Cyclic Fatigue of Brittle Materials with an Indentation-Induced Flaw System

10 Pages·1996·0.56 MB·English

by  Choi, Sung R.

-,Q
_r_//_ _ _ # _/_ _ _
NASA-TM-I12475
Reprinted from
Materials Science and Engineering A208 (1996) 126-130
Cyclic fatigue of brittle materials with an indentation-induced
flaw system
Sung R. Choi a'', Jonathan A. Salem b
aCleveland State University, Cleveland, OH 44115, USA
bNASA Lewis Research Center, Cleveland, OH 44135, USA
Received 1May 1995; in revised form 10October 1995
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ELSEV|ER Materials Science and Engineering A208 [19961126 131)
Cyclic fatigue of brittle materials with an indentation-induced
flaw system
Sung R. Choi a'*, Jonathan A. Salem b
"('h'vehmd State University, Ch'lehmd, OH 44115, USA
hN,4SALe_is Research ('enter, ('leleland. OH 44135, USA
Received I May 1995;in revised form 10October 1995
Abstract
The ratio of static to cyclic fatigue life, or 'h ratio', was obtained numerically for an indentation flaw system subjected to
sinusoidal loading conditions. Emphasis was placed on developing a simple, quick lifetime prediction tool. The solution for the
h ratio was compared with experimental static and cyclic fatigue data obtained from as-indented 96wt.% alumina specimens tested
in room-temperature distilled water.
Keywords:Cyclic fatigue; Static fatigue; Indentation-induced flaw:,Ceramics
I. Introduction The purpose of this study is to analyze cyclic fatigue
of the indentation flaw system under sinusoidal loading
For glass and ceramic materials which have slow crack conditions so that lifetime prediction from one fatigue
growth (stress corrosion) as the unique, time-dependent condition to another is readily feasible. For this purpose,
failure mechanism, it is possible to predict the fatigue life the complete solution of the ratio of static to cyclic
under one loading condition from another. Prediction of fatigue life was obtained numerically in conjunction with
cyclic fatigue lifetime from static lifetime for Griffith flaw fatigue parameter (n) and stress ratio iR ratio). The
system can be done analytically by using the ratio of solution was compared with experimental data that were
static fatigue to cyclic fatigue life, introduced by Evans obtained from static and cyclic fatigue testing of indented
and Fuller [1]. In the case of the indentation flaw system, alumina specimens in room-temperature distilled water.
the solution requires a numerical approach since an The analysis was carried out for material exhibiting a flat
additional driving force appears in the net stress intensity R curve and a power-law crack propagation as a delayed
factor. This term is attributed to residual contact stress failure mechanism.
produced by the elastic/plastic deformation of indenta-
tion [2]. Analyses of dynamic and static fatigue of the
2. Analysis
indentation flaw system were carried out previously for
both postthreshold [3,4] and subthreshold [5] indentation
In many cases slow crack growth of glass and ceramic
flaws. However, no general solution for the cyclic fatigue
materials under Mode I loading conditions is described
of such a flaw system has been found, although some
by the following empirical, power-law relation [4]
cyclic fatigue data on ceramic specimens containing
indentation cracks exist [6 9]. da A_ K, ]" (I)
t_= d7= LK,,,]
where v, a, and t are crack velocity, crack size, and time,
*Corresponding author. Addresscorrespondence to: NASA Senior
Resident Research Associate, Lewis Research ('enter, Cleveland, OH respectively. A and n are the fatigue parameters which
44135, USA. depend on material and environment. K_ is the
0921-5093/96,:'$15.00,*_.1996 Elsevier Science S.A. Allrights reserved
SSDI 0921-5093(95)10068-7

S.R. Choi, J.A. Salem _'Materials Science and Engineering A208 (1996) 126 130 127
Mode I stress intensity factor, and Kw is the Mode I .... I ...... I
critical stress intensity factor or fracture toughness of the
R=IO
material with a flat R curve.
