Cyclic cracking resistance of brittle materials in compressive loading
Fatigue behavior of brittle materials under compression is considered. The findings should be taken into account in the failure probability assessment of components made of materials with limited
 plasticity, which are used in various stress states. Исследованы закономерности усталостного ра...
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Інститут проблем міцності ім. Г.С. Писаренко НАН України
2009
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| Cite this: | Cyclic cracking resistance of brittle materials in compressive loading / A.G. Lanin // Проблемы прочности. — 2009. — № 1. — С. 83-87. — Бібліогр.: 5 назв. — англ. |
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| citation_txt | Cyclic cracking resistance of brittle materials in compressive loading / A.G. Lanin // Проблемы прочности. — 2009. — № 1. — С. 83-87. — Бібліогр.: 5 назв. — англ. |
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| description | Fatigue behavior of brittle materials under compression is considered. The findings should be taken into account in the failure probability assessment of components made of materials with limited
plasticity, which are used in various stress states.
Исследованы закономерности усталостного разрушения хрупких материалов в условиях циклического сжатия. Показано, что полученные результаты следует учитывать при оценке вероятности разрушения конструкционных элементов из материалов с ограниченным ресурсом пластичности при различных напряженных состояниях.
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| first_indexed | 2025-12-07T17:39:46Z |
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UDC 539.4
Cyclic Cracking Resistance of Brittle Materials in Compressive Loading
A. G. L an in
Scientific Institute “Luch,” Podolsk, Russia
Fatigue behavior o f brittle materials under compression is considered. The findings should be taken
into account in the failure probability assessment o f components made o f materials with limited
plasticity, which are used in various stress states.
K e y w o r d s : brittle material, compressive loading, fatigue behavior, cyclic cracking
resistance.
Fatigue o f brittle materials (interstitial phases, oxides, intermetallic
compounds, graphite, etc.) produced m ainly by powder m etallurgy methods, has
been examined far less extensively than that o f metals. The absence o f m acro
plastic deformation in powder metallurgy materials in a wide tem perature range
(in m any cases, up to 0.5-0.8 o f the m elting point [1-3]) limits the extent of
manifestation o f fatigue processes and stresses in the vicinity o f the static strength
[2]. In some experiments [3], the fatigue effect was not recorded at all (specimens
o f brittle materials either failed in the first load cycle or did not fail at all over a
given test time); therefore, it appears that m echanical fatigue does not take place,
and this impression is enhanced by the fact that in some materials (aluminum
oxide [1], silicon nitride) fatigue failure is associated with stress corrosion.
A t the same time, comparative tests on brittle m aterials under long-term
static and cyclic loading, including tests in a highly corrosive atmosphere, e.g.,
tests on alumina, have revealed inherent fatigue processes caused by cyclic
loading. It is evident that the process o f fatigue failure o f brittle m aterials results
from the phenom enon o f inelastic and highly localized deformation [2 ], and the
intensity o f this deformation governs the m icrocrack growth rate in the material.
In the m ajority o f cases, the data on the crack growth rate in brittle materials
were obtained in long-term loading o f specimens o f double cantilever type [2 ].
These data are represented in the form o f a kinetic fatigue failure diagram in the
coordinates o f crack growth rate vs. stress intensity factor (SIF). The reports on
fatigue behavior under other types o f loading, e.g., under compressive loading
which is encountered m ost often in structures made o f pow der metallurgy
materials, are few in number.
The procedure o f constructing a kinetic fatigue failure diagram (KFFD) is
based on the m ethod o f determ ination o f cracking resistance in uniaxial
com pressive loading, which is described in detail in [4].
The experimental data obtained in testing organic silicate glass, graphite, and
zirconium carbide show that compression fracture is o f kinetic nature [5]. The
tests were conducted on flat specimens m easuring 20 X 30 X 4 mm with a central
straight initial crack o f length 2L (2L = 2 -3 mm), positioned at an angle to the
compressive loading axis at a distance d from each other. The growth and
interaction o f cracks in brittle solids under compressive stress state are shown
© A. G. LANIN, 2009
ISSN 0556-171X. Проблемы прочности, 2009, № 1 83
A. G. Lanin
(Fig. 1). From the fracture mechanics standpoint, this process consists o f three
conventional stages occurring successively with increasing compressive load. The
first stage is represented by the equilibrium propagation o f single cracks that
initiate at defects in the m aterial and do not interact with one another. The crack
starts at a critical stress coefficient depending on its initial length and orientation.
