M.A.H. Donners et al.: Adsorption and kinetic effects on crack growth in MnZn ferrites
assuming that the test geometry factors, gS and g, are
called E 42 cores.2 The nominal composition was
71.0 wt% Fe2O3, 20.5 wt% MnO, and 8.5 wt% ZnO. The
nominal grain size, as determined from the mean inter-
cept length, was 7.3 m while the density was 4.8 g/cm3,
corresponding to a relative density of 94%. For the ex-
periments, bars of 3.5 × 4.5 × 42 mm3 without a chamfer
were used. The notches were cut to a depth of 15% of the
specimen height, in one to three passes, using a diamond
saw blade with a width of 100 m. Further material de-
tails are given in Ref. 2.
about equal. If this ratio is a constant for all combinations
of humidity and loading rate, this means that the suscep-
tibility to the effects of humidity is a property of the
material, independent from the type or geometry of de-
fect or specimen. It also implies that the effect of humid-
ity, whether subcritical crack growth, or an adsorption
effect, or a combination of both, manifests itself in the
same way in both strength and SENB fracture toughness
tests, making the latter appropriate to characterize the
effects of humidity on crack growth.
As the stress applied at the notch must be known as
exactly as possible, a four-point test jig with inner and
outer spans of 15 and 36 mm, respectively, was used.
Typically, five specimens were used for testing. The hu-
midity in the test chamber is set by flushing the chamber
surrounding the specimen with dry nitrogen gas or with
humidified air. Alternatively, the test is conducted with
the bar submerged in water. After this, the bar is loaded
with a loading rate of 0.2, 2, or 20 mm min−1, corre-
sponding to 2.3, 26.3, and 275 N s−1, respectively, as was
determined experimentally. After the test, the dimensions
of the bar and the notch were measured using an elec-
tronic micrometer and an optical microscope equipped
with a measuring ocular. The tested bars were subse-
quently subjected to a fractographical analysis to deter-
mine whether they failed “regularly” (i.e., no failure
initiation from pores or other defects on the notch tip).
One series of tests was performed on a four-point bend-
ing test machine, mounted in the vacuum chamber of a
scanning electron microscope (SEM) at a pressure equal
to or lower than 7 × 10−4 Pa, with a loading rate of
9.6 N s−1.
V. ANALYSIS OF DOUBLE TORSION TESTS
In Eq. (46) F denotes the force, h and hn the thickness
and thickness in the groove, w and wm the width of the
specimen and loading span, and Poisson’s ratio ( ס
0.30). The stress intensity of a double torsion (DT) speci-
men is given by10
3
KI = Fwm
,
(46)
ͱ
wh3hn 1 − ͒ ͒
͑
͑
correcting for finite beam thickness with a factor ().
The parameter is given by
2h
=
.
(47)
w
For values of smaller than 1 (square cross section of the
beams), can be approximated by11
ր
͒ = 1 − 0.6302 + 1.20 и e−
,
(48)
͑
with an accuracy of better than 0.1%. Note that the stress
intensity is independent of the crack length. In practice
this only applies in the mid 60% to 70% of the specimen
length.11–13
B. Double torsion experiments
The fracture toughness can be measured by applying a
force causing direct catastrophic fracture, Ff.13–15 If the
initial crack length is sufficiently long, the crack can
grow subcritically, without any influence of the crack
length on the stress intensity. Only the chemical activity
of the reactive species will influence the fracture tough-
ness. In the absence of region II, diffusion limitation to
SCG can be neglected. Therefore, in fact, the adsorption-
Double torsion (DT) specimens measuring nominally
15 × 42 mm2 with a thickness of either 1 or 2 mm were
used. The test jig had three lower bearing points, two
at the line of loading and one support point near the
end of the specimen. A spacer was used for positioning
the specimen on the jig. After applying a small preload
to fixate the specimen, the spacer was removed from
the specimen. The desired test atmosphere humidity
was then set by flushing with dry nitrogen or humidi-
fied air. To measure the fracture toughness, DT speci-
mens of 1 mm thickness were used with a starting notch
length of 14 mm, to ensure that the crack tip, whether the
crack grows subcritically or not, is located in the mid
60% of the specimen length. The specimen was posi-
tioned and preloaded and the humidity was set, as de-
scribed above. Then, the specimen was loaded with a
constant load rate of 0.2 mm min−1. This low loading rate
was chosen to make sure that if subcritical crack growth
would occur, the humidity at the crack tip would remain
constant, at the same value as in the environment.
ˆ
controlled fracture toughness, KIc, is determined by this
method as a function of the environmental humidity, in-
˜
stead of the inert fracture toughness, KIc. This modifies
Eq. (46) to
3
ˆ
KIc = Ffwm
.
(49)
ͱ
wh3hn 1 − ͒ ͒
͑
͑
VI. EXPERIMENTAL PROCEDURES
A. Fracture toughness tests
The experiments were performed on two types of
MnZn ferrite, labeled type 2 and type 4,2 made using
standard mixed-oxide processing and resulting in so-
1382
J. Mater. Res., Vol. 15, No. 6, Jun 2000
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