Session 12-17

Determination of Thermal Expansion Coefficients of High Temperature Materials

Nana-Kwaku Danquah, Patrick Mensah, Samuel Ibekwe, and Guoqiang Li

Mechanical Engineering Department Southern University Baton Rouge

Abstract

Resuscitating a dilatometer that was moved from one laboratory to the other, and has not been used thereafter proved a daunting task in the quest to measure the thermal expansion coefficient of a high temperature material. This poster presents the challenges faced, the solution obtained and the results of the measurement.

Introduction The Harrop Dilatometer System is a complete, compact, easy to use, bench top system comprised of a furnace (for a variety of temperature ranges, including sub-ambient); a sample holder system (fused silica); a control / sample thermocouple; a sample displacement measuring system (probe rod and LVDT sensor); a user-adjustable counterweighted pulley system to provide a constant and uniform contact load on the test sample; a universal furnace controller (user programmable, 4 segment, PID control); an onboard data acquisition computer (stores temperature and displacement data for downloading to an independent computer); software for an independent personal computer system; and a bench-top support structure.

Figure 1. Schematic of Harrop’s Dilatometer. Courtesy of Harrop’s Inc.

In order to run this equipment, a sample specimen is placed in a fused silica sample holder in contact with a freely suspended fused silica movable probe rod. The holder and sample are inserted in the furnace. A control thermocouple is located in close proximity to the heating element for temperature control. The furnace is heated according to a pre-programmed thermal cycle. As the sample temperature changes (as recorded by the sample thermocouple), the sample expands (pushing against the probe rod) or shrinks (pulling away from the probe rod). The probe rod, which is kept in constant pressure contact by the pulley system, transmits the amount of sample movement to the

Proceedings of the 2008 ASEE Gulf-Southwest Annual Conference The University of New Mexico – Albuquerque

Copyright © 2008, American Society for Engineering Education

Figure 2a. Fused Sample holder. Figure 2b. TDA curve electronic displacement sensor (Linear Variable Differential Transformer) located outside of the heated chamber. The LVDT converts the displacement into a proportional voltage signal which is recorded as the Delta-L curve. Then on-board computer would convert the signal to the percent of length change (PLC) and saves it along with the elapsed time and the sample temperature. The stored data can be retrieved using the keypad and displayed. The data can then be analyzed using the TDA Acquisition Software. The basic TDA curve is generated by plotting the percent of length change (PLC) on the Y-axis against the sample temperature. The Harrop TDA Data Analysis Software is an intuitive, easy-to-use executable program that performs standard dilatometric analyses. Data can be printed graphically or in tabular form or exported as an ASCII file.

DATA COLLECTION, CHALLENGES AND SOLUTION During the move of this dilatometer from one laboratory location to another, it sustained damages. The time frame became dysfunctional thereby putting its accuracy and precision in question. Also the onboard data acquisition computer that stores temperature and displacement data for downloading via the supplied RS232 cable to an independent computer system either during the run or after the run and up-to-date data analysis software were missing. Due to the lack of the RS232 cable and data analysis software, an accurate measurement could not be obtained. However most of the dilatometer’s major components such as the furnace, thermocouple connector, slide rail, sample holder, probe rod or push rod and LVDT were undamaged.

Figure 3a. Dial indicator – Courtesy of Brandsonoaia; Figure 3b. Test program ramp

Proceedings of the 2008 ASEE Gulf-Southwest Annual Conference The University of New Mexico – Albuquerque

Copyright © 2008, American Society for Engineering Education

Solution There were two possible solutions to this problem. The first solution was to upgrade the current dilatometer by replacing most of its missing components and upgrading the software to meet current computer requirements. But this solution is unacceptable due to the fact that Harrop Industries, Inc had discontinued their production of this dilatometer model. Also the cost of upgrading into a standard model wasn’t cost effective.

The second solution was to run the dilatometer just as it was without data analysis software but instead manually record the elongation of the sample as it expanses to determine whether or not the equipment was still operational. In order to accomplish this task, the density of the sample has to be determined, followed by appropriate selection of linear thermal expansion coefficient. The elongation of the sample can then be calculated based on its temperature change using this equation:

δT = α(ΔT)L

Where δT = the sample elongation; α = the thermal expansion coefficient ΔT = change in temperature; L = the length of the sample After acquiring the numerical elongation of the sample, the results would then be compared with the recorded results obtained from the dilatometer. However, the question is how do we obtain these results from the dilatometer? This was done using a dial indicator. By placing a dial indicator next to the probe or push-rod, we can record the dimensional changes of the sample over the specified time interval. This second solution procedure was adopted.

