E. Gondar et al. /Journal of the European Ceramic Society 27 (2007)2103-2110 estimate the value of stress in this particular cycle also for input 0080 y03302x+126.33 arameters that have not been simulated y=1,9017x+13089 The aim of this paper is an analysis of thermal shock param eters' influence in a point, which is critical for crack growth ◆ heating time oooling time under the conditions of above described loading Stress analysis was performed also for other 10 points located on vertical axis 25 30 of the specimen, from the heated side down to the cooled side Time [s Presentation of these results. however would increase the vol- ume of this paper too significantly and is beyond the scope of Fig. 15. Linearity of time influence on stress peaks in the fourth cycle the presented topic The results of our analysis are generally applicable for any umber of loading cycles In the case of a specimen with 2 mm width, the value of stress peaks in the critical point becomes stabilized after 16 cycles, 5 hence thermal loading with number y=0.1148X+51367 of cycles higher than this can be already considered as ther mal fatigue. Based on general characteristics and terminology of thermal fatigue it is possible to define maximum stress, min imum stress and the mean stress ● average temperature(△T= const) Cooing temperature(Th=const) 4. Conclusion The influence of repeated thermal shock parameters on stress, 400 450 500 550 600 650 700 750 800 850 generated in silicon nitride was evaluated using parameter of influence(PI)and statistical model. The results show clearly a dominant influence of temperature, followed by the influence of Fig. 16. Linearity of temperature influence on stress peaks in the 20th cycle. temperature difference, and heating and cooling time. This result the results of PI(Figs. 8 and 9). The coefficients of determination on the stress peaks in specific cycle uence on mean stress and again exceed 0.95 The statistical model, obtained using least squares method Figs. 16 and 17 demonstrate the linearity of input parame- howed very high coefficient of determination. The highest value ters influence in the 20th cycle. The influence of temperature is was reached by the equation for mean stress. Despite lower coef again dominant and the coefficients of determination are over ficients of equation for stress peaks in the 4th and 20th cycle, its 0.99. The main difference between the 4th and 20th cycle is value is high enough to prove the prediction reliable. The model the influence of the cooling temperature at Th=const (influence confirmed the surprisingly lower influence of temperature dif- of An). The influence of cooling temperature has an expected ference on the stress and a very low influence of heating and progress. Intersection of both lines in Fig. 16 is not of impor- cooling time tance, it simply indicates that the stress peak in 20th cycle is It is hence important, at least in the conditions of loading for the simulations 1100/750 and 1050/450 almost the same described in this article, to take into account not only the temper (137. 253 MPa and 137.464 MPa, respectively) The influence of heating and cooling time on the stress peaks cooling temperature when evaluating the resistance of technical is in both 4th and 20th cycle negative, which is logical, because ceramics to repeated thermal shocks. The heating and cooling the intensity of thermal shock decreases with increasing time. time should also not be neglected From the point of view of reproducibility of the results, it is important to note the high values of reliability, represented by fatigle nted results are applicable also for conditions of thermal the coefficient of determination. Using the least squares method, we can easily obtain a model equation for any cycle and then References a 1. Ande J. Indentation thermal shock test for ceram- 40958x+144.64 ics..Am. Ceran.Soc.,1996,79,1509-1514 R2=0.9958 2. Koh, Y H, Kim, H. w, Kim, H. E and Halloran, J, Thermal shock resis- ance of fibrous monolithic Si3 N4/BN ceramics. J. Eur. Ceram. Soc., 2004 24.2339-2347 the thermal shock resistance of alumina through the addition of submicron- sized aluminium nitride particles. J. Eur. Ceram Soc., 2004, 24, 2293-2301 T Vedula, V.R., Green, D J, Hellmann, J. R. and Segall, A. E, Test method- ology for thermal shock characterization of ceramics. J. Mater Sci., 1998, Fig. 17. Linearity of time influence on stress peaks in the 20th cycle. 