end of the tube and leave the rotor to strike eight specimens positioned around the perimeter of the apparatus. In the present study the samples were positioned so that the abrasive particles impacted the specimens at 90 ° . It was assumed that the particle velocity was equal to the tip speed of the rotating slinger arm. This assumption has previously been shown to agree within 3% of the velocity as measured by a dual-disc velocity analyzer [4]. Particle velocities up to 100 m s-1 could be achieved. For the high temperature tests (700 and 1000 °C) the erosion cavity with the samples in place was heated by SiC heating elements. The temperature of the specimens was maintained to within + 10 °C. The furnace
197
Fig. 2. An isolated impact site p r o d u c e d in sintered SiC by grit size 46 grit impacting at 37.5 m s- 1 ( 9 0 °; 23 °C).
was shut down immediately following the erosion test and the samples were allowed to cool slowly to room temperature. The number of samples per test condition was 16 and the eroded surface of the samples was coated with mineral oil after erosion to minimize any subcritical crack growth due to aging. Specimens were exposed to a fixed mass of erosion particles, which ranged from 10 to 500 g depending on the grit size and particle velocity. On the basis of preliminary experiments the a m o u n t of grit used in each case was thought to be sufficient to reach steady state erosion conditions. The mass loss by the target during each experiment was measured to at least 1% accuracy with an analytical balance. On the assumption that the SiC particles are spherical, the number of particles impacting a given target was estimated from the mass of SiC abrasives used and the mean particle size and density (3210 kg m -a) of the SiC. The erosive wear (the volume loss per particle impact) was calculated from the mass lost from the specimen per particle impact and the target density (3890 kg m-3). A ball-on-ring biaxial strength test was used to determine the effect of erosion on sample strength without spurious edge effects. An apparatus was constructed based on the design by Wachtman e t al. [5] and was used in
conjunction with a universal testing machine (Instron Corporation, Canton, MA). The support ring was 28.6 mm in diameter and the loading ball was 6.35 mm in diameter. For these strength tests the samples were tested wet with mineral oil using a fast loading rate (about 15 MPa s-1) to minimize any fatigue effects. The appropriate equation to calculate fracture strength is given in ref. 6.
3. R E S U L T S A N D D I S C U S S I O N
3.1. E r o s i v e w e a r
On the assumption that the damage done by the impacting particle is in the form of grain boundary cracking, the energy associated with the formation of a pit will be the grain boundary fracture energy ~/multiplied by the product of the number of grains per pit and surface area per grain. Since the number of grains per pit is proportional to the ratio of the pit volume to the average grain volume, and the surface area per grain is proportional to the square of the average grain diameter d, the size D of the pit will be proportional to the kinetic energy Uk of the impacting particles:
(dUktl/3
D c~ \ ~ - - ]
(1)
198
The volume of material removed per impact (erosive wear) is obtained by taking the cube of the pit diameter; hence, erosive wear V is directly proportional to kinetic energy:
dUk
V ~ -"y
of the erosive wear data on kinetic energy fits the data very well. The results in Fig. 3 also show that the parameters controlling brittle erosion for normal incidence impact are not dependent on temperature up to 1000 °C for sintered A1203. Wiederhorn and Hockey [2] also found that temperature does not play a dominant role in the erosive wear of ceramics. The general validity of eqn. (2) in describing erosive wear of ceramics can be examined by assuming that the grain boundary fracture energy is proportional to the critical stress intensity factor KIc:
(2)
Figure 3 summarizes the erosive wear results for sintered A1203 at normal incidence impact for the three erosion temperatures studied. It should be noted that the kinetic energy in this figure is based on the average particle size since erosion is t h o u g h t to represent a cumulative event [ 7]. The predicted dependence
Kic 2 3, c o E
Uk(J) l o -4 I
10 -6 I
l o -z i
(3)
so that
dEUk
V~ - -
-12.2 .
(4)
gic 2 10 -13
Figure 4, which is based on eqn. (4), shows a material-independent comparison of the erosive wear at 23 °C of a number of polycrystalline ceramics. The erosion data of this study for sintered A1203 and a-SiC obtained in the slinger apparatus are compared with those of Wiederhorn and Hockey [2] who used a high velocity particle-air stream apparatus. It is apparent that eqn. (4) fits both sets of data quite well. The apparent difference in the magnitude of the erosive wear data of this study and those of Wiederhorn
-13.4 .
LOG V (m3)
-10 -14 V
(m 3)
-14.6 .10 -Is
-15.8.
/
/
-do
1
-s:o
-4:0
-3'.0
LOG
Uk(J
-2'.0
)
Fig. 3. Erosive wear of sintered A]203 as a function of kinetic energy of impacting particle: o, 23 °C; A, 700 °C; o, 1000 °C.