2.1. Natural flaws
0
In static fatigue testing a constant applied stress (a) is
employed. Noting that n > 10 for most glass and ceram-
ics, one can derive the following static fatigue equation
[10l 0.1
tfs= B S_' 2or " (2)
where tfs is the time to failure, S, is the inert strength, and (S[NUSOIDAL WAVE) _'_
I /
B is the parameter associated with fracture toughness, lO 100
crack geometry and fatigue parameters.
FATIGUE PARAMETER, n
In cyclic fatigue testing a time-varying, periodic stress
(a(t)) is applied. The time to failure (trc) in cyclic fatigue Fig. I. Numerical solution of the h ratio as a function of fatigue
parameter (n) for different levels of R ratios with the natural flaw
can be expressed as [1]
system. Each line represents a best-fit regression line.
!
.... (3)
is possible to obtain an approximate (but accurate)
lfc = BSi 20 max_1 [f(t)]" dt
relation between log h and log n for a given R ratio by
T
using the regression analysis
where ar,ax is the maximum applied stress, f(t) is a
periodic function defined as a(t) = O'marf(,/) with a range log h = c_log n + fl (6)
of 0<f(t) < 1, and r is the period. The ratio of static
where _ and fl are the regression coefficients.
fatigue to cyclic fatigue life, h, with a condition of a in
Table 1shows the regression coefficients _ and ft. For
static loading equal to O'maxin cyclic loading (a = O'max)
n> 10, the maximum error in h ratio, as compared with
can be obtained from Eqs. (2) and (3)
the exact solution, was 1.0% for R = 0 to 0.7, and 4.5 %
h- tfs -- 1 ['_ [f(t)]" dt (4) for R = 0.8 to 0.9. Therefore, the table gives a convenient
and accurate means of determining the h ratio for a
/re r Jo
natural flaw system for any given value of n, either integer
Sinusoidal loading is the most common and popular
or real. The complication of a lack of a simple analytical
wave form used in cyclic fatigue testing. The periodic
solution to Eq. (5) for real numbers can be eliminated
function fit) for a sinusoidal wave is expressed as
with Eq. (6) and Table 1.
f(t) = [(1 + R)/2 + [(1 - R)/2]sincot], where R isthe stress
(or load) ratio, defined as R = amin/_rmax with amin being
2.2. Indentation flaws
the minimum applied stress, coisthe angular velocity. Eq.
(4) can be solved either analytically or numerically for Because of the residual contact stress produced by
the sinusoidal wave. The h ratio for any other periodic elastic/plastic indentation deformation [2], an addi-
loading wave form such as trapezoidal, triangular or
square can be solved analytically with a straightforward Table 1
procedure [1,11]. Eq. (4) was solved analytically for a Regression coefficients of the h ratio (Eq. (6)) for natural and
sinusoidal wave by using the series expansion technique indentation flaw systems
of Evans and Fuller [1]. Their analytical solution is
Natural flaws Indentation flaws
expressed as
...2. [ n, 1F 1-R 12k(l+R']"
h=k_oL(n-2_)!(k!)2JLZ(l-+--Ri j \-5--/ (5)
0.0 - 0.4939 - 0.2607 --
0.1 -0.4955 -0.2348 -0.4856 -0.1925
Eq. (5) is still complicated to solve and valid only for
0.2 -0.4976 -0.2051 -0.4885 -0.1612
integer values of n. Therefore, it is desirable to solve Eq.
