Subcritical crack growth in oxide and non-oxide ceramics using the Constant Stress Rate Test ✩

Fracture toughness is one of the most important parameters for ceramics description. In some cases, material failure occurs at lower stresses than described by KIc parameter. In these terms, determination of fracture toughness only, proves to be insufficient. This may be due to environmental factors, such as humidity, which might cause subcritical crack propagation in a material. Therefore, it is very important to estimate crack growth velocities to predict lifetime of ceramics used under specific conditions. Constant Stress Rate Test is an indirect method of subcritical crack growth parameters estimation. Calculations are made by using strength data, thus avoiding crack measurement. The expansion of flaws causes reduction of material strength. If subcritical crack growth phenomenon occurs, critical value of crack lengths increases with decreasing stress rate due to longer time for flaw to grow before the critical crack propagation at KIc takes place. Subcritical crack growth phenomenon is particularly dangerous for oxide ceramics due to chemical interactions occurring as a result of exposure to humidity. This paper presents results of Constant Stress Rate Test performed for alumina, zirconia, silicon carbide and silicon nitride in order to demonstrate the differences in subcritical crack propagation phenomenon course.


I. Introduction
In many ceramics crack does not propagate only at applied stress at K Ic , but well below that value.Crack growth at these values is much slower and difficult to detect, but it leads to decrease in material strength and delayed failure [1][2][3][4][5][6] even if it was under strength value determined in standard test methods [7][8][9][10][11].It is an environmentally induced phenomenon.It may vary for different corrosive factors and material types.Water impact on material fracture appears to be particularly dangerous in oxide ceramics used in an environment of high humidity.Water molecules align to the cations at the crack tip surface, with their lone pair orbitals, creating hydrogen bonding.Strained bonds in the material are the enhancing factor.This mechanism leads to bond ✩ Paper presented at 11 th Conference for Young Scientists in Ceramics -SM-2015, Novi Sad, Serbia, 2015 * Corresponding author: tel: +48 69 663 7958, fax: +48 12 633 4630, e-mail: agdudek@agh.edu.plrupture which causes subcritical crack growth induced by stress corrosion [3,12].
Types of tests, used in subcritical crack growth phenomenon description, can be divided into two groups.The first one is a static loading method based on crack growth observations.In this kind of test, measurements might take long time.In discussed phenomenon cracking might start with velocities about 10 -12 m/s.It means that crack growth of 1 µm takes over one week.In the second type of tests, subcritical crack growth parameters are determined on the basis of strength data [13].Strength measurements are performed at different stress rates to allow stress increase in the material for various periods of time.The more time is given, the higher decrease of strength occurs.What is more, there is no need for specific sample preparation, like polishing or introducing cracks.The tests are conducted on sintered ceramics with preexisting flaws (either on the surface or in the material volume) [14].Therefore, these conditions are closer to the actual in the ceramic components.
Relative shortening of testing time and ease of sample preparation (when compared to static fatigue) allows for examination of higher amount of samples, which is statistically advantageous [12].Studies have shown that the amount of thirty samples is minimal until the result is statistically correct [9,15].In contrast, the use of larger quantities is not necessary because it does not affect significantly the changes in the accuracy of results [15,16].
The aim of the paper is the presentation of parameters determined by Constant Stress Rate method for oxide and non-oxide ceramics to demonstrate the differences in subcritical crack growth course.