11.0- -
-
-115120" I
12..5
/" []
130135
o/
log V 14.o
(m3)
/
1
/
S
145 15Do
1
155160
/ 1~'~--16~3
155
1S.0
145
140
135
13.0
125
120
11~
110
1Q~
10.0
9~S
90
EL~
80
Fig. 4. Comparison of erosive wear of various polycrystalline ceramics: line a, data from ref. 2 (A, hot-pressed A1203; o, sintered MgO; o, sintered A1203; *, hot-pressed SiC; 0, hot-pressed Si3N4); line b, this study ($, sintered A1203; o, sintered a-SiC).
199
and H o c k e y is u n d o u b t e d l y related to the d i f f e r e n c e b e t w e e n the t w o erosion apparatuses.
Uk(J)
0.0
3.2. Strength degradation T h e strength o f the e r o d e d samples can be related to the observed erosion damage b y assuming t h a t the pit created by erosion is hemispherical in shape with a radius R and an annular crack o f size L; the a p p r o p r i a t e stress i n t e n s i t y f a c t o r can be given by [8] K I = kt{~)(1.12 -- 0.22 tan-l~)YoL 1/2
1.O
- -
~0.87
-0o6 ~¢~o o,2
o,/ao
LG
~0.76
-o,a
0.66
do
(7)
-s'.o
(a)
o.o
LG
[Z{1.0 + 1 . 2 3 e x p ( - - a . 9 4 ~ U k - 1 / a ) } X
,o,
t=
t 'o -0.87
~o
~,/~ 0.76
-0.12
0.,6.
0.66
6:o
--
10'
2".o
-006
where ~ is a c o n s t a n t . Failure will o c c u r f r o m this p i t - c r a c k d e f e c t w h e n K I -- Kic and the c o r r e s p o n d i n g failure stress is given b y comhining eqns. ( 5 ) - ( 7 ) : -- =
-4:o a'.o LOG Uk (J)
Uk(J)
,,o •
(6)
By assuming t h a t the annular crack has a constant size, t h e n f r o m eqn. (1) = ~Uk -1/a
--
,o'
(5)
where A t (0~) is the stress c o n c e n t r a t i o n f a c t o r for this p i t - c r a c k d e f e c t , ~ = L/R, Y is a g e o m e t r i c c o n s t a n t d e p e n d e n t on loading g e o m e t r y and crack size, and o is the applied stress. The numerical results o f ref. 8 for ]~t (OL) can be expressed b y the following e q u a t i o n : kt(O~ ) = 1 . 0 ~- 1.23 e x p ( - - 3 . 9 4 ( D
,o,'
1V ,
-s'.o
(b)
-io a'o LOG Uk (J)
2:o
o0
× {1.12 -- 0.22 tan-l(~Uk-1/a)} ] -1
(8)
Uk(J) 17 -4
I
where Z is the flaw shape p a r a m e t e r , Co corresponds t o the initial s t r e n g t h - c o n t r o l l i n g flaw size and oo is the initial strength o f the material t h a t is given b y
,1.O
0.0
0.06
ZKIc
O0-
YCol/2
-0.87
o,/~o
L G
(9)
E q u a t i o n (8) can be f i t t e d to the posterosion strength d a t a by n o t i n g that, as U k becomes large, o2/Oo a p p r o a c h e s (Co/L)1/2/2.5Z in the limit and t h a t 02/00 is u n i t y for kinetic energies less t h a n the threshold. Figure 5 shows t h a t eqn. (8) fits the post-erosion strength d a t a for sintered A120 3 well where the as-received strength is 330 MPa.* T h e limit c o n s t a n t (Co/L)l/2/2.5Z can be seen to be *It s h o u l d be n o t e d t h a t t h e k i n e t i c e n e r g y in these s t r e n g t h figures is based o n t h e m a x i m u m particle size since it is these particles t h a t are t h o u g h t t o b e res p o n s i b l e for t h e s t r e n g t h - c o n t r o l l i n g flaw.
~ 0.12
-0.76
o,8
'0.66
6:o
(c)
5'0
-4'.0 3:o LOG Uk (J)
2"0
Fig. 5. S t r e n g t h a f t e r erosion of s i n t e r e d A l 2 0 3 as a f u n c t i o n o f kinetic energy o f i m p a c t i n g particles ( t h e p o s t - e r o s i o n s t r e n g t h is n o r m a l i z e d to the initial s t r e n g t h o f 3 3 0 MPa) (Co/L)l/2/2.5Z= 0.65): (a) 23 °C erosion (/3 = 5.38 × 10 -3 j1/3); (b) 700 °C erosion (/3= 5.38 × 10 -3 j1/3); (c) 1 0 0 0 °C erosion (/3= 1.15 × 10 -2 j1/3).