0.3 -0.5005 -0.1703 -0.4925 -0.1240
(4) numerically to cover any integer or real value of n for 0.4 -0.5049 -0.1282 -0.4977 -0.0804
a full range of R = 0-1.0, even though some limited data 0.5 -0.5112 -0.0765 -0.5049 -0.0268
on the h ratio exist [1,12]. 0.6 -0.5195 -0.0115 -0.5126 -0.0383
0.7 -0.5291 0.0705 -0.5198 0.1172
Fig. 1 shows the results of the numerical solution of
0.8 -0.5353 0.1743 -0.5173 0.2075
Eq. (4) as a function of n for R ratios from R = 0 to 0.9 -0.5138 0.2977 -0.4743 0.2932
R = 1.0. If log h is treated as a linear function of log n, 1.0 0.0000 0.0000 0.0000 0.0000
coefficients of correlation of rcoer> 0.9966 result. Thus it
128
S.R. Choi, J.A. Salem / Materials Science and Engineering A208 (1996) 126 130
tional term appears in the net stress intensity factor and 10e
^S-I.DE.Ti':D 80''do '
an analytical solution of cyclic fatigue for the indenta-
._ 107 CRACKS 40 , 4
tion flaw system is not feasible. The solution needs to
be done via numerical methods, as done previously for " 106 20 ',
both dynamic and static fatigue analyses involving in- 105 10 -I
dentation fracture mechanics [3,4]. As in the previous
04 .._. ":. \ '
studies [3,5], normalized variables are introduced here ...... ",'::.. %,. ,,
I n=5 -.L.:.L.:.:.... "%:_.., '"%,
as follows:
¢_ 102
r_
K*= --K,'l J = -A-t; or*-- O'ma x," C*=-- (./ (7)
KIc am o"m am 101
=¢ 10° (cS,mtcuUeSOFI,Dla_owu,_v.E) q
where K*, J, a* and C* are, respectively, normalized 0 --R= !.O(R'rAI"IC)
z 10 -1 ..... R=o.s
stress intensity factor, normalized time, normalized
........R..-0.1 I
10 -2 , , , , , , ,, I
maximum applied stress and normalized crack size. o-m
0.1 0.3 0.50 1
and am are, respectively, the strength and critical crack
NORMALIZED MAX APPLIED STRESS, o
size in the inert condition. Using these variables, the
crack growth rate of Eq. (1) and net stress intensity Fig. 2. Typical example of numerically obtained normalized failure
factor are expressed as follows: time (Jr) as a function of normalized maximum applied stress (o-*) for
three different R ratios of R=0.1, 0.5 and 1.0 for the indentation
dC* flaw system.
dJ - [K*]"
3 , , I C, 32 which reduces to the relationship in static fatigue of
K* = _oC + _ (8) indentation cracks [4]. This indicates that the relation-
ship between the true (n) and apparent (n') fatigue
, [-1 + R +--1--5-Rsln__)j o'* parameters is independent of R ratio.
Based on the results as shown in Fig. 2, the h ratio
Note that the normalized net stress intensity factor was determined for a given R using the relation h= Jfj
consists of two terms: the first is a function of the Jfc ( = tf_/t,O, where J,-_and Jfc are the normalized time
remote applied stress and the second is related to the to failure corresponding to static and cyclic fatigue,
residual contact stress [2,3]. The differential form of Eq. respectively. Fig. 3 shows a summary of the h ratio as
(8) was solved numerically using a fourth-order a function of n for R ratios from R = 0.1 to R = 1.0,
Runge-Kutta method. The initial condition was C* = where log h was plotted against log n as for the natural
0.3967 at J=0 and the instability conditions were flaw system (Fig. 1). Again the excellent coefficients of
K* = 1 and dK*/dC* > 0. The solution was initiated to correlation of rco_r->0.9911 allow one to obtain a rela-
determine the normalized time to failure (Jr) as a func- tionship based on Eq. (6). The results of such regression
tion of normalized maximum applied stress for the analysis for _ and fl are shown in Table 1. The maxi-
selected values of n = 5-160. This procedure was con-
tinued for the range of stress ratios from R = 0.! to 1.0.
Since the solution is independent of frequency Or) as ' ' ' '1 ' .... I
long as _am/A > 2_zf, any particular values of _am/A R=I.O
satisfying ¢Oam/A _>2_ can be chosen. A value of (Oam/ 1
A = 100 was used in this analysis.
