(632c) Experimental Verification of Solidification Stress Theory

Summary A research program is being conducted to develop a crack-free ceramic waste form (CWF) to be used for long term encasement of fission products and actinides resulting from processing spent nuclear fuel. Cracking usually occurs in the cooldown phase of the glass or ceramic formations. A crack-free formation should have more resistance to leaching than one with many cracks. In the research leading up to producing a CWF, a model was developed that proposes a permanent stress develops when the melt solidifies and that this stress can cause failure as the CWF nears room temperature. This paper reports on how the formation, CWF2, confirms the existence of this stress. The solidification stress is in addition to and of opposite sign of the thermal stress. Its derivation is reported on in Ref. 1. Cracking of the CWF would occur at low temperatures if solidification stress exists but at high temperatures if it doesn't. If solidification stress occurs, then the cooldown rate during solidification should be reduced. If not, it should be reduced when the thermal stresses are highest. Recording cracking sounds confirm the existence of this solidification stress since cracking occurred during the low temperature phase of the cooldown. As a side purpose of this paper, a cooldown rate is proposed that should eliminate cracking in the next experiment, CWF3. CWF2 is a prototype vertical ceramic waste cylinder formed over a period of 10 days by heating a mixture of 75% zeolite, 25% glass frit in an argon atmosphere furnace through melting to 925 C and then cooling through solidification to room temperature. It is approximately 1 m high, 0.5 m in diameter, weighs about 400 kg, and is formed in a stainless steel can 0.5 cm thick. This cylinder developed many cracks on cooldown. At least 15 loud cracks were recorded over a period of 4 days at the end of cooldown when the temperatures were below 400 C. The CWF2 surface and centerline temperatures at mid height were measured which allowed the stress to be calculated. The timing of the cracks was compared to the time the calculated total stress exceeded the tensile stress limit and verified that the cause of the cracking was solidification stress and not thermal stress. Since the CWF is encased in a can in a furnace, the cracks cannot be easily observed but can be detected with sound measurements. Similarly, the stress cannot be measured but only estimated with analysis Temperature Data The cooldown of CWF2 was started but after 4 hours the cooldown and heat transfer from the CWF stopped, resulting in the surface and center temperatures equilibrating over the next hour. This was caused by the coolant fan stopping and staying off for about 8 hours at which time the fan restarted so CWF cooldown started again. The coolant flow is varied to maintain a circulation pump inlet temperature of 100 C or less. The furnace wall continued cooling during this time because the control system kept the heating coils off. As temperatures decreased, the pump stayed on for longer periods of time causing the average coolant flow to increase causing more heat to be removed from the CWF. The largest heat removal occurred during solidification causing a large set-in stress. The temperature difference between the center and the surface during solidification is a measure of the solidification stress which is set-in The CWF3 plan specifies that the temperature difference should decrease during solidification (about 625 C). The data shows the CWF2 temperature difference actually increased. In fact, the largest differences occur during solidification which should have been less than 40 C but the data show a difference near 80 C. This temperature difference resulted in CWF2 cracking. To evaluate the stress, the analytical surface temperature profile was matched to the experimental by varying the heat transfer over time to simulate the pump flow. With this match, centerline temperature, the temperature profile, and stresses developed, both solidification and thermal, could be calculated. Analysis of Stress The thermal stress calculated in the midplane for this cooldown transient. The model used to calculate these stresses are that of Timoshenko and Goodier (Ref. 2). The stresses are shown over 10 evenly spaced radial increments. This stress predicts that the stress will be in tension in the outer radial region of the CWF so that cracking would be expected to start in that region if solidification stress did not exist. The thermal stress at the outer radius exceeds the tensile limit from 32 hours to 48 hours and the stresses slowly dissipate after that. If thermal stress were the cause of cracking in the CWF, it would be expected that cracking would occur during this time period. Sound measurements recorded 15 loud cracks during the course of the cooldown. The first one occurred at 61 hours, much later than the 32 to 48 hours when the thermal stress exceeded the tensile limit. Since all the cracks occurred after the thermal stress exceeded the limit, it cannot be responsible for the damage to the CWF. (Note, only the axial stresses are discussed in this paper. The radial stresses are about the same and the normal stresses are very small. There are no shear stresses.) The solidification stress was calculated using the method presented in Ref. 1. It develops while the CWF is solidifying and occurs because as one layer of the CWF is solidifying, it is attached to an adjacent solidified layer of different length. As the solid then is cooled down to room temperature, all these different lengths are forced to the same length causing stresses. The solidification stress developed is dependent on the temperature profile during solidification but is independent of temperature during the remainder of the cooldown. The maximum solidification stress is about 20000 psi which is well over the tensile stress limit of 12000 psi. The total stress is the sum of the thermal and the solidification stress, and since they are of opposite sign, the thermal stress partially cancels out the solidification stress. Since the thermal stress decreases as the temperature decreases, it cancels out less and less of the solidification stress as the temperature decreases. When the temperature becomes uniform, the thermal stress is zero so the total stress is then equal to the 20000 psi solidification stress at the center of the CWF. This explains why the CWF cracks at low temperature instead of high temperature when the thermal stress is high. That is, the total stress continues to increase as the average temperature decreases and the temperature profile flattens out. Both the solidification stress and the thermal stress add together to obtain the total stress shown in the attached figure. The stress begins at zero at 34 hours after the start of cooldown and increases as the temperature decreases to room temperature. During the initial solidification period, the two stresses almost cancel each other out but the solidification stress is always greater than the thermal stress. Consequently, the inner portion of the cylinder is always in tension. The centerline stress eventually exceeds the tensile limit at 68 hours. The first cracking sound that was recorded occurred at 61 hours. This indicates the stress calculation is close to predicting failure then. The tensile limit shown is only an estimate could be as low as 10000 psi. The damage continued all the way down to room temperature as evidenced with continued cracking, 15 in all. Conclusions A theory has been developed to model a stress which was posited to develop when a ceramic solidifies due to the temperature gradient which exists during the solidification process. An experiment was run which verifies the existence of this stress. Thermal stress alone would have predicted cracking to occur at while temperatures are high but when the solidification stress is added, the total stress calculation predicts cracking of the CWF will occur at low temperatures. Cracking sounds were recorded in this experiment and are used in this paper to show that the existence of this stress is probable since cracking occurred during the low temperature phase of the cooldown. Confirmation of this model allows a cooldown history to be followed which will eliminate cracking. Without including the solidification stress in the calculation, the low cooling rate needed to prevent cracking would be prescribed after solidification and cracking would not be prevented. References 1. Solbrig, C. W., and Bateman, K. J., MODELING SOLIDIFICATION-INDUCED STRESS IN CERAMIC WASTE FORMS CONTAINING NUCLEAR WASTES, to be published in Nuclear Technology 2. Timoshenko, S., and Goodier, J. N. (1970) Theory of Elasticity, Third Edition, McGraw-Hill, New York, NY. Acknowledgement Work supported by the U.S. Department of Energy, Office of Nuclear Energy (NE) under DOE Idaho Operations Office Contract DE-AC07-05ID14517.