200
independent of temperature and equal to 0.65. By taking L to be equal to the average grain size (17 pm) and Z to be 1.30 [8], Co is calculated to be 75/am which is about the size that would be expected for a microstructurally controlled defect [9]. TABLE 1 E f f e c t of a n n e a l i n g o n p o s t - e r o s i o n s t r e n g t h s of s i n t e r e d A1203 a f t e r n o r m a l i n c i d e n c e erosion at 23 °C Kinetic energy (J)
Post-anneal
Mean strength a (MPa)
6 × 1 0 -4 6 × 10 -4 3 × 10 -2 3 x i0 -2
No Yes No Yes
193 278 234 206
(+9) (+23) (+15) (ill)
a T h e n u m e r a l s in p a r e n t h e s e s i n d i c a t e o n e s t a n d a r d deviation.
lO-5
lp
~Uk(J)
~o-3
The threshold constant/3 in Fig. 5 was found to be 5.38 × 10 -3 j1/3 for erosion at 23 and 700 °C and 1.15 × 10 -2 j1/a for erosion at 1000 °C. To investigate why the threshold kinetic energy was greater for erosion at 1000 °C, eight samples each were eroded at 23 °C using kinetic energies of 6 × 1 0 -4 and 3 × 1 0 -2 J. Following erosion, both sets of samples were annealed at 1000 °C for 10 min, which is approximately the time that the samples spent at 1000 °C during erosion at this temperature. These results are summarized in Table 1. The erosion model as discussed above does not include the possibility of a localized residual stress around the pit-crack defect. The results for the higher kinetic energy are consistent with this model since the postannealed strength is not significantly different from the strength of the as-eroded samples. However, the fact that annealing in-
19-2
-H).050.00
100
-0.10-
--0.15
O71
%o 056
0.30
--0.35
-
-
045
0.40 -
-s:oo
-4'25
-3!so
-~!Ts
-2'.00
-,!25
log U k ( J )
Fig. 6. S t r e n g t h (A) a f t e r 23 °C e r o s i o n of s i n t e r e d SiC as a f u n c t i o n o f kinetic energy o f i m p a c t i n g particles (the p o s t - e r o s i o n s t r e n g t h is n o r m a l i z e d to t h e initial s t r e n g t h o f 278 MPa).
201 creased the s t r e n g t h of t h e s a m p l e s e r o d e d at a l o w e r kinetic e n e r g y implies t h a t initially the e r o s i o n d a m a g e c o n t a i n s an e l a s t i c - p l a s t i c c o m p o n e n t t h a t b e c o m e s negligible w h e n intergranular fracture becomes more extensive at t h e higher i m p a c t i n g kinetic energies. T h u s the a p p a r e n t increase in the t h r e s h o l d kinetic e n e r g y at 1 0 0 0 °C is t h o u g h t to be due to stress relief annealing r a t h e r t h a n to an increase in the kinetic e n e r g y to f o r m a p i t crack. Figure 6 is a p l o t o f the s t r e n g t h d a t a o f (~-SiC a f t e r erosion at 23 °C. T h e full line in the figure is t h a t p r e d i c t e d f r o m eqn. (8) w h e r e the limit c o n s t a n t is 0.50 and the t h r e s h o l d c o n s t a n t is 0.32 × 10 -3 j1/3. [n this case the strength d a t a do n o t f o l l o w the t r e n d p r e d i c t e d b y the p i t - c r a c k m o d e l (Fig. 5) b u t instead s t r e n g t h initially decreases and t h e n increases at higher i m p a c t i n g kinetic energies. Close e x a m i n a t i o n of the i m p a c t d a m a g e in this m a t e r i a l shows t h a t relatively shallow, r a t h e r t h a n h e m i s p h e r i c a l , pits are f o r m e d . U n f o r t u n a t e l y , it is difficult to give a m o r e q u a n t i t a t i v e a s s e s s m e n t o f t h e results because (1) K l for an ellipsoidally s h a p e d flaw is n o t k n o w n and (2) t h e d e p e n d e n c e o f the ellipticity (the ratio o f the d e p t h to the d i a m e t e r ) o f t h e pit on kinetic e n e r g y is n o t k n o w n .