Therefore, a simple program, Figure 3b was created to evaluate the equipment in order to determine the working condition of the dilatometer. This program allowed the sample to be heated up from room temperature to 1000°C for 15 minutes, thereafter held at this temperature for 10 minutes. The dimensions of the sample used are shown in Table 1.

After determining the density of the sample and selecting the appropriate metal and its corresponding thermal expansion coefficient. The calculated elongation value as stated above is compared to the actual recorded elongation of the dilatometer. The results do not appear to be consistent especially with sample two; this is due to human error. During the ramping stage of the program, the sample was exposed to ambient temperatures, which results in the samples shrinkage. Also the percentage error from sample one and three indicate that with enough runs the error margin can be sufficiently reduced.

Sample Dimension Length Diameter Density Thermal Expansion Coefficient Sample 1 90 mm 9.4 mm 0.291 lb/in3 11.7×10-6°C Sample 2 92 mm 9.4 mm 0.291 lb/in3 11.7×10-6°CSample 3 92 mm 9.4 mm 0.291 lb/in3 11.7×10-6°C

Proceedings of the 2008 ASEE Gulf-Southwest Annual Conference The University of New Mexico – Albuquerque

Copyright © 2008, American Society for Engineering Education

Sample Results Calculated

ElongationRecorded Elongation from Dilatometer

Percentage Error

Steel Sample 1 1.053 mm .899 mm 14.62% Steel Sample 2 1.076 mm .690 mm 35.87% Steel Sample 3 1.076 mm .984 mm 8.55%

TABLE 1. Results of the sample run.

Summary and Conclusions

Measuring the thermal expansion of the materials in high temperatures is possible with the use of a dilatometer. There are several applications, in which a dilatometer can be used to examine material characteristics such as absolute and relative expansion, linear coefficient of expansion, differential coefficient of expansion, softening range, transformation point, glass transition range, swelling behavior penetration and contraction. This presentation concludes that the Harrop’s dilatometer is still operational. However there are a few aspects that must be taking into considerations in order to make effective measurements. To reduce erroneous results, first, create a cylinder shape sample (recommended) with a diameter exactly 11mm or no less then 10mm with a length between 40mm to 100mm. Having a uniform cylinder sample with these dimensions reduces any irregular expansion results. Secondly, when programming the controller do not exceed a rate of 15°C per minute this will also reduce any erroneous. Third do not attach the thermocouple to the sample, if this occurs the damage sustained to thermocouple will result in inaccurate data. Finally, do not expose the sample to ambient temperature during expansions and secure a location to place the dial indicator directly in contact with the push-rod in order to record the displacement manually. One major flaw associated with this solution approach is using a dial indicator to record elongation manually. To acquire a more precise data the dial indicator must be calibrated to increase its sensitivity to displacement. By implementing these guidelines the operator can reduce the level of errors associated with this method of approach.

This turned out to be a great learning experience involving rehabilitating dysfunctional equipment, improvising reasonable solution methods, and the realization of taking absolute care in relocation of equipment.

Acknowledgement This study was sponsored by a grant from U.S. Department of Energy, Award No. DE-FG52-05N27041. The authors also acknowledge support of Mechanical Engineering Department, Southern University, Baton Rouge. .

Proceedings of the 2008 ASEE Gulf-Southwest Annual Conference The University of New Mexico – Albuquerque

Copyright © 2008, American Society for Engineering Education

References 1. Anter Corporation, “General Dilatometer Maintenance” 1996-2003 <www.anter.com> 2. The Edward Orton Jr. Ceramic Foundation, “Orton Standard Dilatometers” by, May 6, 2006

<www.OrtonCeramic.com> 3. Harrop Industries, Inc., “Instruction Manual for Themodilatometeric Analyzers” pp 1, 6, 9-10. Columbus, Ohio

February, 1994 4. Ferdinand P. Beer, E. Russell Johnson Jr., John T. DeWolf, “ Mechanics of Materials”, 4th ed. The McGraw Hill

Companies, Inc., New York 1981-2006 Pages 74-75. NANA-KWAKU DANQUAH Mr. Danquah is a junior in Mechanical Engineering department, Southern University, Baton Rouge, Louisiana PATRICK MENSAH, SAMUEL IBEKWE, AND GUOQIANG LI Drs. Patrick Mensah, Samuel Ibekwe, and Guoqiang Li are professors in Mechanical Engineering Department at Southern University, Baton Rouge. They are co-PIs on the DOE/NNSA sponsored project.

Proceedings of the 2008 ASEE Gulf-Southwest Annual Conference The University of New Mexico – Albuquerque

Copyright © 2008, American Society for Engineering Education