It follows a curvilinear trajectory approaching asymptotically the compressive
loading axis. The m inim um stress o required for the propagation o f the most
unfavorably oriented defects (at an angle o f 30-45° to the compressive loading
axis) is 2 .5-4 times higher than the stress o t for loading o f an initial crack
perpendicular to the tensile loading axis. Subsequent damage accumulation is
associated w ith the development o f a system o f interacting cracks, where the
paired or multiple interactions between adjacent cracks (the intensity o f these
interactions increasing continuously) m ay lead to a qualitative change in the
nature o f their propagation, i.e., from equilibrium to unstable when the relative
distance X = d /2 L decreases to a critical value. The final stage o f fracture
becomes possible during the increased loading after certain multiple interactions
o f the cracks evolved in equilibrium, and at increased driving stress intensity with
highly unstable crack growth. The load corresponding to fragmentation o f the
solid material is several times greater than the load at w hich the first macrocracks
started to develop.
o?/
15
10
5
0
n.:.' n..'f) n.y.' :.() i/ l
Fig. 1. Fracture diagrams for a system of parallel cracks: (1) X =«>; (2) X = 3; (3) X = 2 (solid lines
3 = 30°, dashed lines j3 = 45°).
Figure 2 shows schematically the sequence o f tests perform ed in air at 20° C
and the variation o f crack growth conditions in a specimen under cyclic
deformation. The specimen w ith an initial notch l о was statically loaded to a
stress triggering the crack propagation from the notch tip. A t that instant, the SIF
reached the critical value K lc and, consequently, the crack “jum ped” and then
stopped as a result o f SIF decreasing to K la which characterizes the crack
inhibition condition in single-cycle loading. Subsequently, the specimen was
subjected to cyclic deformation w ith a constant stress amplitude о co at a stress
ratio equal to zero and w ith a frequency o f approximately 0.1 Hz. This was
accompanied by the fatigue crack growth with the rate slowing down due to the
84 ISSN 0556-171X. Проблемы прочности, 2009, N 1
Cyclic Cracking Resistance o f Brittle Materials
reduction o f the SIF amplitude. For a non-zero cycle, the SIF amplitude was equal
to the m aximum SIF value o f the cycle, i.e., AK i = K imax = K i. _3
W hen the fatigue crack growth rate reached approximately 10 mm/cycles
(the condition o f the acceptable test time), the testing at the stress amplitude o co
was interrupted and the specimen with the fatigue crack length l was statically
loaded to a stress o ci whereby the SIF again reached K ic and the crack that had
completed the “jum p” was arrested. Further cyclic deformation was carried out in
the same m anner w ith the stress amplitude o ci, and so on.
Fig. 2. Sequence of tests and variation of the crack growth conditions during cyclic loading with
uniaxial compression.
To determine the SIF amplitude K i = Y f (o ) 4 l ,the K -calibration o f the Y ( l )
function for each specimen was represented by a dashed line (the dashed line in
Fig. 2) in the fracture diagram in the o-vs.-l/lo coordinates. The inflection points
o f this line correspond to the experimentally determined critical stresses o ci and
crack length l t in the specimen under static loading. Instead o f the absolute value
o f K i, we determined the ratio K i / K Ic ( l iJ-).
The functional relationship between the crack growth rate and the SIF
amplitude was set to be d l / d N = a ( K l / K Ic) n , where a and n are the
phenom enological parameters determined by the present method. Then, the
equation was brought to the form ln ( d l / d N ) = l n a + n ln(K I / K Ic).
Analysis o f test results in the high-amplitude region shows that the log(d l / d N )-
vs.-log(K i / K i c ) functions exhibit a sharp inflection o f K i similar to K i c and
approximating the arithmetic m ean value o f K Ia . It is therefore useful to split the
high-amplitude region o f KFFD into two stages: (i) intensified crack growth at
K I < K Ia , and (ii) cyclic final fracture at K i > K ia .The parameters n and a for
these two stages o f the high-amplitude region, w hich are determined during the
processing o f experimental data, differ greatly.
ISSN 0556-171X. npoôëeMbi npounocmu, 2009, N 1 85
A. G. Lanin
A t the stage o f cyclic final fracture, the value o f param eter n for all the
materials, except for beryllium, is very high (up to 90) in comparison with
n = 1-11 for metals [10]. In fact, in the double logarithmic coordinates this
section o f KFFD degenerates into a vertical straight line: w ith increasing K i the
crack growth rate rapidly increases to a limiting value at K i = K lc .A t the stage
o f intensified crack growth, the value o f n for all the materials, with the
exception o f alumina, steeply decreases and does not exceed 9.5. The param eter a
in transition from the stage o f cyclic final fracture to the stage o f intensified crack
growth decreases as well. Thus, the parameters n and a greatly depend on the
SIF amplitude.
A special feature o f fatigue failure o f ceramic m aterials is that their high
defectiveness and structural heterogeneity together with the limited capacity for
local stress relaxation result in noticeable time and geometrical nonuniform ity of
crack propagation. The crack grows by jum ps due to processes o f microplastic
deformation after a specific num ber o f cycles, which depends on K I . The fact
that the KFFD o f ceramic materials contains the stage o f cyclic final fracture
characterized by the high value o f param eter n causes the fatigue crack growth
rate in the m edium-amplitude region to extremely slow down (at K l / K lc = 0.5 it
is no higher than 2 - 1 0 6 m m /cycles), Fig. 3, and be difficult to record
experim entally even for the fairly ductile beryllium.
log(d//d N ), mm/cycles
Fig. 3. Kinetic fatigue failure diagrams of structural materials for K i / K ic > 0.6: (1) ZrC; (2, 10) Be;
(5) A12O3; (4) GMR graphite; (5) ARV graphite; (6) ZrC + C; (7) aluminum 2024-T6; (8) steel 310;
(9) steel 301; (11) graphite.