4. SUMMARY The damage done by multiparticle impact o f A1203, SiC, Si3N4 a n d MgO was e x p l a i n e d b y a s s u m i n g t h a t t h e kinetic e n e r g y of the imp a c t i n g particles goes into grain b o u n d a r y cracking. T h e s u b s e q u e n t grain fall-out creates a pit w i t h an a n n u l a r c r a c k w h o s e size rem a i n s relatively c o n s t a n t with r e s p e c t t o imp a c t kinetic energy; t h u s the ratio o f t h e c r a c k to pit size decreases as larger pits are f o r m e d at increasing i m p a c t energies. Alt h o u g h this m o d e l a c c u r a t e l y c h a r a c t e r i z e s t h e erosive w e a r results, discrepancies b e t w e e n s t r e n g t h d e g r a d a t i o n results a n d p r e d i c t i o n s were n o t e d . F u r t h e r research is n e e d e d to
refine this p r o p o s e d m o d e l to a c c o u n t f o r t h e effects o f residual stress a n d ellipticity o f the pit on t h e stress i n t e n s i t y f a c t o r o f this c r a c k - p i t i m p a c t flaw. ACKNOWLEDGMENT This research was s u p p o r t e d b y the U.S. D e p a r t m e n t o f E n e r g y u n d e r C o n t r a c t DE AC02-81ER10950. REFERENCES 1 J. E. Ritter, Jr., P. Strzepa, K. Jakus, L. Rosenfeld and K. J. Buckman, Erosion damage in glass and alumina, J. Am. Ceram. Soc., 67 (11) (1984) 769774. 2 S. M. Wiederhorn and B. J. Hockey, Effect of material parameters on the erosion resistance of brittle materials, J. Mater. Sci., 18 (1983) 766 780. 3 M. E. Gulden, Solid particle erosion of high technology (Si3N4, glass-bonded A1203, and MgF2). In W. F. Adler (ed.), Erosion: Prevention and Useful Application, in A S T M Spec. Tech. Publ. 664, 1979, pp. 101-122. 4 T. H. Kosel, R. O. Scattergood and A. P. L. Turner, An electron microscope study of erosion wear. In K. C. Ludema, W. A. Glaeser and S. K. Rhee (eds.), Proc. Int. Conf. on the Wear o f Materials, Dearborn, MI, April 1979, American Society of Mechanical Engineers, New York, 1979, pp. 192-204. 5 J. B. Wachtman, Jr., W. Capps and J. Mandel, Biaxial flexure tests of ceramic substrates, J. Mater., 7 (2) (1972) 188-194. 6 D. K. Shetty, A. R. Rosenficld, P. McGuide, G. K. Bansal and W. H. Duckworth, Biaxial flexure tests for ceramics, Am. Ceram. Soc., Bull., 59 (12) (1980) 1193-1197. 7 D. B. Marshall, A. G. Evans, M. E. Gulden, J. L. Routbort and R. O. Scattergood, Particle size distribution effects on solid particle erosion in brittle materials, Wear, 71 (1981)363 373. 8 F. I. Barratta, Refinement of stress intensity factor estimates for a peripherally cracked spherical void and a hemispherical surface pit, J. Am. Ceram. Soc., 64 (1) (1981) C-3-C-4. 9 B. R. Lawn, S. W. Freiman, T. L. Baker, D. D. Cobb and A. G. Gonzales, Study of microstructural effects in the strength of alumina using controlled flaws, J. Am. Ceram. Soc., 67 (4) (1984) C-67C-68.
195
Erosion Damage in Structural Ceramics* JOHN E. RITTER
Mechanical Engineering Department, University of Massachusetts, Amherst, MA 01003 (U.S.A.) (Received October 30, ]984)
ABSTRACT
The erosion damage (material removal and strength degradation) in a variety of structural ceramics (Al20 s, SiC, SizN 4 and MgO) as a function of kinetic energy o f the impacting particle is compared. Based on this data an erosion damage model is developed by assuming that the kinetic energy of the impacting particle goes into grain boundary cracking and the subsequent grain fall-out creates a hemispherical pit with an annular crack o f about a grain diameter in size. The model predicts that, as kinetic energy increases, larger pits are formed; however, the ratio of the annular crack to pit size decreases, causing the stress intensity factor for this pit-crack defect to become insensitive to the size o f the pit. Thus, strength degradation is predicted to level o f f at high kinetic energies. The dependence of the erosive wear data on the kinetic energy of the impacting particle and the grain size and toughness of the target material agreed well with the model, as well as the strength degradation results o f sintered AlzO s. However, the post-erosion strength of sintered SiC showed an increase at high impacting kinetic energies. This discrepancy was thought to be related to the fact that, in SiC, relatively shallow, rather than hemispherical, pits were formed on erosion.
1. INTRODUCTION Erosion of ceramic materials by hard sharp particles is a co mp l ex process in which material is lost from the target surface by brittle fracture. The sizes and types of cracks that *Paper presented at the International Symposium on Engineering Ceramics, Jerusalem, Israel, December 16-20, 1984. 0025-5416/85/$3.30
form in the target surface during impact can lead to erosive wear as well as to strength degradation, causing a deterioration in performance or even worse failure of ceramic components. Thus, when ceramic materials are considered for structural applications, their response to particle impact during service must be understood. Ceramic materials eroded at an impingem ent angle of 90 ° exhibit a rough chipped surface indicative of material removal by a fracture process [1, 2]. Figure 1 shows a typical isolated impact site for sintered A120 3. The damage zone is characterized by a relatively deep pit formed primarily through intergranular chipping with no evidence of any radial or lateral cracking around this zone. Figure 2 similarly shows a pit created by particle impact of sintered SiC. It is possible t hat t he cont act stresses generated by these impacts did not exceed the threshold for elastic-plastic fracture; however, the estimated impact loads are at least an order of magnitude greater than those necessary to initiate indentation cracks with a Vickers indenter. It is also i m p o r t a n t to note that other researchers [2, 3] have observed similar surface damage m o r p h o l o g y after erosion of polycrystalline ceramics. On the basis of the microstructural observations of the nature of the impact damage produced in polycrystalline A1203, erosive wear and strength degradation have been explained by assuming that the kinetic energy of the impacting particles is absorbed by the target material through grain boundary cracking adjacent to the impact site [1]. The subsequent grain fall-out produces a pit surrounded by an annular crack with a length equal to about a grain diameter. While this view of erosion damage may be oversimplified considering the com pl exi t y of the process, it can be used to model the damage and to de© Elsevier Sequoia/Printed in The Netherlands
196 [ 1] of impact damage in explaining erosive wear and strength degradation results of structural ceramics.
