FRACTOGRAPHIC ANALYSIS OF CONDITIONS LEADING TO
THE CRACK FORMATION DURING THE INDENTATION
LOADING
Horváthová, J., Olejníčková, L., Jonšta, Z., Mazanec, K.
Institute of Materials Engineering, TU Ostrava, Czech Republic
Abstract
The contribution is devoted to the indentation fracture toughness evaluation of technical
ceramics (Si3N4, Al2O3). The evaluation of fracture toughness was realised by use of
method developed by Liang et al., which is not dependent on type of formed cracks. The
study is also devoted to the evaluation of indentation fatigue characteristics. The
mechanism of lateral crack initiation and its influence on fatigue durability are presented.
The importance of chipping formation by repeated loading is analysed. The ceramography
of investigated ceramic material is included in this contribution using a special etching
technique.
Keywords: indentation fracture toughness, indentation fatigue, ceramographic analysis,
lateral crack, chipping formation
Introduction
In recent years, the indentation techniques have found a broad application field for testing
of ceramic materials. It is a consequence like of deeper knowledge elaboration concerning
the behaviour of brittle (ceramic) materials in the vicinity of indent, like of broader ceramic
material application and the necessity to determine its quality level as possible in the
highest degree. Indentation techniques are applied to the finding, besides hardness values,
fracture toughness and fracture surface energy in larger temperature range. The indentation
creep and fatigue response are also evaluated successfully [1,2]. Before the presentation of
some basic aspects detected by the evaluation of indentation fracture toughness and
indentation fatigue (repeated loading) response, the analysis of chosen aspects of modelling
by the indentation crack formation will be carried out.
The advantages of indentation techniques are obvious, the needed equipment is available in
many laboratories using small testing specimens [3,4].
Crack formation around the Vickers indent in ceramic (brittle) material
This part of our contribution is devoted to the description of process realised during the
indentation loading. As mentioned above, the analysis is made with the aim to elucidate the
physical conditions influencing the response of ceramic materials to indentation loading in
detail. In this connection, Vickers sharp indenter is used. This indenter has an angle
between pyramidal edges of -2-. The section across the Vickers indentation, including the
indentation cavity and crack system initiated in its vicinity, is presented in Fig. 1 [2].
Pr
Plastic zone
aa
c
Radial crack
Lateral crack
b
l
l
Trace of median
crack front
Edge view of
median crack
Indentation
impression
Fig. 1: Schematic representation of the indentation impression and crack system produced
by Vickers indenter
The knowledge of the indent diagonal length, indicated -2a- in connection with the -angle value makes possible to determine the volume of ceramic material -V- which is
displaced during the course of indent cavity formation.
2
V   a 3  cot 
(1)
3
This volume is accommodated by the plastic deformation realised in narrow plastic zone
situated around the considered indentation cavity. It is supposed that this zone is
hemispherical with the radius -b-. To maintain the constant volume of material displaced by
the formation of indentation cavity, the plastic zone is compressed elastically. The residual
force -Pr- acting outwards in opposite direction to the indentation loading is induced at the
free surface. Simultaneously, the residual forces -Pm- induced beneath the plastic zone
produce tensile stresses there. The maximum values of -Pr- and -Pm- indicated as -Pr0- and
-Pm0-, respectively, are found at the stage of full indenter load -P-. The cracks are initiated if
above discussed parameters attain the critical values. The force -Pr0- participates in the
development of lateral cracks (in depth -h-) after relieving the indenter loading. The force
-Pm0- takes part in the initiation of the median/radial cracks. During the lateral crack growth
to the equilibrium length -l-, the induced residual force indicated as -Pr0-, is decreasing to
reach down to equilibrium value -P- [5].
Figure 1 shows the crack location around the Vickers indent. The very important parameter
is the size (extend) of induced plastic zone -b-. Its size can be expressed using the following
relationship:
1
b
 E   cotg  3
  