Fig. 2 shows a typical example of the normalized
time to failure as a function of normalized maximum o
applied stress for stress ratios of R = 1.0, 0.5 and 0.1.
n,,
Fatigue susceptibility increases with increasing R ratio, .c
yielding a maximum at R = 1.0 (static fatigue). Note
0.1
that regardless of R ratio the curves converge to a* =
1.0, in which the inert strength with no slow crack
AS-INDENTED CRACKS "_
growth is defined. Similar to the previous static fatigue
- (SINUSOIDAL WAVE)
analysis [4], the slope in Fig. 2 is not representative of
i ,A[ ..... f
a 'true' fatigue parameter of n, due to the effect of 10 100
residual contact stress. The slope in Fig. 2, which is
FATIGUE PARAMETER, n
called 'apparent' fatigue parameter (n'), was found to
have the following approximate relation Fig. 3. Numerical solution of the h ratio as a function of fatigue
parameter (n) for different R ratios with the indentation flaw system.
n = 4/3n' - 2/3 (9) Each line represents a best-fit regression line.
S.R. Choi, J.A. Sah'm .;Materials Science and Engineering A208 (1996) 126 130 129
mum error associated in the h ratio was observed to be 107 ' I '
967. ALUMINA
about 4%, occurring at R=0.9 for n> 10. Hence, 106 _ (as-indented;
lifetime prediction of an indentation flaw system with one 'W RT water)
fatigue loading condition can be done quickly and 105 Static
accurately from another by using Eq. (6) in conjunction
104 n'=35.4
with Table 1.
,..1 103
2.3. Evaluation oJfittigue parameters Jor indentation n'=32.9 _ Cyclic
o 102
f[LIWS
• cyclic B
101 {3 static O
The "true" fatigue parameter n for both static and
[3
cyclic fatigue can be determined using Eq. (9) once the 100
"apparent" fatigue parameter n' is determined from the
10-1 , , , , I
slope of fatigue data. The fatigue parameter A in static 50 60 70 8090100 200 300
fatigue was determined previously [4]
(MAX) APPLIED STRESS, (7[MPa]
A = (2-_-']] _..a..,,zq1,-- (10)
t.') Fig. 4. Results of static and cyclic fatigue testing obtained from
indented 96 wt.% alumina flexure specimens tested in room-tempera-
where 5_[is the intercept of static fatigue data, expressed lure distilled water. The solid lines represent the best-ill lines in a plot
as tr_a'"= 2_. Since the following relation for the inden- of log t_vs. log a,,,,_.
tation flaw system holds
perature distilled water are depicted in Fig. 4. Consis-
Jl+ _ tf+ z"+o- ,,, -)-_=h (ll) tent with the results shown in Fig. 3, the alumina is
slightly more susceptible to fatigue in static loading
where 2'< is the intercept of cyclic fatigue data as
than in cyclic loading within the experimental range
trio-n.'... = z"_¢. Hence, from Eqs. (10) and (11), the parame-
used. The "apparent" fatigue parameter was obtained
ter A in cyclic fatigue is obtained
from the data as n' = 32.92_+ 6.01 and 35.37 +4.79,
t/2_'_12 ,, I respectively, for static and cyclic fatigue. The corre-
A = tp_7 ) O'm(/m _,ch (12) sponding "true" fatigue parameter was obtained from
Eq. (9) as n=43.23 _+8.01 and 46.49_+ 6.39, respec-
3. Experimental procedure tively, for static and cyclic fatigue• The prediction of
cyclic fatigue from static fatigue data can be done using
Static and cyclic fatigue tests of indented alumina (96 Eq. (6) together with Table 1.The prediction thus made
wt.%, ALSIMAG 614, General Electrical Ceramics)
is presented in Fig. 5, where the cyclic fatigue data
flexure specimens were carried out in room-temperature obtained from the experiments are included for com-
distilled water using a four-point bend fixture of 6.05 mm parison. The prediction somewhat overestimates (less
inner and 19.05 mm outer spans. The nominal dimen-
sions of the test specimens were 4 mm by 5 mm by 25
mm, respectively, in height, width, and length. The center 107
(5 mm side) of each specimen was indented in air for I 96X ALUMINA
about 20 s using a Vickers microhardness indenter 106 \_ (as-indented;
_, RTwater)
(Zwick, model 3212, Germany) with an indentation load
105 Best fit_ \\"_
of 49 N. Static fatigue testing was conducted by loading of .static \_'_ Best fitof
indented specimens in a lever-arm creep machine (ATS) _e_d 104 fahgue _-_"" cyclic fatigue
with constant stress levels of 95 to 133 MPa. Cyclic
103
fatigue testing of indented specimens was conducted by .<
i_. _ Predicted
sinusoidal loading with a stress ratio of R = 0.5 and a o 102
_ _".."_(from static.
