ondar et al. Journal of the European Ceramic Society 27(2007)2103-2110 Necessary condition when evaluating PI is that only one input parameter can be changed at a time. Other parameters must remain constant. The parameter of influence is only suitable for comparing of parameters'influence, it cannot be used to determine the absolute influence of a parameter. The evaluation using PI has been developed because we could not find a suit able widely used method. There was a possibility of using the ANOVA method 6(analysis of variance), but this method only evaluates, whether or not a parameter has infuence on the out- put quantity. It does not compare the infuence of the parameters Another disadvantage is, that it can only be used for cases with a finite number of values Our aim was not only to analyze the results, but also to predict the value of stress in the critical point. Based on the analysis of Fig. 4. Stress progress in critical point of a 20 mm thick specimen. our results, most suitable method was the least squares method Using this method, we were able to obtain the parameters'esti mates in a linear regression model in the form o=aTh+bTc+cth+ dte +e+E (2) where a, b, c, d and e are regression coefficients and e is the methods commonly used for statistical analysis of results. I7 e normally distributed random error. This method is one of 3. Results and discussion Results for 20 mm thick specimen are shown in Table 1. First 0020002500300035004000 line, containing reference parameters, is marked bold Changed 5001000 parameter is introduced in the third column, with its percentual change given in the fourth one. Most intense shocks, which can Fig. 5. Stress progress in critical point of a 2 mm thick specimen. be experimentally achieved, are caused by reference parame- ters. For this reason the changed input parameters caused lower practical experiments, because mean stress is not responsible intensity of thermal shock. The influence of heating temperature for unstable crack growth. We evaluated the influence of input was studied by decreasing Th by 100C, maintaining constant parameters on the stress peaks in the 4th and 20th cycle temperature difference, hence the cooling temperature had to be For both specimen thicknesses, the influence of input param- lowered of the same amount as well(simulations 2 and 3).The eters on the stress can be described by a so-called parameter influence of temperature difference was evaluated by increasing of influence(PD). The PI is a ratio of the change of stress to the cooling temperature while keeping the heating temperature the change of input parameter. This change(expressed in %)is constant(simulations 4 and 5). The influence of heating and understood with respect to the reference parameters. Thus, when cooling time was studied by increasing both quantities, lower- looking for example for the influence of heating temperature on ing thus again the intensity of thermal shock (simulations 6-9) the value of stress. the pi will be calculated as The next two columns of the table contain the values of the mean △σ[% stress in critical point and the percentual change with respect to (1) the value obtained at reference parameters. Parameter of influ △i[%] ence(Pl) is given in the last column. From Table 1 it can be Table Calculation of Pl from simulations output for a 20 mm thick specimen Simulation number Changed paramet Change of the parameter(%) Change of omean(%) 1100/500-16/6 28.97 1000/400-16/6 Th=1000°C 13.92 1530 900300-16/6 Th=900°C 32.46 1100/600-16/6 △T=500°C 0.370 1100700-166 △T=400°C 32.53 0.369 1100/500-20/6 h=20s 1100/500-25/6 0.004 t=10s 66.7 0.1 0.002E. Gondar et al. / Journal of the European Ceramic Society 27 (2007) 2103–2110 2105 Fig. 4. Stress progress in critical point of a 20 mm thick specimen. Fig. 5. Stress progress in critical point of a 2 mm thick specimen. practical experiments, because mean stress is not responsible for unstable crack growth. We evaluated the influence of input parameters on the stress peaks in the 4th and 20th cycle. For both specimen thicknesses, the influence of input param￾eters on the stress can be described by a so-called parameter of influence (PI). The PI is a ratio of the change of stress to the change of input parameter. This change (expressed in %) is understood with respect to the reference parameters. Thus, when looking for example for the influence of heating temperature on the value of stress, the PI will be calculated as: PI = σ[%] Th[%] (1) Necessary condition when evaluating PI is that only one input parameter can be changed at a time. Other parameters must remain constant. The parameter of influence is only suitable for comparing of parameters’ influence, it cannot be used to determine the absolute influence of a parameter. The evaluation using PI has been developed because we could not find a suit￾able widely used method. There was a possibility of using the ANOVA method16 (analysis of variance), but this method only evaluates, whether or not a parameter has influence on the out￾put quantity. It does not compare the influence of the parameters. Another disadvantage is, that it can only be used for cases with a finite number of values. Our aim was not only to analyze the results, but also to predict the value of stress in the critical point. Based on the analysis of our results, most suitable method was the least squares method. Using this method, we were able to obtain the parameters’ esti￾mates in a linear regression model in the form: σ = aTh + bTc + cth + dtc + e + ε (2) where a, b, c, d and e are regression coefficients and ε is the normally distributed random error. This method is one of the methods commonly used for statistical analysis of results.17 3. Results and discussion Results for 20 mm thick specimen are shown in Table 1. First line, containing reference parameters, is marked bold. Changed parameter is introduced in the third column, with its percentual change given in the fourth one. Most intense shocks, which can be experimentally achieved, are caused by reference parame￾ters. For this reason the changed input parameters caused lower intensity of thermal shock. The influence of heating temperature was studied by decreasing Th by 100 ◦C, maintaining constant temperature difference, hence the cooling temperature had to be lowered of the same amount as well (simulations 2 and 3). The influence of temperature difference was evaluated by increasing the cooling temperature while keeping the heating temperature constant (simulations 4 and 5). The influence of heating and cooling time was studied by increasing both quantities, lower￾ing thus again the intensity of thermal shock (simulations 6–9). The next two columns of the table contain the values of the mean stress in critical point and the percentual change with respect to the value obtained at reference parameters. Parameter of influ￾ence (PI) is given in the last column. From Table 1 it can be Table 1 Calculation of PI from simulations output for a 20 mm thick specimen Simulation number Input parameters Changed parameter Change of the parameter (%) σmean Change of σmean (%) PI 1 1100/500-16/6 – – 28.97 – 2 1000/400-16/6 Th = 1000 ◦C 9.1 25.43 13.92 1.530 3 900/300-16/6 Th = 900 ◦C 18.2 21.87 32.46 1.784 4 1100/600-16/6 T = 500 ◦C 16.7 30.76 6.18 0.370 5 1100/700-16/6 T = 400 ◦C 33.3 32.53 12.29 0.369 6 1100/500-20/6 th = 20 s 25 29.00 0.1 0.004 7 1100/500-25/6 th = 25 s 56.3 28.98 0.03 0.001 8 1100/500-16/8 tc = 8 s 33.3 29.01 0.14 0.004 9 1100/500-16/10 tc = 10 s 66.7 29.00 0.1 0.002