(2)
 

a
 HV    
in which -- and -m- are constants, determined experimentally. The term [(cotg)/]1/3
relates the Vickers indentation semidiagonal length -a- to the radius -r0- of hemispherical
indentation cavity having the same volume. This conversion is based on the fact, that the
formed plastic zone is always spherical and the corresponding volume accommodation of
indent cavity (regardless of indenter geometry) is applied.
Figure 2 shows the dependence between -b- and -a-. The radius of plastic zone -b- is
estimated from the depth of lateral cracks in vertical section of Vickers indent. The values
determined by Reece and Guiu [2] for Al2O3 and our results obtained for Si3N4 are included
in Fig. 2. The dependence -b- vers. -a- is linear and its slope makes possible to express
corresponding relationship. In case of Al2O3 its value is 0,88, approximately, while in case
m
of Si3N4 the determined slope b/a is a little higher, around 1. The graph plotted in Fig. 3
demonstrates the dependence of relative radius of induced plastic zone, expressed as b/r 0 on
the value E/HV, where E is Young’s modulus and HV expresses the corresponding Vickers
hardness value in SI units.
1
Chiang’s results
Results obtained by
Reece a Guiu
0,07
0,06
0,8
Our results
obtained for
silicon nitride
ceramics
0,05
0,04
0,03
log(b/r0)
plastic zone radius -b[ mm]
0,08
0,02
Our results – silicon nitride
ceramic
Our results WC+Co
0,6
0,4
Our results - steel
0,2
0,01
0
0
0
0,02
0,04
0,06
semidiagonal length -a-
0,08
[mm]
0,1
0,5
1
1,5
2
2,5
3
log(E/HV)
Fig. 2: Dependence of plastic zone radius vers. Fig. 3: Dependence of relative plastic zone
indentation semidiagonal length
radius (b/r0) on (E/HV)determined
for different material types
The dependence presented in Fig. 3 include the data obtained by Chiang et al. [6] and
results, which we found by testing of Si3N4 ceramics. Simultaneously in this figure, the
additional data of cutting material (WC/Co) and heat-treated structural steel (Rm=950 MPa)
are plotted. The dependence (b/r0) vers. (E/HV) presented in logarithmic co-ordinates is
linear. This graph shows that the present dependence has a general validity. It is possible to
found the values of constants -m- and -- (eqn.(2)). The value of above-mentioned
constant are m=0,34 and =0,74, what is in very good agreement with data given in [2].
Application of indentation techniques-indentation fracture toughness
The indentation method of fracture toughness determination is very easy to realise (as it
was said above) in comparison with the conventional technique based on the application of
fracture mechanics parameter measurements. In excess of a critical indentation load, the
cracks are formed around the indent. The evaluation is based on the finding of crack lengths
formed in the arms of the indenter impression. Over the years a number of indentation
models have been reported [1]. However the validity of obtained results after application of
these techniques is limited as it results from the formation of different crack types in
ceramics. For this reason, it is necessary to determine the type of cracks and use appropriate
equation to calculate the fracture toughness values [1,4]. To the solution of this situation,
Liang et al. have contributed very significantly [7]. Liang et al. provided a refined
expression, which applies to different types of cracks and predicts the indentation fracture
toughness very accurately. Liang’s et al. formula is used preferentially in the evaluation of
fracture toughness from indentation test data, due to its universality irrespective of
indentation crack type.
The principles of preparation technique of applied ceramic materials are described in
former works in detail and for this reason is not included in this contribution [8]. Knowing
the crack length -c- and the indentation semidiagonal length -a- the fracture toughness can
be computed using Liang’s et al. expression [7]:
 cl

1, 51

0, 4


KC
 HV 
 c   18a 




(3)