II. Experimental
The idea was to fabricate two oxide and two nonoxide materials for comparative purposes.In the first group α-alumina samples (TAIMEI Chemicals, TM-DAR) sintered at 1400 °C for 2 hours, and tetragonal zirconia samples (TOSOH, TZ-3Y) sintered at 1500 °C for 2 hours, were prepared.As representatives of nonoxide ceramics, silicon carbide (SIKA FCP 15, Saint-Gobain) sintered at 1800 °C ( 10  3 ).Relative density for silicon carbide samples was calculated considering content of phases arising due to oxides addition.Fracture toughness was obtained in SENB method.
Subcritical crack growth parameters were estimated in Constant Stress Rate Test.Calculations were based on power law equation for subcritical crack growth velocity: where ν is crack velocity, K I is stress intensity factor, K Ic is fracture toughness, n is stress corrosion susceptibility parameter, A and A * are constant depending on material properties and environmental factors, respectively [17,18].In this method no crack length measurement is required.Estimations are carried out by using strength data.Strength measurements were performed by using Zwick/Roell 2.5 with biaxial loading support.Four stress rates were used: 0.1, 1, 10 and 200 MPa/s.If there is no influence of the environment (no water impact), strength is called inert.It occurs at high stress rates or in inert environments.In this case, the tests were made at 20 °C and humidity in range of 40-50% and the strength results at stress rate of 200 MPa/s were found to be inert [4,19,20].Dependence between strength and stress rate is shown by: where σ f is flexural strength, σ is stress rate, n is subcritical crack growth equation exponent (Eq. 1) and D is subcritical crack growth parameter depending on material type and environmental factors.
Strength measurement results are presented on logarithmic dependence graphs, in which the designation of the regression equation allows to calculate n and D parameters.To calculate other parameters from Eq. 1, the following formulas were used: where Y is shape factor (for circular samples 1.13 [21]), α is slope, β is intercept and σ i is inert strength [14,19].
Irwin-Griffith formula allows critical crack length calculation [22]: By expressing crack velocity as a change of crack length in time and knowing needed parameters, calculation of corresponding stress intensity factor is possible [14].

III. Results and discussion
The results of density and fracture toughness were summarized in Table 1.Sintering of the alumina and zirconia lead to high densification, while densification of both non-oxide ceramics was lower, however, it was considered to be sufficient to conduct experiments.
Figures 1 and 2 demonstrate that subcritical crack growth occurs in both oxide materials.It is proved by increase in material strength for increasing stress rates.It can be explained by reduction of testing time for higher stress rates, leading to reduction of crack growth.
For the silicon nitride (Fig. 3) and silicon carbide (Fig. 4) no increase of strength with increasing stress rate was observed.For confidence, additional strength measurements at 0.01 MPa/s for the silicon carbide were  made.This was to prolong loading to see if there is any effect of water.The measurements showed that these strengths were on the same level as others.It may be concluded, that for the non-oxide materials tested in presented conditions (20 °C, 40-50% RH) no subcritical crack growth occurred.Further calculations were possible only for oxide sintered ceramics, in which subcritical crack propagation occurred.Using the slope and intercept of fitting line for strength -stress rate dependences n and D parameters were calculated from Eq. 2 (Table 2).For the zirconia n value was higher.That means that change of material strength for different stress rate was less significant.Crack velocities and corresponding stress intensity factor values (estimated as it was explained before) combined with the knowledge of n parameters (inducing the slope) allowed to create crack velocity vs. K I /K Ic plot (Fig. 5).It shows that for the alumina, cracking starts at relatively low K I /K Ic ratio.It may be perceived as a smaller subcritical crack propagation resistance of the alumina compared to the zirconia.

IV. Conclusions
The presented study confirmed that the phenomenon of subcritical crack propagation occurred in sintered oxide ceramic as opposed to non-oxide.This conclusion was made on the basis of log flexural strengthlog stress rate dependence graphs.For the investigated alumina and zirconia samples there was noticeable increase of strength for increasing stress rates.It means that when the material is loaded for a longer time in corrosive environment (in this case 20 °C and 40-50% RH) its strength decreases as a result of expanded flaw sizes.However, this was not observed for both non-oxide materials -SiC and Si 3 N 4 .For every stress rate strength value was at the same level.Even if the measurement time was prolonged for SiC, by using 0.01 MPa/s stress rate, no change occurred.This indicates that these materials are subcritical crack growth resistant under presented conditions.Constant Stress Rate Test allowed estimating subcritical crack propagation parameters using strength data.It was possible for the alumina and zirconia.Change of material strength generated the slope of fitting line which indicated n parameter.This case shows that for the material with higher n value (zirconia) cracking starts at higher K I /K Ic values compared to the alumina.This means that zirconia has lower susceptibility for subcritical cracking.The reason of this phenomenon might be higher energy of chemical bonding in zirconia and well-known input of polymorphic transformation (tetragonal to monoclinic) in energy dissipation on the crack tip.

Figure 3 .Figure 4 .
Figure 3. Log flexural strength -log stress rate dependence graph of sintered silicon nitride

Figure 5 .
Figure 5. Log crack velocity -log K I /K Ic dependence plot for sintered alumina and zirconia

Table 1 .
Results of relative density and fracture toughness

Table 2 .
Values of n and D parameters calculated for alumina and zirconia