A,'_ fatigue data)
frequency of f= 5 Hz with a servohydraulic testing
10 _
machine (|nstron, Model 8562). The maximum applied F • cyclic data
stress in cyclic fatigue ranged from 100 to 130 MPa. The 10 o
sinusoidal wave shape was frequently checked and ver-
10 -1 , _ _ , I
ified by a digital storage oscilloscope.
50 60 70 80 90100 200 300
(MAX) APPLIED STRESS, (7[MPa]
4. Results and discussion
Fig. 5. Prediction of cyclic fatigue lifetime from static fatigue data for
The results of the static and cyclic fatigue testing of indented 96 wt.% alumina specimens tested in room-temperature
the indented 96 wt.% alumina specimens in room-tem- distilled water.
130
S,R. Choi, J.A. Salem / Materials Science and Engineering A208 (1996) 126 130
than one order of magnitude) the actual cyclic time to compared with static and cyclic fatigue data obtained
failure. from indented 96 wt.% alumina specimens tested in
It has been reported that, for certain ceramic materi- room-temperature distilled water.
als, damage accumulation and/or fatigue synergisms
can be active in cyclic fatigue, resulting in more fatigue
susceptibility in cyclic than in static loading [8,13-16].
Acknowledgements
If such synergies exist or if creep at elevated tempera-
tures is simultaneous with cyclic fatigue, the analysis
The authors are grateful to R. Pawlik for the experi-
given in this paper may not be valid. However, the
mental work. This work was sponsored in part by the
analysis may still provide, by comparing with experi-
Ceramic Technology Project, DOE Office of Trans-
mental data and by using fractographic analysis, some
portation Technologies, under contract DE-AC05-
clues with which the prevailing mechanism associated
84OR21400 with Martin Marietta Energy System, Inc.
with failure can be pinpointed. It should be noted that
most of glass and ceramic materials under static fatigue
loading conditions in a room-temperature moisture en-
References
vironment are subjected to one failure mechanism,
stress corrosion. Therefore, in view of the reasonable
[1] A.G. Evans and E.R. Fuller, Crack propagation in ceramic
agreement between the static and cyclic fatigue data
materials under cyclic loading conditions, Metall. Trans., 5
shown here, it can be stated that stress corrosion is a
(1974) 27-33.
governing failure mechanism, either in static or in cyclic [2] B.R. Lawn, A.G. Evans and D.B. Marshall, Elastic/plastic in-
loading conditions. This is supported by the fact that dentation damage in ceramics: the median/radial crack system, J.
the material contains a large amount of glassy phase, Am. Ceram. Soc., 63 (1980) 574-581.
[3] B.R. Lawn, D.B. Marshall, G.R. Anstis and T.P. Dabbs, Fa-
which is highly susceptible to stress corrosion in an
tigue analysis of brittle materials using indentation flaws, Part I.
aqueous environment. The fatigue parameters for this
General theory, J. Mater. Sci., 16 (1981) 2846 2854.
material system, therefore, can be obtained by using [4] E.R. Fuller, B.R. Lawn and R.F. Cook, Theory of fatigue for
either static or cyclic fatigue testing. In terms of testing brittle flaws originating from residual stress concentrations, J.
economy, however, static fatigue is preferred because of Am. Ceram. Soe., 66 (1983) 314 321.