2. EXPERIMENTAL PROCEDURE
Fig. 1. An isolated impact site produced in sintered A1203 by grit size 46 impacting at 75 m s-1 (90°; 23 °C): (a) overall pit; (b) interior of pit.
velop equations that predict erosive wear and strength degradation as a function of projectile kinetic energy and target parameters. The purpose of this paper is to demonstrate the general applicability of this pit-crack model
Sintered A1203 (AD995, Coors Porcelain Co., Golden, CO) and SiC (Hexoloy SA, Carborundum Co., Niagara Falls, NY) were used as the target material. The A1203 samples were manufactured from the same powder lot in the form of discs 38.1 mm in diameter and 2.54 mm in thickness. The faces of the specimens were polished by the manufacturer to a 2.54 pm r.m.s, surface finish. The SiC sample discs were 38.1 mm in diameter and 15.0 mm in thickness. They were given a stress relief anneal (1500 °C for 2 h) and then lightly polished with grade 600 SiC grit paper. The eroding particles were a commercial grade SiC abrasive grain (type RA, Carborundum Co., Niagara Falls, NY). Three different grit sizes were used: 16, 46 and 150. The particle size distribution for each grit size was determined by sieve analysis. The average particle diameters for the three grits were 1530 pm, 400 pm and 90 pm respectively. The m a x i m u m particle sizes, corresponding to the largest 5% of the particles in the distribution, were 1850 pm, 510 pm and 130 pm respectively. Erosion tests were conducted in air using a slinger-type erosion apparatus similar in design to that described by Kosel et al. [4]. In this apparatus, abrasive particles are fed into the center of a tubular rotor 50.8 cm in diameter rotating in a horizontal plane, accelerate to the end of the tube and leave the rotor to strike eight specimens positioned around the perimeter of the apparatus. In the present study the samples were positioned so that the abrasive particles impacted the specimens at 90 ° . It was assumed that the particle velocity was equal to the tip speed of the rotating slinger arm. This assumption has previously been shown to agree within 3% of the velocity as measured by a dual-disc velocity analyzer [4]. Particle velocities up to 100 m s-1 could be achieved. For the high temperature tests (700 and 1000 °C) the erosion cavity with the samples in place was heated by SiC heating elements. The temperature of the specimens was maintained to within + 10 °C. The furnace
197
Fig. 2. An isolated impact site p r o d u c e d in sintered SiC by grit size 46 grit impacting at 37.5 m s- 1 ( 9 0 °; 23 °C).
was shut down immediately following the erosion test and the samples were allowed to cool slowly to room temperature. The number of samples per test condition was 16 and the eroded surface of the samples was coated with mineral oil after erosion to minimize any subcritical crack growth due to aging. Specimens were exposed to a fixed mass of erosion particles, which ranged from 10 to 500 g depending on the grit size and particle velocity. On the basis of preliminary experiments the a m o u n t of grit used in each case was thought to be sufficient to reach steady state erosion conditions. The mass loss by the target during each experiment was measured to at least 1% accuracy with an analytical balance. On the assumption that the SiC particles are spherical, the number of particles impacting a given target was estimated from the mass of SiC abrasives used and the mean particle size and density (3210 kg m -a) of the SiC. The erosive wear (the volume loss per particle impact) was calculated from the mass lost from the specimen per particle impact and the target density (3890 kg m-3). A ball-on-ring biaxial strength test was used to determine the effect of erosion on sample strength without spurious edge effects. An apparatus was constructed based on the design by Wachtman e t al. [5] and was used in
conjunction with a universal testing machine (Instron Corporation, Canton, MA). The support ring was 28.6 mm in diameter and the loading ball was 6.35 mm in diameter. For these strength tests the samples were tested wet with mineral oil using a fast loading rate (about 15 MPa s-1) to minimize any fatigue effects. The appropriate equation to calculate fracture strength is given in ref. 6.