HV  a 1 / 2  E   
a
Where  =14{1-8[(4-0,5)/(1+)]4}, -- is a non – dimensional constant related to the
Poisson’s ratio -- , -- is a constraint factor (according [7]  = 3, approximately). From
elementary dimensional study, the hardness was calculated in SI units using the
dependence:
P
HV 
(4)
2a 2
in which -P- is the indentation load.
The evaluation was performed using two types of ceramic material. The cutting ceramics of
Si3N4 type represents the first variant of the investigated ceramics. The grain size is in units
of 10-6 m. The minimum volume fraction of glassy phases is in the microstructure as it can
be assessed from high etching resistance.
Fig. 4a: Microstructure of Si3N4 ceramics
Fig. 4b: Microstructure of Al2O3 ceramics
Figure 4a shows the microstructure of Si3N4 after etching in water free melt of NaOH
(350°C/3 min.) [9]. The second investigated ceramic variant is Al2O3. The microstructure of
this ceramic material is given in Fig. 4b. In this case, the investigated ceramic was etched in
boiling 85% phosphoric acid (250°C/2 min.) [9].
The results of indentation fracture toughness evaluation in dependence on indentation load
are summarised in Fig. 5.
7
KC (MPa m1/2 )
Si3N4
5
4
Al2O3
3
2
1
ln(ln(1/(1-P)))
2
6
1
0
-1
-2
-3
-4
0
0
50
100
150
200
250
Load (N)
Fig. 5: Dependence of indentation fracture
toughness on indentation load
1,4
1,65
y = 15,37x - 26,515
ln(KC)
1,9
Fig. 6: Dependence of ln[ln(l/(1-P))] on
ln(K C)
This figure demonstrates, the values of indentation fracture toughness (KC) in the applied
load range are constant with minimum scattering (7 measurements were performed at
chosen loads). Simultaneously, the statistical elaboration of experimental data was made.
The distribution of fracture toughness values corresponds to Weibull distribution having
following form:
  K m 
P( x )  1  exp   C  
(5)
  K C 0  
where -KC- is investigated value of fracture toughness and -KC0- expresses the threshold
value. After double logarithmic calculation, the expression in eqn. (5) has the form:
  1 
(6)
ln ln 
  m  ln K C   m  ln K C 0 
  1  P 
1/2
KC [MPa m ]
which makes possible to determine the value of Weibull’s modulus. This modulus
describes the scattering of measured values. The example of realised evaluation (for load of
200 N, Si3N4) is given in Fig. 6. In this case, the value of m=15,37. The summarising data
obtained by the measurements in load range 20-200 N show that in case of Si3N4 the values
of -m- are 10-35, while in case of Al2O3, Weibull’s modulus is situated in the range 10-33,
with majority values around 20.
The above presented values of indentation fracture toughness are compared with KC values
determined using conventional fracture mechanics technique (three point bending of
specimens with very sharp -chevron- notch) [10]. The achieved results of this measurement
are summarised in Fig. 7. The comparison demonstrates that the level of indentation
fracture toughness is a little conservative then the conventional measurement of these
values. This finding corresponds to the in general applied standpoint concerning the
determined indentation values of fracture toughness.
4,5
4
3,5
3
2,5
2
1,5
1
0,5
0
0
1
2
3
4
5
6
7
Measurement number
Fig. 7: Values of KC determined on Al2O3 – application of conventional fracture mechanics
specimen (chevron notch)
Indentation fatigue evaluation
Indentation fatigue measurement is carried out by repeated indentation process onto the
same point of the specimen surface. In order to eliminate the difficulties by the evaluation
process, which are connected with the different depth of the subsurface lateral crack
initiation [5] due to the different level of applied standard loading, the pre-indentation was
applied. In our case, the used pre-indentation is 200 and/or 300 N. The criterion of fatigue
durability is the chip formation defined as a number of repeated loading at its given level.
The critical indentation number (corresponding to the indentation number necessary to
Load [N]
350
300
-pre-indentation of 300 N
250
-pre-indentation of 200 N
200
150
100
50
0
0
10
20
30
40
50
60
0,16
0,14
0,12
0,1
0,08
0,06
0,04
0,02
0
0,25
0,2
0,15
0,1
0,05
0
0
50
Number of cycles
100
150
200
Lateral crack growth
rate [mm/cycle]
Length of chips [mm]
produce chipping) is increasing with a lowering of applied indentation load (for constant
pre-loading value). The threshold fatigue load decreases as the standardised pre-loading is
lowered and this parameter corresponds to the level load below which the chipping
formation is suppressed [11].
Two types of cracks initiated during the repeated indentation loading can be found.