The quantitative agreement between the present findings and the data
obtained on the W OL-type specimens and double cantilever beam indicates that
the fracture mechanisms under compression, tension, and bending conditions are
similar in nature. However, the crack propagation kinetics in cyclic compressive
86 ISSN 0556-171X. npo6n.eMH npounocmu, 2009, N 1
Cyclic Cracking Resistance o f Brittle Materials
loading have a num ber o f special features attributable m ainly to the fact that the
value o f K i decreases with increasing crack length. Consequently, the stress
variation rate becomes comparable to the low rate o f relaxation o f local stresses;
the probability o f local deformation occurring and accumulating in the defective
volume o f a m aterial increases, thus ensuring the equilibrium subcritical
(K i < K ic ) crack growth. The resultant residual tensile stresses during unloading
add up with the stresses resulting from the applied load, and in subsequent
loading cycles these residual stresses m ay also support subcritical crack growth.
I f d K 1 1 d l > 0 , the stress relaxation rate is considerably lower than the stress
growth rate and the fatigue effect m ay not take place.
The results should be taken into account during the assessment o f failure
probability for components m ade o f materials w ith lim ited plasticity, w hich are
used in various stress states. i t is evident that the m ethod o f cyclic compressive
loading makes it possible to determine more accurately the relationships governing
the fatigue failure o f low-ductility materials in the case o f changes o f the
structural parameters and chemical composition.
1. R. A. Andrievskii, A. G. Lanin, and G. A. Rymashevsky, S tre n g th o f
R e fr a c to r y C o m p o u n d s [in Russian], M etallurgiya, M oscow (1974).
2. A. G. Lanin, S tre n g th a n d T h e rm a l S tr e s s R e s is ta n c e o f S tr u c tu r a l C e ra m ic
[in Russian], M oscow State Engineering Physics Institute, M oscow (1998).
3. A. G. Lanin and I. I. Fedik, T h e rm a l S tr e s s R e s is ta n c e o f M a te r ia ls [in
Russian], Podolsk (2005).
4. A. G. Lanin, V. A. Sokolov, and N. A. Bochkov, “Determ ination o f crack
resistance o f brittle m aterials,” S tre n g th M a te r . , 16, No. 2, 161-165 (1984).
5. A. G. Lanin, N. A. Bochkov, V. S. Egorov, and B. A. Sokolov, “Brittle
fracture o f materials in compression,” Ib id , 17, No. 9, 1274-1281 (1986).
Received 11. 06. 2008
ISSN 0556-171X. npoöneMbi npoHHocmu, 2009, № 1 87
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| id | nasplib_isofts_kiev_ua-123456789-48472 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0556-171X |
| language | English |
| last_indexed | 2025-12-07T17:39:46Z |
| publishDate | 2009 |
| publisher | Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| record_format | dspace |
| spelling | Lanin, A.G. 2013-08-20T04:02:29Z 2013-08-20T04:02:29Z 2009 Cyclic cracking resistance of brittle materials in compressive loading / A.G. Lanin // Проблемы прочности. — 2009. — № 1. — С. 83-87. — Бібліогр.: 5 назв. — англ. 0556-171X https://nasplib.isofts.kiev.ua/handle/123456789/48472 539.4 Fatigue behavior of brittle materials under compression is considered. The findings should be taken into account in the failure probability assessment of components made of materials with limited
 plasticity, which are used in various stress states. Исследованы закономерности усталостного разрушения хрупких материалов в условиях циклического сжатия. Показано, что полученные результаты следует учитывать при оценке вероятности разрушения конструкционных элементов из материалов с ограниченным ресурсом пластичности при различных напряженных состояниях. en Інститут проблем міцності ім. Г.С. Писаренко НАН України Проблемы прочности Научно-технический раздел Cyclic cracking resistance of brittle materials in compressive loading Циклическая трещиностойкость хрупких материалов при нагружении сжатием Article published earlier |
| spellingShingle | Cyclic cracking resistance of brittle materials in compressive loading Lanin, A.G. Научно-технический раздел |
| title | Cyclic cracking resistance of brittle materials in compressive loading |
| title_alt | Циклическая трещиностойкость хрупких материалов при нагружении сжатием |
| title_full | Cyclic cracking resistance of brittle materials in compressive loading |
| title_fullStr | Cyclic cracking resistance of brittle materials in compressive loading |
| title_full_unstemmed | Cyclic cracking resistance of brittle materials in compressive loading |
| title_short | Cyclic cracking resistance of brittle materials in compressive loading |
| title_sort | cyclic cracking resistance of brittle materials in compressive loading |
| topic | Научно-технический раздел |
| topic_facet | Научно-технический раздел |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/48472 |
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