3. R E S U L T S A N D D I S C U S S I O N
3.1. E r o s i v e w e a r
On the assumption that the damage done by the impacting particle is in the form of grain boundary cracking, the energy associated with the formation of a pit will be the grain boundary fracture energy ~/multiplied by the product of the number of grains per pit and surface area per grain. Since the number of grains per pit is proportional to the ratio of the pit volume to the average grain volume, and the surface area per grain is proportional to the square of the average grain diameter d, the size D of the pit will be proportional to the kinetic energy Uk of the impacting particles:
(dUktl/3
D c~ \ ~ - - ]
(1)
198
The volume of material removed per impact (erosive wear) is obtained by taking the cube of the pit diameter; hence, erosive wear V is directly proportional to kinetic energy:
dUk
V ~ -"y
of the erosive wear data on kinetic energy fits the data very well. The results in Fig. 3 also show that the parameters controlling brittle erosion for normal incidence impact are not dependent on temperature up to 1000 °C for sintered A1203. Wiederhorn and Hockey [2] also found that temperature does not play a dominant role in the erosive wear of ceramics. The general validity of eqn. (2) in describing erosive wear of ceramics can be examined by assuming that the grain boundary fracture energy is proportional to the critical stress intensity factor KIc:
(2)
Figure 3 summarizes the erosive wear results for sintered A1203 at normal incidence impact for the three erosion temperatures studied. It should be noted that the kinetic energy in this figure is based on the average particle size since erosion is t h o u g h t to represent a cumulative event [ 7]. The predicted dependence
Kic 2 3, c o E
Uk(J) l o -4 I
10 -6 I
l o -z i
(3)
so that
dEUk
V~ - -
-12.2 .
(4)
gic 2 10 -13
Figure 4, which is based on eqn. (4), shows a material-independent comparison of the erosive wear at 23 °C of a number of polycrystalline ceramics. The erosion data of this study for sintered A1203 and a-SiC obtained in the slinger apparatus are compared with those of Wiederhorn and Hockey [2] who used a high velocity particle-air stream apparatus. It is apparent that eqn. (4) fits both sets of data quite well. The apparent difference in the magnitude of the erosive wear data of this study and those of Wiederhorn
-13.4 .
LOG V (m3)
-10 -14 V
(m 3)
-14.6 .10 -Is
-15.8.
/
/
-do
1
-s:o
-4:0
-3'.0
LOG
Uk(J
-2'.0
)
Fig. 3. Erosive wear of sintered A]203 as a function of kinetic energy of impacting particle: o, 23 °C; A, 700 °C; o, 1000 °C.
11.0- -
-
-115120" I
12..5
/" []
130135
o/
log V 14.o
(m3)
/
1
/
S
145 15Do
1
155160
/ 1~'~--16~3
155
1S.0
145
140
135
13.0
125
120
11~
110
1Q~
10.0
9~S
90
EL~
80
Fig. 4. Comparison of erosive wear of various polycrystalline ceramics: line a, data from ref. 2 (A, hot-pressed A1203; o, sintered MgO; o, sintered A1203; *, hot-pressed SiC; 0, hot-pressed Si3N4); line b, this study ($, sintered A1203; o, sintered a-SiC).
199
and H o c k e y is u n d o u b t e d l y related to the d i f f e r e n c e b e t w e e n the t w o erosion apparatuses.
Uk(J)
0.0
3.2. Strength degradation T h e strength o f the e r o d e d samples can be related to the observed erosion damage b y assuming t h a t the pit created by erosion is hemispherical in shape with a radius R and an annular crack o f size L; the a p p r o p r i a t e stress i n t e n s i t y f a c t o r can be given by [8] K I = kt{~)(1.12 -- 0.22 tan-l~)YoL 1/2
1.O
- -
~0.87
-0o6 ~¢~o o,2
o,/ao
LG
~0.76
-o,a
0.66
do
(7)
-s'.o
(a)
o.o
LG
[Z{1.0 + 1 . 2 3 e x p ( - - a . 9 4 ~ U k - 1 / a ) } X
,o,
t=
t 'o -0.87
~o
~,/~ 0.76
-0.12
0.,6.