Median/radial crack growth can be observed at the surface of specimens using optical
microscopy in periodic intervals. Further, the propagation of subsurface lateral cracks is
realised. The number of cycles to chipping formation represents the final stage of the lateral
crack propagation. The size of chipping area, defined as the distance from the centre of
indent to the end of chipping region, can be also evaluated using optical microscope. Figure
8 show repeated indentation data for two levels of pre-indentation (Si3N4). The application
of higher level of pre-indentation, connected with a deeper lateral crack initiation, results in
a higher delaying intensity to the damage process in ceramic materials realised by way of
chips formation [8].
250
Load [N]
Fig. 8: Repeated indentation data – two
levels of pre-indentation (Si3N4)
Fig. 9: Dependence of chip length and lateral
crack growth rate on indentation load
(Si3N4)
Figure 9 shows the dependence between the indentation load -P- and the mean values of
chipping length (derived from chipping area size) as it corresponds to the growth process of
lateral cracks. Simultaneously, the lateral crack growth rate in dependence on -P- is plotted
in this figure. These dependencies demonstrate, the size of chips is decreasing with the
lowering of applied load [12]. The propagation of lateral cracks during the repeated loading
process is given in Fig. 10, schematically.
Surface
Indenter
Lateral crack
U1 L2 U2 L3 U3 L4
Plastic
deformation zone
Median/radial crack
Fig. 10: Lateral crack propagation (schematic presentation)
The first indentation loading cycle leads to the formation of median/radial cracks, while by
subsequent unloading the lateral cracks are initiated, this is based on the analysis of the
indentation stress field presented by Chiang at al. [6]. In the second indentation, the slight
propagation process of median/radial crack can be detected, because the new stress field
different from that formed in the first loading due to initiation and propagation of the lateral
cracks. The lateral crack propagates during the second indentation. At this crack
propagation stage, a shear stress acts on the lateral crack and causes a shift of material zone
being above crack face. The crack growth via mode II is a result of this operation. Such
lateral crack growth during the loading process produces a new residual stress field what
leads to the lateral crack propagation in the cause of unloading operation. It is supposed that
this growth mechanism is realised repeatedly up to the chipping formation (Fig.10). The
described mechanism leads to the conclusion, the achieved values of indentation fracture
toughness take part in the resistance to the development of fatigue process in ceramic
materials in a high degree. As found in [12], toughness improving in engineering ceramics
is an important parameter characterising the protection against the indentation fatigue.
Conclusions
This work summarises the fundamental results concerning the behaviour of ceramic
materials inclusive of the contribution to the elucidation of processes, which take part by
repeated loading. The presented results confirm the usefulness of the indentation techniques
to determine mechanical properties of technical ceramics. Simultaneously, the paper
contributes to the complex understanding like physical characteristics of indentation
fracture toughness, like material principles influencing the response on indentation repeated
(fatigue) loading.
Acknowledgements
The autors are grateful to the Ministry of Education of Czech Republic for financial support
of the project LN 00B029.
References
[1]
Matzke, M.: Key Eng. Materials, 56-57,(1991),365.
[2]
Reece, M., Guiu, F.: Jnl. Amer. Ceram. Soc., 73, (1990), 1004.
[3]
Quinn, G. D.: Adv. Mater. Process, 154, (1998), No8, 23.
[4]
Muchtar, A., Lim, L. C.: Acta Mater., 46, (1998), 1683.
[5]
Marshall, D. B., Lawn, B. R., Evans, A. G.: Jnl. Amer. Ceram. Soc., 65, (1982),
561.
[6]
Chiang, S. S., Marshall, D. B., Evans, A. G.: Jnl. Applied Physics, 53, (1982), 312.
[7]
Liang, K. M. , Orange, G. , Fantozzi, G. : Jnl. Mater. Sci. , 25, (1990), 207.
[8]
Olejníčková, L., Jonšta, Z., Mazanec, K.: Key Eng. Materials, 223, (2002), 247.
[9]
Täffner, U., Carle, V., Schäffer, U., Predel, F., Petzow, G.: Prakt. Metalogr., 29,
(1991), 592.
[10]
Dlouhý, I., Holzmann, M., Man, J., Válka, L.: Metall. Mater., 32, (1994), 3.
[11]
Vaughan, D. A. J., Guiu, F., Dalman, M. R.: Jnl. Mater. Sci. Letters, 6, (1987),
689.
[12]
Takakura, E., Horibe, S.: Mater. Trans., JIM, 32, (1991), 495.