210 E Gondar et al Joumal of the European Ceramic Society 27(2007)2103-2110 0,3690,37 20量 0001000400020004 ange of th change of te change ofaT change dTh change af AT 6. Graphical representation of PI for a 20 mm thick specimen, the two Fig. 7. Graphical representation of PI for a 20 mm thick specimen, the two most columns showing the infiuence of change of heating temperature Th rightmost columns showing the influence of change of average temperature Tavg seen that the reference parameters, which we stated as the most ntense ones. caused a lower value of mean stress in most simula tions(4-9). However, the reference parameters were determined as most intense not for mean stress, but for stress peak Graphical representation of the results is shown in Fig. 6. It can be seen that the heating and cooling time has generally the lowest influence on the mean stress pi is low because a significant change of these parameters caused only a negligible of Omean. Most important conclusion from this series of simulations is that the temperature difference does not have the most significant influence on the resulting stress. Pi reached its highest value with the change of heating temperature. The difference between the two values(1.53 and 1.784)represents 16.6%, which indicates only a relative suitability of Pl change of th change of aT change of Tavg change of Th The main reason for such a high PI in the case of change of heating temperature is probably that in fact two parameters Fig 8. Graphical representation of Pl on mean stress for a 2 mm thick specimen (heating and cooling temperature) were changed at a time in order to maintain a constant temperature difference(Table 1 lines 2 and 3). However, during the definition of PI we declared progress in this case, more simulations were performed for this eter can thickness. The results for mean stress can be seen in table 2 which describes the change of both temperatures is in this and Fig 8. The change of both heating and cooling temperature case simply their average value Tavg. Parameters Tmax, Tmin simulations 2-7)is again expressed also with the average tem- and Tavg are characteristic for thermal fatigue. The aim of our perature Tavg as an input parameter. The results for stress peaks work, however, is analysis of parameters within a small number in the 4th and 20th cycle are shown in Figs. 9 and 10 thermal fatigue, although our testing method is suitable also of parameters on the mean stress and on stress peaks in the 4th for this case. Let us replace lines 2 and 3 of the previous table. and 20th cycle. The only exceptionis the cooling time, especially Simulation number Input parameters Changed parameter Change of the parameter(o) Change of mean(%) 1100/500-16/6 Tavg=800°C 28.97 Tawg=700°C 900/300-166 New results are shown in Fig. 7. The influence of temper- atures, expressed by their average value, is lower. However, when comparing its influence on the mean stress and on the also the average temperature has more significant infuence on stress in fourth cycle( Figs. and 9). However, the influence is the mean stress than the temperature difference. The difference in both cases low, hence, this difference cannot be considered between the values of Pl(1.1l and 1.3)again casts doubt up decisive the Pl method as an absolute of parameters'influence The dominant influence of temperatures has been confirmed Next series of simulations was performed for a specimen also when taking into account the average temperature as an with thickness of 2 mm. Because of a more complicated stress input parameter. This can be considered a significant addition to2106 E. Gondar et al. / Journal of the European Ceramic Society 27 (2007) 2103–2110 Fig. 6. Graphical representation of PI for a 20 mm thick specimen, the two rightmost columns showing the influence of change of heating temperature Th. seen that the reference parameters, which we stated as the most intense ones, caused a lower value of mean stress in most simula￾tions (4–9). However, the reference parameters were determined as most intense not for mean stress, but for stress peaks. Graphical representation of the results is shown in Fig. 6. It can be seen that the heating and cooling time has generally the lowest influence on the mean stress, PI is low because a significant change of these parameters caused only a negligible change of σmean. Most important conclusion from this series of simulations is that the temperature difference does not have the most significant influence on the resulting stress. PI reached its highest value with the change of heating temperature. The difference between the two values (1.53 and 1.784) represents 16.6%, which indicates only a relative suitability of PI. The main reason for such a high PI in the case of change of heating temperature is probably that in fact two parameters (heating and cooling temperature) were changed at a time in order to maintain a constant temperature difference (Table 1, lines 2 and 3). However, during the definition of PI we declared that only one parameter can be changed at a time. A parameter which describes the change of both temperatures is in this case simply their average value Tavg. Parameters Tmax, Tmin and Tavg are characteristic for thermal fatigue. The aim of our work, however, is analysis of parameters within a small number of repeated thermal shocks, which cannot be considered as thermal fatigue, although our testing method is suitable also for this case. Let us replace lines 2 and 3 of the previous table. Simulation number Input parameters Changed parameter Change of the parameter (%) σmean Change of σmean (%) PI 1 1100/500-16/6 Tavg = 800 ◦C – 28.97 – 2 1000/400-16/6 Tavg = 700 ◦C 12.5 25.43 13.92 1.11 3 900/300-16/6 Tavg = 600 ◦C 25 21.87 32.46 1.30 New results are shown in Fig. 7. The influence of temper￾atures, expressed by their average value, is lower. However, also the average temperature has more significant influence on the mean stress than the temperature difference. The difference between the values of PI (1.11 and 1.3) again casts doubt upon the PI method as an absolute of parameters’ influence. Next series of simulations was performed for a specimen with thickness of 2 mm. Because of a more complicated stress Fig. 7. Graphical representation of PI for a 20 mm thick specimen, the two rightmost columns showing the influence of change of average temperature Tavg. Fig. 8. Graphical representation of PI on mean stress for a 2 mm thick specimen. progress in this case, more simulations were performed for this thickness. The results for mean stress can be seen in Table 2 and Fig. 8. The change of both heating and cooling temperature (simulations 2–7) is again expressed also with the average tem￾perature Tavg as an input parameter. The results for stress peaks in the 4th and 20th cycle are shown in Figs. 9 and 10. The results show only small difference between the influence of parameters on the mean stress and on stress peaks in the 4th and 20th cycle. The only exception is the cooling time, especially when comparing its influence on the mean stress and on the stress in fourth cycle (Figs. 8 and 9). However, the influence is in both cases low, hence, this difference cannot be considered decisive. The dominant influence of temperatures has been confirmed also when taking into account the average temperature as an input parameter. This can be considered a significant addition to