[5] S.R. Choi, J.E. Ritter and K. Jakus, Failure of glass with
the much higher testing costs associated with cyclic
subthreshold flaws, J. Am. Ceram. Soc., 73 (1990) 268-274.
fatigue testing.
[6] C.-K.J. Lin and D.F. Socie, Static and cyclic fatigue of alumina
As mentioned before, the analytical solution of the h at high temperatures, J. ,4m. Ceram. Soe., 74 (1991) 1511 1518.
ratio for other loading functions such as trapezoidal, [7] S. Lathabai, Y.-W. Mai and BR. Lawn, Cyclic fatigue behavior
triangular and square wave forms can be easily ob- of an alumina ceramic with crack-resistance characteristics, J.
Am. Ceram. Soc., 72 (1989) 1760 1763.
tained for the natural flaw system because of their
[8] S. Horibe and R. Hirahara, Cyclic fatigue of ceramic materials:
mathematical simplicity [1,11]. However, the conven-
influence of crack path and fatigue mechanisms, Acta Metall.
tional numerical solution for these loading functions Mater., 39 (1991) 1309-1317.
may not be simple for the indentation flaw system, [9] R.H. Dauskardt, R.R. James, J.R. Porter and R.O. Ritchie,
since the functions, unlike the sinusoidal wave, are not Cyclic fatigue-crack growth in SiC whisker-reinforced alumina
ceramic composite: long- and small-crack behavior, J. Am. Ce-
continuous but discontinuous in nature. In this case,
ram. Soc., 75 (1992) 759-771.
each discontinuous periodic function should be con-
[10] (a) J.E. Ritter, P.B. Oates, ER. Fuller and S.M. Wiederhorn,
verted into a continuous periodic function so that nu- Proof testing of ceramics, Part I Experiment, J. Mater. Sci., 15
merical solution is feasible. This may be done by using (1980) 2275-2281. (b) E.R. Fuller, S.M. Wiederhorn, J.E. Ritter
the Fourier analysis from which a discontinuous func- and P.B. Oates, Proof testing of ceramics, Part 2 Theory, J.
Mater. Sci., 15 (1980) 2282-2295.
tion can be approximated into a continuous function.
[11] J.A. Salem and S.R. Choi, Bimonthly Progress Report, April/
May 1994, Ceramic Technology Project, Oak Ridge National
Laboratory, Oak Ridge, TN.
[12] T. Kawakubo and K. Komeya, Static and cyclic fatigue behavior
4. Conclusions
of a sintered silicon nitride at room temperature, Metall. Trans.,
70 (1987) 400-405.
The ratio of static to cyclic fatigue life, or h ratio, [13] D.A. Krohn and D.P.H. Hasselman, Static and cyclic fatigue
behavior of a polycrystalline alumina, J. Am. Ceram. Soc., 55
was obtained numerically with an emphasis on the
(1972) 208-21 I.
indentation flaw system subjected to sinusoidal loading
[14] L. Ewart and S. Suresh, Crack propagation in ceramics under
conditions. The h ratio decreases with increasing n and cyclic loads, J. Mater. Sei. Lett., 22 (1987) 1173-1192.
decreasing R ratio. The solution provides a simple and [15] M.J. Reece, F. Guiu and M.F.R. Sammur, Cyclic fatigue crack
quick methodology to predict the lifetime of one fatigue propagation in alumina under direct tension-compression load-
ing, J. Am. Ceram. Soc., 72(1989) 348-352.
condition from another for indentation flaw systems (as
[16] R.H. Dauskardt, D.B. Marshall and R.O. Ritchie, Cyclic fa-
well as the natural flaw system) when the governing
tigue-crack propagation in magnesia-partially-stabilized zirconia
failure mechanism is stress corrosion. The solution was
ceramics, J. Am. Ceram. Soc., 73 (1990) 893-903.
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