0.66
6:o
--
10'
2".o
-006
where ~ is a c o n s t a n t . Failure will o c c u r f r o m this p i t - c r a c k d e f e c t w h e n K I -- Kic and the c o r r e s p o n d i n g failure stress is given b y comhining eqns. ( 5 ) - ( 7 ) : -- =
-4:o a'.o LOG Uk (J)
Uk(J)
,,o •
(6)
By assuming t h a t the annular crack has a constant size, t h e n f r o m eqn. (1) = ~Uk -1/a
--
,o'
(5)
where A t (0~) is the stress c o n c e n t r a t i o n f a c t o r for this p i t - c r a c k d e f e c t , ~ = L/R, Y is a g e o m e t r i c c o n s t a n t d e p e n d e n t on loading g e o m e t r y and crack size, and o is the applied stress. The numerical results o f ref. 8 for ]~t (OL) can be expressed b y the following e q u a t i o n : kt(O~ ) = 1 . 0 ~- 1.23 e x p ( - - 3 . 9 4 ( D
,o,'
1V ,
-s'.o
(b)
-io a'o LOG Uk (J)
2:o
o0
× {1.12 -- 0.22 tan-l(~Uk-1/a)} ] -1
(8)
Uk(J) 17 -4
I
where Z is the flaw shape p a r a m e t e r , Co corresponds t o the initial s t r e n g t h - c o n t r o l l i n g flaw size and oo is the initial strength o f the material t h a t is given b y
,1.O
0.0
0.06
ZKIc
O0-
YCol/2
-0.87
o,/~o
L G
(9)
E q u a t i o n (8) can be f i t t e d to the posterosion strength d a t a by n o t i n g that, as U k becomes large, o2/Oo a p p r o a c h e s (Co/L)1/2/2.5Z in the limit and t h a t 02/00 is u n i t y for kinetic energies less t h a n the threshold. Figure 5 shows t h a t eqn. (8) fits the post-erosion strength d a t a for sintered A120 3 well where the as-received strength is 330 MPa.* T h e limit c o n s t a n t (Co/L)l/2/2.5Z can be seen to be *It s h o u l d be n o t e d t h a t t h e k i n e t i c e n e r g y in these s t r e n g t h figures is based o n t h e m a x i m u m particle size since it is these particles t h a t are t h o u g h t t o b e res p o n s i b l e for t h e s t r e n g t h - c o n t r o l l i n g flaw.
~ 0.12
-0.76
o,8
'0.66
6:o
(c)
5'0
-4'.0 3:o LOG Uk (J)
2"0
Fig. 5. S t r e n g t h a f t e r erosion of s i n t e r e d A l 2 0 3 as a f u n c t i o n o f kinetic energy o f i m p a c t i n g particles ( t h e p o s t - e r o s i o n s t r e n g t h is n o r m a l i z e d to the initial s t r e n g t h o f 3 3 0 MPa) (Co/L)l/2/2.5Z= 0.65): (a) 23 °C erosion (/3 = 5.38 × 10 -3 j1/3); (b) 700 °C erosion (/3= 5.38 × 10 -3 j1/3); (c) 1 0 0 0 °C erosion (/3= 1.15 × 10 -2 j1/3).
200
independent of temperature and equal to 0.65. By taking L to be equal to the average grain size (17 pm) and Z to be 1.30 [8], Co is calculated to be 75/am which is about the size that would be expected for a microstructurally controlled defect [9]. TABLE 1 E f f e c t of a n n e a l i n g o n p o s t - e r o s i o n s t r e n g t h s of s i n t e r e d A1203 a f t e r n o r m a l i n c i d e n c e erosion at 23 °C Kinetic energy (J)
Post-anneal
Mean strength a (MPa)
6 × 1 0 -4 6 × 10 -4 3 × 10 -2 3 x i0 -2
No Yes No Yes
193 278 234 206
(+9) (+23) (+15) (ill)
a T h e n u m e r a l s in p a r e n t h e s e s i n d i c a t e o n e s t a n d a r d deviation.
lO-5
lp
~Uk(J)
~o-3
The threshold constant/3 in Fig. 5 was found to be 5.38 × 10 -3 j1/3 for erosion at 23 and 700 °C and 1.15 × 10 -2 j1/a for erosion at 1000 °C. To investigate why the threshold kinetic energy was greater for erosion at 1000 °C, eight samples each were eroded at 23 °C using kinetic energies of 6 × 1 0 -4 and 3 × 1 0 -2 J. Following erosion, both sets of samples were annealed at 1000 °C for 10 min, which is approximately the time that the samples spent at 1000 °C during erosion at this temperature. These results are summarized in Table 1. The erosion model as discussed above does not include the possibility of a localized residual stress around the pit-crack defect. The results for the higher kinetic energy are consistent with this model since the postannealed strength is not significantly different from the strength of the as-eroded samples. However, the fact that annealing in-
19-2
-H).050.00
100
-0.10-
--0.15
O71
%o 056
0.30
--0.35
-
-
045
0.40 -
-s:oo
-4'25
-3!so
-~!Ts
-2'.00
-,!25
log U k ( J )
Fig. 6. S t r e n g t h (A) a f t e r 23 °C e r o s i o n of s i n t e r e d SiC as a f u n c t i o n o f kinetic energy o f i m p a c t i n g particles (the p o s t - e r o s i o n s t r e n g t h is n o r m a l i z e d to t h e initial s t r e n g t h o f 278 MPa).