33.5427-5432E. Gondar et al. / Journal of the European Ceramic Society 27 (2007) 2103–2110 2109 Fig. 15. Linearity of time influence on stress peaks in the fourth cycle. Fig. 16. Linearity of temperature influence on stress peaks in the 20th cycle. the results of PI (Figs. 8 and 9). The coefficients of determination again exceed 0.95. Figs. 16 and 17 demonstrate the linearity of input parame￾ters influence in the 20th cycle. The influence of temperature is again dominant and the coefficients of determination are over 0.99. The main difference between the 4th and 20th cycle is the influence of the cooling temperature at Th = const (influence of T). The influence of cooling temperature has an expected progress. Intersection of both lines in Fig. 16 is not of impor￾tance, it simply indicates that the stress peak in 20th cycle is for the simulations 1100/750 and 1050/450 almost the same (137.253 MPa and 137.464 MPa, respectively). The influence of heating and cooling time on the stress peaks is in both 4th and 20th cycle negative, which is logical, because the intensity of thermal shock decreases with increasing time. From the point of view of reproducibility of the results, it is important to note the high values of reliability, represented by the coefficient of determination. Using the least squares method, we can easily obtain a model equation for any cycle and then Fig. 17. Linearity of time influence on stress peaks in the 20th cycle. estimate the value of stress in this particular cycle also for input parameters that have not been simulated. The aim of this paper is an analysis of thermal shock param￾eters’ influence in a point, which is critical for crack growth under the conditions of above described loading. Stress analysis was performed also for other 10 points located on vertical axis of the specimen, from the heated side down to the cooled side. Presentation of these results, however, would increase the vol￾ume of this paper too significantly and is beyond the scope of the presented topic. The results of our analysis are generally applicable for any number of loading cycles. In the case of a specimen with 2 mm width, the value of stress peaks in the critical point becomes stabilized after 16 cycles,15 hence thermal loading with number of cycles higher than this can be already considered as ther￾mal fatigue. Based on general characteristics and terminology of thermal fatigue it is possible to define maximum stress, min￾imum stress and the mean stress. 4. Conclusion The influence of repeated thermal shock parameters on stress, generated in silicon nitride was evaluated using parameter of influence (PI) and statistical model. The results show clearly a dominant influence of temperature, followed by the influence of temperature difference, and heating and cooling time. This result was the same for evaluation of the influence on mean stress and on the stress peaks in specific cycles. The statistical model, obtained using least squares method, showed very high coefficient of determination. The highest value was reached by the equation for mean stress. Despite lower coef- ficients of equation for stress peaks in the 4th and 20th cycle, its value is high enough to prove the prediction reliable. The model confirmed the surprisingly lower influence of temperature dif￾ference on the stress and a very low influence of heating and cooling time. It is hence important, at least in the conditions of loading described in this article, to take into account not only the temper￾ature difference, but primarily the absolute values of heating and cooling temperature when evaluating the resistance of technical ceramics to repeated thermal shocks. The heating and cooling time should also not be neglected. Presented results are applicable also for conditions of thermal fatigue. References 1. Andersson, T. and Rowcliffe, D. J., Indentation thermal shock test for ceram￾ics. J. Am. Ceram. Soc., 1996, 79, 1509–1514. 2. Koh, Y. H., Kim, H. W., Kim, H. E. and Halloran, J., Thermal shock resis￾tance of fibrous monolithic Si3N4/BN ceramics. J. Eur. Ceram. Soc., 2004, 24, 2339–2347. 3. Nieto, M. I., Martinez, R., Mazerolles, L. and Baudin, C., Improvement in the thermal shock resistance of alumina through the addition of submicron￾sized aluminium nitride particles. J. Eur. Ceram. Soc., 2004, 24, 2293–2301. 4. Vedula, V. R., Green, D. J., Hellmann, J. R. and Segall, A. E., Test method￾ology for thermal shock characterization of ceramics. J. Mater. Sci., 1998, 33, 5427–5432.