201 creased the s t r e n g t h of t h e s a m p l e s e r o d e d at a l o w e r kinetic e n e r g y implies t h a t initially the e r o s i o n d a m a g e c o n t a i n s an e l a s t i c - p l a s t i c c o m p o n e n t t h a t b e c o m e s negligible w h e n intergranular fracture becomes more extensive at t h e higher i m p a c t i n g kinetic energies. T h u s the a p p a r e n t increase in the t h r e s h o l d kinetic e n e r g y at 1 0 0 0 °C is t h o u g h t to be due to stress relief annealing r a t h e r t h a n to an increase in the kinetic e n e r g y to f o r m a p i t crack. Figure 6 is a p l o t o f the s t r e n g t h d a t a o f (~-SiC a f t e r erosion at 23 °C. T h e full line in the figure is t h a t p r e d i c t e d f r o m eqn. (8) w h e r e the limit c o n s t a n t is 0.50 and the t h r e s h o l d c o n s t a n t is 0.32 × 10 -3 j1/3. [n this case the strength d a t a do n o t f o l l o w the t r e n d p r e d i c t e d b y the p i t - c r a c k m o d e l (Fig. 5) b u t instead s t r e n g t h initially decreases and t h e n increases at higher i m p a c t i n g kinetic energies. Close e x a m i n a t i o n of the i m p a c t d a m a g e in this m a t e r i a l shows t h a t relatively shallow, r a t h e r t h a n h e m i s p h e r i c a l , pits are f o r m e d . U n f o r t u n a t e l y , it is difficult to give a m o r e q u a n t i t a t i v e a s s e s s m e n t o f t h e results because (1) K l for an ellipsoidally s h a p e d flaw is n o t k n o w n and (2) t h e d e p e n d e n c e o f the ellipticity (the ratio o f the d e p t h to the d i a m e t e r ) o f t h e pit on kinetic e n e r g y is n o t k n o w n .
4. SUMMARY The damage done by multiparticle impact o f A1203, SiC, Si3N4 a n d MgO was e x p l a i n e d b y a s s u m i n g t h a t t h e kinetic e n e r g y of the imp a c t i n g particles goes into grain b o u n d a r y cracking. T h e s u b s e q u e n t grain fall-out creates a pit w i t h an a n n u l a r c r a c k w h o s e size rem a i n s relatively c o n s t a n t with r e s p e c t t o imp a c t kinetic energy; t h u s the ratio o f t h e c r a c k to pit size decreases as larger pits are f o r m e d at increasing i m p a c t energies. Alt h o u g h this m o d e l a c c u r a t e l y c h a r a c t e r i z e s t h e erosive w e a r results, discrepancies b e t w e e n s t r e n g t h d e g r a d a t i o n results a n d p r e d i c t i o n s were n o t e d . F u r t h e r research is n e e d e d to
refine this p r o p o s e d m o d e l to a c c o u n t f o r t h e effects o f residual stress a n d ellipticity o f the pit on t h e stress i n t e n s i t y f a c t o r o f this c r a c k - p i t i m p a c t flaw. ACKNOWLEDGMENT This research was s u p p o r t e d b y the U.S. D e p a r t m e n t o f E n e r g y u n d e r C o n t r a c t DE AC02-81ER10950. REFERENCES 1 J. E. Ritter, Jr., P. Strzepa, K. Jakus, L. Rosenfeld and K. J. Buckman, Erosion damage in glass and alumina, J. Am. Ceram. Soc., 67 (11) (1984) 769774. 2 S. M. Wiederhorn and B. J. Hockey, Effect of material parameters on the erosion resistance of brittle materials, J. Mater. Sci., 18 (1983) 766 780. 3 M. E. Gulden, Solid particle erosion of high technology (Si3N4, glass-bonded A1203, and MgF2). In W. F. Adler (ed.), Erosion: Prevention and Useful Application, in A S T M Spec. Tech. Publ. 664, 1979, pp. 101-122. 4 T. H. Kosel, R. O. Scattergood and A. P. L. Turner, An electron microscope study of erosion wear. In K. C. Ludema, W. A. Glaeser and S. K. Rhee (eds.), Proc. Int. Conf. on the Wear o f Materials, Dearborn, MI, April 1979, American Society of Mechanical Engineers, New York, 1979, pp. 192-204. 5 J. B. Wachtman, Jr., W. Capps and J. Mandel, Biaxial flexure tests of ceramic substrates, J. Mater., 7 (2) (1972) 188-194. 6 D. K. Shetty, A. R. Rosenficld, P. McGuide, G. K. Bansal and W. H. Duckworth, Biaxial flexure tests for ceramics, Am. Ceram. Soc., Bull., 59 (12) (1980) 1193-1197. 7 D. B. Marshall, A. G. Evans, M. E. Gulden, J. L. Routbort and R. O. Scattergood, Particle size distribution effects on solid particle erosion in brittle materials, Wear, 71 (1981)363 373. 8 F. I. Barratta, Refinement of stress intensity factor estimates for a peripherally cracked spherical void and a hemispherical surface pit, J. Am. Ceram. Soc., 64 (1) (1981) C-3-C-4. 9 B. R. Lawn, S. W. Freiman, T. L. Baker, D. D. Cobb and A. G. Gonzales, Study of microstructural effects in the strength of alumina using controlled flaws, J. Am. Ceram. Soc., 67 (4) (1984) C-67C-68.